Team:Shenzhen BGIC ATCG/modeling

From 2013.igem.org

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<ul id="myGallery1">
<ul id="myGallery1">
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           <li><img src="https://static.igem.org/mediawiki/2012/b/b5/Yao.result.jpg" />
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           <li><img src="https://static.igem.org/mediawiki/2013/e/e7/Kd%3D0.png" title="Phase Specific Promoter + XFP" description="Different XFPs emerge at different phases with its own degradation rate"/>
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           <li><img src="https://static.igem.org/mediawiki/2012/7/77/Yao.012-001.jpg" />
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           <li><img src="https://static.igem.org/mediawiki/2013/b/bc/P%2BD.png" title="Phase Specific Promoter + XFP + Degradation Tag" description="Different XFPs emerge at different phases with a faster degradation rate"/>
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            <li><img src="https://static.igem.org/mediawiki/2012/1/1b/Result_yao_genome_p2.jpg" />
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          <li><img src="https://static.igem.org/mediawiki/2013/c/c7/3D.png" title="Phase Specific Promoter + XFP + Degradation Tag + Targeting Peptide" description="Different XFPs emerge at different phases with faster degradation rate and are transported to different organelles"/>
</ul></div>
</ul></div>
     <div id="box1" class="box">
     <div id="box1" class="box">
         <h3>Blueprint</h3>
         <h3>Blueprint</h3>
<p>Our project based a lot on cell cycle, especially the cyclin-promoters and cyclin-degradation tags. Through modelling Cell cycle is one of the most complex network in biology world. Better understanding of cell cycle and it’s regulation, to some extent, faciliate the fermentation industry because we can easily accelarate or decelarate a cell cycle or even one phase in the cycle which are important for metabolism product synthesis. In order to simulation and predict the experimets of the effeciency of Sic1, alternative splicing and degradation tags in the whole cell cycle, we build tree ordinary differential equation system models.</p>
<p>Our project based a lot on cell cycle, especially the cyclin-promoters and cyclin-degradation tags. Through modelling Cell cycle is one of the most complex network in biology world. Better understanding of cell cycle and it’s regulation, to some extent, faciliate the fermentation industry because we can easily accelarate or decelarate a cell cycle or even one phase in the cycle which are important for metabolism product synthesis. In order to simulation and predict the experimets of the effeciency of Sic1, alternative splicing and degradation tags in the whole cell cycle, we build tree ordinary differential equation system models.</p>
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<p>With the use of cyclins' promoters, we got the simulation of period XFP.
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</p>
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<img src="https://static.igem.org/mediawiki/2013/e/e7/Kd%3D0.png">
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<center><p>Figure. Simulation Result of Phase Specific Promoter + XFP
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</p></center>
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<p>Each XFP will finally merge together so it's hard to tell part. So degradation tags were introduced. Degradation tags were also obtained from cyclins because cyclins should degrade fast enough to avoid binding to cdc28 and delaying its own phase. From our simulation we can find out that transformed proteins can also be degraded at a convenient speed.
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</p>
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<center><p><b>Parameter Table
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</b></p></center>
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<table>
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<td><p>Parameter</p></td>
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<td><p>Rate(min<sup>-1</sup>)</p></td>
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<td><p>Citation</p></td>
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<tr>
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<td><p>D(PEST1)</p></td>
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<td><p>0.12</p></td>
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<td><p> Chen et al. (2004) </p></td>
