http://2013.igem.org/wiki/index.php?title=Special:Contributions/NanoWu&feed=atom&limit=50&target=NanoWu&year=&month=2013.igem.org - User contributions [en]2024-03-28T18:07:22ZFrom 2013.igem.orgMediaWiki 1.16.5http://2013.igem.org/Team:USTC_CHINA/PartsTeam:USTC CHINA/Parts2013-09-27T22:42:44Z<p>NanoWu: </p>
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Project</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Parts">Parts</a></div></div><br />
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<h1>TD1, Transdermal peptide</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074000">BBa_K1074000</a></h2><br />
<p align="center">TD1 is a short synthetic peptide(ACSSSPSKHCG) identified by in vivo phage display, facilitated efficient transdermal protein delivery through intact skin...</p><br />
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<div class="part-col-1"><br />
<h1>Pgrac+RBS+SamyQ+TD1<br>+GFP</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074006">BBa_K1074006</a></h2><br />
<p align="center">This is the main circuit of our project to allow high expression of target protein(antigen,adjuvant).GFP can be substituted by various proteins...</p><br />
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<div class="part-col-2"><br />
<h1>PHT43</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074001">BBa_K1074001</a></h2><br />
<p align="center">PHT43 is a E.coli-B.subtilis shuttle vector allowing high-level expression of secreted proteins in B.subtilis... </p><br />
</div><br />
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<div class="part-col-2"><br />
<h1>HBsAg</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074002">BBa_K1074002</a></h2> <br />
<p align="center">HBsAg is the surface antigen of the hepatitis B virus (HBV). It indicates current hepatitis B infection...</p><br />
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<h1>Ag85b</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074003">BBa_K1074003</a></h2> <br />
<p align="center">The antigen 85 proteins (FbpA, FbpB, FbpC) are responsible for the high affinity of mycobacteria for fibronectin... </p><br />
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<div class="part-col-2"><br />
<h1>Protective Antigen Domain 4</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074004">BBa_K1074004</a></h2> <br />
<p align="center">Protective antigen (PA) is the central component of the three-part protein toxin secreted by Bacillus anthracis, the organism responsible for anthrax... </p><br />
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<div class="part-col-2"><br />
<h1>LTB</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074005">BBa_K1074005</a></h2> <br />
<p align="center">This eltB gene encodes for the Heat-labile enterotox(LT) in certain virulent strains of E.coli...</p><br />
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<h1>Pctc+RBS+<br>amilCP</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074007">BBa_K1074007</a></h2> <br />
<p align="center">Promoter ctc(BBa_K143010) is a sigma factor B-dependent promoter in B. subtilis. activated by endogenous sigma factor B ...</p><br />
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<div class="part-col-2"><br />
<h1>SdpA,SdpB,<br>SpbC</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074009">BBa_K1074009</a></h2> <br />
<p align="center">Killing factor of Bacillus subtilis ,SpbC Induces the lysis of other B.subtilis cells that have not entered the sporulation pathway...</p><br />
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<h1>Pgrac+RBS+SDP</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074010">BBa_K1074010</a></h2> <br />
<p align="center">Spbc in SDP(sdpA,sdpB,spbC)(BBa_K1074009)operon is a killing factor of Bacillus subtilis...</p><br />
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<div class="clear"></div><br />
<div class="part-col-2"><br />
<h1>PsdpRI+RBS<br>+SDP</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074011">BBa_K1074011</a></h2> <br />
<p align="center">We construct this gene circuit as our kill switch to kill the engineered Bacillus subtilis for the safety purpose...</p><br />
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<div class="part-col-2"><br />
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<h1>Pgrac promoter</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074012">BBa_K1074012</a></h2> <br />
<p align="center">Prgac promoter(consisting of the groE promoter,the lacO operator and the gsiBSD sequence) allow induction by addition of ITPG... </p><br />
</div><br />
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<div class="part-col-2"><br />
<h1>promoter sdpR/I</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074013">BBa_K1074013</a></h2> <br />
<p align="center">This part is a sigma factor A-dependent promotor of the gene sdpR derived from the B.subtilis...</p><br />
</div><br />
<div class="part-col-2"><br />
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<h1>SamyQ</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074014">BBa_K1074014</a></h2> <br />
<p align="center">SamyQ is the signal peptide of the amyQ gene encoding an α-amylase in Bacillus subtilis WB800N...</p><br />
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<div class="part-col-2"><br />
<h1>RBS for Pgrac</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074015">BBa_K1074015</a></h2> <br />
<p align="center">An efficient RBS for promoter Pgrac(BBa_K1074012) in Bacillus subtilis.../p><br />
</div><br />
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<div class="part-col-2"><br />
<h1>RBS for Pctc</h1><br />
<h2><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K1074016">BBa_K1074016</a></h2> <br />
<p align="center">This is an efficient RBS for promoter Pctc(BBa_K143010) in Bacillus subtilis...</p><br />
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<div class="port-sidebar-border"><h>Project</h></div><br />
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<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Overview</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Background">Background</a></div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/ModelingTeam:USTC CHINA/Modeling2013-09-27T22:37:20Z<p>NanoWu: </p>
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<h1>Modeling on the suicide mechanism of the reporter system</h1><br />
<p>To eliminate potential safety problem, we constructed a suicide system on engineered bacteria to ensure biosafety. As the only one loaded with kill switch, the engineered reporter bacteria is responsible for eliminating all siblings in T-vaccine.<br />
Killing is mediated by the exported toxic protein SdpC. Extracellular SdpC induces the synthesis of an immunity protein, SdpI, which protects toxin-producing cells from being killed. SdpI, a polytopic membrane protein, is encoded by a two-gene operon under sporulation control that contains the gene for an autorepressor, SdpR.</p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">read more about Kill Switch</a><br />
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<h1>The best growing condition for Bacillus subtilis WB800N</h1><br />
</div><br />
<div><br />
To ensure the expression of our T-vaccine, we do some experiments to find out the best growing condition for Bacillus subtilis WB800N, we finally choose five independent factors: temperature, inoculation time, peptone, yeast extract and NaCl. The following table displays their levels:<br />
<table width="400" border="1px"<br />
<tr><br />
<th align="left">Factor</th><br />
<th align="right">Low</th><br />
<th align="right">High</th><br />
</tr><br />
<tr><br />
<td align="left">Temperature</td><br />
<td align="right">25℃</td><br />
<td align="right">35℃</td><br />
</tr><br />
<tr><br />
<td align="left">Time</td><br />
<td align="right">12h</td><br />
<td align="right">24h</td><br />
</tr><br />
<tr><br />
<td align="left">Peptone</td><br />
<td align="right">5</td><br />
<td align="right">15</td><br />
</tr><br />
<tr><br />
<th align="left">Yeast Extract</th><br />
<th align="right">2.5</th><br />
<th align="right">7.5</th><br />
</tr><br />
<tr><br />
<th align="left">NaCl</th><br />
<th align="right">5</th><br />
<th align="right">15</th><br />
</tr><br />
</table><br />
<br />
</div><br />
<br><br><br />
<div><br />
<br />
Roughly, we could consider the treatment of No. 15 medium (Temperature 35℃, Time 12h, Peptone 15, Yeast Extract 7.5, NaCl 15)as the maximal condition for Bacillus subtilis.<br />
<br><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">read more about B.Subtilis Culture</a><br />
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<h1>Designs of Immune Experiments</h1><br />
<p>Our mice experiment has primarily proven the validity of our project. However, just like most scientific immune experiments on animals, the aim of our mice experiment was verification instead of exploring the optimal conditions for the production of our vaccine. In fact, fewer optimization experiments have been done by pure scientific researches, as most scientists care about facts and theories only, whereas exploring the optimal conditions is often viewed as the task of pharmaceutical factories. Yet since igem itself frequently involves industrial fields, which make igem seems like more an engineering competition than a science competition sometimes. </p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">read more about Designs of Immune Experiments</a><br />
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<div class="port-sidebar-border"><h>Modeling</h></div><br />
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<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs Of Immune Experiments</a></div><br />
</div></div></div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/Team:USTC CHINA/Modeling/2013-09-27T22:35:52Z<p>NanoWu: </p>
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<h1>Modeling on the suicide mechanism of the reporter system</h1><br />
<p>To eliminate potential safety problem, we constructed a suicide system on engineered bacteria to ensure biosafety. As the only one loaded with kill switch, the engineered reporter bacteria is responsible for eliminating all siblings in T-vaccine.<br />
Killing is mediated by the exported toxic protein SdpC. Extracellular SdpC induces the synthesis of an immunity protein, SdpI, which protects toxin-producing cells from being killed. SdpI, a polytopic membrane protein, is encoded by a two-gene operon under sporulation control that contains the gene for an autorepressor, SdpR.</p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">read more about Kill Switch</a><br />
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<br><br><br />
<div><br />
<h1>The best growing condition for Bacillus subtilis WB800N</h1><br />
</div><br />
<div><br />
To ensure the expression of our T-vaccine, we do some experiments to find out the best growing condition for Bacillus subtilis WB800N, we finally choose five independent factors: temperature, inoculation time, peptone, yeast extract and NaCl. The following table displays their levels:<br />
<table width="400" border="1px"<br />
<tr><br />
<th align="left">Factor</th><br />
<th align="right">Low</th><br />
<th align="right">High</th><br />
</tr><br />
<tr><br />
<td align="left">Temperature</td><br />
<td align="right">25℃</td><br />
<td align="right">35℃</td><br />
</tr><br />
<tr><br />
<td align="left">Time</td><br />
<td align="right">12h</td><br />
<td align="right">24h</td><br />
</tr><br />
<tr><br />
<td align="left">Peptone</td><br />
<td align="right">5</td><br />
<td align="right">15</td><br />
</tr><br />
<tr><br />
<th align="left">Yeast Extract</th><br />
<th align="right">2.5</th><br />
<th align="right">7.5</th><br />
</tr><br />
<tr><br />
<th align="left">NaCl</th><br />
<th align="right">5</th><br />
<th align="right">15</th><br />
</tr><br />
</table><br />
<br />
</div><br />
<br><br><br />
<div><br />
<br />
Roughly, we could consider the treatment of No. 15 medium (Temperature 35℃, Time 12h, Peptone 15, Yeast Extract 7.5, NaCl 15)as the maximal condition for Bacillus subtilis.<br />
<br><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">read more about B.Subtilis Culture</a><br />
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<br><br><br />
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<h1>Designs of Immune Experiments</h1><br />
<p>Our mice experiment has primarily proven the validity of our project. However, just like most scientific immune experiments on animals, the aim of our mice experiment was verification instead of exploring the optimal conditions for the production of our vaccine. In fact, fewer optimization experiments have been done by pure scientific researches, as most scientists care about facts and theories only, whereas exploring the optimal conditions is often viewed as the task of pharmaceutical factories. Yet since igem itself frequently involves industrial fields, which make igem seems like more an engineering competition than a science competition sometimes. </p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">read more about Designs of Immune Experiments</a><br />
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<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs Of Immune Experiments</a></div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINATeam:USTC CHINA2013-09-27T22:30:36Z<p>NanoWu: </p>
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<h1>In Situ Transdermal Vaccine</h1><br />
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<p>Fresh Expression, No Purification<br />Standardized, Block-based Design<br />Easy-transportation, Low Storage External Costs<br />Almost No Demand For Medical Conditions And Proferssionals<br /><br />
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<a class="button-home" href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview"><span>Project </span></a><br />
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<h1>Motivation</h1><br />
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We hope to develop a fresh-expression transdermal vaccination.<br />
<br />We hope everyone in this world could equally enjoy the benefit of medical progress.<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Background">more</a><br />
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<h1>Design of Project</h1><br />
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With the support of <span><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Background#" target="_blank">TD-1</a></span>, a special polypeptide which can greatly facilitate macromolecule transdermal delivery through intact skin, we construct three different fuctional engineered bacillus subtilis; besides, we design a reporter system, including a kill switch, in the fouth type B.subtilis to improve usability and ensure biosafety.</div><br />
<div id="ls" class="pro-col"><br />
<img class="img-left" src="https://static.igem.org/mediawiki/2013/0/02/2013ustc-china_66.png" width="16" height="14" /><br />
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<span>ANTIGEN</span><br /><br />
As the core of our in-situ system,<br /> TD1-antigen expresser is designed<br /> and will share a great percentage of<br /> the total bacteria in our "band-aid".<br />
<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">more</a><br />
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<span>LTB</span><br /><br />
As one kind of our adjuvant expresser,<br />TD1-LTB is used to enhance the antigenicity.<br /> For LTB has so many advantages, it's a wild using adjuvant for most of exsiting injected vaccine.<br />
<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">more</a><br />
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<span>TNFα</span><br /><br />
TNFαis a chemotactic factor that recruits Langerhans Cells, antigen presenting cells beneath the skin barrier. The TNFα expresser is responsible for immigrating LC and triggering more intense immune responses.<br />
<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">more</a><br />
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<span>REPORTER</span><br /><br />
Reporter notifies users whether the status of vaccine patch is all right and when they can stick the patches to arms . Further more killing switch is conveyed in them as a biosafety guard.<br />
<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">more</a><br />
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<h1>Experimental Measurement</h1><br />
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<span>Molecules part</span><br /><br />
We took E.coli and the PET vector as the positive control and realized our ideas in the B.subtilis expression system based on PHT43 shuttle vector.<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Results">more</a><br />
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<span>Protein part</span><br /><br />
Before we achieve fresh expression, we use purified protein to obtain accurate data to verify our assumptions.<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Results">more</a><br />
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<span>Mice experiments</span><br /><br />
The most obvious character of our 2013USTC iGEM team is that we have not only achieved a series of molecule experiments but also tried mice experiments, which could be divided into transdermal experiments in vitro and animate mice experiments<br /><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Project/Results/FurthurWork">more</a><br />
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<h1>Modeling</h1><br />
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<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Suicide mechanism of the reporter system</a></h2><br />
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<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">The optimal culture conditions of Bacillus subtilis</a></h2><br />
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<h3 id="sponsors-title" align="center"><em>Thanks to the sponsors</em></h3><br><br />
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<p align="center">Deutsche Bank, China</p><br />
<div align="center"><a href="https://china.db.com/index_e.html" target="_blank"><img src="https://static.igem.org/mediawiki/2013/a/a7/2013ustc-china_Db-logo.png" alt="Deutsche Bank, China" height="65px" align="absmiddle" width="280px"></a><br />
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<p align="center">School of Life Sciences, USTC</p><br />
<div align="center"><a href="http://en.biox.ustc.edu.cn/" target="_blank"><img src="https://static.igem.org/mediawiki/2013/9/98/2013ustc-china_Life-logo.png" alt="School of Life Sciences, USTC" height="65px" align="absmiddle" width="280px"></a><br />
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<p align="center">USTC<span style="color:#fcc644">IF</span></p><br />
<div align="center"><a href="http://www.ustcif.org/" target="_blank"><img src="https://static.igem.org/mediawiki/2013/3/3c/2013ustc-china_Ustcif-logo.png" height="65px" align="absmiddle" width="280px"></a><br />
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<p align="center">School of the Gifted Young, USTC</p><br />
<div align="center"><a href="http://en.scgy.ustc.edu.cn/" target="_blank"><img src="https://static.igem.org/mediawiki/2013/c/c1/2013ustc-china_Gifted_young.jpg" height="65px" align="absmiddle" width="280px"></a><br />
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<p align="center">School of physics, USTC</p><br />
<div align="center"><a href="http://en.physics.ustc.edu.cn/" target="_blank"><img src="https://static.igem.org/mediawiki/2013/6/68/2013ustc-china_Physics-logo.png" height="65px" align="absmiddle" width="280px"></a><br />
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<p align="center">Teaching Affairs Office of USTC</p><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/TeamTeam:USTC CHINA/Team2013-09-27T21:05:16Z<p>NanoWu: </p>
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<div id="igemlogo"><a href="https://2013.igem.org/Main_Page" target="_blank"><img src="https://static.igem.org/mediawiki/2013/2/26/2013ustcigem_IGEM_basic_Logo.png" alt="igem home page" width="50" height="40" /></a></div><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Project</a><br />
<ul class="subs"><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Overview</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Background">Background</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">Design</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Results">Results</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Parts">Parts</a></li><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook">Notebook</a><br />
<ul class="subs"><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Timeline">Timeline</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols">Protocols</a></li><br />
</ul><br />
</li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a><br />
<ul class="subs"><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs of Immune Experiments</a></li><br />
