http://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&feed=atom&action=historyTeam:USTC CHINA/Modeling/KillSwitch - Revision history2024-03-29T08:30:08ZRevision history for this page on the wikiMediaWiki 1.16.5http://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=345727&oldid=prevKndtmsl at 12:59, 28 October 20132013-10-28T12:59:50Z<p></p>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=345717&oldid=prevKndtmsl at 12:58, 28 October 20132013-10-28T12:58:40Z<p></p>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=345704&oldid=prevKndtmsl at 12:57, 28 October 20132013-10-28T12:57:22Z<p></p>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=345676&oldid=prevKndtmsl at 12:53, 28 October 20132013-10-28T12:53:30Z<p></p>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=345665&oldid=prevKndtmsl at 12:52, 28 October 20132013-10-28T12:52:28Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We designed a circuit of killing switch based on its endogenous genetic system.</br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We designed a circuit of killing switch based on its endogenous genetic system.</br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In B.subtilis, when stationary phase begins, the environmental pressure increases and nutrition becomes limited, forcing B.subtilis to produce spores. Then the community will be divided into two different parts. One is trying to kill the other one for adequate nutrient, delaying the production of spores and obtaining competitive advantages. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. As a membrane protein, SdpI could bind free SdpC and autopressor SdpR, removing SdpR’s inhibition against I and R, producing more SdpI to offset SdpC and finally guaranteeing the subgroup alive, thereby delaying the spores production.</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In <ins class="diffchange diffchange-inline"><i></ins>B.subtilis<ins class="diffchange diffchange-inline"></i></ins>, when stationary phase begins, the environmental pressure increases and nutrition becomes limited, forcing <ins class="diffchange diffchange-inline"><i></ins>B.subtilis<ins class="diffchange diffchange-inline"></i> </ins>to produce spores. Then the community will be divided into two different parts. One is trying to kill the other one for adequate nutrient, delaying the production of spores and obtaining competitive advantages. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. As a membrane protein, SdpI could bind free SdpC and autopressor SdpR, removing SdpR’s inhibition against I and R, producing more SdpI to offset SdpC and finally guaranteeing the subgroup alive, thereby delaying the spores production.</br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p>We transfered SdpC, which is fused with promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling, the amount of SdpC can increase beyond the accommodation of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p>We transfered SdpC, which is fused with promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling, the amount of SdpC can increase beyond the accommodation of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>References</h1></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>References</h1></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Parallel pathways of repression and antirepression governing the transition to stationary phase in Bacillus subtilis</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Parallel pathways of repression and antirepression governing the transition to stationary phase in <ins class="diffchange diffchange-inline"><i></ins>Bacillus subtilis<ins class="diffchange diffchange-inline"></i></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>AV Banse, A Chastanet, L Rahn-Lee…,PNAS ,2008 </p></div></td></tr>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=328560&oldid=prevKndtmsl at 14:00, 25 October 20132013-10-25T14:00:56Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p>We transfered SdpC, which is fused with promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling, the amount of SdpC can increase beyond the accommodation of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p>We transfered SdpC, which is fused with promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling, the amount of SdpC can increase beyond the accommodation of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We also designed a test circuit, which contains promotor grac and sdpABC <del class="diffchange diffchange-inline">soly</del>, to check the toxicity of SdpC.</p></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We also designed a test circuit, which contains promotor grac and sdpABC <ins class="diffchange diffchange-inline">solely</ins>, to check the toxicity of SdpC.</p></div></td></tr>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=328530&oldid=prevKndtmsl at 13:49, 25 October 20132013-10-25T13:49:49Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><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>, but we <del class="diffchange diffchange-inline">suppose </del>both of them <del class="diffchange diffchange-inline">are </del>much smaller than k<sub>10</sub> because SdpI is a membrane protein inherently, and rarely exists as free protein;</li></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><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>, but we <ins class="diffchange diffchange-inline">supposed </ins>both of them <ins class="diffchange diffchange-inline">were </ins>much smaller than k<sub>10</sub> because SdpI is a membrane protein inherently, and rarely exists as free protein;</li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>The primary values of all the six variables are very small or strictly zero. We expect this as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally.</li></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>The primary values of all the six variables are very small or strictly zero. We expect this as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally.</li></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><div style="float:left; margin-left:330px;margin-top:-350px;width:270px;align="justify;">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 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/><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><div style="float:left; margin-left:330px;margin-top:-350px;width:270px;align="justify;">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 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/><br/></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, I<sub>f</sub> 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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, I<sub>f</sub> 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 <ins class="diffchange diffchange-inline">the </ins>corresponding graph:</div></div></br></br></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Although the derivative of I<sub>m</sub> is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated that 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, <del class="diffchange diffchange-inline">and hence </del>the copy number of SdpC must be larger.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Although the derivative of I<sub>m</sub> is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated that 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, <ins class="diffchange diffchange-inline">which requires </ins>the copy number of SdpC must be larger.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></p></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/1/19/Suicide7.png"></br></br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">where </del>we increased the primary concentration of SdpC and the normal expression rate of SdpI.