Difference between revisions of "Team:HUST-China/Modeling on Cellular Level"

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    <div align="center" class="description"><a name="1"></a><br>
+
  <div align="center" class="description"><a name="1"></a><br>
 
     <div class="dongxi"></div>
 
     <div class="dongxi"></div>
        With the benefit of synthetic biology, we built up our network with some characterized parts to carry out the mission of sand solidification. However, whether our circuit will be able to achieve its goal depends on the key to the following questions.<br>
+
    <h2 style="color:black" align="left"><b>Modeling on Cellular Level</b></h2><br>
- Will the darkness induction system be able to switch efficiently to control the expression of target proteins?<br>
+
    <p>With the benefit of synthetic biology, we built up our network with some characterized parts to carry out the mission of sand solidification. However, whether our circuit will be able to achieve its goal depends on the key to the following questions.<br>
- How much Si-tag and Mcfp-3 our strains produce in the end?<br>
+
- Will the darkness induction system be able to switch efficiently to control the expression of target proteins?<br>
- What strategy should we take in practice to make full use of our product?<br>
+
- How much Si-tag and Mcfp-3 our strains produce in the end?<br>
 +
- What strategy should we take in practice to make full use of our product?<br>
 +
        </p>
 +
<p>The answer to these questions will be shown in our modeling as well as the guidance for future wet-lab experiments.</p>
  
<p>The answer to these questions will be shown in our modeling as well as the guidance for future wet-lab experiments.</p>
+
<p>To ensure that our circuit is capable, we built a DDEs (Delay Differential Equations) model based on Michaelis-Menten equation and Chemical reaction rate equation, which includes three parts, to get the insight of how each part works cooperatively.</p>
 +
<a href="#"><b> The code of our DDEs model can be downloaded here.</b></a>
  
<p>To ensure that our circuit is capable, we built a DDEs (Delay Differential Equations) model based on Michaelis-Menten equation and Chemical reaction rate equation, which includes three parts, to get the insight of how each part works cooperatively.</p>
+
<br><br><br>
<a><p> The code of our DDEs model can be downloaded here.</p></a>
+
  
<h3 style="color:black" align="left"><b>Basic Parts</b></h3><br>
+
    <h3 style="color:black" align="left"><b>Parameters</b></h3><br>
             <h4 style="color:black" align="left"><b>1.Light Control</b></h4><br>
+
             The description of parameters, their values and the references involved in this model are listed in a table.<br>
 +
            <a href="#"><b>The parameters table (1) can be downloaded here.</b></a>
  
        <table border="1">
+
</div>
            <tr>
+
<div align="center" class="description"><a name="2"></a><br>
<th>Part Number</th>
+
    <div class="dongxi"></div>
<th>Description</th>
+
        <h2 style="color:black" align="left"><b>Part one: the Darkness Induction System</b></h2><br>
<th>Abbreviation</th>
+
          <p>First of all, we intended to simulate the whole pathway to approximate the final expression rate of target proteins as well as the property of the darkness induction system. To achieve this, we need to translate our biological processes to chemical reactions and finally represent it with mathematical equations. </p>
</tr>
+
<p>The Darkness Induction System pathway contains the following reactions:</p>
<tr>
+
<br><br><br>
<td><a href="http://parts.igem.org/Part:BBa_K1592005">BBa_K1592005</a></td>
+
<td>GalBD-CRY2 Fusion for Yeast-Two-Hybrid</td>
+
<td>BD-CRY2</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592006">BBa_K1592006</a></td>
+
<td>GalAD-CIB1 Fusion for Yeast-Two-Hybrid</td>
+
<td>AD-CIB1</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592015">BBa_K1592015</a></td>
+
<td>photoreceptor cryptochrome 2</td>
+
<td>CRY2</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592016">BBa_K1592016</a></td>
+
<td>a basic helix-loop-helix protein</td>
+
<td>CIB1</td>
+
</tr>
+
</table>
+
<p>Our light-control system is based on the Yeast-Two-Hybrid system. Cryptochrome 2 (CRY2) is a blue light stimulated photoreceptor, when exposed to blue light, it would interact with CIB1. A Gal4 DNA sequence was fused to their C terminus, thus the interaction between two proteins would activate the downstream expression.<br>
+
We measured β-galactosidase activity as the validation test of our Light-control system.
+
  </p>
+
    [[File:Codon_Frequency_Distribution.png|thumb|center|1200px| Fig.2-1-3 The percentage distribution of codons in computed codon quality groups. The value of 100 is set for the codon with the highest usage frequency for a given amino acid in the desired expression organism. Codons with values lower than 30 are likely to hamper the expression efficiency.]]
+
  