</ul><br />
</li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice">Human Practice</a><br />
<ul class="subs"><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice/Communication" >Communication</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice/Activity">Activity</a></li><br />
</ul><br />
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<li class="active"><a href="https://2013.igem.org/Team:USTC_CHINA/Team">Team</a><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Team">Members</a></li><br />
<li><a href="https://igem.org/Team.cgi?year=2013&team_name=USTC_CHINA">Profile</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Attributions">Attributions</a></li><br />
<li><a href="https://igem.org/2013_Judging_Form?id=1074#iGEM_Medals">Achievements</a></li><br />
</ul><br />
</li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Safety">Safety</a></li><br />
</ul><br />
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<br />
<div class="content" align="center" style="margin-bottom: 50px"><br />
<h2>Students</h2><br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/2/21/Zhangsitao1.JPG" alt="Zhang Sitao"> <br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao"><br />
<div class ="nameplate"><a href="#">Zhang Sitao</a> </div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao" align="left"><p>Our labor leader weighs various matters, leads the overall trend and plays our cards right. He leaves a strong impression in others’ mind. However, His friends found that the leader is very cute.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/0/02/Zhaochanglong1.JPG" alt="Changlong Zhao"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" ><br />
<div class ="nameplate"><a href="#">Changlong Zhao</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" align="left"><p>There’s no doubt that we can give full stars for Changlong’s fighting capacity. The roads leading to success will never be smooth and Changlong is a perfect companion to travel with.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/9/91/Xionghanjin1.JPG" alt="Hanjin Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" ><br />
<div class ="nameplate"><a href="#">Hanjin Xiong</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" align="left"><p>As the keynote speaker of our team, he always keeps a clear head with extraordinary creativity and expressiveness. He said, “It is shameful if you haven’t burnt the midnight oil for iGEM.” Moving forward bravely, he shows us overwhelming power which nobody can stop it.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/2/23/Limingyue1.JPG" alt="Mingyue Li"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li"><br />
<div class ="nameplate"><a href="#">Mingyue Li</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li" align="left"><p>“Mingyue Bacteria” is the spokesperson of our bacterium, handling the destiny of those little lives. We all agreed that, Mingyue with rubber gloves is GORGEOUSNESS!</p></div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/8/85/Shenshengqi1.JPG" alt="Shen Shengqi"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" ><br />
<div class ="nameplate"><a href="#">Shen Shengqi</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" align="left"><p>Everyone considers that it is honored to be a friend of “Brother Face” as he is a totally “local tyrant”. Actually,” Brother Shen” is warmth, nice, really expert in digging shortcuts in the experiments. He is a sharp soldier of our team as he adheres to the “more with less” principle.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c1/Madanyi1.JPG" alt="Danyi Ma"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" ><br />
<div class ="nameplate"><a href="#">Danyi Ma</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" align="left"><p>”Aunty Ma” takes charge of our finance and safety, which calls for much patience and responsibility. In the experiment, she also plays an absolutely necessary role.</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/8/87/Zhangheng1.JPG" alt="Zhang Heng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" ><br />
<div class ="nameplate"><a href="#">Zhang Heng</a> </div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" align="left"><p>He is a man full of responsibility, we could 100% trust him! Bro, it’s you that bring us positive energy!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f9/Yuanye1.JPG" alt="Yvette Yuan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" ><br />
<div class ="nameplate"><a href="#">Yvette Yuan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" align="left"><p>As a s pronoun for efficient, Yuan Ye is studious and decisive. And what makes her best is that she always brings us delicious oranges.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/a3/Xinghuayue1.JPG" alt="Huayue Xing"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" ><br />
<div class ="nameplate"><a href="#">Huayue Xing</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" align="left"><p>With my little eyes, I see bacterium; with my little eyes, I see TD-1; with my little eyes, I see vaccine secreted out; with my little eyes, I see the future without needles. Carefulness, earnest, and a little bit of acting cute, I am XHY.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/ad/Xionglei1.JPG" alt="Lei Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" ><br />
<div class ="nameplate"><a href="#">Lei Xiong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" align="left"><p>Despite the fact that it is me who always breaks test tubes, loses beakers, and pours reagent onto the skin of my hands, I have the enthusiasm for science. I love to explore and pursue knowledge. As long as there is a chance to see the tip of the iceberg, it doesn't matter how many test tubes I am going to break.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/7/76/Panminghao1.JPG" alt="Minghao Pan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" ><br />
<div class ="nameplate"><a href="#">Minghao Pan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" align="left"><p>I love physics and biology.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c8/Dongbo1.JPG" alt="Bo Dong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" ><br />
<div class ="nameplate"><a href="#">Bo Dong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" align="left"><p>He is an earnest boy, he always work hard that every bros and sis like him, he is our team’s MVP! <br />
Hey, bro! It our pleasure to be with you!</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/3/3f/Chenzhaoxiong1.JPG" alt="Zhaoxiong Chen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen"><br />
<div class ="nameplate"><a href="#">Zhaoxiong Chen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen" align="left"><p>This smart boy is good at playing all kinds of computer systems. We believe that he will refresh the history of wikis!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/15/Wuming1.JPG" alt="Min Wu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu"><br />
<div class ="nameplate"><a href="#">Min Wu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu" align="left"><p>I love experiments. I love music. I love USTC iGEMers. We never walk alone.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/14/Wangshiwei1.JPG" alt="Shiwei Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang"><br />
<div class ="nameplate"><a href="#">Shiwei Wang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang" align="left"><p>Again, a quiet boy is coming! He love experiment, he is Bo Dong’s loyal friend. We all believe in him, without his help we cannot achieve our goal! Thanks a lot ,my bro! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/e/e4/Fansijia1.JPG" alt="Sijia Fan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan"><br />
<div class ="nameplate"><a href="#">Sijia Fan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan" align="left"><p>Black humorist, and sadly, the leader is always shouting at me:” Hurry! Hurry!”.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/d/df/Pengyali1.JPG" alt="Yali Peng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng"><br />
<div class ="nameplate"><a href="#">Yali Peng</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng" align="left"><p>She is a quiet girl, she likes smile, she loves doing experiments peacefully and slowly. As the best partner of Mingyue Li, every trouble become easy! Hey, little pretty we all love you! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/5/52/Longjie1.JPG" alt="Long jie"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie"><br />
<div class ="nameplate"><a href="#">Long jie</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie" align="left"><p>Clever and hard-working, I cannot agree more to do experiments with him. You never let us down!</p><br />
</div><br />
</div><br />
</div><br />
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<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/b/bd/Caoqinjingwen1.JPG" alt="Cao Qinjingwen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen"><br />
<div class ="nameplate"><a href="#">Cao Qinjingwen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen" align="left"><p>Excellent! Without these kinds of words, how can I say anything to describe her? As our elder sister, she always gives us self-confident, hey soul sister!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/60/Shaoxueying1.JPG" alt="Shao Xueying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying"><br />
<div class ="nameplate"><a href="#">Shao Xueying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying" align="left"><p>Competent and independent, Shao Xueying has unique ideas about colors and graphics. At the same time, she is a good lecturer. She edits our wiki and make presentation for us. </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/49/Qiuyanning1.JPG" alt="Yanning Qiu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu"><br />
<div class ="nameplate"><a href="#">Yanning Qiu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu" align="left"><p>Our little sister holds the trump cards. She always knows what do with all the words and pictures. Brave and creative, Yanning enjoys the days with new skills and knowledge. Our team was painted colorfully with the lively girl.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/9/9a/Wangzeyu1.JPG" alt="Zeyu Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang"><br />
<div class ="nameplate"><a href="#">Zeyu Wang</a></div><br />
<div class = "details"><a href="http://home.ustc.edu.cn/~wangzeyu/contact%20me.htm"><img src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang" align="left"></a><p>Although I was a freshman and initially came to USTC iGEM , I did some experiment in molecular cloning.I took part in human practice and wiki writing.I also helped with presentation. Thank you,USTC iGEMers!<br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xiaozhuyun1.JPG" alt="Xiao Zhuyun"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun"><br />
<div class ="nameplate"><a href="#">Xiao Zhuyun</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun" align="left"><p>Sincere and straightforward, “piggy”, the curve wrecker in our eyes, puts all her efforts into research and study. Only when you get close to her, will you find that she also loves to play, that she also loves life.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f3/Yanggege1.JPG" alt="Gege Yang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang"><br />
<div class ="nameplate"><a href="#">Gege Yang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang" align="left"><p> She is majoring in Life Sciences. She is in charge of the construction of one type of engineering bacteria producing fusion protein. As a member of the wet lab, she enjoys the work as well as meets new friends this summer.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/62/Hanyingying1.JPG" alt="Han Yingying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying"><br />
<div class ="nameplate"><a href="#">Han Yingying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying" align="left"><p>Tender as a new-born kitty, Yingying doesn’t like to stand in the spotlight. She’s a diligent brain instead of a silken tongue. We believe that gold will shine no matter where it is. </p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/1/18/Chenzhuo1.JPG" alt="Chen Zhuo"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo"><br />
<div class ="nameplate"><a href="#">Chen Zhuo</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo" align="left"><p>Always, he is still of tongue, but he is not only a genius of experiment, but also a brilliant living library. I cannot say more but admire! </p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xuehao1.JPG" alt="Hao Xue"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue"><br />
<div class ="nameplate"><a href="#">Hao Xue</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue" align="left"><p>Laughing, he is still laughing! What on hill? Oh god, negative results, but how… But bro, thank you for giving us positive energy, you really raise us up! My bro! </p><br />
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<h2>Advisers</h2> <br />
<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu"><br />
<div class ="nameplate"><a href="#">Haiyan Liu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu" align="left"><p>Haiyan Liu was born in Sichuan Province, China. He received his BS degree in Biology in 1990 and PhD degree in Biochemistry and Molecular Biology in 1996, both from USTC. Between 1993 and 1995 he was a visiting graduate student in Laboratory of Physical Chemistry of ETH, Zurich (Switzerland). Since 2001, he has been a professor of computational biology at School of Life Sciences, USTC. </p><br />
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<img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong"><br />
<div class ="nameplate"><a href="#">Jiong Hong</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong" align="left"><p> I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. My ongoing project is to identify biomarkers in order to detect the progress stages of the diabetes. In addition, I have planed to analyze the genetic and environmental factors and their interactions during the progressing of the type 2 diabetes with systems-biology approaches.</p><br />
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<img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu"><br />
<div class ="nameplate"><a href="#">Jiarui Wu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu" align="left"><p>Since the research strategy of systems biology is well fit to analyze the biological complex systems. I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. We have developed systematic approaches based on proteomics and bioinformatics to analyze human normal and diabetic serum.</p><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/TeamTeam:USTC CHINA/Team2013-09-27T21:01:40Z<p>NanoWu: </p>
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<h2>Students</h2><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/2013/2/21/Zhangsitao1.JPG" alt="Zhang Sitao"> <br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao"><br />
<div class ="nameplate"><a href="#">Zhang Sitao</a> </div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao" align="left"><p>Our labor leader weighs various matters, leads the overall trend and plays our cards right. He leaves a strong impression in others’ mind. However, His friends found that the leader is very cute.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/2013/0/02/Zhaochanglong1.JPG" alt="Changlong Zhao"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" ><br />
<div class ="nameplate"><a href="#">Changlong Zhao</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" align="left"><p>There’s no doubt that we can give full stars for Changlong’s fighting capacity. The roads leading to success will never be smooth and Changlong is a perfect companion to travel with.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/2013/9/91/Xionghanjin1.JPG" alt="Hanjin Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" ><br />
<div class ="nameplate"><a href="#">Hanjin Xiong</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" align="left"><p>As the keynote speaker of our team, he always keeps a clear head with extraordinary creativity and expressiveness. He said, “It is shameful if you haven’t burnt the midnight oil for iGEM.” Moving forward bravely, he shows us overwhelming power which nobody can stop it.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/2/23/Limingyue1.JPG" alt="Mingyue Li"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li"><br />
<div class ="nameplate"><a href="#">Mingyue Li</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li" align="left"><p>“Mingyue Bacteria” is the spokesperson of our bacterium, handling the destiny of those little lives. We all agreed that, Mingyue with rubber gloves is GORGEOUSNESS!</p></div><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/8/85/Shenshengqi1.JPG" alt="Shen Shengqi"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" ><br />
<div class ="nameplate"><a href="#">Shen Shengqi</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" align="left"><p>Everyone considers that it is honored to be a friend of “Brother Face” as he is a totally “local tyrant”. Actually,” Brother Shen” is warmth, nice, really expert in digging shortcuts in the experiments. He is a sharp soldier of our team as he adheres to the “more with less” principle.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c1/Madanyi1.JPG" alt="Danyi Ma"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" ><br />
<div class ="nameplate"><a href="#">Danyi Ma</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" align="left"><p>”Aunty Ma” takes charge of our finance and safety, which calls for much patience and responsibility. In the experiment, she also plays an absolutely necessary role.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/2013/8/87/Zhangheng1.JPG" alt="Zhang Heng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" ><br />
<div class ="nameplate"><a href="#">Zhang Heng</a> </div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" align="left"><p>He is a man full of responsibility, we could 100% trust him! Bro, it’s you that bring us positive energy!</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f9/Yuanye1.JPG" alt="Yvette Yuan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" ><br />
<div class ="nameplate"><a href="#">Yvette Yuan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" align="left"><p>As a s pronoun for efficient, Yuan Ye is studious and decisive. And what makes her best is that she always brings us delicious oranges.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/a3/Xinghuayue1.JPG" alt="Huayue Xing"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" ><br />
<div class ="nameplate"><a href="#">Huayue Xing</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" align="left"><p>With my little eyes, I see bacterium; with my little eyes, I see TD-1; with my little eyes, I see vaccine secreted out; with my little eyes, I see the future without needles. Carefulness, earnest, and a little bit of acting cute, I am XHY.</p><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/ad/Xionglei1.JPG" alt="Lei Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" ><br />
<div class ="nameplate"><a href="#">Lei Xiong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" align="left"><p>Despite the fact that it is me who always breaks test tubes, loses beakers, and pours reagent onto the skin of my hands, I have the enthusiasm for science. I love to explore and pursue knowledge. As long as there is a chance to see the tip of the iceberg, it doesn't matter how many test tubes I am going to break.</p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/7/76/Panminghao1.JPG" alt="Minghao Pan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" ><br />
<div class ="nameplate"><a href="#">Minghao Pan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" align="left"><p>I love physics and biology.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c8/Dongbo1.JPG" alt="Bo Dong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" ><br />
<div class ="nameplate"><a href="#">Bo Dong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" align="left"><p>He is an earnest boy, he always work hard that every bros and sis like him, he is our team’s MVP! <br />
Hey, bro! It our pleasure to be with you!</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/3/3f/Chenzhaoxiong1.JPG" alt="Zhaoxiong Chen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen"><br />
<div class ="nameplate"><a href="#">Zhaoxiong Chen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen" align="left"><p>This smart boy is good at playing all kinds of computer systems. We believe that he will refresh the history of wikis!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/15/Wuming1.JPG" alt="Min Wu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu"><br />