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<tr>
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<td><p>D(PEST2)</p></td>
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<td><p>0.12</p></td>
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<td><p> Chen et al. (2004) </p></td>
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<tr>
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<td><p>D(PEST3)</p></td>
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<td><p>0.14</p></td>
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<td><p> Belli, Gari, Aldea, & Herrero (2001) </p></td>
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<tr>
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<td><p>D(D-box)</p></td>
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<td><p>Vdb5</p></td>
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<td><p> Chen et al. (2004) </p></td>
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</table>
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<p></p>
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<img src="https://static.igem.org/mediawiki/2013/b/bc/P%2BD.png">
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<center><p>Figure. Simulation Result of Phase Specific Promoter + XFP + Degradation Tag
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</p></center>
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<p>As Degradation tags could not fully help tell apart each phase by the light of XFP, we built targeting peptide into model to make a more distinguishable visual result. As shown here, we present a 3D simulation result by adding another axis to specify different organelles.
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</p>
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<img src="https://static.igem.org/mediawiki/2013/c/c7/3D.png">
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<center><p>Figure. Simulation Result of Phase Specific Promoter + XFP + Degradation Tag + Targeting Peptide
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</p></center>
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</div>
</div>
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<div class="media">
<div class="media">
<ul id="myGallery2">
<ul id="myGallery2">
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           <li><img src="https://static.igem.org/mediawiki/2012/b/b5/Yao.result.jpg" title="YAO.Genome"/>
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           <li><img src="https://static.igem.org/mediawiki/2013/7/70/Original_Cell_Cycle.png" title="Original Cell Cycle Simulation" description="Simulation of appearance and disappearance of different proteins"/>
</ul></div>
</ul></div>
     <div id="box2" class="box">
     <div id="box2" class="box">
         <h3>Cell Cycle</h3>
         <h3>Cell Cycle</h3>
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<p>To make a precise prediction of our project and analyze its feasibility, we build a cell cycle model based on Chen's work Chen et al. (2004). By simulating the periodic cycle, we obtained the promoters we could make use of.
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</p>
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<p>Promoters are selected by observing the appearance and disappearance of proteins shown in cell cycle model.
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</p>
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<img src="https://static.igem.org/mediawiki/2013/7/70/Original_Cell_Cycle.png">
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<center><p>Figure. Simulation Result of Original Cell Cycle
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</p></center>
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<p>Both the model and related papers show that cln1, 2 and clb1, 2, 5, 6 appear at a periodic rhythm because of the appearance of their transcription factors. There are some other proteins (such as NET1) shown this features, but their mechanisms are also related to some protein-protein interactions.
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</p>
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<img src="https://static.igem.org/mediawiki/2013/b/bd/NET.png">
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<center><p>Figure. Simulation Result of NET1 and NET1T
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</p></center>
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     </div>
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<div class="media">
<div class="media">
<ul id="myGallery3">
<ul id="myGallery3">