            <h4 style="color:black" align="left"><b>2.Viscous Protein</b></h4><br>
+
        <h3 style="color:black" align="left"><b>Formulary</b></h3><br>
            <p><b>Mcfp</b></p>
+
          <p>1. Generation of active CIB1_AD</p>
          <table border="1">
+
          <img class="picture" src="https://static.igem.org/mediawiki/2015/7/70/HUST_Formulary1.png"><br>
            <tr>
+
          <p>2. Generation of active CRY2_BD</p>
<th>Part Number</th>
+
          <img class="picture" src="https://static.igem.org/mediawiki/2015/4/41/HUST-Formulary2.png"><br>
<th>Description</th>
+
          <p>3. Activation of promoter Anb1</p>
<th>Abbreviation</th>
+
          <img class="picture" src="https://static.igem.org/mediawiki/2015/9/9e/HUST-Formulary3.png"><br>
</tr>
+
       
<tr>
+
        <br><br><br>
<td><a href="http://parts.igem.org/Part:BBa_K1592001">BBa_K1592001</a></td>
+
        <p>The corresponding DDEs of darkness induction system are listed below:</p>
<td>Mytilus californianus foot protein 3(Mcfp3) variant 3</td>
+
        <p>1. Generation of CIB1_AD</p>
<td>Mcfp3</td>
+
        <img class="picture" src=""><br>
</tr>
+
        <img class="picture" src=""><br>
<tr>
+
        <img class="picture" src=""><br>
<td><a href="http://parts.igem.org/Part:BBa_K1592003">BBa_K1592003</a></td>
+
        <p>2. Generation of CRY2_BD</p>
<td>Mcfp3 with LIP2 prepro</td>
+
        <img class="picture" src=""><br>
<td>LIP-Mcfp</td>
+
        <img class="picture" src=""><br>
</tr>
+
        <img class="picture" src=""><br>
<tr>
+
        <p>3. Activation of promoter Anb1</p>
<td><a href="http://parts.igem.org/Part:BBa_K15920017">BBa_K1592017</a></td>
+
        <img class="picture" src=""><br>
<td>Mcfp3 with XPR2 pre</td>
+
        <p>If exposed to light</p>
<td>XPR2-Mcfp</td>
+
        <img class="picture" src=""><br>
</tr>
+
        <p>Elseif in darkness</p>
</table>
+
        <img class="picture" src=""><br>
<p>Mcfp-3 is foot protein secreted from Mytilus californianus. The protein is of significance to the formation of byssus to help mussels permanently or temporarily tether to the surface of solid surface of reef or ship-body.<br>
+
       
LIP2 and XPR2 are signal peptides. Signal peptide is added to the behind of Mcfp3 sequence, thus Mcfp can be secreted out of cell.
+
            <br><br><br>
            </p>
+
 +
            <h3 style="color:black" align="left"><b>Results</b></h3><br>
 +
          <p>Before the circuit was determined, there were two kinds of darkness induction system for choice: the CRY2-CIB1 system and the PhyA-FHL system. To find out the system that suits our circuit better, we simulated both of them with the DDEs model and printed some figures with MATLAB. </p>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/8/8e/HUST-result1.png"><br>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/6/65/HUST-result2.png"><br>
 +
          <p>We can safely derive the following conclusions from the figures above.<br>
 +
- The photoactive subjects are of low concentration but they remain at a certain level.<br>
 +
- Compared to the PhyA-FHL system, the CRY2-CIB1 system is more sensitive to light exposure (The peak of CRY2-CIB1 system appears earlier than the one of PhyA-FHL system) and the PhyA-FHL system has a time-lag for photoactivation. <br>
 +
- The rate of Rox1 degradation in CRY2-CIB1 system is higher than the one in PhyA-FHL system, which means the darkness induction could shut down quickly so that the downstream systems could be activated.<br>
 +
Hence, we considered CRY2-CIB1 system more advantageous and applied it to our project.<br>
 +
</p>
 +
</div>
  