<div class ="nameplate"><a href="#">Min Wu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu" align="left"><p>I love experiments. I love rock music. I love F.Alonso. Call me Nano.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/14/Wangshiwei1.JPG" alt="Shiwei Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang"><br />
<div class ="nameplate"><a href="#">Shiwei Wang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang" align="left"><p>Again, a quiet boy is coming! He love experiment, he is Bo Dong’s loyal friend. We all believe in him, without his help we cannot achieve our goal! Thanks a lot ,my bro! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/e/e4/Fansijia1.JPG" alt="Sijia Fan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan"><br />
<div class ="nameplate"><a href="#">Sijia Fan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan" align="left"><p>Black humorist, and sadly, the leader is always shouting at me:” Hurry! Hurry!”.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/d/df/Pengyali1.JPG" alt="Yali Peng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng"><br />
<div class ="nameplate"><a href="#">Yali Peng</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng" align="left"><p>She is a quiet girl, she likes smile, she loves doing experiments peacefully and slowly. As the best partner of Mingyue Li, every trouble become easy! Hey, little pretty we all love you! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/5/52/Longjie1.JPG" alt="Long jie"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie"><br />
<div class ="nameplate"><a href="#">Long jie</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie" align="left"><p>Clever and hard-working, I cannot agree more to do experiments with him. You never let us down!</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/b/bd/Caoqinjingwen1.JPG" alt="Cao Qinjingwen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen"><br />
<div class ="nameplate"><a href="#">Cao Qinjingwen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen" align="left"><p>Excellent! Without these kinds of words, how can I say anything to describe her? As our elder sister, she always gives us self-confident, hey soul sister!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/60/Shaoxueying1.JPG" alt="Shao Xueying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying"><br />
<div class ="nameplate"><a href="#">Shao Xueying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying" align="left"><p>Competent and independent, Shao Xueying has unique ideas about colors and graphics. At the same time, she is a good lecturer. She edits our wiki and make presentation for us. </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/49/Qiuyanning1.JPG" alt="Yanning Qiu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu"><br />
<div class ="nameplate"><a href="#">Yanning Qiu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu" align="left"><p>Our little sister holds the trump cards. She always knows what do with all the words and pictures. Brave and creative, Yanning enjoys the days with new skills and knowledge. Our team was painted colorfully with the lively girl.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/9/9a/Wangzeyu1.JPG" alt="Zeyu Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang"><br />
<div class ="nameplate"><a href="#">Zeyu Wang</a></div><br />
<div class = "details"><a href="http://home.ustc.edu.cn/~wangzeyu/contact%20me.htm"><img src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang" align="left"></a><p>Although I was a freshman and initially came to USTC iGEM , I did some experiment in molecular cloning.I took part in human practice and wiki writing.I also helped with presentation. Thank you,USTC iGEMers!<br />
<br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xiaozhuyun1.JPG" alt="Xiao Zhuyun"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun"><br />
<div class ="nameplate"><a href="#">Xiao Zhuyun</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun" align="left"><p>Sincere and straightforward, “piggy”, the curve wrecker in our eyes, puts all her efforts into research and study. Only when you get close to her, will you find that she also loves to play, that she also loves life.</p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f3/Yanggege1.JPG" alt="Gege Yang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang"><br />
<div class ="nameplate"><a href="#">Gege Yang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang" align="left"><p> She is majoring in Life Sciences. She is in charge of the construction of one type of engineering bacteria producing fusion protein. As a member of the wet lab, she enjoys the work as well as meets new friends this summer.</p><br />
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<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/62/Hanyingying1.JPG" alt="Han Yingying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying"><br />
<div class ="nameplate"><a href="#">Han Yingying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying" align="left"><p>Tender as a new-born kitty, Yingying doesn’t like to stand in the spotlight. She’s a diligent brain instead of a silken tongue. We believe that gold will shine no matter where it is. </p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/1/18/Chenzhuo1.JPG" alt="Chen Zhuo"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo"><br />
<div class ="nameplate"><a href="#">Chen Zhuo</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo" align="left"><p>Always, he is still of tongue, but he is not only a genius of experiment, but also a brilliant living library. I cannot say more but admire! </p><br />
</div><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xuehao1.JPG" alt="Hao Xue"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue"><br />
<div class ="nameplate"><a href="#">Hao Xue</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue" align="left"><p>Laughing, he is still laughing! What on hill? Oh god, negative results, but how… But bro, thank you for giving us positive energy, you really raise us up! My bro! </p><br />
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<h2>Advisers</h2> <br />
<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu"><br />
<div class ="nameplate"><a href="#">Haiyan Liu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu" align="left"><p>Haiyan Liu was born in Sichuan Province, China. He received his BS degree in Biology in 1990 and PhD degree in Biochemistry and Molecular Biology in 1996, both from USTC. Between 1993 and 1995 he was a visiting graduate student in Laboratory of Physical Chemistry of ETH, Zurich (Switzerland). Since 2001, he has been a professor of computational biology at School of Life Sciences, USTC. </p><br />
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<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong"><br />
<div class ="nameplate"><a href="#">Jiong Hong</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong" align="left"><p> I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. My ongoing project is to identify biomarkers in order to detect the progress stages of the diabetes. In addition, I have planed to analyze the genetic and environmental factors and their interactions during the progressing of the type 2 diabetes with systems-biology approaches.</p><br />
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<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu"><br />
<div class ="nameplate"><a href="#">Jiarui Wu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu" align="left"><p>Since the research strategy of systems biology is well fit to analyze the biological complex systems. I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. We have developed systematic approaches based on proteomics and bioinformatics to analyze human normal and diabetic serum.</p><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC-ChinaTeam:USTC-China2013-09-27T20:36:56Z<p>NanoWu: Blanked the page</p>
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<div></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/HumanPractice/ActivityTeam:USTC CHINA/HumanPractice/Activity2013-09-27T20:30:49Z<p>NanoWu: </p>
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<div>{{USTC-China/hidden}}<br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Project</a><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Overview">Overview</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Background">Background</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design">Design</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Project/Results">Results</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Parts">Parts</a></li><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook">Notebook</a><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Timeline">Timeline</a></li><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a><br />
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></li><br />
<li><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs of Immune Experiments</a></li><br />
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<li class="active"><a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice">Human Practice</a><br />
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<div id="tlogo"><img src="https://static.igem.org/mediawiki/2013/f/f8/2013ustc-china_T-VACCINE.png" width="100%" height="123" /><br />
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt;<a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice">Human Practice</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/HumanPractice/Activity">Activity</a></div></div><br />
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<h1>May Festival</h1><br />
<p>As one of iGEMers’ classical activities, our lab is open to public at one weekend on May 18th, we welcomed 18 groups of high school students and 11 groups of primary school students. We welcomed over 500 normal.<br />
In order to show our lab work and popularize synthetic biology, we rearranged our lab and created several kids’ games about iGEM.<br />
</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/b/b2/2013ustc-china_may_festival1.jpg"/width="500"height="375"><br />
<img src="https://static.igem.org/mediawiki/igem.org/1/16/2013ustc-china_may_festival_2.jpg"width="500"height="600"><br />
<p>Blowing the gloves? Are you kidding? It comes true in USTC iGEM’s lab! DIY+gloves=amazing!<br />
Who say that we just have machine and reagents here? Welcome to USTC iGEM’s lab 363! What we have created is far more than fairytales!<br />
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<img src="https://static.igem.org/mediawiki/igem.org/1/10/2013ustc-china_may_festival_3.jpg"width="500"height="355"><br />
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<imgg src="https://static.igem.org/mediawiki/igem.org/b/be/2013ustc-china_may_festival5.jpg"width="500"height="325"><br />
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<h1>Super-taster</h1><br />
<p>Biosensor has been a classical topic in iGEM and Synthetic Biology. Many biosensor cases have been known by public, for example, detecting pollutants in the environment and fluorescent coloring. Therefore, biosensor is a good example to explain the ideology of iGEM. USTC iGEMers are always devoted into popularizing synthetic biology. After last year’s Hefei Genetically Modified (GM) Knowledge Competition, we host an activity named ”Super Taster” to recruit more people to take a brief glance at iGEM. Are we better taster than engineered bacterial? We provided others a chance to see and feel “biosensor”. Come on! Join us! </p><br />
<img src="https://static.igem.org/mediawiki/igem.org/7/7a/2013ustc-china_taster_1.jpg" width="500" height="420" /><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/ea/2013ustc-china_taster_2.jpg"width="500"height="325"/><br />
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<h1>Lecture</h1><br />
<p>As the most classical way to display, the lecture is indispensable! To meet thr requirement of different people, we used 3D film to show the world inside the cell, and we also show them one of our iGEM team’s clay movie, so that children can understand iGEM.Of course, our own propaganda video was also shown. Here we would like to thank USTC Alumni Foundation for helping us make an elegant propaganda video!</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/a/a8/2013ustc-china_lecture1.jpg" width="500" height="375" /><br />
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<h1>Art of T-vaccine</h1><br />
<p>Our souvenir</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/e8/2013ustc-china_igem_art1.jpg" width="500" height="300" /><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/e7/2013ustc-china_art_device_2.jpg"width="500"height="350"/><br />
<img src="https://static.igem.org/mediawiki/igem.org/f/ff/2013ustc-china_art_device_3.jpg"width="500"height="325"/><br />
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<h1>Device</h1><br />
<p>Our device for storing and activating T-Vaccine patches.</p><br />
<p>We designed a “Bacteria Box” as our assistance device for instant production. Covered with sterile membrane, the box contains dry powder of engineering bacteria and dehydrated medium, and once adequate water is added, the bacteria will be activated and ready to produce. Then we further enhance the device and invent the new double-layer device “Bacteria Box II”, in which the dehydrated medium and bacteria are stored at different layers. All we are required to do is to extract the division plate between layers and the bacteria and medium will naturally mix up. Compared with the former one, the bacteria and medium are separated, thus facilitating transportation and avoiding potential contamination.</p><br />
<img src="https://static.igem.org/mediawiki/2013/6/6b/2013_ustc-china_device6.jpg"width="500"height="375"/><br />
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</html></div>NanoWuhttp://2013.igem.org/File:Device_3D.JPGFile:Device 3D.JPG2013-09-27T20:30:18Z<p>NanoWu: </p>
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<div></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Project/ResultsTeam:USTC CHINA/Project/Results2013-09-27T19:48:43Z<p>NanoWu: </p>
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<h1>Stage one:Basal experiments</h1><br />
<h2>Introduction</h2><br />
<p>As the construction and concentration of recombinant plasmid rely heavily on E.coli system in current molecule experiment protocols of Bacillus subtilis, Bacillus subtilis acts only as the secretory expression vector. Therefore, to verify the practicality of our locus and the transdermal function of recombinant transdermal protein on top of its original functions, we conducted basic experiments on E.coli to verify our assumptions. </p><br />
<p>The following figure shows the stages of our basal experiments:</p><br />
<div align="center"><img src="https://static.igem.org/mediawiki/2013/0/0e/First_experiments.png" width="300" height="400"/></div><br />
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<h2>Results</h2><br />
<h3>1. Verifying the validity of our circuit by GFP</h3><br />
<p>E.coli BL21 proved that the standard transdermal locus does work with GFP.</p><br />
<img src="https://static.igem.org/mediawiki/2013/8/82/2013ustc-china_genecircuit5.png" width="580" height="125"/><br />
<p>Using GFP to prove the validity of a newly designed circuit is a classical way to verify the expressing of this circuit. As expressions in E.coli involve neither secretory nor sequential problems, we hoped to verify the practicality of our locus by the expression of TD1-GFP. Thus we selected pET22b, which is a common recombinant vector for plasmid construction, as our recombinant vector and E.coli BL21 as engineered bacteria . We fused sequence TD1-GFP with T7 promoter from pET22b downstream and succeeded in expressing fusion protein TD1-GFP. </p><br />
<div class="atfigure" align="center"><img src="https://static.igem.org/mediawiki/2013/d/d7/2013ustc-chinajiaotuTD1-GFP.jpg"></br></br><br />
Fig1. SDS PAGE shows the molecule weight of TD1-GFP</div><br />
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<div style="float:left;width:290px;"><br />
<img src="https://static.igem.org/mediawiki/igem.org/2/20/2013ustc-china_ygt%28GFP%29.png" width="290" height="290"/><br />
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<div class="atfigure" align="center" style="width:580px">Fig 2. The expression of GFP under fluorescence microscope</br>A.BL21 colony Induced by IPTG; B.BL21 colony without IPTG<br />
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<div class="basic-bar"><br />
<h3 style="font-size:24px;line-height:20px;">2. TD1-fusion protein expression</h3><br />
<p>The expression of recombinant antigen and adjuvant in E.coli BL21.</p><br />
<img src="https://static.igem.org/mediawiki/2013/4/4d/2013ustc-china_genecircuit.png" width="580" height="120"/><br />
<p>The practicality of our locus afforded by TD1-GFP enabled our to express recombinant antigen TD1-HBsAg and recombinant adjuvant TD1-LTB successfully. So far our basic molecule experiments have ended with perfection.</p><br />
<div style="float:left;width:200px;"><br />
<img src="https://static.igem.org/mediawiki/2013/6/6f/2013ustc-chinasdsTD1-LTB.png" width="200" height="300"/><br />
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<div style="float:left;width:380px;"><br />
<img src="https://static.igem.org/mediawiki/2013/7/73/2013ustc-chinasdsTD1-HBsAg.png" width="300" height="300"/><br />
</div><br />
<br />
<br />
<div class="atfigure" align="center" style="width:580px">Fig3. SDS PAGE shows the expression of LTB(L)、HBsAg(R)</div><br />
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<br />
<div class="basic-bar"><br />
<h3 style="font-size:24px;line-height:20px;">3. Verified the antigenicity of TD1-antibody by ELISA</h3><br />
<p>Verified the antigenicity of TD1-HBsAg by ELISA. The antigenicity of the TD1-antigen(fusion protein)strongly proved our theoretical basis. </p><br />
<img src="https://static.igem.org/mediawiki/2013/a/a9/ELISA.jpg" width="580" height="380"/><br />
<div class="atfigure" align="center" style="width:">Fig 4. Verify the antigenicity of TD1-HBsAg with ELISA</div><br />
</div><br />
<br />
<div class="basic-bar"><br />
<h3 style="font-size:24px;line-height:20px;">4. Transdermal experiment</h3><br />
<p>TD1-HBsAg is able to penetrate the skin and keep its antigenicity: </p><br />
<br><br />
<div style="float:left;width:106px;height:170px;padding:5px"><br />
<img src="https://static.igem.org/mediawiki/2013/0/0b/2013ustc-china_transdevice.png" width="106" height="150" /><br />
<div class="atfigure" align="center" style="width:106px">Fig 5. Special transdermal device</div></div><br />
<p>To prove that TD1-HBsAg is able to pass across the skin and keep its antigenicity, we utilized a <span>special device</span> in the picture below, whose upper tube and lower tube can be separated by fresh skin peeled from mice, and all we were required to do was fastening the device, adding protein solution to the upper tube and extracting appropriate volume of liquid from the physiological saline in the lower tube to check the concentration of TD1-HBsAg which had crossed the skin during diverse periods.</p><br />
<img src="" width="" height="" /><br />
<div class="atfigure" align="center" style="width:">Fig 6. Check the concentration of TD1-HBsAg in the liquid under the skin during diverse periods with ELISA</div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitchTeam:USTC CHINA/Modeling/KillSwitch2013-09-27T19:13:31Z<p>NanoWu: </p>
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
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</div><br />
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<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<div class="port-sidebar-border"><h>Modeling</h></div><br />
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<div id="t1"><a class="active" href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitchTeam:USTC CHINA/Modeling/KillSwitch2013-09-27T19:11:02Z<p>NanoWu: </p>
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a>&gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div></div><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br></br></br></br></br></br></br></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br></br></br></br></br></br></br></br></br></br></br></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
</div><br />
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<div class="rightbar"><br />
<div class="port-sidebar-border"><h>Modeling</h></div><br />
<div class="clear"></div><br />
<div id="t1"><a class="active" href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs of Immune Experiments</a></div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitchTeam:USTC CHINA/Modeling/KillSwitch2013-09-27T19:06:33Z<p>NanoWu: </p>
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a>&gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div></div><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
</div><br />
<br />
</div><br />
</div><br />