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           <li><img src="https://static.igem.org/mediawiki/2012/b/b5/Yao.result.jpg" />
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           <li><img src="https://static.igem.org/mediawiki/2013/8/89/G1_delay.png" title="G1 Phase Delay" description="G1 phase will delay with galactose induced sic1p expression">
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          <li><img src="https://static.igem.org/mediawiki/2013/9/98/SIC1_Time.png" title="Plateau Stage of sic1p" description="Plateau Stage of sic1p by inducing sic1p expression">
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          <li><img src="https://static.igem.org/mediawiki/2013/1/1a/Tp_ka_kd.png" title="Influence of Ka and Kd to Tp">
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          <li><img src="https://static.igem.org/mediawiki/2013/1/1f/Lp_ka_kd.png" title="Influence of Ka and Kd to Lp">
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          <li><img src="https://static.igem.org/mediawiki/2013/9/9a/Synchronization.png" title="Synchronization" description="Synchronization result of multiple cells">
</ul></div>
</ul></div>
     <div id="box3" class="box">
     <div id="box3" class="box">
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<p>Previously study reported the introduction of sic1p could prevent the cell to enter S phase. Based on the sic1 system in yeast, we developed an artificial sic1 system (SIC1_Art). By adding galactose or modifying the phosphorylated sites, we can regulate the synthesis (Ka) and degradation (Kd) rates of the sic1_Art. We are trying to utilize this artificial system to precisely regulate the phase in yeast cell cycle, and our goal is to understand the synchronization behavior in yeast.
<p>Previously study reported the introduction of sic1p could prevent the cell to enter S phase. Based on the sic1 system in yeast, we developed an artificial sic1 system (SIC1_Art). By adding galactose or modifying the phosphorylated sites, we can regulate the synthesis (Ka) and degradation (Kd) rates of the sic1_Art. We are trying to utilize this artificial system to precisely regulate the phase in yeast cell cycle, and our goal is to understand the synchronization behavior in yeast.
</p>
</p>
 +
<img src="https://static.igem.org/mediawiki/2013/1/10/SIC1.png">
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<center><p>Figure. SIC1 Model
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</p></center>
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<img src="https://static.igem.org/mediawiki/2013/8/89/G1_delay.png">
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<center><p>Figure. G1 Phase Delay
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</p></center>
<h4>SIC1_Art on G1 stage</h4>
<h4>SIC1_Art on G1 stage</h4>
<h5>G1 length:</h5>
<h5>G1 length:</h5>
<p>To understand the temporal effect of SIC1_Art on the length G1 phase, we performed parameter scan on the amount of time of adding SIC1_Art (DeltaT). By setting Ka=0.12 and Kd=0.016, we estimated the relationship between DeltaT and the length of G1 phase. Our computation simulation showed that, as we added SIC1_Art into the yeast, the amount of SIC1_Art will increase at first, and then it will enter a plateau stage. After the plateau stage, SIC1_Art will decrease gradually, which subsequently followed by the leaving of G1 stage (900 min). Our result suggests a positive correlation between DeltaT and the length of G1 phase in the first 900 min, and we discovered an upper bound at the length of G1 phase.
<p>To understand the temporal effect of SIC1_Art on the length G1 phase, we performed parameter scan on the amount of time of adding SIC1_Art (DeltaT). By setting Ka=0.12 and Kd=0.016, we estimated the relationship between DeltaT and the length of G1 phase. Our computation simulation showed that, as we added SIC1_Art into the yeast, the amount of SIC1_Art will increase at first, and then it will enter a plateau stage. After the plateau stage, SIC1_Art will decrease gradually, which subsequently followed by the leaving of G1 stage (900 min). Our result suggests a positive correlation between DeltaT and the length of G1 phase in the first 900 min, and we discovered an upper bound at the length of G1 phase.
</p>
</p>
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<p>两幅图</p>
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<img src="https://static.igem.org/mediawiki/2013/3/38/SIC1_G1L.png">
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<center><p>Figure. Curve Fitting of SIC1_Art and G1 Phase Length
