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<h3>★  ALERT! </h3>
 
<p>This page is used by the judges to evaluate your team for the <a href="https://2017.igem.org/Judging/Medals">medal criterion</a> or <a href="https://2017.igem.org/Judging/Awards"> award listed above</a>. </p>
 
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<h1> Modeling</h1>
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
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<a href="#mazef">MazEF modeling</a>
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<li><a href="#ov">Overview</a></li>
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<li><a href="#pd">Part description pBAD</a></li>
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<li><a href="#con">Conclusion</a></li>
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<h2>MazEF modeling</h2>
 
</div>
 
</div>
<div class="clear"></div>
 
  
<div class="column half_size">
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<div id="ov">
<h3> Gold Medal Criterion #3</h3>
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<div class="aaa"></div>
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<h3>Overview</h3>
 
<p>
 
<p>
To complete for the gold medal criterion #3, please describe your work on this page and fill out the description on your <a href="https://2017.igem.org/Judging/Judging_Form">judging form</a>. To achieve this medal criterion, you must convince the judges that your team has gained insight into your project from modeling. You may not convince the judges if your model does not have an effect on your project design or implementation.  
+
This year modeling plays a great role on our project because we used it to predict the precise time in which our systems start functioning. We showed two essential part modeling below, one is <i>E. coli DH5α</i> and the other one is B. subtilis B. subtilis strain 168(ATCC ® 23857). The showing data will demonstrate our project working result.
 
</p>
 
</p>
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</div>
  
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<div id="pd">
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<div class="aaa"></div>
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<h3>Part description pBAD</h3>
 
<p>
 
<p>
Please see the <a href="https://2017.igem.org/Judging/Medals"> 2017 Medals Page</a> for more information.  
+
pBAD is the promoter regulated by both arabinose and the araC gene product. Since that araC gene protein regulates expression is also activated by arabinose, pBAD promoter is enormously effected by arabinose. We modeling the relationship between pBAD activity and arabinose concentration for finding out how to let pBAD reach it maximal activity.<br/>
 +
We assumed that our system reacts as the following chemical system:<br/>
 +
</p>
 +
<img src="https://static.igem.org/mediawiki/2017/a/a8/Ccum1.png" style="display:block; margin:auto;"><br/>
 +
<img src="https://static.igem.org/mediawiki/2017/f/f8/Ccum2.png" style="display:block; margin:auto;"><br/>
 +
<p>
 +
Assume that AraC is always in large concentration, the binding reaction between AraC and arabinose is very fast. Thus, we don’t have to consider the concentration of arabinose and AraC. We only need to focus on concentration of Arabinose AraC.
 +
To describe the transcription of mRNA, we used Michaelis- Mentin kinetics and get the follow differential equation.
 +
</p>
 +
<img src="https://static.igem.org/mediawiki/2017/d/da/Ccum3.png" style="display:block; margin:auto;"><br/>
 +
<img src="https://static.igem.org/mediawiki/2017/8/89/Ccum4.png" style="display:block; margin:auto;"><br/>
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<style type="text/css">
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.tg  {border-collapse:collapse;border-spacing:0;border-color:#ccc;}
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.tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#ccc;color:#333;background-color:#fff;}
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.tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#ccc;color:#333;background-color:#f0f0f0;}
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.tg .tg-4eph{background-color:#f9f9f9}
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</style>
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<table class="tg">
 +
  <tr>
 +
    <th class="tg-031e">α</th>
 +
    <th class="tg-031e">Translation rate</th>
 +
    <th class="tg-031e">15ntds−1/length of sequence</th>
 +
  </tr>
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  <tr>
 +
    <td class="tg-4eph">γ1</td>
 +
    <td class="tg-4eph">Combineddegradation and dilution rate,of mRNA</td>
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    <td class="tg-4eph">2.2×10-3(S-1)</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-031e">γ2</td>
 +
    <td class="tg-031e">Combineddegradation and,dilution rate of GFP</td>
 +
    <td class="tg-031e">5.2×10-4(S-1)</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-4eph">Kmax</td>
 +
    <td class="tg-4eph">Maximal transcription rate</td>
 +
    <td class="tg-4eph">50ntd,S-1/length of sequence</td>
 +
  </tr>
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  <tr>
 +
    <td class="tg-031e">Khalf</td>
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    <td class="tg-031e">Half-maximal transcription,rate</td>
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    <td class="tg-031e">160μM</td>
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  </tr>
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  <tr>
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    <td class="tg-4eph">n</td>
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    <td class="tg-4eph">Hill coefficient</td>
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    <td class="tg-4eph">2.65</td>
 +
  </tr>
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</table>
 +
<p>The above data is all from 2015 Oxford iGEM modeling<br/><br/>
 +
Using Polymath, we can get the different signal of GFP in different concentration of Arabinose-AraC.
 +
</p>
 +
<img src="https://static.igem.org/mediawiki/2017/4/46/Ccum5.png" style="display:block; margin:auto;"><br/>
 +
<p>Figure 1 The respond of GFP in different concentration of Arabinose-AraC. Range 0.13 μM~10μM<br/>
 +
We can see that different concentration of Arabinose-AraC will affect the maximum amount of GFP production. We also can see that they reach maximum signal at the same time at approximate 60 minute.
 +
</p>
 +
<img src="https://static.igem.org/mediawiki/2017/c/c2/Ccum6.png" style="display:block; margin:auto;"><br/>
 +
<p>Figure 2 The respond of GFP in different concentration of Arabinose-AraC. Range 6000 μM~130000μM<br/>
 +
In high concentration of arabinose, we can see that all the line will overlap. The signal of GFP isn’t changing.
 