<br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitchTeam:USTC CHINA/Modeling/KillSwitch2013-09-27T19:03:37Z<p>NanoWu: </p>
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png" width="450" height="350" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="600" height="400" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="600" height="400" /></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"width="500" height="150" /></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="260" height="150" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="260" height="150" /></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="290" height="150" /></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitchTeam:USTC CHINA/Modeling/KillSwitch2013-09-27T18:54:59Z<p>NanoWu: </p>
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<li><a href="https://2013.igem.org/Team:USTC_CHINA/Safety">Safety</a></li><br />
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a>&gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div></div><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
<div></br></br></br></br></br></br></br></br>In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<div id="breadcrumb"><a href="https://2013.igem.org/Team:USTC_CHINA">Home</a> &gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/">Modeling</a>&gt; <a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div></div><br />
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<div style="margin-top:20px;"><br />
<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
<div>Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br></div><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
<div></br></br></br></br></br></br>In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Stage one:Basal experiments</h1><br />
<h2>Introduction</h2><br />
<p>As the construction and concentration of recombinant plasmid rely heavily on E.coli system in current molecule experiment protocols of Bacillus subtilis, Bacillus subtilis acts only as the secretory expression vector. Therefore, to verify the practicality of our locus and the transdermal function of recombinant transdermal protein on top of its original functions, we conducted basic experiments on E.coli to verify our assumptions. </p><br />
<p>The following figure shows the stages of our basal experiments:</p><br />
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<h2>Results</h2><br />
<h3>1. Verifying the validity of our circuit by GFP</h3><br />
<p>E.coli BL21 proved that the standard transdermal locus does work with GFP.</p><br />
<img src="https://static.igem.org/mediawiki/2013/8/82/2013ustc-china_genecircuit5.png" width="580" height="125"/><br />
<p>Using GFP to prove the validity of a newly designed circuit is a classical way to verify the expressing of this circuit. As expressions in E.coli involve neither secretory nor sequential problems, we hoped to verify the practicality of our locus by the expression of TD1-GFP. Thus we selected pET22b, which is a common recombinant vector for plasmid construction, as our recombinant vector and E.coli BL21 as engineered bacteria . We fused sequence TD1-GFP with T7 promoter from pET22b downstream and succeeded in expressing fusion protein TD1-GFP. </p><br />
<div class="atfigure" align="center"><img src="https://static.igem.org/mediawiki/2013/d/d7/2013ustc-chinajiaotuTD1-GFP.jpg"></br></br><br />
Fig1. SDS PAGE shows the molecule weight of TD1-GFP</div><br />
<br><br><br />
<div style="float:left;width:290px;"><br />
<img src="https://static.igem.org/mediawiki/igem.org/2/20/2013ustc-china_ygt%28GFP%29.png" width="290" height="290"/><br />
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<div class="atfigure" align="center" style="width:580px">Fig 2. The expression of GFP under fluorescence microscope</br>A.BL21 colony Induced by IPTG; B.BL21 colony without IPTG<br />
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<h3 style="font-size:24px;line-height:20px;">2. TD1-fusion protein expression</h3><br />
<p>The expression of recombinant antigen and adjuvant in E.coli BL21.</p><br />
<img src="https://static.igem.org/mediawiki/2013/4/4d/2013ustc-china_genecircuit.png" width="580" height="120"/><br />
<p>The practicality of our locus afforded by TD1-GFP enabled our to express recombinant antigen TD1-HBsAg and recombinant adjuvant TD1-LTB successfully. So far our basic molecule experiments have ended with perfection.</p><br />
<div style="float:left;width:200px;"><br />
<img src="https://static.igem.org/mediawiki/2013/6/6f/2013ustc-chinasdsTD1-LTB.png" width="200" height="300"/><br />
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<img src="https://static.igem.org/mediawiki/2013/7/73/2013ustc-chinasdsTD1-HBsAg.png" width="300" height="300"/><br />
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<br />
<br />
<div class="atfigure" align="center" style="width:580px">Fig3. SDS PAGE shows the expression of LTB(L)、HBsAg(R)</div><br />
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<h3 style="font-size:24px;line-height:20px;">3. Verified the antigenicity of TD1-antibody by ELISA</h3><br />
<p>Verified the antigenicity of TD1-HBsAg by ELISA. The antigenicity of the TD1-antigen(fusion protein)strongly proved our theoretical basis. </p><br />
<img src="https://static.igem.org/mediawiki/2013/a/a9/ELISA.jpg" width="580" height="380"/><br />
<div class="atfigure" align="center" style="width:">Fig 4. Verify the antigenicity of TD1-HBsAg with ELISA</div><br />
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<h3 style="font-size:24px;line-height:20px;">4. Transdermal experiment</h3><br />
<p>TD1-HBsAg is able to penetrate the skin and keep its antigenicity: </p><br />
<br><br />
<div style="float:left;width:106px;height:170px;padding:5px"><br />
<img src="https://static.igem.org/mediawiki/2013/0/0b/2013ustc-china_transdevice.png" width="106" height="150" /><br />
<div class="atfigure" align="center" style="width:106px">Fig 5. Special transdermal device</div></div><br />
<p>To prove that TD1-HBsAg is able to pass across the skin and keep its antigenicity, we utilized a <span>special device</span> in the picture below, whose upper tube and lower tube can be separated by fresh skin peeled from mice, and all we were required to do was fastening the device, adding protein solution to the upper tube and extracting appropriate volume of liquid from the physiological saline in the lower tube to check the concentration of TD1-HBsAg which had crossed the skin during diverse periods.</p><br />
<img src="" width="" height="" /><br />
<div class="atfigure" align="center" style="width:">Fig 6. Check the concentration of TD1-HBsAg in the liquid under the skin during diverse periods with ELISA</div><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
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<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
<div>At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</div></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
<div>In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</div></div></br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
<br />
<br />
<div></br></br>The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
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</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h2>Project Safety</h2><br />
<h3>Would any of your project ideas raise safety issues in terms of researcher safety,public safety or environmental safety?</h3><br />
<p>To ensure biosafety, we design a <a href="https://2013.igem.org/Team:USTC_CHINA/Project/Design" target="_blank" >kill switch</a> in Bacillus for the first time in iGEM. The very type B.subtilis, which contains kill switch circuit, can elimate their siblings and commit suicide when the switch is activated, and thus prevent gene contamination and raise project safty in terms of researcher safety, public safety and environmental safety.</p><br />
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<h2>Parts Safety</h2><br />
<h3>Do any of the new BioBrick part (or devices) that you made this year raise any safety issues?</h3><br />
<p>The only safety issue associated with our new BioBrick parts is researcher safety in testing the parts. We've revised a strict Lab operation standard to raise safty.<br><br />
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<h2>Safty Supervision</h2><br />
<h3>Is there a local biosafety group, committee, or review board at your institution? </h3><br />
<p>Yes.Supervised by biosafety committee,we accepted their advice and abandoned intention to use HBV genome as template to amplify HBsAg antigen. With their help,we obtained plasmid fused HBsAg antigen eventually.</p><br />
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<h1>Attributions</h1><br />
<br />
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<br />
<p> <br />
In the last two months,thanks to our devotion and the support of various professors and scientific institutions ,our team achieved proud results.<br><br />
In the summer vacation,we used the gene material donated by scientific institutions and individuals to standardize and splice.we standardized and spliced transdermal peptide and gene circuits consists of various fusion protein of antigen.Meanwhile,we expressed TD1-GFP、TD1-HBsAg、TD1-LTB and all of expression of them was verified by in the E.coli. TD1-PA、TD1-HBsAg、TD1-Ag85b and TD1-LTB constructed circuits of the secretion vector,WB800N.Firstly,the transdermal experiment outside human body succeeded.Secondly,we also try to do experiment in living mice.Generally,we construct 16 new parts,we set a foundation for toolkit.Also our standardized BBa_K1074006 set a frame for other secretion expression researchers,theoretically users can use TD1 to merge any protein,to made the target protein have the function of secretion and transdermal permeation.<br><br />
<br> <br />
Thanks to the following individuals and institutions:<br><br />
1.Gene donation<br><br />
Standardized antigen:Chinese Centre for Disease<br><br />
TD-1 short chain poly peptide:Professor Longping Wen<br><br />
2.Theoretically support:<br><br />
Consultation of Bacillus subtilis:Professor Xin Run,Nanjing Agriculture University<br><br />
Consultation of transdermal experiment:Professor Longping Wen<br><br />
Training of mice experiment:Professor Ting Yue<br><br />
<br />
3.Preliminary Partner:Hualan Biology Co.,ltd.<br><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/TeamTeam:USTC CHINA/Team2013-09-27T18:17:26Z<p>NanoWu: </p>
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<h2>Students</h2><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/2/21/Zhangsitao1.JPG" alt="Zhang Sitao"> <br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao"><br />
<div class ="nameplate"><a href="#">Zhang Sitao</a> </div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/0/0d/Zhangsitao2.JPG" alt="Zhang Sitao" align="left"><p>Our labor leader weighs various matters, leads the overall trend and plays our cards right. He leaves a strong impression in others’ mind. However, His friends found that the leader is very cute.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/0/02/Zhaochanglong1.JPG" alt="Changlong Zhao"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" ><br />
<div class ="nameplate"><a href="#">Changlong Zhao</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/7/7e/Zhaochanglong2.JPG" alt="Changlong Zhao" align="left"><p>There’s no doubt that we can give full stars for Changlong’s fighting capacity. The roads leading to success will never be smooth and Changlong is a perfect companion to travel with.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/9/91/Xionghanjin1.JPG" alt="Hanjin Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" ><br />
<div class ="nameplate"><a href="#">Hanjin Xiong</a></div><br />
<div class = "details"><br />
<img src="https://static.igem.org/mediawiki/2013/d/d9/Xionghanjin2.JPG" alt="Hanjin Xiong" align="left"><p>As the keynote speaker of our team, he always keeps a clear head with extraordinary creativity and expressiveness. He said, “It is shameful if you haven’t burnt the midnight oil for iGEM.” Moving forward bravely, he shows us overwhelming power which nobody can stop it.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/2/23/Limingyue1.JPG" alt="Mingyue Li"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li"><br />
<div class ="nameplate"><a href="#">Mingyue Li</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/05/Limingyue2.JPG" alt="Mingyue Li" align="left"><p>“Mingyue Bacteria” is the spokesperson of our bacterium, handling the destiny of those little lives. We all agreed that, Mingyue with rubber gloves is GORGEOUSNESS!</p></div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/8/85/Shenshengqi1.JPG" alt="Shen Shengqi"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" ><br />
<div class ="nameplate"><a href="#">Shen Shengqi</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/4/44/Shenshengqi2.JPG" alt="Shen Shengqi" align="left"><p>Everyone considers that it is honored to be a friend of “Brother Face” as he is a totally “local tyrant”. Actually,” Brother Shen” is warmth, nice, really expert in digging shortcuts in the experiments. He is a sharp soldier of our team as he adheres to the “more with less” principle.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c1/Madanyi1.JPG" alt="Danyi Ma"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" ><br />
<div class ="nameplate"><a href="#">Danyi Ma</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/1/19/Madanyi2.JPG" alt="Danyi Ma" align="left"><p>”Aunty Ma” takes charge of our finance and safety, which calls for much patience and responsibility. In the experiment, she also plays an absolutely necessary role.</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/8/87/Zhangheng1.JPG" alt="Zhang Heng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" ><br />
<div class ="nameplate"><a href="#">Zhang Heng</a> </div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/6/63/Zhangheng2.JPG" alt="Zhang Heng" align="left"><p>He is a man full of responsibility, we could 100% trust him! Bro, it’s you that bring us positive energy!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f9/Yuanye1.JPG" alt="Yvette Yuan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" ><br />
<div class ="nameplate"><a href="#">Yvette Yuan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/8/81/Yuanye2.JPG" alt="Yvette Yuan" align="left"><p>As a s pronoun for efficient, Yuan Ye is studious and decisive. And what makes her best is that she always brings us delicious oranges.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/a3/Xinghuayue1.JPG" alt="Huayue Xing"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" ><br />
<div class ="nameplate"><a href="#">Huayue Xing</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/ae/Xinghuayue2.JPG" alt="Huayue Xing" align="left"><p>With my little eyes, I see bacterium; with my little eyes, I see TD-1; with my little eyes, I see vaccine secreted out; with my little eyes, I see the future without needles. Carefulness, earnest, and a little bit of acting cute, I am XHY.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/a/ad/Xionglei1.JPG" alt="Lei Xiong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" ><br />
<div class ="nameplate"><a href="#">Lei Xiong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/b/b2/Xionglei2.JPG" alt="Lei Xiong" align="left"><p>Despite the fact that it is me who always breaks test tubes, loses beakers, and pours reagent onto the skin of my hands, I have the enthusiasm for science. I love to explore and pursue knowledge. As long as there is a chance to see the tip of the iceberg, it doesn't matter how many test tubes I am going to break.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/7/76/Panminghao1.JPG" alt="Minghao Pan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" ><br />
<div class ="nameplate"><a href="#">Minghao Pan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/ed/Panminghao2.JPG" alt="Minghao Pan" align="left"><p>I love physics and biology.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/c/c8/Dongbo1.JPG" alt="Bo Dong"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" ><br />
<div class ="nameplate"><a href="#">Bo Dong</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/0/08/Dongbo2.JPG" alt="Bo Dong" align="left"><p>He is an earnest boy, he always work hard that every bros and sis like him, he is our team’s MVP! <br />
Hey, bro! It our pleasure to be with you!</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/3/3f/Chenzhaoxiong1.JPG" alt="Zhaoxiong Chen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen"><br />
<div class ="nameplate"><a href="#">Zhaoxiong Chen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/d/dc/Chenzhaoxiong2.JPG" alt="Zhaoxiong Chen" align="left"><p>This smart boy is good at playing all kinds of computer systems. We believe that he will refresh the history of wikis!</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/15/Wuming1.JPG" alt="Min Wu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu"><br />
<div class ="nameplate"><a href="#">Min Wu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/b/be/Wuming2.JPG" alt="Min Wu" align="left"><p>I love experiments. I love games. I love Weibo.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/1/14/Wangshiwei1.JPG" alt="Shiwei Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang"><br />
<div class ="nameplate"><a href="#">Shiwei Wang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/e/e2/Wangshiwei2.JPG" alt="Shiwei Wang" align="left"><p>Again, a quiet boy is coming! He love experiment, he is Bo Dong’s loyal friend. We all believe in him, without his help we cannot achieve our goal! Thanks a lot ,my bro! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/2013/e/e4/Fansijia1.JPG" alt="Sijia Fan"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan"><br />
<div class ="nameplate"><a href="#">Sijia Fan</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/2013/5/57/Fansijia2.JPG" alt="Sijia Fan" align="left"><p>Black humorist, and sadly, the leader is always shouting at me:” Hurry! Hurry!”.</p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/d/df/Pengyali1.JPG" alt="Yali Peng"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng"><br />
<div class ="nameplate"><a href="#">Yali Peng</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/0c/Pengyali2.JPG" alt="Yali Peng" align="left"><p>She is a quiet girl, she likes smile, she loves doing experiments peacefully and slowly. As the best partner of Mingyue Li, every trouble become easy! Hey, little pretty we all love you! </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/5/52/Longjie1.JPG" alt="Long jie"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie"><br />
<div class ="nameplate"><a href="#">Long jie</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/9/96/Longjie2.JPG" alt="Long jie" align="left"><p>Clever and hard-working, I cannot agree more to do experiments with him. You never let us down!</p><br />
</div><br />
</div><br />
</div><br />
<br />
<br />
<div class ="row"><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/b/bd/Caoqinjingwen1.JPG" alt="Cao Qinjingwen"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen"><br />
<div class ="nameplate"><a href="#">Cao Qinjingwen</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/f/f9/Caoqinjingwen2.JPG" alt="Cao Qinjingwen" align="left"><p>Excellent! Without these kinds of words, how can I say anything to describe her? As our elder sister, she always gives us self-confident, hey soul sister!</p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/60/Shaoxueying1.JPG" alt="Shao Xueying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying"><br />
<div class ="nameplate"><a href="#">Shao Xueying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/e/e9/Shaoxueying2.JPG" alt="Shao Xueying" align="left"><p>Competent and independent, Shao Xueying has unique ideas about colors and graphics. At the same time, she is a good lecturer. She edits our wiki and make presentation for us. </p><br />
</div><br />
</div><br />
<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/49/Qiuyanning1.JPG" alt="Yanning Qiu"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu"><br />
<div class ="nameplate"><a href="#">Yanning Qiu</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/d/df/Qiuyanning2.JPG" alt="Yanning Qiu" align="left"><p>Our little sister holds the trump cards. She always knows what do with all the words and pictures. Brave and creative, Yanning enjoys the days with new skills and knowledge. Our team was painted colorfully with the lively girl.</p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/9/9a/Wangzeyu1.JPG" alt="Zeyu Wang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang"><br />
<div class ="nameplate"><a href="#">Zeyu Wang</a></div><br />