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</p></center>
<h5>Plateau, the definition:</h5>
<h5>Plateau, the definition:</h5>
<p>Based on the relation between DeltaT and the cellular level of SIC1_Art, we defined plateau stage as the time space within which the amount of SIC1_Art is less than the maximum SIC_Art amount during the G1 phase (SIC1_Amax) and greater than (SIC1_Amax - Kd*5min). During this time space, the temporal difference of SIC1_Art degradation is less than 5 min, which we considered the minimum requirement of synchronization.
<p>Based on the relation between DeltaT and the cellular level of SIC1_Art, we defined plateau stage as the time space within which the amount of SIC1_Art is less than the maximum SIC_Art amount during the G1 phase (SIC1_Amax) and greater than (SIC1_Amax - Kd*5min). During this time space, the temporal difference of SIC1_Art degradation is less than 5 min, which we considered the minimum requirement of synchronization.
</p>
</p>
 +
<img src="https://static.igem.org/mediawiki/2013/9/98/SIC1_Time.png">
 +
<center><p>Figure. Plateau Stage of SIC1_Art
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</p></center>
<img src="https://static.igem.org/mediawiki/2013/9/99/SIC1_Art_Time.png">
<img src="https://static.igem.org/mediawiki/2013/9/99/SIC1_Art_Time.png">
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<center><p>Figure. Plateau Stage of SIC1_Art with Different Galatose Input Time
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</p></center>
<h5>Ka/Kd, Entering Plateau:</h5>
<h5>Ka/Kd, Entering Plateau:</h5>
<p>To examine the relation between the synthesis and degradation rate and the timing of entering plateau stage (Tp), we performed parameter scan on Ka and Kd. We found that the Tp is negatively correlated with Ka and positively correlated with Kd.
<p>To examine the relation between the synthesis and degradation rate and the timing of entering plateau stage (Tp), we performed parameter scan on Ka and Kd. We found that the Tp is negatively correlated with Ka and positively correlated with Kd.
</p>
</p>
<img src="https://static.igem.org/mediawiki/2013/1/1a/Tp_ka_kd.png">
<img src="https://static.igem.org/mediawiki/2013/1/1a/Tp_ka_kd.png">
 +
<center><p>Figure. Influence of Ka and Kd to Tp
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</p></center>
<h5>Ka/kd, Length of Plateau:</h5>
<h5>Ka/kd, Length of Plateau:</h5>
<p>To further explore the optimal Ka/Kd in SIC1_Art system, we investigated the influence of Ka/Kd on the length of plateau domain (Lp).
<p>To further explore the optimal Ka/Kd in SIC1_Art system, we investigated the influence of Ka/Kd on the length of plateau domain (Lp).
</p>
</p>
<img src="https://static.igem.org/mediawiki/2013/1/1f/Lp_ka_kd.png">
<img src="https://static.igem.org/mediawiki/2013/1/1f/Lp_ka_kd.png">
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<center><p>Figure. Influence of Ka and Kd to Lp
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</p></center>
<h4>Synchronization in yeast cell cycle</h4>
<h4>Synchronization in yeast cell cycle</h4>
<p>Using the result of above analysis, we chose Ka=0.219, Kd=0.048 as the optimal parameters, which give rise to short entering plateau time and long enough plateau stage (Tp = 61 min, Lp=355 min ).
<p>Using the result of above analysis, we chose Ka=0.219, Kd=0.048 as the optimal parameters, which give rise to short entering plateau time and long enough plateau stage (Tp = 61 min, Lp=355 min ).
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</p>
</p>
<img src="https://static.igem.org/mediawiki/2013/9/9a/Synchronization.png">
<img src="https://static.igem.org/mediawiki/2013/9/9a/Synchronization.png">
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<center><p>Figure. Simulation Result of Multiple Cells' Synchronization
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</p></center>
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<img src="https://static.igem.org/mediawiki/2013/2/29/Viability.png">
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<p><center>Figure. Viability Simulation</center></p>
     </div>
     </div>
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<div class="media">
<div class="media">
<ul id="myGallery4">
<ul id="myGallery4">
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           <li><img src="https://static.igem.org/mediawiki/2012/b/b5/Yao.result.jpg"/>
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           <li><img src="https://static.igem.org/mediawiki/igem.org/0/01/Kass1_eq_kdis1.png" title="Simulation Result of Kass1 and Kdis1" description="Kass1 = Kids1">