            <p><b>Si-tag Collection</b></p>
 
    <table border="1">
 
            <tr>
 
<th>Part Number</th>
 
<th>Description</th>
 
<th>Abbreviation</th>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592007">BBa_K1592007</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (1-60) + YLcwp3 Fusion</td>
 
<td>Si-tag1-his</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592008">BBa_K1592008</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (61-202) + YLcwp3 Fusion</td>
 
<td>Si-tag2-his</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592009">BBa_K159209</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (203-273) + YLcwp3 Fusion</td>
 
<td>Si-tag3-his</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K15920010">BBa_K1592010</a></td>
 
<td>LIP2 prepro + E. coli ribosomal protein L2 (1-202)+ YLcwp3 Fusion</td>
 
<td>ST12</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592011">BBa_K1592011</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (61-273) + YLcwp3 Fusion</td>
 
<td>ST23</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592012">BBa_K159212</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (1-60,203-273) + YLcwp3 Fusion</td>
 
<td>ST13</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592013">BBa_K1592013</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (1-60,GS linker,202-273) + YLcwp3</td>
 
<td>ST1L3-his</td>
 
</tr>
 
<tr>
 
<td><a href="http://parts.igem.org/Part:BBa_K1592014">BBa_K1592014</a></td>
 
<td>LIP prepro + E. coli ribosomal protein L2 (1-273) + YLcwp3</td>
 
<td>ST123</td>
 
</tr>
 
</table>
 
            <p>This collection consists of several Si-tag proteins. Si-tag is 50S ribosomal protein L2 in the genome of E.coli, which was found to bind tightly to silicon particles. The Si-tag consists of three domains showing different binding strength. We combined the single domain, and tested their final binding strength.
 
            </p>
 
          <div>
 
          <img class="picture" src="https://static.igem.org/mediawiki/2015/8/8e/HUST_part2.png">
 
          </div>
 
<p>Besides, we added LIP prepro and YLcwp3(see below) to the terminals of Si-tag, thus Si-tag can be secreted then surface displayed on the cell wall.</p>
 
  
<p><a href="https://2015.igem.org/Team:HUST-China/Results#4">Click HERE or part number to see more details.</a></p>
 
  
    <h4 style="color:black" align="left"><b>3.Secrete and Surface display</b></h4><br>
+
<div align="center" class="description"><a name="3"></a><br>
           <table border="1">
+
    <div class="dongxi"></div>
 +
        <h2 style="color:black" align="left"><b>Part two: the Surface Display System of Si-tag</b></h2><br>
 +
        <p>With the simulation of Darkness Induction System above, we are able to determine when the Surface Display System of Si-tag would be activated. However, to predict whether Si-tag would be sufficient in the end and to provide essential parameters for the next model, we need to simulate the Surface Display System of Si-tag. </p>
 +
<br><br><br>
 +
 