<div class = "details"><a href="http://home.ustc.edu.cn/~wangzeyu/contact%20me.htm"><img src="https://static.igem.org/mediawiki/igem.org/5/53/Wangzeyu2.JPG" alt="Zeyu Wang" align="left"></a><p>Although I was a freshman and initially came to USTC iGEM , I did some experiment in molecular cloning.I took part in human practice and wiki writing.I also helped with presentation. Thank you,USTC iGEMers!<br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xiaozhuyun1.JPG" alt="Xiao Zhuyun"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun"><br />
<div class ="nameplate"><a href="#">Xiao Zhuyun</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/1/1d/Xiaozhuyun2.JPG" alt="Xiao Zhuyun" align="left"><p>Sincere and straightforward, “piggy”, the curve wrecker in our eyes, puts all her efforts into research and study. Only when you get close to her, will you find that she also loves to play, that she also loves life.</p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/f/f3/Yanggege1.JPG" alt="Gege Yang"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang"><br />
<div class ="nameplate"><a href="#">Gege Yang</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/2/25/Yanggege2.JPG" alt="Gege Yang" align="left"><p> She is majoring in Life Sciences. She is in charge of the construction of one type of engineering bacteria producing fusion protein. As a member of the wet lab, she enjoys the work as well as meets new friends this summer.</p><br />
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<div class ="row"><br />
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<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/6/62/Hanyingying1.JPG" alt="Han Yingying"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying"><br />
<div class ="nameplate"><a href="#">Han Yingying</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/c/ca/Hanyingying2.JPG" alt="Han Yingying" align="left"><p>Tender as a new-born kitty, Yingying doesn’t like to stand in the spotlight. She’s a diligent brain instead of a silken tongue. We believe that gold will shine no matter where it is. </p><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/1/18/Chenzhuo1.JPG" alt="Chen Zhuo"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo"><br />
<div class ="nameplate"><a href="#">Chen Zhuo</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/a/af/Chenzhuo2.JPG" alt="Chen Zhuo" align="left"><p>Always, he is still of tongue, but he is not only a genius of experiment, but also a brilliant living library. I cannot say more but admire! </p><br />
</div><br />
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<div class ="profilewrap"><br />
<img class ="normal" src="https://static.igem.org/mediawiki/igem.org/4/4a/Xuehao1.JPG" alt="Hao Xue"><br />
<img class ="crazy" src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue"><br />
<div class ="nameplate"><a href="#">Hao Xue</a></div><br />
<div class = "details"><img src="https://static.igem.org/mediawiki/igem.org/0/08/Xuehao2.JPG" alt="Hao Xue" align="left"><p>Laughing, he is still laughing! What on hill? Oh god, negative results, but how… But bro, thank you for giving us positive energy, you really raise us up! My bro! </p><br />
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<h2>Advisers</h2> <br />
<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu"><br />
<div class ="nameplate"><a href="#">Haiyan Liu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/f/f0/Haiyan_Liu.jpg" alt="Haiyan Liu" align="left"><p>Haiyan Liu was born in Sichuan Province, China. He received his BS degree in Biology in 1990 and PhD degree in Biochemistry and Molecular Biology in 1996, both from USTC. Between 1993 and 1995 he was a visiting graduate student in Laboratory of Physical Chemistry of ETH, Zurich (Switzerland). Since 2001, he has been a professor of computational biology at School of Life Sciences, USTC. </p><br />
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<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong"><br />
<div class ="nameplate"><a href="#">Jiong Hong</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/0/09/Hongjiong.PNG" alt="Jiong Hong" align="left"><p> I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. My ongoing project is to identify biomarkers in order to detect the progress stages of the diabetes. In addition, I have planed to analyze the genetic and environmental factors and their interactions during the progressing of the type 2 diabetes with systems-biology approaches.</p><br />
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<div class ="profilewrap" style="width:160px;margin:60px 80px 5px;"><br />
<img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu"><br />
<div class ="nameplate"><a href="#">Jiarui Wu</a></div><br />
<div class = "details"><img style="width:160px" src="https://static.igem.org/mediawiki/2013/4/46/Wujiarui.PNG" alt="Jiarui Wu" align="left"><p>Since the research strategy of systems biology is well fit to analyze the biological complex systems. I am applying this strategy on the mechanism of the complex diseases such as cancer and diabetes. We have developed systematic approaches based on proteomics and bioinformatics to analyze human normal and diabetic serum.</p><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/HumanPractice/CommunicationTeam:USTC CHINA/HumanPractice/Communication2013-09-27T18:15:54Z<p>NanoWu: </p>
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<h1>Talking with peers</h1><br />
<p>Communication makes science attractive, and learning from each other lights up iGEM competition. It says, a single conversation across the table with a wise man worth a month's study of books. Talking with peers bridges the gap between us and promotes our cooperation. We had visited five iGEM teams, (SJTU,FDU,NJU,WHU and PKU,) thus we travelled almost all over China within half a year. Moreover, in order to increase iGEM’s popularity in China, we also be invited to two universities which are good at Biosciences (Nanjing Agricultural University, Henan Normal University) to give speeches about iGEM.<br />
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<img src="https://static.igem.org/mediawiki/2013/a/aa/SAM_2942.JPG"/width="500"height="325"><br />
<p>Visitor from SDU</p><br />
<img src="https://static.igem.org/mediawiki/2013/f/ff/Large_0XWJ_273300001606118f.jpg"width="500"height="325"><br />
<img src="https://static.igem.org/mediawiki/2013/6/6f/Large_DWC7_265300000920118e.jpg"width="500"height="325"><br />
<img src="https://static.igem.org/mediawiki/2013/4/4e/Large_pFgp_256b00000914118e.jpg"width="500"height="325"><br />
<p>Visit FDU</p><br />
<img src="https://static.igem.org/mediawiki/2013/8/82/SJTU1.jpg"width="500"height="375"><br />
<img src="https://static.igem.org/mediawiki/2013/6/6a/SJTU2.jpg"width="500"height="375"><br />
<p>Visit SJTU</p><br />
<img src="https://static.igem.org/mediawiki/2013/0/08/WHU.jpg"width="500"height="275"><br />
<p>Visit WHU</p><br />
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<h1>Consulting professors</h1><br />
<p>To find the best project and improve the subject, we visited three universities (Nanjing Agricultural University, Wuhan University, Henan Agricultural University), and we went to four institute which affiliated to Chinese academy of sciences (China Center for Disease Control and Prevention, Virus Research Institute of Chinese Academy of Sciences, Chinese Academy of Sciences Institute of Aquatic Organisms, Guangzhou Pharmaceutical Research Institute) for help, consulting 17 senior professors. We also established a preliminary cooperative relationship with a famous biotechnology company (Hualan bio-engineering: research and development base of H1N1 vaccine).</p><br />
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<h1>May festival</h1><br />
<p>As one of iGEMers’ classical activities, our lab is open to public at one weekend on May 18th, we welcomed 18 groups of high school students and 11 groups of primary school students. We welcomed over 500 normal.<br />
In order to show our lab work and popularize synthetic biology, we rearranged our lab and created several kids’ games about iGEM.<br />
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<img src="https://static.igem.org/mediawiki/igem.org/b/b2/2013ustc-china_may_festival1.jpg"/width="500"height="375"><br />
<img src="https://static.igem.org/mediawiki/igem.org/1/16/2013ustc-china_may_festival_2.jpg"width="500"height="600"><br />
<p>Blowing the gloves? Are you kidding? It comes true in USTC iGEM’s lab! DIY+gloves=amazing!<br />
Who say that we just have machine and reagents here? Welcome to USTC iGEM’s lab 363! What we have created is far more than fairytales!<br />
</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/1/10/2013ustc-china_may_festival_3.jpg"width="500"height="355"><br />
<img src="https://static.igem.org/mediawiki/igem.org/d/dc/2013ustc-china_may_festival_4.jpg"width="500"height="325"><br />
<imgg src="https://static.igem.org/mediawiki/igem.org/b/be/2013ustc-china_may_festival5.jpg"width="500"height="325"><br />
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<h1>Super-taster</h1><br />
<p>Biosensor has been a classical topic in iGEM and Synthetic Biology. Many biosensor cases have been known by public, for example, detecting pollutants in the environment and fluorescent coloring. Therefore, biosensor is a good example to explain the ideology of iGEM. USTC iGEMers are always devoted into popularizing synthetic biology. After last year’s Hefei Genetically Modified (GM) Knowledge Competition, we host an activity named ”Super Taster” to recruit more people to take a brief glance at iGEM. Are we better taster than engineered bacterial? We provided others a chance to see and feel “biosensor”. Come on! Join us! </p><br />
<img src="https://static.igem.org/mediawiki/igem.org/7/7a/2013ustc-china_taster_1.jpg" width="500" height="420" /><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/ea/2013ustc-china_taster_2.jpg"width="500"height="325"/><br />
<div class="atfigure" align="center" style="width:;"></div><br />
<br />
<br />
<div class="basic-bar"><br />
<h1>Lecture</h1><br />
<p>As the most classical way to display, the lecture is indispensable! To meet thr requirement of different people, we used 3D film to show the world inside the cell, and we also show them one of our iGEM team’s clay movie, so that children can understand iGEM.Of course, our own propaganda video was also shown. Here we would like to thank USTC Alumni Foundation for helping us make an elegant propaganda video!</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/a/a8/2013ustc-china_lecture1.jpg" width="500" height="375" /><br />
<img src="https://static.igem.org/mediawiki/igem.org/7/78/2013ustc-china_lecture_2.jpg"width="500" height="350" /><br />
<div class="atfigure" align="center" style="width:;"></div><br />
</div><br />
</div><br />
<div class="basic-bar"><br />
<h1>Art of T-vaccine</h1><br />
<p>Our souvenir</p><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/e8/2013ustc-china_igem_art1.jpg" width="500" height="300" /><br />
<img src="https://static.igem.org/mediawiki/igem.org/e/e7/2013ustc-china_art_device_2.jpg"width="500"height="350"/><br />
<img src="https://static.igem.org/mediawiki/igem.org/f/ff/2013ustc-china_art_device_3.jpg"width="500"height="300"/><br />
<div class="basic-bar"><br />
<h1>Device</h1><br />
<p>Our device for storing and activating T-Vaccine patches.</p><br />
<p>We designed a “Bacteria Box” as our assistance device for instant production. Covered with sterile membrane, the box contains dry powder of engineering bacteria and dehydrated medium, and once adequate water is added, the bacteria will be activated and ready to produce. Then we further enhance the device and invent the new double-layer device “Bacteria Box II”, in which the dehydrated medium and bacteria are stored at different layers. All we are required to do is to extract the division plate between layers and the bacteria and medium will naturally mix up. Compared with the former one, the bacteria and medium are separated, thus facilitating transportation and avoiding potential contamination.</p><br />
<img src="https://static.igem.org/mediawiki/2013/6/6b/2013_ustc-china_device6.jpg"width="500"height="375"/><br />
<div class="atfigure" align="center" style="width:;"></div><br />
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<br />
</body><br />
</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/HumanPracticeTeam:USTC CHINA/HumanPractice2013-09-27T18:14:39Z<p>NanoWu: </p>
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<div class="part-tittle"><h>Communication</h></div><br />
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<p>USTC_CHINA 2013<br><br />
Travel almost<span> all </span>over China within half a year<br><br />
Visit<span> Five </span>igem teams,<span> Four </span>CAS institutes,<span> Seventeen </span>senior professors<br><br />
Give special report in<span> Four </span>universities and establish a preliminary cooperative relationship with<span> One </span>famous biotechnology company.<br></p></div><br />
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<br />
<div class="pin pin-down" data-xpos="170" data-ypos="100"> <br />
<h2>North America</h2> <br />
<ul><br />
<li><b>Area (km�):</b> 24,490,000</li><br />
<li><b>Population:</b> 528,720,588</li><br />
<br />
</ul><br />
</div><br />
<br />
<div class="pin" data-xpos="270" data-ypos="320"> <br />
<h2>South America</h2> <br />
<ul><br />
<li><b>Area (km�):</b> 17,840,000</li><br />
<li><b>Population:</b> 382,000,000</li><br />
<br />
</ul> <br />
</div><br />
<br />
<div class="pin pin-down" data-xpos="450" data-ypos="110"> <br />
<h2>Europe</h2> <br />
<ul><br />
<li><b>Area (km�):</b> 10,180,000</li><br />
<li><b>Population:</b> 731,000,000 </li><br />
<br />
</ul><br />
</div><br />
<br />
<div class="pin" data-xpos="450" data-ypos="250"> <br />
<h2>Africa</h2> <br />
<ul><br />
<li><b>Area (km�):</b> 30,370,000</li><br />
<li><b>Population:</b> 1,022,011,000</li><br />
<br />
</ul> <br />
</div><br />
<br />
<div class="pin pin-down" data-xpos="650" data-ypos="130"> <br />
<h2>Asia</h2> <br />
<ul><br />
<li><b>Area (km�):</b> 43,820,000</li><br />
<li><b>Population:</b> 3,879,000,000</li><br />
<br />
</ul><br />
</div><br />
<br />
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<h2>Australia</h2> <br />
<ul><br />
<li><b><img src="images/拼图.png" width="200" height="100" />Area (km):</b> 9,008,500</li><br />
<li><b>Population:</b> 31,260,000</li><br />
<br />
</ul> <br />
</div><br />
</div> <br />
<div class="part"><br />
<div class="part-tittle"><h>Activity</h></div><br />
<div class="part-content"><br />
<p>USTC_CHINA 2013</br><br />
Travel almost<span> all </span>over China within half a year<br /><br />
Visit<span> Five </span>igem teams,<span> Four </span>CAS institutes,<span> Seventeen </span>senior professors<br /><br />
Give special report in<span> Four </span>universities and establish a preliminary cooperative relationship with<span> A </span>famous biotechnology company.<br /></p></div><br />
<div class="part-details"><br />
<a href="#">Details</a><br />
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</div><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperimentsTeam:USTC CHINA/Modeling/DesignsofImmuneExperiments2013-09-27T18:13:17Z<p>NanoWu: </p>
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<div style="margin-top:20px;"><br />
<h1>Introduction</h1><br />
<p>Our mice experiment has primarily proven the validity of our project. However, just like most scientific immune experiments on animals, the aim of our mice experiment was verification instead of exploring the optimal conditions for the production of our vaccine. In fact, fewer optimization experiments have been done by pure scientific researches, as most scientists care about facts and theories only, whereas exploring the optimal conditions is often viewed as the task of pharmaceutical factories. Yet since igem itself frequently involves industrial fields, which make igem seems like more an engineering competition than a science competition sometimes.</br> <br />
<br />
We investigated the methodology of Design of Experiment (DOE) in our project, and realized although most papers claim the wide application of DOE, the popularity of DOE is much lower in scientific fields compared with that in engineered fields. Perhaps the disparity of ideology between science and engineering determines this puzzling phenomenon. Consider the dual qualities of igem, we decided to explore on DOE further and design further experiments for pharmaceutical factories. We have also utilized DOE on our optimization of Bacillus subtilis medium experiment. Various designs have been made, and the overall runs of them all are too large for our laboratory.</br> <br />
But generally factories have adequate time and equipment to fulfill our designs, and different designs meet the requirement of different situations.<br />
</br> <br />
</p><br />
</div><br />
<div><br />
<h1>Sweeping factors</h1><br />
The final effects of the vaccine hinge on various factors, in fact perhaps over ten factors. Yet the more factors, the more runs. In our laboratory, an experiment involving over five factors is hard to design, whatever the method. Fortunately we were designing experiments for pharmaceutical factories, which enabled us to take more factors into account without sacrificing accuracy too much.<br />
The first step of any method in DOE is to make a list of controllable factors, and the second step is to find out levels of each factors. In our design, we finally selected eight factor as follows:</br><br />
The rate of four engineered bacteria, which produce antigen, LTB, KNFα and reporter respectively;(We selected the concentration of antigen as our standard, fixed at 1, and the rates of other three bacteria to engineered bacteria produced antigen provides three independent factor);</br><br />
<ul><br />
<li>The area of the sticky vaccine;</li><br />
<li>The concentration of bacteria per unit area;</li><br />
<li>The body temperature of the vaccinees;</li><br />
<li>The time consumed for culturing the bacteria;</li><br />
<li>The molecule weight of the antigen;</li><br />
</ul></br><br />
The ranges of these factor is given as follows:</li><br />
<table border="1" cellspacing="0" cellpadding="0"><br />
<tr><br />
<td width="190" valign="top"><p>Factor</p></td><br />
<td width="190" valign="top"><p>Level Values</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>LTB</p></td><br />
<td width="190" valign="top"><p>-1 0 1</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>KNFα </p></td><br />
<td width="190" valign="top"><p>-1 0 1</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Reporter</p></td><br />
<td width="190" valign="top"><p>-4 -3</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Temperature/℃ </p></td><br />
<td width="190" valign="top"><p>35.5 36 36.5 37 37.5</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Time/h</p></td><br />
<td width="190" valign="top"><p>4 5 6 7 </p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Area/ </p></td><br />
<td width="190" valign="top"><p>1 3 7 10</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Concentration(the number of engineered bacteria per square centimeter )</p></td><br />
<td width="190" valign="top"><p>7 8 9 </p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Molecule Weight(K D)</p></td><br />
<td width="190" valign="top"><p>10 20 40 80</p></td><br />
</tr><br />
</table></br><br />
<h4>Note: </h4>The ranges of rates and concentration of engineered bacteria were too large, and thus we used the common logarithms instead of the original values. For example, the low level of LTB was -1, meaning the lowest rate of LTB to antigen was 0.1.</br><br />
<br />
</div><br />
<br />
<br />
<br />
<div><br />
<h1>Abstract of DOE methods</h1><br />
The classification standards of DOE methods are not unified, and according to one classification the DOE methods can be classifies into three plots:</br><br />
Factorial Designs: Factorial Design is the most traditional method of DOE, and theoretically all other plots origin from it. Factorial Design is recommended when the ranges of factors is too large.</br><br />
Response Surface Designs: Response Surface utilizes response surface and excels in data analysis. </br><br />
Taguchi Designs: Taguchi Designs utilizes orthogonal table to decrease runs, and emphasizes the stability of qualities. Some mathematicians doubt the accuracy of this method, yet its wide success has proven its power.</br><br />
<br />
We have tried them all in our project.</br><br />
<br />
<br />
<br />
</div><br />
<div><br />
<h1>Factorial Designs</h1><br />
To some extent, all DOE methods are branches of Factorial Designs. The easiest subplot of Factorial Designs is Full Factorial Designs, meaning making a list of all combinations of all levels, which in fact does nothing to minimizing the runs. Surly the overall runs of Full Factorial Designs is larger than any other method, yet it does provide the most detailed information, so it is recommended when the factory does not care about money and time.</br><br />
Generally Full Factorial Design has nothing mathematically sophisticated, all required is to list the specific values of all factors without any limitation on levels, which grants us more flexibility and freedom. Here is our table of levels of factors:</br><br />