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          <li><img src="https://static.igem.org/mediawiki/igem.org/a/ad/Parameter_scan_of_b_%28gal%29.png" title="Parameter Scan of b with Galactose Input">
</ul></div>
</ul></div>
     <div id="box4" class="box">
     <div id="box4" class="box">
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         <h3>Alternative Splicing by CRISPRi</h3><br/>
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         <h3>Alternative Splicing by CRISPRi</h3>
<p>To predict the alternative outcome, we also made an intron model to show different results due to incubating in different media. In our project, intron can be spliced in two different ways, providing a completely different outcome because of frame-shift, and this result is not a change like 1-0 to 0-1, but somehow more like a change between 0.4-0.6 and 0.8-0.2.
<p>To predict the alternative outcome, we also made an intron model to show different results due to incubating in different media. In our project, intron can be spliced in two different ways, providing a completely different outcome because of frame-shift, and this result is not a change like 1-0 to 0-1, but somehow more like a change between 0.4-0.6 and 0.8-0.2.
</p>
</p>
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<img src="https://static.igem.org/mediawiki/2013/9/96/DCas9.png">
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<center><p>Figure. dCas9 Controlled SRC1 Intron Splicing
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</p></center>
<h4>Reactions:</h4>
<h4>Reactions:</h4>
<img src="https://static.igem.org/mediawiki/2013/a/af/Formula1.png">
<img src="https://static.igem.org/mediawiki/2013/a/af/Formula1.png">
<img src="https://static.igem.org/mediawiki/2013/0/03/Formula2.png">
<img src="https://static.igem.org/mediawiki/2013/0/03/Formula2.png">
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</h4>Parameter Table:</h4>
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<h4>Parameter Table:</h4>
<table>
<table>
<td><p>Parameter</p></td>
<td><p>Parameter</p></td>
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<tr>
<tr>
</table>
</table>
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<p>There are 4 parameters that we cannot find during our research, including kass, kdis representing the association and dissociation rate of CRISPRi system, and kass1 and kdis1 representing the association and dissociation rate of Hub1p and spliceosome.
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</p>
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<p></p>
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<p>We run parameter scan for each system individually, and found out that with CRISPRi system is more efficient with higher kass and lower kdis, as expected.
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</p>
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<p></p>
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<p>And about the alternative splicing model, we attempted to fit simulation result to experimental one. In Hub1 expressed system, L-mRNA will rise at first but descend to an equilibrium stage while S-mRNA will directly rise to its own equilibrium stage.
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</p>
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<p>kass1 should be larger than kdis1, or L-mRNA will be produced more than S-mRNA instead of a ratio of 40-60.
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</p>
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<img src="https://static.igem.org/mediawiki/igem.org/2/2b/Kass1_lt_kdis1.png">
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<center><p>Figure. Simulation Result of Two mRNA when Kass1<Kdis1
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</p></center>
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<p>Also, kass1 should not be too smaller than kdis1, or their ratio will be much larger than 40-60.
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</p>
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<img src="https://static.igem.org/mediawiki/igem.org/e/ec/Kass1_gt_kdis1.png">
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<center><p>Figure. Simulation Result of Two mRNA when Kass1>Kdis1
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</p></center>
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<p>Finally we set down that kass1 = kdis1.
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</p>
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<img src="https://static.igem.org/mediawiki/igem.org/0/01/Kass1_eq_kdis1.png">