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 <ins class="diffchange diffchange-inline">in which </ins>we increased the primary concentration of SdpC and the normal expression rate of SdpI.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In sum, the ODE model <del class="diffchange diffchange-inline">of </del>singular cell indicates following results:</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In sum, the ODE model <ins class="diffchange diffchange-inline">on </ins>singular cell indicates following results:</br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><ol></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><ol></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li>The <del class="diffchange diffchange-inline">character </del>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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li>The <ins class="diffchange diffchange-inline">concentration </ins>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></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li>The influence of the value of <del class="diffchange diffchange-inline">Imax </del>and k<sub>2</sub> is much limited;</li></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li>The influence of the value of <ins class="diffchange diffchange-inline">I<sub>max</sub> </ins>and k<sub>2</sub> is much limited;</li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>The amount of free SdpI is always near zero;</li></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>The amount of free SdpI is always near zero;</li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>SdpC will not increase limitlessly however we transform parameters;</li></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li>SdpC will not increase limitlessly however we transform parameters;</li></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li>To ensure <del class="diffchange diffchange-inline">the success of </del>suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li>To ensure <ins class="diffchange diffchange-inline">successful </ins>suicide, it is required k<sub>0</sub>>>k<sub>4</sub>>>k<sub>7</sub>;</li></div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><p style="width:300px; margin-left:300px; align="justify"">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 <del class="diffchange diffchange-inline">hand</del>, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the <del class="diffchange diffchange-inline">bacteria</del>.</p></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><p style="width:300px; margin-left:300px; align="justify"">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, if #4 engineered bacteria are not able to commit suicide, we can try to boost the expression of SdpI to adjust the <ins class="diffchange diffchange-inline">kill switch</ins>.</p></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Discussion on colonies</h1></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Discussion on colonies</h1></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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. <del class="diffchange diffchange-inline">Assume </del>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.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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. <ins class="diffchange diffchange-inline">We assume </ins>the diffusion of toxin among cells comply with diffusion law, that is, the diffusion rate is proportionate with the gradient of concentration. Further <ins class="diffchange diffchange-inline">we </ins>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.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>As long the coefficient of diffusion is large enough, any engineered <del class="diffchange diffchange-inline">bacterias</del>, 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 <del class="diffchange diffchange-inline">locus</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>As long the coefficient of diffusion is large enough, any engineered <ins class="diffchange diffchange-inline">bacteria</ins>, 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 <ins class="diffchange diffchange-inline">circuit</ins>.</div></td></tr>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=328505&oldid=prevKndtmsl at 13:36, 25 October 20132013-10-25T13:36:00Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>The ODE model of singular cells</h1></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>The ODE model of singular cells</h1></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” circuit itself is to kill their siblings rather than themselves and ensure the survival of themselves. Surely they can kill their siblings, but can they finally eliminate themselves, as we expect? 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 circuit theoretically. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>There is no denying fact that the essential goal of engineered bacterias who carry this so called “suicide” circuit itself is to kill their siblings rather than themselves and ensure the survival of themselves. Surely they can kill their siblings, but can they finally eliminate themselves, as we expect? 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 <ins class="diffchange diffchange-inline">limited </ins>laboratory. Fortunately, we could resort to mathematical models to verify the validity of this circuit theoretically. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>There are six independent variables in individual cells, and 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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>There are six independent variables in individual cells, and 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></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">the process of </del>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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 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></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>According to the law of mass action, we got six independent differential equations of the variables:</br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>According to the law of mass action, we got six independent differential equations of the variables:</br></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Discussions on the constants</h2></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Discussions on the constants</h2></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 own expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in <del class="diffchange diffchange-inline">person</del>. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to <del class="diffchange diffchange-inline">afford </del>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, while in fact the latter one is impossible. 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.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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<ins class="diffchange diffchange-inline">, </ins>and observing the influence of the concentration of SdpC on its own expression. Yet any modification on genome is notoriously time-consuming, which inhibited us from measuring them in <ins class="diffchange diffchange-inline">our tiny laboratory</ins>. We also looked up oceans of papers to confer their approximate ranges, but almost all papers are too fragmental to <ins class="diffchange diffchange-inline">provide </ins>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, while in fact the latter one is impossible. 