<table border="1" cellspacing="0" cellpadding="0"><br />
<tr><br />
<td width="190" valign="top"><p>Factor</p></td><br />
<td width="190" valign="top"><p>Level Values</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>LTB</p></td><br />
<td width="190" valign="top"><p>-1 0 1</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>KNFα </p></td><br />
<td width="190" valign="top"><p>-1 0 1</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Reporter</p></td><br />
<td width="190" valign="top"><p>-4 -3</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Temperature/℃ </p></td><br />
<td width="190" valign="top"><p>35.5 36 36.5 37 37.5</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Time/h</p></td><br />
<td width="190" valign="top"><p>4 5 6 7 </p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Area/ </p></td><br />
<td width="190" valign="top"><p>1 3 7 10</p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Concentration(the number of engineered bacteria per square centimeter )</p></td><br />
<td width="190" valign="top"><p>7 8 9 </p></td><br />
</tr><br />
<tr><br />
<td width="190" valign="top"><p>Molecule Weight(K D)</p></td><br />
<td width="190" valign="top"><p>10 20 40 80</p></td><br />
</tr><br />
</table></br>And we got our first design, whose number of overall runs is 17820! </br><br />
<a href="https://static.igem.org/mediawiki/2013/2/22/Full_Factorial_Designs_17280runs.XLS">Full Factorial Designs 17280 runs</a></br><br />
In reality we did not deem this level values table was detailed enough, but the number of runs was already enormous. Perhaps only the biggest pharmaceutical factory can afford this design.</br><br />
<br />
Next we turned to traditional Factional Factorial Designs. To minimize the runs, the levels of all factors were fixed at 2. A general 2-level-8-factor Full Factorial design contains 2^8=256 treatments, but we can further decrease the runs by defining alias. That is to say, define some specific factors as logical operation results of other factor.</br><br />
Here we got a half and a quater Factional Factorial Designs, and the numbers of runs of them are 128 and 64.</br><br />
<a href="https://static.igem.org/mediawiki/2013/e/ed/Factorial_Designs_64runs.XLS"> Factorial Designs 64runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/3/3c/Factorial_Designs_128runs.XLS"> Factorial Designs 128 runs</a></br><br />
Any effort trying to decrease runs will inevitably lower the cogency of the experiments, and this influence is irreversible. Factories are supposed to strike a balance between the accuracy of experiments and the costs they can afford when designing experiments.</br><br />
<br />
<br />
<br />
<br />
<br />
</div><br />
<div><br />
<h1>Plackett-Burman Design</h1><br />
As an important subplot of Factorial Designs, Plackett-Burman Design is excellent in dealing with mass factors. Generally it was applied in the primary experiments to select the key factors for further experiments. The number of runs can be controlled at very low values, yet it is hard to get the best treatment from Plackett-Burman Design. </br><br />
Naturally the levels of all factors were two. On most occasions it is combined with other DOE methods, like RSM. In our project, we made three Plackett-Burman Designs of 12 runs, 20 runs and 48 runs. The more runs, the more reliable results will be get, but even the last design still requires further designs.</br><br />
<a href="https://static.igem.org/mediawiki/2013/b/b3/Plackett-Burman_20_runs.XLS">Plackett-Burman 20 runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/3/3f/Plackett-Burman_12_runs.XLS">Plackett-Burman 12 runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/e/e0/Plackett-Burman_48_runs.XLS">Plackett-Burman 48 runs</a></br><br />
</br><br />
<br />
<br />
</div><br />
<div><br />
<h1>Response Surface Design</h1><br />
Utilized response surface and gradient, Response Surface Design excels in analysis of data, which makes it more mathematically gracefully than Taguchi Designs, and this accounts for why we selected it for our experiments on the optimization of medium<br />
The most widespread subplots of Response Surface Design is Central Composite Design and Box-Behnken Designs, both of which were considered when we designed our experiments on medium. The number of factors of Box-Behnken Designs is fixed on some given values, which does not include eight, therefore we had to turn to Central Composite Design (CCD). CCD itself contains three subplots, namely Central Composite Circumscribed Design (CCC), Central Composite Inscribed Design (CCI) and Central Composite Face-centered Design (CCF). Only CCC is rotatable, and thus CCC is mathematically preferred. We designed the experiments on CCC and CCF. The numbers of runs in half CCC and CCF designs were 154, whereas in quarter designs 90.</br><br />
<a href="https://static.igem.org/mediawiki/2013/0/02/CCC-90runs.XLS">CCC 90runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/b/bc/CCC-154runs.XLS">CCC 154runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/c/ce/CCF-90runs.XLS">CCF 90runs</a></br><br />
<a href="https://static.igem.org/mediawiki/2013/7/75/CCF-154runs.XLS">CCF 154runs</a></br><br />
In spite of the mathematical advantages of CCC, the alpha value, which means the distance from axial point to the center point, is larger than one, some absurd treatment might be yielded. In our half CCC design the alpha value was 3.364, while in quarter CCC design 2.828. In both designs, some treatments are irrational, for their area or concentration were negative, which contradicts the common sense. However, factories can still adopt these CCC designs by giving up the irrational treatments.</br><br />
<br />
<br />
</div><br />
<div><br />
<h1>Taguchi Design</h1><br />
Taguchi Designs use orthogonal table to decrease the runs. Created by Doctor Taguchi, it has obtained wide success all over the world, especially in Asia. Different from Response Surface Design, it does not aim to calculate a fitting surface or function but just find out the best level value of each factor. Generally the number of runs is smaller compared with RSM, yet the range of factors in Taguchi Design is relatively smaller.</br><br />
We tried to make Taguchi Designs but our tool software minitab is unable to make the design with eight factor. Additionally, our ranges of factors were too large for Taguchi Design, therefore we gave up this method in our design.</br><br />
<br />
If our vaccine is fortunate enough to be produced at mass scale, we hope our designs could help these pharmaceutical factories. </br><br />
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<br />
<br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
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</div><br />
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<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<br />
<br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
<br />
<br />
<h1>References</h1><br />
AV Banse, A Chastanet, L Rahn-Lee….Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis,PNAS ,2008 </br><br />
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<h1>Why Do We Design This Experiment</h1><br />
<p>Bacillus subtilis has been widely applied as engineered bacteria, especially in food industry and pharmaceutical industry, for its safety and excellent secretion capacity. Therefore, after comparing characters of distinct mutants we selected Bacillus subtilis WB800N mutant as our engineered bacteria and looked up plenty of papers to select the optimal conditions for our experiment. To our disappointment, very few experiments have been done on WB800N mutant, and most optimization experiments regarding Bacillus subtilis focus solely on the optimization of production of specific proteins produced by Bacillus subtilis. Consider the final goal of our project, it is imperative to design this experiment on our own to find out the best condition for Bacillus subtilis WB800N.</p><br />
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<div><br />
<h1>Methodology</h1><br />
Any optimization designs will inevitably involve the ideology of Design of Experiment (DOE), which includes several dependent plots. Among them Orthogonal Design and Response Surface Design, RSM for short, are the most common two in biological experiments. Generally, Orthogonal Design consumes less time and has been used more widely, yet it is not logically rigorous in mathematics, and sometimes it overlooks interactions and alias between or among factors. In contrast, RSM is constructed on rigorous mathematical theories and excels in data analysis. Having weighing the features of the two methods carefully, we finally chose RSM.<br />
</div><br />
<br />
<div><br />
<h1>Sweeping Factors</h1><br />
The first step of any methods of DOE is to investigate all variables that affect the results and select controllable factors for the experiment. In terms of this experiment, all factors can be categorized into two kinds: environment factors, like temperature, the rotation speed of the shaker, and the components of the medium. We have looked up several papers about the optimization experiments on Bacillus subtilis, finding the rotation speed of shakers ranging from 100 r/min to 250 r/min, and generally rotation speed only plays a tiny role. Additionally, our lab has only two shakers. While we can place twenty different mediums into one shaker at a time, we must run the shakers every time we alert the speed, which surely consumes longer time. Thus, we fixed the rotation speed of shakers at 200r/min.However, temperature and inoculation time are both vital environment factors whose effects cannot be ignored.</br><br />
Inoculation amount and pack amount are also two factors that affect results slightly. We fixed them at 5 percent and 30mL/500mL respectively according to earlier authentic experiments.</br><br />
A typical medium consists of carbon source, nitrogen source and inorganic salt, all of which are essential to ensure the regular metabolism of engineered bacteria. Finally in light of convenience, we infered the components of typical LB medium and determined three independent medium factors: peptone, yeast extract and sodium chloride (NaCl). Peptone provides nitrogen and carbon for the colonies, while yeast extract contains most required inorganic salt, therefore we did not list any inorganic salt except NaCl. We had no idea why NaCl is listed alone, and we suspected the influence of NaCl as yeast extract had already contains sodium.</br><br />
Thus, we had five independent factors: temperature, inoculation time, peptone, yeast extract and NaCl. We further investigated some papers and defined their ranges. The following table displays their levels, and the unit of peptone, yeast extract and NaCl is g/L:<br />
</br><br />
<br />
<br />
<table border="1" cellspacing="0" cellpadding="0" width="577" backgroud-color="transparent"><br />
<tr><br />
<td>Factor</td><br />
<td>Low</td><br />
<td>High</td><br />
</tr><br />
<tr><br />
<td>Temperature</td><br />
<td>25℃</td><br />
<td>35℃</td><br />
</tr><br />
<tr><br />
<td>25℃</td><br />
<td>12h</td><br />
<td>24h</td><br />
</tr><br />
<tr><br />
<td>Peptone</td><br />
<td>5</td><br />
<td>15</td><br />
</tr><br />
<tr><br />
<td>Yeast Extract</td><br />
<td>2.5</td><br />
<td>7.5</td><br />
</tr><br />
<tr><br />
<td>NaCl</td><br />
<td>5</td><br />
<td>15</td><br />
</tr><br />
</table><br />
<b>Table 1.</b> Factors and their values of our design<br />
</div><br />
<div><br />
<h1>Designs&Results</h1><br />
The methodology of RSM can be divided into two subplots: Central Composite Designs (CCD) and Box-Behnken Designs. Generally the overall runs of Box-Behnken Designs is fewer when the factors are fixed, but Central composite designs are often recommended when the design plan calls for sequential experimentation because these designs can incorporate information from a properly planned factorial experiment. In our experiment, time is more precious than reagents, and as time itself is also an independent factor, Box-Behnken Designs would not have saved any time if adopted. Thus we selected CCD.</br><br />
CCD itself can also be classified into three subplots: Central Composite Circumscribed Design (CCC), Central Composite Inscribed design(CCI) and Central Composite Face-centered Design(CCF). The alpha value of CCC is related to the number of factors, whereas in CCF α is fixed at 1, and only CCC is rotatable. The rotational invariance empowers CCC to be mathematically preferred, yet the value of alpha in a five-factor-CCC is over 2. In other words, if we adopted CCC, we would get some absurd treatments where the concentration of some specific actual material were negative. If we narrowed down the range to ensure any concentration is positive, the ranges of all three medium factors would be too narrow to yield cogent results. Therefore, we finally selected CCF.</br><br />
We conducted our experiments according to the following table, which was calculated by Minitab, and the results, which were measure by OD value, were also included:</br><br />
<table border="1" cellspacing="0" cellpadding="0" width="577"><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="left">No.</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="left">Temperature</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="left">Time</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="left">Peptone</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="left">Yeast extract</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="left">NaCl</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="left">OD</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.511</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.625</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.783</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">4</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.74</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.317</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">6</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.4</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">7</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.912</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">8</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">9</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.169</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.77</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">11</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.371</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.7</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">13</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.754</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">14</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.58</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3.128</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">16</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.38</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">17</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">19</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.75</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">20</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">21</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.082</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">22</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.75</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">23</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.508</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.6</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.989</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">26</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.8</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">27</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.782</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">28</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.7</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">29</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.508</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.338</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">31</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3.061</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">32</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.2</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">33</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.167</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">34</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.53</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">0.555</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">36</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.9</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">37</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">38</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">39</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">40</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.957</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">41</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">25</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">1.907</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">42</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">35</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">43</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">12</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.652</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">44</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">24</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">45</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.726</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">46</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3.042</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">47</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">2.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.598</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">48</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">7.5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">3.124</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">49</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.999</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">50</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">15</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.834</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">51</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">52</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">53</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
<tr><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">54</p></td><br />
<td width="83" nowrap="nowrap" valign="bottom"><p align="right">30</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">18</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="107" nowrap="nowrap" valign="bottom"><p align="right">5</p></td><br />
<td width="100" nowrap="nowrap" valign="bottom"><p align="right">10</p></td><br />
<td width="72" nowrap="nowrap" valign="bottom"><p align="right">2.908</p></td><br />
</tr><br />
</table><b> Table 2.</b> Treatments and results of our experiment<br />
<br /><br />
The result of No.42 medium is destroyed due to some unfortunate reason. Additionally, multiple center points, which means conducting multiple experiments at the center points with identical treatments, is a very common phenomenon in DOE, yet we decided to do only experiment at the center point and reuse its result due to our limited time and reagents.</br><br />
<b>Estimated Regression Coefficients for OD</br></b><br />
<table border="1" cellspacing="0" cellpadding="0" width="100%"><br />
<tr><br />
<td width="43%" valign="top"><p><a name="OLE_LINK9" id="OLE_LINK9"></a><a name="OLE_LINK8" id="OLE_LINK8">Term </a></p></td><br />
<td width="16%" valign="top"><p>Coef</p></td><br />
<td width="15%" valign="top"><p>SE Coef </p></td><br />
<td width="13%" valign="top"><p>T </p></td><br />
<td width="11%" valign="top"><p>P</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Constant </p></td><br />
<td width="16%" valign="top"><p> 2.87625 </p></td><br />
<td width="15%" valign="top"><p>0.07126 </p></td><br />
<td width="13%" valign="top"><p>40.361 </p></td><br />
<td width="11%" valign="top"><p>0.000</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature </p></td><br />
<td width="16%" valign="top"><p> 0.60225 </p></td><br />
<td width="15%" valign="top"><p>0.05210 </p></td><br />
<td width="13%" valign="top"><p>11.560 </p></td><br />
<td width="11%" valign="top"><p>0.000</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Time </p></td><br />
<td width="16%" valign="top"><p> 0.28447 </p></td><br />
<td width="15%" valign="top"><p>0.05072 </p></td><br />
<td width="13%" valign="top"><p>5.608 </p></td><br />
<td width="11%" valign="top"><p>0.000</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Peptone </p></td><br />