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<center><p>Figure. Simulation Result of Two mRNA when Kass1=Kdis1
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</p></center>
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<p>When inhibiting the expression of HUB1, there is still a background splicing of 5’S site, so we need another parameter b in S-splicing.
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</p>
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<p>Background S-splicing parameter b is mostly related to the ratio of spliceosome and Hub1p-modified spliceosome (Hub1_spliceosome) at equilibrium state. With higher b, L-mRNA and S-mRNA will come closer at equilibrium stat while it influence no-Hub1p situation more than Hub1p situation.
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</p>
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<img src="https://static.igem.org/mediawiki/igem.org/a/ad/Parameter_scan_of_b_%28gal%29.png">
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<center><p>Figure. Parameter Scan of b with Galactose Input
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</p></center>
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<img src="https://static.igem.org/mediawiki/igem.org/e/ea/Parameter_scan_of_b_%28no_gal%29.png">
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<center><p>Figure. Parameter Scan of b without Galactose Input
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</p></center>
     </div>
     </div>
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           <li><img src="https://static.igem.org/mediawiki/2013/0/0a/Curve_fitting.png" title="Simulation Result of Degradation Rate  v.s. Protein Concentration Ratio">
 +
          <li><img src="https://static.igem.org/mediawiki/2013/1/19/3fitting.png" title="Experimental Result Curve Fitting">
</ul></div>
</ul></div>
     <div id="box5" class="box">
     <div id="box5" class="box">
         <h3>Degradation Rate</h3>
         <h3>Degradation Rate</h3>
-
<p>Degradation tags were also obtained from cyclins because cyclins should degrade fast enough to avoid binding to cdc28 and delaying its own phase. From our simulation we can find out that transformed proteins can also be degraded at a convenient speed.
+
<p>Through light intensity we want to convert it to protein concentration as well as calculate its degradation rate, so we made another model to achieve that.</p>
-
</p>
+
<h4>Reaction</h4>
-
<p><b>Parameter Table
+
<img src="https://static.igem.org/mediawiki/2013/c/cf/Formula.png">
-
</b></p>
+
<p>Through formula deviation, we obtain the relationship between protein degradation rate and ratio of protein tagged with degradation tags or not.</p>
-
<table>
+
<img src="https://static.igem.org/mediawiki/2013/8/8f/Deviation.png">
-
<td><p>Parameter</p></td>
+
<p>Since the degradation tags we use is too short when compared to XFP, we simplify our question to:</p>
-
<td><p>Rate(min<sup>-1</sup>)</p></td>
+
<img src="https://static.igem.org/mediawiki/2013/a/a3/Simplify.png">
-
<td><p>Citation</p></td>
+
<img src="https://static.igem.org/mediawiki/2013/0/0a/Curve_fitting.png">
-
<tr>
+
<center><p>Figure. Simulation Result of Degradation Rate  v.s. Protein Concentration Ratio
-
<td><p>D(PEST1)</p></td>
+
</p></center>
-
<td><p>0.12</p></td>
+
<img src="https://static.igem.org/mediawiki/2013/1/19/3fitting.png">
-
<td><p> Chen et al. (2004) </p></td>
+
<center><p>Figure. Experimental Result Curve Fitting
-
<tr>
+
</p></center>
-
<td><p>D(PEST2)</p></td>
+
<p>From experimental fitting curve we got its half-life of our protein 6.88 min. So the degradation rate should be: </p>
-
<td><p>0.12</p></td>
+
<img src="https://static.igem.org/mediawiki/2013/9/94/Hl-rate.png">
-
<td><p> Chen et al. (2004) </p></td>
+
<p>While in simulation, we obtained the degradation rate by calculating with [P1_P]/[P2_P]:</p>
-
<tr>
+
<img src="https://static.igem.org/mediawiki/2013/b/ba/Simulation_result.png">
-
<td><p>D(PEST3)</p></td>
+
<p>Simulation result did mate with our experimental result.</p>
-
<td><p>0.14</p></td>
+
-
<td><p> Belli, Gari, Aldea, & Herrero (2001) </p></td>
+
-
<tr>
+
-
<td><p>D(D-box)</p></td>
+
-
<td><p>Vdb5</p></td>
+
-
<td><p> Chen et al. (2004) </p></td>
+
-
</table>
+
-
<p></p>
+
-
<img src="https://static.igem.org/mediawiki/2013/b/bc/P%2BD.png">
+
-
<p>As Degradation tags could not fully help tell apart each phase by the light of XFP, we built targeting peptide into model to make a more distinguishable visual result. As shown here, we present a 3D simulation result by adding another axis to specify different organelles.
+
-
</p>
+
</div>
</div>