 +
        <h3 style="color:black" align="left"><b>Formulary</b></h3><br>
 +
           <p>1. Generation of active CIB1_AD</p>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/c/c9/HUST-Formulary4.png"><br>
 +
          <p>2. Generation of active CRY2_BD</p>
 +
          <img class="picture" src=""><br>
 +
          <p>3. Activation of promoter Anb1</p>
 +
          <img class="picture" src=""><br>
 +
          <br><br><br>
 +
        <p>The corresponding DDEs of darkness induction system are listed below:</p>
 +
        <img class="picture" src=""><br>
 +
        <h3 style="color:black" align="left"><b>Results</b></h3><br>
 +
          <p>With the DDEs model we built, we could run the simulation of the expression of Si-tag and determine its amount at any time. To test the function of our darkness induction system, the timeline would be set as darkness-light-darkness. We printed the result figure with MATLAB.</p>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/3/39/HUST-result3.png"><br>
 +
          <p>From the figure above, we can see that the Si-tag remains at a low concentration and the Displayed Si-tag accumulates very efficiently when Euk.Cement is in darkness for the first time (0-200min). However, when exposed to light (200-500min), the expression of Si-tag is blocked and the rate of Displayed Si-tag accumulation decreases greatly. After light exposure (500-1500min), the expression of Si-tag and the rate of Displayed Si-tag accumulation gradually recover. Generally speaking, the darkness induction system is capable of controlling the downstream system and the expression of Si-tag is sufficient.
 +
</p>
 +
</div>
 +
 
 +
<div align="center" class="description"><a name="3"></a><br>
 +
    <div class="dongxi"></div>
 +
        <h2 style="color:black" align="left"><b>Part three: the Expression of Mcfp-3</b></h2><br>
 +
        <p>Besides Si-tag, Mcfp-3 is another important product that we must quantify its amount. It’s promoter is the same with the promoter of Si-tag and therefore, we could easily simulate it with the DDEs model and MATLAB.</p>
 +
<br><br><br>
 +
        <h3 style="color:black" align="left"><b>Formulary</b></h3><br>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/a/a4/HUST-Formulary5.png"><br>
 +
          <p>The corresponding DDEs of the expression of Mcfp-3 are listed below</p>
 +
          <img class="picture" src=""><br><br>
 +
 
 +
          <h3 style="color:black" align="left"><b>Results</b></h3><br>
 +
          <p>To test the darkness induction system again as well as to quantify the amount of Mcfp-3, we set the same timeline with that of Si-tag and run the simulation with MATLAB.</p>
 +
          <img class="picture" src="https://static.igem.org/mediawiki/2015/7/73/HUST-result4.png"><br>
 +
          <p>As we can see in the figure, the amount of Mcfp-3 was approximately twice as Si-tag and the darkness induction system took effect again.</p>
 +
          <br><br><br>
 +
          <h3 style="color:black" align="left"><b>Conclusions</b></h3><br>
 +
          <p>With our DDEs model, we can safely conclude that: <br>
 +
- Our darkness induction system could switch efficiently from darkness to light to shut down the downstream systems. However, it takes some time to switch back from light to darkness. <br>
 +
- Our strains could produce sufficient Si-tag as well as Mcfp-3 to do the job.<br>
 +
- We can quantify the amount of Si-tag and Mcfp-3 at any time so that we can move on to the next model with these data.<br>
 +
</p>
 +
        <br><br><br>
 +
<h3 style="color:black" align="left"><b>Robustness and Parameter Sensitivity Analysis</b></h3><br>
 +
          <p>Considering there are some parameters whose value is uncertain and may have effect on our model, we used numerical solutions to analyze the robustness and parameter sensitivity of our DDEs model.
 +
</p>
 +
<br><br><br>
 +
<h3 style="color:black" align="left"><b>τ1 &τ2</b></h3><br>
 +
          <p>Since τ1 and τ2 are variables that we could not determine their accurate values (0.1-3min), we run the DDEs model with different values ofτ1 and τ2 to find out what effect they have on our DDEs model.
 +
</p>
 +
<table border="1">
 
             <tr>
 
             <tr>
<th>Part Number</th>
+
<th>Parameters</th>a
<th>Description</th>
+
<th colspan="4">Values of each figure</th>
<th>Abbreviation</th>
+
 