<td width="16%" valign="top"><p> 0.18665 </p></td><br />
<td width="15%" valign="top"><p>0.05072 </p></td><br />
<td width="13%" valign="top"><p>3.680 </p></td><br />
<td width="11%" valign="top"><p>0.001</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Yeast Extract </p></td><br />
<td width="16%" valign="top"><p>0.16776 </p></td><br />
<td width="15%" valign="top"><p>0.05072 </p></td><br />
<td width="13%" valign="top"><p>3.308 </p></td><br />
<td width="11%" valign="top"><p>0.002</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>NaCl </p></td><br />
<td width="16%" valign="top"><p>-0.01626 </p></td><br />
<td width="15%" valign="top"><p>0.05072 </p></td><br />
<td width="13%" valign="top"><p>-0.321 </p></td><br />
<td width="11%" valign="top"><p>0.751</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature*Temperature </p></td><br />
<td width="16%" valign="top"><p>-0.54900 </p></td><br />
<td width="15%" valign="top"><p>0.24585 </p></td><br />
<td width="13%" valign="top"><p>-2.233 </p></td><br />
<td width="11%" valign="top"><p>0.033</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Time*Time </p></td><br />
<td width="16%" valign="top"><p>-0.18725 </p></td><br />
<td width="15%" valign="top"><p>0.19289 </p></td><br />
<td width="13%" valign="top"><p>-0.971 </p></td><br />
<td width="11%" valign="top"><p>0.339</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Peptone*Peptone </p></td><br />
<td width="16%" valign="top"><p> -0.08325 </p></td><br />
<td width="15%" valign="top"><p>0.19289 </p></td><br />
<td width="13%" valign="top"><p>-0.432 </p></td><br />
<td width="11%" valign="top"><p>0.669</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Yeast Extract*Yeast Extract </p></td><br />
<td width="16%" valign="top"><p>-0.10625 </p></td><br />
<td width="15%" valign="top"><p>0.19289 </p></td><br />
<td width="13%" valign="top"><p>-0.551 </p></td><br />
<td width="11%" valign="top"><p>0.586</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>NaCl*NaCl </p></td><br />
<td width="16%" valign="top"><p> -0.05075 </p></td><br />
<td width="15%" valign="top"><p>0.19289 </p></td><br />
<td width="13%" valign="top"><p>-0.263 </p></td><br />
<td width="11%" valign="top"><p>0.794</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature*Time </p></td><br />
<td width="16%" valign="top"><p>-0.358338</p></td><br />
<td width="15%" valign="top"><p>0.05228</p></td><br />
<td width="13%" valign="top"><p>-6.579</p></td><br />
<td width="11%" valign="top"><p>0.000</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature*Peptone </p></td><br />
<td width="16%" valign="top"><p>0.17881</p></td><br />
<td width="15%" valign="top"><p>0.05228</p></td><br />
<td width="13%" valign="top"><p>3.420</p></td><br />
<td width="11%" valign="top"><p>0.002</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature*Yeast Extract </p></td><br />
<td width="16%" valign="top"><p> 0.04544 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>0.869 </p></td><br />
<td width="11%" valign="top"><p>0.391</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Temperature*NaCl </p></td><br />
<td width="16%" valign="top"><p>0.01550</p></td><br />
<td width="15%" valign="top"><p>0.05228</p></td><br />
<td width="13%" valign="top"><p>0.296</p></td><br />
<td width="11%" valign="top"><p>0.769</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Time*Peptone </p></td><br />
<td width="16%" valign="top"><p> 0.02575 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>0.493 </p></td><br />
<td width="11%" valign="top"><p>0.626</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Time*Yeast Extract </p></td><br />
<td width="16%" valign="top"><p>.06112 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>1.169 </p></td><br />
<td width="11%" valign="top"><p>0.261</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Time*NaCl </p></td><br />
<td width="16%" valign="top"><p> -0.00144 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>-0.027 </p></td><br />
<td width="11%" valign="top"><p>0.978</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Peptone*Yeast Extract </p></td><br />
<td width="16%" valign="top"><p>-0.07469 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>-1.429 </p></td><br />
<td width="11%" valign="top"><p>0.163</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Peptone*NaCl </p></td><br />
<td width="16%" valign="top"><p>0.09150 </p></td><br />
<td width="15%" valign="top"><p>0.05228</p></td><br />
<td width="13%" valign="top"><p>1.750</p></td><br />
<td width="11%" valign="top"><p>0.090</p></td><br />
</tr><br />
<tr><br />
<td width="43%" valign="top"><p>Yeast Extract*NaCl </p></td><br />
<td width="16%" valign="top"><p>-0.04450 </p></td><br />
<td width="15%" valign="top"><p>0.05228 </p></td><br />
<td width="13%" valign="top"><p>-0.851 </p></td><br />
<td width="11%" valign="top"><p>0.401</p></td><br />
</tr><br />
<br />
<big><b>S = 0.295758 PRESS = 7.78904</br><br />
R-Sq = 92.25% R-Sq(pred) = 78.45% R-Sq(adj) = 87.41%</b></big></br><br />
<br><br />
</table><br />
<b> Table 3.</b> Estimated Regression Coefficients for OD<br />
<br /><br />
Suppose we redefine the factors according to the following table:</br><br />
<table border="1" cellspacing="0" cellpadding="0" width="557"><br />
<tr><br />
<td width="279" valign="top"><p>Term</p></td><br />
<td width="279" valign="top"><p>Mark</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>OD</p></td><br />
<td width="279" valign="top"><p>F</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>Temperature</p></td><br />
<td width="279" valign="top"><p>T</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>Time</p></td><br />
<td width="279" valign="top"><p>T</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>Peptone</p></td><br />
<td width="279" valign="top"><p>P</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>Yeast Extract</p></td><br />
<td width="279" valign="top"><p>Y</p></td><br />
</tr><br />
<tr><br />
<td width="279" valign="top"><p>NaCl</p></td><br />
<td width="279" valign="top"><p>C</p></td><br />
</tr><br />
</table><br />
<br /><b> Table 4.</b> Mark for each term<br />
According to the ANOVA calculated by minitab, we got the expression of OD:</br><br />
<img src="https://static.igem.org/mediawiki/2013/9/96/BS_formation.png"></br><br />
P represents confidence coefficient, which is a key judgment to check the reliability of the fitting function. In other words, if P=0.05, the probability that this term is wrong is 5%. The coefficient of determination (R) was calculated to be 0.9225, indicating that the model could explain 92% of the variability .From the above table we can identify eight statistically significant and reliable terms:</br><br />
<ul><br />
<li>Constant;</li><br />
<li>Temperature;</li><br />
<li>Time;</li><br />
<li>Yeast Extract;</li><br />
<li>Peptone;</li><br />
<li>Temperature*Temperature;</li><br />
<li>Temperature*Time;</li><br />
<li>Temperature*Yeast Extract;</li><br />
</ul><br />
<br />
The influences of linear terms predominated, except NaCl, which substantiated our suspicion whereas most square terms and interaction terms were ignorable and statistically unreliable. Temperature and time and two most influential factor.</br><br />
As our world is three-dimensional but the intact response surface is six-dimensional, it is impossible to draw the intact surface. Yet we could fix some factors to lower the dimensional, which empowers us to imagine the full surface. Here are some surfaces and contours of our fitting surface, we can extrapolate this super surface by combining these pictures:</br><br />
<br />
<img src="https://static.igem.org/mediawiki/2013/2/24/%E6%9E%AF%E8%8D%891.png"></br><br />
<b> Figure 1.</b> Surface plots of OD vs time and temperature.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/d/d0/%E6%9E%AF%E8%8D%892.png"></br><br />
<b> Figure 2.</b> Contour plots of OD vs time and temperature.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/1/1f/%E6%9E%AF%E8%8D%893.png"></br><br />
<b> Figure 3.</b> Surface plots of OD vs time and peptone.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/9/9f/%E6%9E%AF%E8%8D%894.png"></br><br />
<b> Figure 4.</b> Contour plots of OD vs time and peptone.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/22/%E6%9E%AF%E8%8D%895.png"></br><br />
<b> Figure 5.</b> Surface plots of OD vs peptone and temperature.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/5/54/%E6%9E%AF%E8%8D%896.png"></br><br />
<b> Figure 6.</b> Contour plots of OD vs peptone and temperature.</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/40/%E6%9E%AF%E8%8D%897.png"></br><br />
<b> Figure 7.</b> Conyour plots of OD vs yeast extract and temperature.</br><br />
<img src="https://static.igem.org/mediawiki/2013/4/40/%E6%9E%AF%E8%8D%897.png"></br><br />
<b> Figure 8.</b> Contour plots of OD vs yeast extract and temperature.</br></br></br><br />
The following four pictures illustrate the distribution of residual error:</br></br><br />
<img src="https://static.igem.org/mediawiki/2013/b/b1/%E6%9E%AF%E8%8D%899.png"></br><br />
<b> Figure 9.</b> Residual error vs order</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/0/04/%E6%9E%AF%E8%8D%8910.png"></br><br />
<b> Figure 10.</b> Histogram of residual error</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/29/%E6%9E%AF%E8%8D%8911.png"></br><br />
<b> Figure 11.</b> Residual error vs fits</br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/5/50/%E6%9E%AF%E8%8D%8912.png"></br><br />
<b> Figure 12.</b> Normal probability plot of residual error</br></br></br><br />
</div><br />
<br />
<div><br />
<h1>Optimization</h1><br />
One remarkable character of CCD is that it is sequential, and this is also the essence of RSM. Since we had got the fitting function, the next step is to calculate the gradient of the function, and define a small number as step length. Further experiments are supposed to be conducted from the beginning point according to the gradient and step length, and the final maximal treatment would be made sure. The methodology of RSM seems like climbing a mountain whose peak is unknown, and we adjust our orientation according to the topography. The fitting surface, which can be often a super surface in higher dimensional spaces, can be likened to the mountain without clear peaks, and calculating gradient to orientating.</br><br />
Unfortunately our remaining time is not enough to support further experiments,and as we looked up other researches utilizing RSM, none of which did second round experiment, and we realized perhaps that was the difference between a scientific research and a real industrial procedure. Yet the analytical methodology of response surface still acted as a powerful tool for ANOVA. Roughly, we could consider the treatment of No. 15 medium (Temperature 35℃, Time 12h, Peptone 15, Yeast Extract 7.5, NaCl 15)as the maximal condition for Bacillus subtilis.<br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<br />
<br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
<br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<br />
<br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
<br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
<br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Introduction</h1><br />
To be more user-friendly, 4# circuit contains a reporting system. After melting in water, the spores germinate and express blue pigment protein to report the best using time.</br><br />
Meanwhile, 4# circuit could also ensure biosafety. Because other circuit do not have self-killing device, 4# engineering bacterial should kill all the bacterial after using.</br><br />
<br />
</div><br />
<br />
<div><br />
<h1>Designing of the suicide system</h1><br />
We design a circuit of killing switch based on its endogenous genetic system.</br><br />
In B.subtilis, when it comes to the stationary phase, the environmental pressure increases and nutrition becomes limited, so B begin to produce spores. Now the community will be divided into two different parts. One of them are trying to kill others to get enough nutrient , delaying the production of spores and achieving a competitive advantage. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. SdpI could bind free SdpC and autopressor SdpR, to remove SdpR’s inhibition against I and R, to produce more SdpI to offset SdpC, finally guaranteeing the subgroup alive, thereby delaying the spores production.</br><br />
<img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"><br />
<p>We transfer SdpC which is fused by promoter SdpI/R into high copy plasmids in order to damage the balance of the system, thereby killing whole colony. When SdpC appears, SdpI on the membrane will bind free SdpC and adsorb SdpR to cease its inhibition against SdpI P/R, trying to produce more SdpI. At the same time, it will activate the promoter SdpR/I in our circuits and generate more SdpC.The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC increases beyond the ability of SdpI.Thus,the cells with protection mechanism will crack and die because of too much SdpC. All above forms the killing device.<br />
We Also designed a test circuit,which contains promotor grac and sdpABC only,aiming to determine the ability of SdpC.</p><br />
<br />
<div></br></br><br />
There are both positive and negative feedback loops in this process. On the one hand, SdpI is unable to sequestrate the autorepressor, SdpR, until it captures the toxin, SdpC. The accumulation of SdpC will thus facilitate SdpI to capture more SdpR and thereby relieve the repression of SdpR, stimulating the expression of itself. This is the positive feedback loop which leads to the increasing accumulation of SdpC and finally the death of the bacteria. On the other hand, the removal of SdpR also enhance the expression of SdpI and accelerate the sequestration of SdpC, which forms a negative feedback loop whose effects contradict the positive feedback loop. However, since the copy number of SdpC is much higher, it is believed that the positive loop is strong enough to outweigh the negative one, which guarantees this mechanism will finally leads to collapse instead of equilibrium.<br />
</div><br />
<div><br />
<h1>The ODE model of singular cells</h1><br />
There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” locus itself is to kill their siblings rather than themselves to ensure the survival of themselves. Surly they can kill their siblings, but can they finally eliminate themselves, as we expects? The trivial experiment protocol and huge uncertainty had put off our experiment, and as expected, we failed to achieve the construction of complete reporter system in our laboratory. Fortunately, we could resort to mathematical models to verify the validity of this locus theoretically. <br />
There are six independent variables in individual cells, and the theoretically if the initial conditions are fixed, all of them will be the univariate functions of time. The following table illustrates the mark and meaning of each variable:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub></td><br />
<td >Mole number of free SdpI in cytoplasm</a>.</td><br />
</tr><br />
<tr><br />
<td >I<sub>m</sub> </td><br />
<td >Mole number of SdpI in the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >C<sub>f</sub></td><br />
<td >Mole number of free SdpC in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >C<sub>i</sub></td><br />
<td >Mole number of SdpC captured by SdpI.</td><br />
</tr><br />
<tr><br />
<td >R<sub>f</sub></td><br />
<td >Mole number of free SdpR in cytoplasm.</td><br />
</tr><br />
<tr><br />
<td >R<sub>i</sub> </td><br />
<td >Mole number of SdpR captured by SdpI</td><br />
</tr><br />
</table><br />
</br></br><br />
<div>To construct reasonable ordinary differential equation (ODE) model to describe and predict the operation of the suicide system, we followed the law of mass action, one basic law of chemistry and biology.</br><br />
Taken as a statement about kinetics, the law states that the rate of an elementary reaction (a reaction that proceeds through only one transition state, which is one mechanistic step) is proportional to the product of the concentrations of the participating molecules. In modern chemistry this is derived using statistical mechanics. Despite the complicated chemical reactions involved in the process of transcription and translation, it is common and logically sound to view the expression of one particular gene as an elementary reaction and assume the repression effects of the protein itself encodes and the repressor are both linear.</br><br />
According to the law of mass action, we got six independent differential equation of the variables:</br><br />
<img src="https://static.igem.org/mediawiki/2013/e/e8/For1%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/2/23/For2%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/4/48/For3%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/7/71/For4%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/3/31/For5%281%29.png"></br></br></br><br />
<img src="https://static.igem.org/mediawiki/2013/c/cb/For6%281%29.png"></br></br></br><br />
The following table explain the constants in the above ODE groups:</br></br></div><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td >Mark</td><br />
<td >Meaning</td><br />
</tr><br />
<tr><br />
<td >I<sub>max</sub> </td><br />
<td >The maximal number of SdpI than can be fixed on the cell membrane.</td><br />
</tr><br />
<tr><br />
<td >k<sub>0</sub></td><br />
<td >Constant describes the normal expression rate of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>1</sub> </td><br />
<td >Constant describes the self-repression effects of SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>2</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpC.</a></td><br />
</tr><br />
<tr><br />
<td >k<sub>3</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpC</td><br />
</tr><br />
<tr><br />
<td >k<sub>4</sub> </td><br />
<td >Constant describes the normal expression rate of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>5</sub> </td><br />
<td >Constant describes the self-repression effects of SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>6</sub> </td><br />
<td >Constant describes the rate of SdpI capturing SdpR</td><br />
</tr><br />
<tr><br />
<td >k<sub>7</sub> </td><br />
<td >Constant describes the normal expression rate of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>8</sub> </td><br />
<td >Constant describes the self-repression effects of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>9</sub> </td><br />
<td >Constant describes the repression of SdpR on the expression of SdpI</td><br />
</tr><br />
<tr><br />
<td >k<sub>10</sub> </td><br />
<td >Constant describes the rate of SdpI binding to the cell membrane</td><br />
</tr><br />
</table><br />
<br />
<br />
<br />
<br />
</div><br />
<div class="clear"></div><br />
<div><br />
<h2>Discussions on the constants</h2><br />
All the constants given above is steady and theoretically measurable when all the conditions are constant. For example, we could measure k<sub>0</sub> by constructing a new engineered bacteria, which contains the gene encoding SdpC and marker gene alone and observing the influence of the concentration of SdpC on its expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in person. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to afford any valid information. Therefore, we decided to assume all these constant according to our limited information and make a qualitative analysis instead of quantifiable analysis. All units and dimensions were temporarily ignored. In other words, our model aims at justifying the validity of this suicide mechanism rather than predicting the exact time or any other parameters of the system.<br />
<br />
Despite the fact that we have hardly any accurate data on these constants, there are some limitations that we extrapolated from known information before we further explore this model:</br><br />
<ol><br />
<li>k<sub>0</sub>>>k<sub>4</sub>≈k<sub>7</sub>: k<sub>0</sub>,k<sub>4</sub> and k<sub>7</sub> represent the normal expression rate of SdpC, SdpR and SdpC separately, and the copy number of SdpC is much larger than that of SdpR and SdpI, whereas the value of the latter two is approximately equal;</li><br />
<li>k<sub>2</sub>>>k<sub>9</sub>: the existence of free SdpR represses the expression of both SdpI and SdpC, and similarly, since the copy number of SdpC is much higher, we expected the repression effect was stronger accordingly;</li><br />
<li>k<sub>10</sub>>>k<sub>3</sub>,k<sub>6</sub>:it is hard to predict the value of k<sub>3</sub> and k<sub>8</sub>, yet we suppose both of them is much smaller than k<sub>10</sub> because SdpI is a kind of membrane protein inherently, and rarely exists as free protein</li><br />
<li>The primary values of all the six variables are very small or strictly zero. We expect it as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li><br />
</ol><br />
</br></br><br />
<h2>Stimulation and discussion</h2><br />
<br />