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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><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>, <del class="diffchange diffchange-inline">yet </del>we suppose both of them <del class="diffchange diffchange-inline">is </del>much smaller than k<sub>10</sub> because SdpI is a membrane protein inherently, and rarely exists as free protein;</li></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><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>, <ins class="diffchange diffchange-inline">but </ins>we suppose both of them <ins class="diffchange diffchange-inline">are </ins>much smaller than k<sub>10</sub> because SdpI is a membrane protein inherently, and rarely exists as free protein;</li></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li>The primary values of all the six variables are very small or strictly zero. We expect <del class="diffchange diffchange-inline">it </del>as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally</li></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li>The primary values of all the six variables are very small or strictly zero. We expect <ins class="diffchange diffchange-inline">this </ins>as the most logical initial status. If the primary value of any variable is relatively large, the suicide mechanism may not run normally<ins class="diffchange diffchange-inline">.</ins></li></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Stimulation and discussion</h2></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Stimulation and discussion</h2></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 descriptions 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 accounting 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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 descriptions 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 accounting for the unexpected results: our model is too rough to include some assignable factor; or there are some implicit but objective limitation inside <ins class="diffchange diffchange-inline">this </ins>model, which may be substantiate by later experiments or papers.</br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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:</p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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:</p></div></td></tr>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=328486&oldid=prevKndtmsl at 13:24, 25 October 20132013-10-25T13:24:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Introduction</h1></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Introduction</h1></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">best </del>using time.</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 <ins class="diffchange diffchange-inline">optimal </ins>using time.</br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Meanwhile, 4# circuit could also ensure biosafety. Since other <del class="diffchange diffchange-inline">circuit </del>do not <del class="diffchange diffchange-inline">have </del>self-killing device, 4# engineered bacterial <del class="diffchange diffchange-inline">should </del>kill all the bacterial after being used.</p></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Meanwhile, 4# circuit could also ensure biosafety. Since other <ins class="diffchange diffchange-inline">circuits </ins>do not <ins class="diffchange diffchange-inline">contain </ins>self-killing device, 4# engineered bacterial <ins class="diffchange diffchange-inline">would </ins>kill all the bacterial after being used.</p></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Designing of the suicide system</h1></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h1>Designing of the suicide system</h1></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We <del class="diffchange diffchange-inline">design </del>a circuit of killing switch based on its endogenous genetic system.</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We <ins class="diffchange diffchange-inline">designed </ins>a circuit of killing switch based on its endogenous genetic system.</br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In B.subtilis, when stationary phase begins, the environmental pressure increases and nutrition becomes limited, forcing B.subtilis to produce spores. Then the community will be divided into two different parts. One is trying to kill the <del class="diffchange diffchange-inline">others </del>for <del class="diffchange diffchange-inline">enough </del>nutrient, delaying the production of spores and obtaining competitive advantages. 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, removing SdpR’s inhibition against I and R, producing more SdpI to offset SdpC and finally guaranteeing the subgroup alive, thereby delaying the spores production.</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In B.subtilis, when stationary phase begins, the environmental pressure increases and nutrition becomes limited, forcing B.subtilis to produce spores. Then the community will be divided into two different parts. One is trying to kill the <ins class="diffchange diffchange-inline">other one </ins>for <ins class="diffchange diffchange-inline">adequate </ins>nutrient, delaying the production of spores and obtaining competitive advantages. Killing is mediated by the exported toxic protein SdpC. SdpI will appear on the membrane surface to avoid itself from being damaged. <ins class="diffchange diffchange-inline">As a membrane protein, </ins>SdpI could bind free SdpC and autopressor SdpR, removing SdpR’s inhibition against I and R, producing more SdpI to offset SdpC and finally guaranteeing the subgroup alive, thereby delaying the spores production.</br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img src="https://static.igem.org/mediawiki/2013/2/2b/Reporter_3.png" width="500" height="350"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><p>We <del class="diffchange diffchange-inline">transfer </del>SdpC, which is fused <del class="diffchange diffchange-inline">by </del>promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling ,the amount of SdpC <del class="diffchange diffchange-inline">increases </del>beyond the <del class="diffchange diffchange-inline">ability </del>of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><p>We <ins class="diffchange diffchange-inline">transfered </ins>SdpC, which is fused <ins class="diffchange diffchange-inline">with </ins>promoter SdpI/R into high copy plasmids, to damage the balance of the system and kill 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 circuit and generate more SdpC. The system would fall into an infinite loop, and according to our modeling, the amount of SdpC <ins class="diffchange diffchange-inline">can increase </ins>beyond the <ins class="diffchange diffchange-inline">accommodation </ins>of SdpI. Thus, the cells with protection mechanism will finally collapse due to too much SdpC. All above forms the killing device.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We also designed a test circuit, <del class="diffchange diffchange-inline">containing </del>promotor grac and sdpABC <del class="diffchange diffchange-inline">only</del>, to check the <del class="diffchange diffchange-inline">ability </del>of SdpC.</p></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We also designed a test circuit, <ins class="diffchange diffchange-inline">which contains </ins>promotor grac and sdpABC <ins class="diffchange diffchange-inline">soly</ins>, to check the <ins class="diffchange diffchange-inline">toxicity </ins>of SdpC.</p></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 the death of the colony. On the other hand, the removal of SdpR also <del class="diffchange diffchange-inline">enhance </del>the expression of SdpI and <del class="diffchange diffchange-inline">accelerate </del>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, <del class="diffchange diffchange-inline">it is believed </del>that the positive loop is strong enough to outweigh the negative one, which guarantees this circuit will finally leads to collapse instead of equilibrium.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 the death of the colony. On the other hand, the removal of SdpR also <ins class="diffchange diffchange-inline">enhances </ins>the expression of SdpI and <ins class="diffchange diffchange-inline">accelerates </ins>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, <ins class="diffchange diffchange-inline">we believe </ins>that the positive loop is strong enough to outweigh the negative one, which guarantees this circuit will finally leads to collapse instead of equilibrium.</div></td></tr>