Latest revision as of 03:35, 29 October 2013


Ball Ball

Playing with my eyes
aren't you?

Hi I am Dr. Mage!
A "budding" yeast cell!

Blueprint

Our project based a lot on cell cycle, especially the cyclin-promoters and cyclin-degradation tags. Through modelling Cell cycle is one of the most complex network in biology world. Better understanding of cell cycle and it’s regulation, to some extent, faciliate the fermentation industry because we can easily accelarate or decelarate a cell cycle or even one phase in the cycle which are important for metabolism product synthesis. In order to simulation and predict the experimets of the effeciency of Sic1, alternative splicing and degradation tags in the whole cell cycle, we build tree ordinary differential equation system models.

With the use of cyclins' promoters, we got the simulation of period XFP.

Figure. Simulation Result of Phase Specific Promoter + XFP

Each XFP will finally merge together so it's hard to tell part. So degradation tags were introduced. Degradation tags were also obtained from cyclins because cyclins should degrade fast enough to avoid binding to cdc28 and delaying its own phase. From our simulation we can find out that transformed proteins can also be degraded at a convenient speed.

Parameter Table

Parameter

Rate(min-1)

Citation

D(PEST1)

0.12

Chen et al. (2004)

D(PEST2)

0.12

Chen et al. (2004)

D(PEST3)

0.14

Belli, Gari, Aldea, & Herrero (2001)

D(D-box)

Vdb5

Chen et al. (2004)

Figure. Simulation Result of Phase Specific Promoter + XFP + Degradation Tag

As Degradation tags could not fully help tell apart each phase by the light of XFP, we built targeting peptide into model to make a more distinguishable visual result. As shown here, we present a 3D simulation result by adding another axis to specify different organelles.

Figure. Simulation Result of Phase Specific Promoter + XFP + Degradation Tag + Targeting Peptide

Cell Cycle

To make a precise prediction of our project and analyze its feasibility, we build a cell cycle model based on Chen's work Chen et al. (2004). By simulating the periodic cycle, we obtained the promoters we could make use of.

Promoters are selected by observing the appearance and disappearance of proteins shown in cell cycle model.

Figure. Simulation Result of Original Cell Cycle

Both the model and related papers show that cln1, 2 and clb1, 2, 5, 6 appear at a periodic rhythm because of the appearance of their transcription factors. There are some other proteins (such as NET1) shown this features, but their mechanisms are also related to some protein-protein interactions.

Figure. Simulation Result of NET1 and NET1T

Cell Synchronization

Previously study reported the introduction of sic1p could prevent the cell to enter S phase. Based on the sic1 system in yeast, we developed an artificial sic1 system (SIC1_Art). By adding galactose or modifying the phosphorylated sites, we can regulate the synthesis (Ka) and degradation (Kd) rates of the sic1_Art. We are trying to utilize this artificial system to precisely regulate the phase in yeast cell cycle, and our goal is to understand the synchronization behavior in yeast.

Figure. SIC1 Model

Figure. G1 Phase Delay

SIC1_Art on G1 stage

G1 length:

To understand the temporal effect of SIC1_Art on the length G1 phase, we performed parameter scan on the amount of time of adding SIC1_Art (DeltaT). By setting Ka=0.12 and Kd=0.016, we estimated the relationship between DeltaT and the length of G1 phase. Our computation simulation showed that, as we added SIC1_Art into the yeast, the amount of SIC1_Art will increase at first, and then it will enter a plateau stage. After the plateau stage, SIC1_Art will decrease gradually, which subsequently followed by the leaving of G1 stage (900 min). Our result suggests a positive correlation between DeltaT and the length of G1 phase in the first 900 min, and we discovered an upper bound at the length of G1 phase.

Figure. Curve Fitting of SIC1_Art and G1 Phase Length

Plateau, the definition:

Based on the relation between DeltaT and the cellular level of SIC1_Art, we defined plateau stage as the time space within which the amount of SIC1_Art is less than the maximum SIC_Art amount during the G1 phase (SIC1_Amax) and greater than (SIC1_Amax - Kd*5min). During this time space, the temporal difference of SIC1_Art degradation is less than 5 min, which we considered the minimum requirement of synchronization.

Figure. Plateau Stage of SIC1_Art

Figure. Plateau Stage of SIC1_Art with Different Galatose Input Time

Ka/Kd, Entering Plateau:

To examine the relation between the synthesis and degradation rate and the timing of entering plateau stage (Tp), we performed parameter scan on Ka and Kd. We found that the Tp is negatively correlated with Ka and positively correlated with Kd.

Figure. Influence of Ka and Kd to Tp

Ka/kd, Length of Plateau:

To further explore the optimal Ka/Kd in SIC1_Art system, we investigated the influence of Ka/Kd on the length of plateau domain (Lp).

Figure. Influence of Ka and Kd to Lp

Synchronization in yeast cell cycle

Using the result of above analysis, we chose Ka=0.219, Kd=0.048 as the optimal parameters, which give rise to short entering plateau time and long enough plateau stage (Tp = 61 min, Lp=355 min ).