</tr>
 
</tr>
 
<tr>
 
<tr>
<td><a href="http://parts.igem.org/Part:BBa_K1592000">BBa_K1592000</a></td>
+
<td>τ1</a></td>
<td>LIP2 prepro(signal peptide)</td>
+
<td>0.1</td>
<td>LIP2 prepro</td>
+
<td>3</td>
 +
<td>0.1</td>
 +
<td>3</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
<td><a href="http://parts.igem.org/Part:BBa_K1592002">BBa_K1592002</a></td>
+
<td>τ2</a></td>
<td>Yarrowia lipolytica cell wall protein 3</td>
+
<td>0.1</td>
<td>YLcwp3</td>
+
<td>0.1</td>
 +
<td>3</td>
 +
<td>3</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
<p>LIP2 prepro is a signal peptide. When fused to the N-terminal of interest protein, the expression products will be secreted out of cell.</p>
+
        <img class="picture" src="https://static.igem.org/mediawiki/2015/5/52/HUST-result5.png"><br>
 
+
        <img class="picture" src="https://static.igem.org/mediawiki/2015/4/43/HUST-result6.png"><br>
<p>YLcwp3, also as an anchor domain, is a cell wall protein. When fused to the C-terminal of interest protein, the expression products will be displayed on the cell wall.</p>
+
        <img class="picture" src="https://static.igem.org/mediawiki/2015/c/cc/HUST-result7.png"><br>
 
+
        <img class="picture" src="https://static.igem.org/mediawiki/2015/2/22/HUST-result8.png"><br>
<h4 style="color:black" align="left"><b>4.Others</b></h4><br>
+
        <h3 style="color:black" align="left"><b>Results</b></h3><br>
<table border="1">
+
          <p>Apparently, even the max value of τ1 and τ2 couldn’t produce noticeable time-lag for the whole system, because the time-lag produced byτ1 and τ2 is approximately 5 minutes while the whole simulation process has the timeline of 1.5 thousands minutes. Therefore, we can conclude that our DDEs model has the robustness ofτ1 and τ2 .</p>
            <tr>
+
<br><br><br>
<th>Part Number</th>
+
<th>Description</th>
+
<th>Abbreviation</th>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592004">BBa_K1592004</a></td>
+
<td>promoter hp4d</td>
+
<td>Php4d</td>
+
</tr>
+
</table>
+
<p>Promoter hp4d is a recombinant promotor which can strongly promote gene expression in any culture medium. The gene promoted by Php4d usually expresses at the early stage of stabilization</p>
+
 
+
        <p><b>Improved part</b></p>
+
<table border="1">
+
            <tr>
+
<th>Part Number</th>
+
<th>Description</th>
+
<th>Abbreviation</th>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592020">BBa_K1592020</a></td>
+
<td>Ptrp mutant1</td>
+
<td>Ptrp1</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592021">BBa_K1592021</a></td>
+
<td>Ptrp mutant2</td>
+
<td>Ptrp2</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592022">BBa_K1592022</a></td>
+
<td>Ptrp mutant3</td>
+
<td>Ptrp3</td>
+
</tr>
+
</table>
+
 
+
        <p>Ptrp is a promoter with trp operator. It will be repressed by trpR and LovTAP.
+
<br>We improved BBa_K191007, remove the illegal sites without affecting its function by site-directed mutagenesis for meeting the requirements of RFC10. Finally we constructed three ptrp mutant, called Ptrp mutant1, Ptrp mutant2, and Ptrp mutant3.
+
</p>
+
<p>(These promoters didn’t really applied to our project, for they were our reserve choices)</p>
+
    </div>
+
 
+
 
+
<div class="description"><a name="2"></a><br>
+
<div class="dongxi"></div>
+
<h2 style="color:black" align="left"><b>Composite part</b></h2>
+
  <table border="1">
+
            <tr>
+
<th>Part Number</th>
+
<th>Description</th>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592018">BBa_K1592018</a></td>
+
<td>Pgal1+rox1+cyc1_terminator</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592019">BBa_K1592019</a></td>
+
<td>Panb1+XPR2 pre-Mcfp3</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592023">BBa_K1592023</a></td>
+
<td>Ptrp mutant1+RBS+GFP</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592024">BBa_K1592024</a></td>
+
<td>Ptrp mutant2+RBS+GFP</td>
+
</tr>
+
<tr>
+
<td><a href="http://parts.igem.org/Part:BBa_K1592025">BBa_K1592025</a></td>
+
<td>Ptrp mutant3+RBS+GFP</td>
+
</tr>
+
</table>
+
+
  