Simple and rough as the above model is, it does theoretically sound. To test the validity of this model, we first tried to get analytic solution of the ODE set. If this analytic solution exists, we could further investigate the interaction among those variables, and draw some phase planes to get accurate and mathematically perfect description of this model. Unfortunately but expectedly, the existence of analytic solution was negated by MATLAB, and we had to assume groups of values for these constants in advance and analyze the arithmetic solutions instead. These arithmetic solutions not only justified this mechanism is effective enough to commit cell suicide but also indicated some unexpected, or even weird results that beyond our wildest imagination. There are two possibility account for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside model, which may be substantiate by later experiments or papers.</br><br />
When we explored the arithmetic solutions of this ODE set, we received nearly one hundred warnings from MATLAB and for many times our most powerful computer ran out of its 8GB memory, but sometimes we can receive the solution within seconds. We had adjusted our parameters for several times before we got our first solution. Here is the values of parameters for this group, and the graph of arithmetic solutions is also given:</br><br />
<div style="margin-top:20px;"><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>50</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table><br />
</div></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png"></br></br><br />
At the first glance this graph seemed fine. Initially the concentration of SdpC decreased slightly due to the capturing of SdpI and the repression of float SdpR, but gradually the positive feedback loop works, and C<sub>f</sub> increases rapidly. But when we turned our attention to the curves of other parameters, things seemed not so perfect:</br><br />
<div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png"></br></br><br />
The curve of I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub> contradicted our common sense severely. First, I<sub>m</sub>>C<sub>i</sub>>R<sub>i</sub> is expected to be tenable all the time, which precludes the intersects among the three curves; Second, there is no mechanism in this system that could decrease their concentration, and all of them are increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.<br />
<br />
Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.<br />
Here we listed another representative group of parament values and relative graph:</div></br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/7/7d/Suicide3.png/800px-Suicide3.png"></br></br><br />
In this group, we gave up one former assumption and set k<sub>2</sub> equal to k<sub>9</sub>. We also gave positive values to I<sub>m</sub>, C<sub>i</sub> and R<sub>i</sub>, which were considered to be zero at first. And by groups of stimulations we realized the value of k<sub>2</sub> does matter, as the derivative of C<sub>f</sub> only increased slightly as k<sub>2</sub> lowers, and the positive values failed to avoid the weird phenomenon in the latter three curves.<br />
We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, If dropped into approximately zero extremely rapidly at the initial stage and remained balanced, which might account for why the derivatives of the latter curves were abnormally negative. Thus we modified another assumption and increased k<sub>7</sub>. Here is another group of values and corresponding graph:</br></br><br />
<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>100</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/1/15/Suicide4.png/800px-Suicide4.png" style="width:600; height:400;"></br></br><br />
Although the derivative of Im is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful “suicide.” Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.<br />
We kept all other parameters constant and gradually augmented k<sub>0</sub>. The larger k<sub>0</sub>, the more perfect the curve seemed, and here are the values table and graph where k<sub>0</sub> equals 400, 80 times larger than k<sub>4</sub>.</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>400</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>5</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/thumb/3/33/Suicide5.png/800px-Suicide5.png"></br></br><br />
Take the curve of C<sub>f</sub> and R<sub>f</sub> separately, the curves seemed more perfect:</br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/9/9f/Suicide6.png"></br></br><br />
<br />
In wild bacteria who are unable to produced SdpC, naturally k<sub>0</sub> equals zero. We expected C<sub>f</sub> would decreased gradually and finally approximate zero, and here are the corresponding table and graph:</br></br><br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>30</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br><br />
Wired but not surprising, there were intersects among the latter three curve, and C<sub>f</sub> decreases continually when it is negative. We continued to try groups of these parameters, and this is the best one where we increased the primary concentration of SdpC and the normal expression rate of SdpI.<br />
<table border="1" align="center" frame="box"><br />
<tr><br />
<td>k<sub>0</sub></td><br />
<td>k<sub>1</sub></td><br />
<td>k<sub>2</sub></td><br />
<td>k<sub>3</sub></td><br />
<td>k<sub>4</sub></td><br />
<td>k<sub>5</sub></td><br />
<td>k<sub>6</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>8</sub></td><br />
<td>k<sub>9</sub></td><br />
<td>k<sub>10</sub></td><br />
<td>I<sub>max</sub></td><br />
<td>C<sub>f0</sub></td><br />
<td>R<sub>f0</sub></td><br />
<td>I<sub>f0</sub></td><br />
<td>I<sub>m0</sub></td><br />
<td>C<sub>i0</sub></td><br />
<td>R<sub>i0</sub></td><br />
</tr><br />
<tr><br />
<td>0</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>5</td><br />
<td>20</td><br />
<td>500</td><br />
<td>8</td><br />
<td>5</td><br />
<td>1</td><br />
<td>5</td><br />
<td>3</td><br />
<td>2</td><br />
</tr><br />
</table></br></br><br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/8/8e/Suicide8.png"></br></br><br />
The curve of C<sub>f</sub> and R<sub>f</sub> alone:<br />
<img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br><br />
In spite of minimal abnormal phenomenon (C<sub>f</sub> was negative in later stage), this graph roughly testified that in wild bacterial the concentration of float SdpC will drop to nearly zero quickly.<br />
In sum, the ODE model of singular cells indicate following results:</br><br />
<ol><br />
<li>The character of free SdpC is most affected by k<sub>0</sub>, if the copy number of SdpC is large enough, it is theoretically reasonable to commit suicide;</li><br />
<li>The influence of the value of Imax and k<sub>2</sub> is much limited;</li><br />
<li>The amount of free SdpI is always near zero;</li><br />
<li>SdpC will not increase limitlessly however we transform parameters;</li><br />
<li>To ensure the success of suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li><br />
The last conclusion was our biggest windfall, and we have verified the validity of this suicide mechanism in math. On the one hand, if further experiments proven #4 engineered bacteria will kill both siblings and themselves, it is highly like that the expression rate SdpI is much larger than SdpR even if they share the same promoter; on the other hand, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the bacteria.<br />
</ol><br />
<br />
<div><br />
<h1>Discussion on colonies</h1><br />
<br />
In reality, the engineered bacteria aims at killing its siblings instead of itself, and at first almost all toxin SdpC will be secreted outside the bacteria. Assume the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further assume the death concentration of SdpC is same to all bacteria expect those who contain this locus, the average life expectancy is bacteria will hinge on the rate and distribution of engineered bacteria, and the distribution of life expectancy of bacteria is similar to that of average free path of gas molecules.<br />
As long the coefficient of diffusion is large enough, any engineered bacterias, no matter how few, is adequate to devastate the whole colony. Alike to the average free path of thin gas, the average suicide time of the whole reporter system is inversely proportional with the square root of the rate of engineer bacteria containing this locus.<br />
</div><br />
<br />
<h1>References</h1><br />
Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis<br />
AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </br><br />
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<h1>Modeling on the suicide mechanism of the reporter system</h1><br />
<p>To eliminate potential safety problem, we constructed a suicide system on engineered bacteria to ensure biosafety. As the only one loaded with kill switch, the engineered reporter bacteria is responsible for eliminating all siblings in T-vaccine.<br />
Killing is mediated by the exported toxic protein SdpC. Extracellular SdpC induces the synthesis of an immunity protein, SdpI, which protects toxin-producing cells from being killed. SdpI, a polytopic membrane protein, is encoded by a two-gene operon under sporulation control that contains the gene for an autorepressor, SdpR.</p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">read more about Kill Switch</a><br />
</div><br />
<br />
<br><br><br />
<div><br />
<h1>The best growing condition for Bacillus subtilis WB800N</h1><br />
</div><br />
<div><br />
To ensure the expression of our T-vaccine, we do some experiments to find out the best growing condition for Bacillus subtilis WB800N, we finally choose five independent factors: temperature, inoculation time, peptone, yeast extract and NaCl. The following table displays their levels:<br />
<table width="400" border="1px"<br />
<tr><br />
<th align="left">Factor</th><br />
<th align="right">Low</th><br />
<th align="right">High</th><br />
</tr><br />
<tr><br />
<td align="left">Temperature</td><br />
<td align="right">25℃</td><br />
<td align="right">35℃</td><br />
</tr><br />
<tr><br />
<td align="left">Time</td><br />
<td align="right">12h</td><br />
<td align="right">24h</td><br />
</tr><br />
<tr><br />
<td align="left">Peptone</td><br />
<td align="right">5</td><br />
<td align="right">15</td><br />
</tr><br />
<tr><br />
<th align="left">Yeast Extract</th><br />
<th align="right">2.5</th><br />
<th align="right">7.5</th><br />
</tr><br />
<tr><br />
<th align="left">NaCl</th><br />
<th align="right">5</th><br />
<th align="right">15</th><br />
</tr><br />
</table><br />
<br />
</div><br />
<br><br><br />
<div><br />
图无法导出<br />
Roughly, we could consider the treatment of No. 15 medium (Temperature 35℃, Time 12h, Peptone 15, Yeast Extract 7.5, NaCl 15)as the maximal condition for Bacillus subtilis.<br />
<br><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">read more about B.Subtilis Culture</a><br />
</div><br />
<br />
<br><br><br />
<br />
<div><br />
<h1>Designs of Immune Experiments</h1><br />
<p>Our mice experiment has primarily proven the validity of our project. However, just like most scientific immune experiments on animals, the aim of our mice experiment was verification instead of exploring the optimal conditions for the production of our vaccine. In fact, fewer optimization experiments have been done by pure scientific researches, as most scientists care about facts and theories only, whereas exploring the optimal conditions is often viewed as the task of pharmaceutical factories. Yet since igem itself frequently involves industrial fields, which make igem seems like more an engineering competition than a science competition sometimes. </p><br />
<a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">read more about Designs of Immune Experiments</a><br />
</div><br />
<br />
<br />
</div><br />
<br />
<div class="rightbar"><br />
<div class="port-sidebar-border"><h>Modeling</h></div><br />
<div class="clear"></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/KillSwitch">Kill Switch</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/B.SubtilisCulture">B.Subtilis Culture</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Modeling/DesignsofImmuneExperiments">Designs Of Immune Experiments</a></div><br />
</div></div></div><br />
<br />
</body><br />
</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Notebook/ProtocolsTeam:USTC CHINA/Notebook/Protocols2013-09-27T18:04:41Z<p>NanoWu: </p>
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<h>Gene Clone</h><br />
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<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Gel Extraction">Gel Extraction</a></h1><br />
<h1>DNA digestion</h1><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Single Digestion">Single Digestion</a></h2><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Double Digestion">Double Digestion</a></h2><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Colony PCR">Colony PCR</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/PCR">PCR</a></h1><br />
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<h1>Transformation</h1><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/The transformation of E.coli">The transformation of E.coli</a></h2><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/The transformation of Bacillus subtilis">The transformation of Bacillus subtilis</a></h2><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Overlap PCR">Overlap PCR</a></h1><br />
<h1>Extracting plasmids</h1><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Extracting plasmids from gram-positive bacterium">Extracting plasmids from gram-positive bacterium</a></h2><br />
<h2><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Extracting plasmids from gram-negative bacterium">Extracting plasmids from gram-negative bacterium</a><h2></div><br />
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<h>Expression of proteins</h><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Expression of proteins in Bacillus subtilis">Expression of proteins in Bacillus subtilis</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Expression of proteins in Escherichia coli">Expression of proteins in Escherichia coli</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Concentrating proteins">Concentrating proteins</a></h1><br />
</div><br />
<div class="protocol-col-2"><br />
<h>Transdermal experiments</h><br />
<h>Immunity&Tests</h><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/ELISA">ELISA</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Sample analysis">Sample analysis</a></h1><br />
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<h>Medium</h><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/LB media">LB media</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/10*S base">10*S base</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/HS media">HS media</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/LS media">LS media</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/2*YT media">2*YT media</a></h1><br />
</div><br />
<div class="protocol-col-2"><br />
<h>Measurement</h><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Constitutive promoter measurements">Constitutive promoter measurements</a></h1><br />
<h1><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols/Plac promoter response to IPTG or Glucose">Plac promoter response to IPTG or Glucose</a></h1><br />
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</html></div>NanoWuhttp://2013.igem.org/Team:USTC_CHINA/Notebook/TimelineTeam:USTC CHINA/Notebook/Timeline2013-09-27T18:04:11Z<p>NanoWu: </p>
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<div id="title" align="center"><h>2013 USTC_CHINA iGEM Chronology</h></div><br />
<div class="main" align="left" style="background:#fff;border-radius:1em 1em 1em 1em;border:1px solid rgb(68,68,68);margin:20px auto 20px auto;"><br />
<div class="history"><br />
<div class="history-date"><br />
<ul><br />
<h2 class="first">2012</h2><br />
<br />
<li><br />
<h3><span>2012</span></h3><br />
<dl><br />
<dt><br />
</dt><br />
</dl><br />
</li><br />
<br />
<li class="green"><br />
<h3>Dec.15th<span>2012</span></h3><br />
<dl><br />
<dt>annual recruiting season<br />
<span>brought a large number of inquisitive mind <br />to USTC igem team. </span><br />
</dt><br />
</dl><br />
</li><br />
</ul><br />
</div><br />
<br />
<div class="history-date"><br />
<ul><br />
<h2 class="date02">2013</h2><br />
<li><br />
<h3>Jan.26th<span>2013</span></h3><br />
<dl><br />
<dt>systematic training begin<br />
<span>senior team members gave systematic training to the fresh<br /> and assigned responsibilities for every individual.</span><br />
</dt><br />
</dl><br />
</li><br />
<li><br />
<h3>Feb.17th<span>2013</span></h3><br />
<dl><br />
<dt>second training course<br />
<span>we held a simulated iGEM competition.<br /> Everyone was serious about the task he or she received,<br /> and gained a lot from the simulated competition.<br /> In the end, the team leader was elected by us.</span><br />
</dt><br />
</dl><br />
</li><br />
<li><br />
<h3>Mar.2nd<span>2013</span></h3><br />
<dl><br />
<dt>grouping and brain storming<br />
<span> All the members were divided into several groups<br /> according to each person's specialty and interest,<br /> and were motivated in the mobilization meeting.<br /> Everyone was ready for the coming activities.</span><br />
</dt><br />
</dl><br />
</li><br />
<li><br />
<h3>Mar.30th<span>2013</span></h3><br />
<dl><br />
<dt>Preliminary identified <br />several projects<br />
<span>algae produce H<sub>2</sub>, natural competence<br /> and magnetosome application <br />were preliminary identified as the promising projects.</span><br />
</dt><br />
</dl><br />
</li><br />
<li><br />
<h3>May.15th<span>2013</span></h3><br />
<dl><br />
<dt>SDI Conference <br />
<span>through heated discussion, we selected <br />optimization of blue-green algae produce H<sub>2</sub> as our subject.</span><br />
</dt><br />
</dl><br />
</li><br />
<li><br />
<h3>May.31th<span>2013</span></h3><br />
<dl><br />
<dt>halmatogenesis<br />
<span>A recently published paper has already done<br /> what we prepared to do, and we started to<br /> search another competitve project.</span><br />
</dt><br />
</dl><br />
</li><br />
<li class="green"><br />
<h3>June.5th<span>2013</span></h3><br />
<dl><br />
<dt>In situ transdermal vaccine<br />born<br />
</dt><br />
</dl><br />
</li><br />
<li class="green"><br />
<h3>July.10th-Apr.14th<span>2013</span></h3><br />
<dl><br />
<dt>experiment pet part<br />
<span>Introduce plasmid containing the GFP sequence into E.coli<br /><br />
Extract the plasmid after verified by PCR<br /><br />
Connect GFP gene with TD-1 via PCR<br /><br />
Connect the fragment with RBS and locus of restriction<br /> enzyme digestion via PCR<br /><br />
Digest the sequence and the plasmid <br />with same restriction endonuclease<br /><br />
Connect the sequence and the plasmid with DNA ligase<br /><br />
Verify the recombined plasmid by PCR<br /><br />
Sequence the plasmid<br /><br />
Introduce recombined plasmid into E.coli<br /><br />
Verify the bacterium by PCR<br /><br />
Induce protein expression<br /><br />
Verify the protein by SDS-page<br /><br />
Secret protein abundantly<br /><br />
Concentrate the protein via nickel column<br /><br />
Verify the protein by SDS-page<br /><br />
Transdermal experiments</span><br />
</dt><br />
</dl><br />
<br />
</li><br />
<li class="green"><br />
<h3>Apr.15th-Sept.10th<span>2013</span></h3><br />
<dl><br />
<dt>experiment B.subtilis part<br />
<span>Get the GFP sequence via PCR<br /><br />
Connect GFP gene with part of TD-1 via PCR<br /><br />
Connect the fragment with another part of TD-1 via PCR<br /><br />
Connect the fragment with promoter and <br />signal peptide via PCR<br /><br />
Digest the sequence and the plasmid with<br />same restriction endonuclease<br /><br />
Connect the sequence and the plasmid with DNA ligase<br /><br />
Verify the recombined plasmid by PCR<br /><br />
Sequence the plasmid<br /><br />
Introduce recombined plasmid into B.subtilis<br /><br />
Verify the bacterium by PCR<br /><br />
Induce protein expression<br /><br />
Concentrate the protein via TCA<br /><br />
Verify the protein by SDS-page<br /><br />
Secret protein abundantly<br /><br />
Concentrate by centrifuging<br /><br />
Verify the protein by SDS-page<br /><br />
Transdermal experiments</span><br />
</dt><br />
</dl><br />
</li><br />
<br />
<li class="green"><br />
<h3>Sept.14th<span>2013</span></h3><br />
<dl><br />
<dt>in vivo Transdermal antigen <br />antibody response validation<br />
</dt><br />
</dl><br />
</li><br />
</ul><br />
</div><br />
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<div class="port-sidebar-border"><h>Notebook</h></div><br />
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<div id="t1"><a class="active" href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Timeline">Timeline</a></div><br />
<div id="t1"><a href="https://2013.igem.org/Team:USTC_CHINA/Notebook/Protocols">Protocols</a></div></div><br />
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