We simulated the multi-cell behavior in yeast cell cycle: we started with cells in different phases, Art_time = 990 min, we added galactose into the systems, which initiated the synthesis of SIC1_Art and subsequently stopped all the cells at G1 phase. At time=1030 min, we stopped adding galactose and subsequently caused fast degradation of SIC1_Art. This process made all the yeasts into the phase and consequently achieved synchronization.

Figure. Simulation Result of Multiple Cells' Synchronization

Figure. Viability Simulation

Alternative Splicing by CRISPRi

To predict the alternative outcome, we also made an intron model to show different results due to incubating in different media. In our project, intron can be spliced in two different ways, providing a completely different outcome because of frame-shift, and this result is not a change like 1-0 to 0-1, but somehow more like a change between 0.4-0.6 and 0.8-0.2.

Figure. dCas9 Controlled SRC1 Intron Splicing

Reactions:

Parameter Table:

Parameter

Explanation

P(dCas9_m)

dCas9 mRNA transcription rate

P(sgRNA)

sgRNA transcription rate

P(dCas9p)

dCas9 protein translation rate

D(RNA)

Average degradation rate of RNA

Kass

Association rate of CRISPRi system

Kass

Association rate of CRISPRi system

Kdis

Dissociation rate of CRISPRi system

Kass1

Association rate of modified spliceosome

Kdis1

Dissociation rate of modified spliceosome

Kdis1

Dissociation rate of modified spliceosome

K

Splicing rate

P(Hub1_m)

Hub1 mRNA transcription rate

P(Hub1_P)

Hub1 protein translation rate

P(pre-mRNA)

pre-mRNA transcription rate

P(ProteinL)

5’L protein translation rate

P(ProteinS)

5’S protein translation rate

D(Protein)

Average degradation rate of protein

There are 4 parameters that we cannot find during our research, including kass, kdis representing the association and dissociation rate of CRISPRi system, and kass1 and kdis1 representing the association and dissociation rate of Hub1p and spliceosome.

We run parameter scan for each system individually, and found out that with CRISPRi system is more efficient with higher kass and lower kdis, as expected.

And about the alternative splicing model, we attempted to fit simulation result to experimental one. In Hub1 expressed system, L-mRNA will rise at first but descend to an equilibrium stage while S-mRNA will directly rise to its own equilibrium stage.

kass1 should be larger than kdis1, or L-mRNA will be produced more than S-mRNA instead of a ratio of 40-60.

Figure. Simulation Result of Two mRNA when Kass1

Also, kass1 should not be too smaller than kdis1, or their ratio will be much larger than 40-60.

Figure. Simulation Result of Two mRNA when Kass1>Kdis1

Finally we set down that kass1 = kdis1.

Figure. Simulation Result of Two mRNA when Kass1=Kdis1

When inhibiting the expression of HUB1, there is still a background splicing of 5’S site, so we need another parameter b in S-splicing.

Background S-splicing parameter b is mostly related to the ratio of spliceosome and Hub1p-modified spliceosome (Hub1_spliceosome) at equilibrium state. With higher b, L-mRNA and S-mRNA will come closer at equilibrium stat while it influence no-Hub1p situation more than Hub1p situation.

Figure. Parameter Scan of b with Galactose Input

Figure. Parameter Scan of b without Galactose Input

Degradation Rate

Through light intensity we want to convert it to protein concentration as well as calculate its degradation rate, so we made another model to achieve that.

Reaction

Through formula deviation, we obtain the relationship between protein degradation rate and ratio of protein tagged with degradation tags or not.

Since the degradation tags we use is too short when compared to XFP, we simplify our question to:

Figure. Simulation Result of Degradation Rate v.s. Protein Concentration Ratio

Figure. Experimental Result Curve Fitting

From experimental fitting curve we got its half-life of our protein 6.88 min. So the degradation rate should be:

While in simulation, we obtained the degradation rate by calculating with [P1_P]/[P2_P]:

Simulation result did mate with our experimental result.