<!--图片-->
+
<h3 style="color:black" align="left"><b>Rate of pAnb1 basic transcription</b></h3><br>
<div>
+
          <p>Since promoter Anb1 has basic transcription rate, Rox1, Si-tag and Mcfp-3 would be expressed even in darkness. Hence, to figure out how it takes effect on our model, we run the simulation with different rate of pAnb1 basic transcription (0.1*Vmax to 0.2*Vmax with step of 0.005*Vmax).</p>
    <p>BBa_K1592018</p>
+
            <img class="picture" src=""><br>
<img class="picture" src="https://static.igem.org/mediawiki/2015/8/88/HUST_part3.png">
+
<br><br><br>
</div>
+
<div>
+
    <p>BBa_K1592018</p>
+
<img class="picture" src="https://static.igem.org/mediawiki/2015/9/90/HUST_part4.png">
+
</div>
+
<div>
+
    <p>BBa_K1592018</p>
+
<img class="picture" src="https://static.igem.org/mediawiki/2015/c/cf/HUST_part5.png">
+
</div>
+
  
+
<h3 style="color:black" align="left"><b>Results</b></h3><br>
 +
          <p>Obviously, our DDEs model is quite sensitive to the amount of basic transcription of pAnb1. If the rate of pAnb1 basic transcription increases from 0.100*Vmax to 0.200*Vmax, the amount of Rox1 would become 125 percent. Therefore, with less basic transcription of pAnb1, less Rox1 would be expressed and the repressed expression of Si-tag and Mcfp-3 would recover more quickly. We can conclude that our circuit could be improved by reducing the basic transcription of pAnb1.</p>
 +
<br><br><br>
  
 
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Revision as of 12:20, 14 September 2015

Team:HUST-China:Results


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Modeling on Cellular Level


With the benefit of synthetic biology, we built up our network with some characterized parts to carry out the mission of sand solidification. However, whether our circuit will be able to achieve its goal depends on the key to the following questions.
- Will the darkness induction system be able to switch efficiently to control the expression of target proteins?
- How much Si-tag and Mcfp-3 our strains produce in the end?
- What strategy should we take in practice to make full use of our product?

The answer to these questions will be shown in our modeling as well as the guidance for future wet-lab experiments.

To ensure that our circuit is capable, we built a DDEs (Delay Differential Equations) model based on Michaelis-Menten equation and Chemical reaction rate equation, which includes three parts, to get the insight of how each part works cooperatively.

The code of our DDEs model can be downloaded here.


Parameters


The description of parameters, their values and the references involved in this model are listed in a table.
The parameters table (1) can be downloaded here.

Part one: the Darkness Induction System


First of all, we intended to simulate the whole pathway to approximate the final expression rate of target proteins as well as the property of the darkness induction system. To achieve this, we need to translate our biological processes to chemical reactions and finally represent it with mathematical equations.

The Darkness Induction System pathway contains the following reactions:




Formulary


1. Generation of active CIB1_AD


2. Generation of active CRY2_BD


3. Activation of promoter Anb1





The corresponding DDEs of darkness induction system are listed below:

1. Generation of CIB1_AD




2. Generation of CRY2_BD




3. Activation of promoter Anb1


If exposed to light


Elseif in darkness





Results


Before the circuit was determined, there were two kinds of darkness induction system for choice: the CRY2-CIB1 system and the PhyA-FHL system. To find out the system that suits our circuit better, we simulated both of them with the DDEs model and printed some figures with MATLAB.



We can safely derive the following conclusions from the figures above.
- The photoactive subjects are of low concentration but they remain at a certain level.
- Compared to the PhyA-FHL system, the CRY2-CIB1 system is more sensitive to light exposure (The peak of CRY2-CIB1 system appears earlier than the one of PhyA-FHL system) and the PhyA-FHL system has a time-lag for photoactivation.
- The rate of Rox1 degradation in CRY2-CIB1 system is higher than the one in PhyA-FHL system, which means the darkness induction could shut down quickly so that the downstream systems could be activated.
Hence, we considered CRY2-CIB1 system more advantageous and applied it to our project.