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</table>Kndtmslhttp://2013.igem.org/wiki/index.php?title=Team:USTC_CHINA/Modeling/KillSwitch&diff=326784&oldid=prevKndtmsl at 15:27, 24 October 20132013-10-24T15:27:37Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Discussions on the constants</h2></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Discussions on the constants</h2></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 <ins class="diffchange diffchange-inline">own </ins>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<ins class="diffchange diffchange-inline">, while in fact the latter one is impossible</ins>. 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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><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 <del class="diffchange diffchange-inline">kind of </del>membrane protein inherently, and rarely exists as free protein</li></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><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 membrane protein inherently, and rarely exists as free protein<ins class="diffchange diffchange-inline">;</ins></li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Stimulation and discussion</h2></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><h2>Stimulation and discussion</h2></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">description </del>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 <del class="diffchange diffchange-inline">account </del>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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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 <ins class="diffchange diffchange-inline">descriptions </ins>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 <ins class="diffchange diffchange-inline">accounting </ins>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></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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:</p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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:</p></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/2/26/Suicide1.png" width="450" height="350" /></br></br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><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 <del class="diffchange diffchange-inline">perfect</del>:</div></br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><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 <ins class="diffchange diffchange-inline">platonic</ins>:</div></br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/c/cf/Suicide2.png" width="450" height="350" /></br></br></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><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.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><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 <ins class="diffchange diffchange-inline">expected to be </ins>increasing function; Third and most serious, never will them be negative, as they represent the concentration of real substances.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Then we adjusted the parameters slightly for several times. To eliminate those absurd curves, we reconsidered some assumptions.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here we listed another representative group of parament values and relative graph:</div></div></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here we listed another representative group of parament values and relative graph:</div></div></br></br></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></table></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></table></br></br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><div style="float:left; margin-left:330px;margin-top:-350px;width:270px;align="justify;">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 <del class="diffchange diffchange-inline">to be </del>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/><br/></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><div style="float:left; margin-left:330px;margin-top:-350px;width:270px;align="justify;">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 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/><br/></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, <del class="diffchange diffchange-inline">If </del>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></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We also found that however we adjusted the primary value of I<sub>f</sub> and other parameters, <ins class="diffchange diffchange-inline">I<sub>f</sub> </ins>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></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><p align="justify"></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Although the derivative of <del class="diffchange diffchange-inline">Im </del>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 <del class="diffchange diffchange-inline">“suicide</del>.<del class="diffchange diffchange-inline">” </del>Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Although the derivative of <ins class="diffchange diffchange-inline">I<sub>m</sub> </ins>is not seriously positive constantly, the three latter curves seemed much more reasonable. Hence, we extrapolated <ins class="diffchange diffchange-inline">that </ins>although SdpI and SdpR share the same promoter, the expression of SdpI must much faster than SdpR to ensure successful <ins class="diffchange diffchange-inline">“suicide”</ins>. Additionally, the increase of k<sub>7</sub> also represses SdpC, and hence the copy number of SdpC must be larger.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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></p></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table border="1" align="center" frame="box"></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><table border="1" align="center" frame="box"></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><img class="linegraph" src="https://static.igem.org/mediawiki/2013/e/eb/Suicide9.png"></br></br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In sum, the ODE model of singular <del class="diffchange diffchange-inline">cells indicate </del>following results:</br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In sum, the ODE model of singular <ins class="diffchange diffchange-inline">cell indicates </ins>following results:</br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><ol></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><ol></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><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></div></td></tr>
</table>Kndtmsl