Part two: the Surface Display System of Si-tag


With the simulation of Darkness Induction System above, we are able to determine when the Surface Display System of Si-tag would be activated. However, to predict whether Si-tag would be sufficient in the end and to provide essential parameters for the next model, we need to simulate the Surface Display System of Si-tag.




Formulary


1. Generation of active CIB1_AD


2. Generation of active CRY2_BD


3. Activation of promoter Anb1





The corresponding DDEs of darkness induction system are listed below:


Results


With the DDEs model we built, we could run the simulation of the expression of Si-tag and determine its amount at any time. To test the function of our darkness induction system, the timeline would be set as darkness-light-darkness. We printed the result figure with MATLAB.


From the figure above, we can see that the Si-tag remains at a low concentration and the Displayed Si-tag accumulates very efficiently when Euk.Cement is in darkness for the first time (0-200min). However, when exposed to light (200-500min), the expression of Si-tag is blocked and the rate of Displayed Si-tag accumulation decreases greatly. After light exposure (500-1500min), the expression of Si-tag and the rate of Displayed Si-tag accumulation gradually recover. Generally speaking, the darkness induction system is capable of controlling the downstream system and the expression of Si-tag is sufficient.


Part three: the Expression of Mcfp-3


Besides Si-tag, Mcfp-3 is another important product that we must quantify its amount. It’s promoter is the same with the promoter of Si-tag and therefore, we could easily simulate it with the DDEs model and MATLAB.




Formulary



The corresponding DDEs of the expression of Mcfp-3 are listed below



Results


To test the darkness induction system again as well as to quantify the amount of Mcfp-3, we set the same timeline with that of Si-tag and run the simulation with MATLAB.


As we can see in the figure, the amount of Mcfp-3 was approximately twice as Si-tag and the darkness induction system took effect again.




Conclusions


With our DDEs model, we can safely conclude that:
- Our darkness induction system could switch efficiently from darkness to light to shut down the downstream systems. However, it takes some time to switch back from light to darkness.
- Our strains could produce sufficient Si-tag as well as Mcfp-3 to do the job.
- We can quantify the amount of Si-tag and Mcfp-3 at any time so that we can move on to the next model with these data.




Robustness and Parameter Sensitivity Analysis


Considering there are some parameters whose value is uncertain and may have effect on our model, we used numerical solutions to analyze the robustness and parameter sensitivity of our DDEs model.




τ1 &τ2


Since τ1 and τ2 are variables that we could not determine their accurate values (0.1-3min), we run the DDEs model with different values ofτ1 and τ2 to find out what effect they have on our DDEs model.

a
ParametersValues of each figure
τ1 0.1 3 0.1 3
τ2 0.1 0.1 3 3




Results


Apparently, even the max value of τ1 and τ2 couldn’t produce noticeable time-lag for the whole system, because the time-lag produced byτ1 and τ2 is approximately 5 minutes while the whole simulation process has the timeline of 1.5 thousands minutes. Therefore, we can conclude that our DDEs model has the robustness ofτ1 and τ2 .




Rate of pAnb1 basic transcription


Since promoter Anb1 has basic transcription rate, Rox1, Si-tag and Mcfp-3 would be expressed even in darkness. Hence, to figure out how it takes effect on our model, we run the simulation with different rate of pAnb1 basic transcription (0.1*Vmax to 0.2*Vmax with step of 0.005*Vmax).





Results


Obviously, our DDEs model is quite sensitive to the amount of basic transcription of pAnb1. If the rate of pAnb1 basic transcription increases from 0.100*Vmax to 0.200*Vmax, the amount of Rox1 would become 125 percent. Therefore, with less basic transcription of pAnb1, less Rox1 would be expressed and the repressed expression of Si-tag and Mcfp-3 would recover more quickly. We can conclude that our circuit could be improved by reducing the basic transcription of pAnb1.