</p>
 
</p>
 
</div>
 
</div>
  
<div class="column half_size">
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<div id="con">
<h3>Best Model Special Prize</h3>
+
<div class="aaa"></div>
 
+
<h3>Conclusion:</h3>
 
<p>
 
<p>
To compete for the <a href="https://2017.igem.org/Judging/Awards">Best Model prize</a>, please describe your work on this page  and also fill out the description on the <a href="https://2017.igem.org/Judging/Judging_Form">judging form</a>. Please note you can compete for both the gold medal criterion #3 and the best model prize with this page.  
+
Assume that we want to make a difference in our system, the amount of arabinose shouldn’t be too large, and the interval should be too large either. Because pBAD system is very sensitive to arabinose, a trivial change can result in drastic impact. And we found out that the system would reach equilibrium at approximately 60 mins. So we learned that the kill switch would be activated after 1 hour. So the sampling point interval can be roughly 1 hour.
<br><br>
+
You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
+
 
</p>
 
</p>
 
 
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<div class="clear"></div>
 
  
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+
<div id="ref">
<h5> Inspiration </h5>
+
<div class="aaa"></div>
 +
<h3>Reference:</h3>
 
<p>
 
<p>
Here are a few examples from previous teams:
+
1. Ben-Samoun, K., Leblon, G., & Reyes, O. (1999). Positively regulated expression of the Escherichia coli araBAD promoter in Corynebacterium glutamicum. FEMS microbiology letters, 174(1), 125-130. <br/>
 +
2. Guzman, L.-M., Belin, D., Carson, M. J., & Beckwith, J. (1995). Tight regulation, modulation, and high-level expression by vectors containing the arabinose PBAD promoter. Journal of bacteriology, 177(14), 4121-4130. <br/>
 +
3. https://2015.igem.org/Team:Oxford/Modeling
 
</p>
 
</p>
<ul>
 
<li><a href="https://2016.igem.org/Team:Manchester/Model">Manchester 2016</a></li>
 
<li><a href="https://2016.igem.org/Team:TU_Delft/Model">TU Delft 2016  </li>
 
<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">ETH Zurich 2014</a></li>
 
<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">Waterloo 2014</a></li>
 
</ul>
 
  
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Latest revision as of 03:59, 2 November 2017

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MazEF modeling

Overview

This year modeling plays a great role on our project because we used it to predict the precise time in which our systems start functioning. We showed two essential part modeling below, one is E. coli DH5α and the other one is B. subtilis B. subtilis strain 168(ATCC ® 23857). The showing data will demonstrate our project working result.

Part description pBAD

pBAD is the promoter regulated by both arabinose and the araC gene product. Since that araC gene protein regulates expression is also activated by arabinose, pBAD promoter is enormously effected by arabinose. We modeling the relationship between pBAD activity and arabinose concentration for finding out how to let pBAD reach it maximal activity.
We assumed that our system reacts as the following chemical system:



Assume that AraC is always in large concentration, the binding reaction between AraC and arabinose is very fast. Thus, we don’t have to consider the concentration of arabinose and AraC. We only need to focus on concentration of Arabinose AraC. To describe the transcription of mRNA, we used Michaelis- Mentin kinetics and get the follow differential equation.



α Translation rate 15ntds−1/length of sequence
γ1 Combineddegradation and dilution rate,of mRNA 2.2×10-3(S-1)
γ2 Combineddegradation and,dilution rate of GFP 5.2×10-4(S-1)
Kmax Maximal transcription rate 50ntd,S-1/length of sequence
Khalf Half-maximal transcription,rate 160μM
n Hill coefficient 2.65

The above data is all from 2015 Oxford iGEM modeling

Using Polymath, we can get the different signal of GFP in different concentration of Arabinose-AraC.


Figure 1 The respond of GFP in different concentration of Arabinose-AraC. Range 0.13 μM~10μM
We can see that different concentration of Arabinose-AraC will affect the maximum amount of GFP production. We also can see that they reach maximum signal at the same time at approximate 60 minute.


Figure 2 The respond of GFP in different concentration of Arabinose-AraC. Range 6000 μM~130000μM
In high concentration of arabinose, we can see that all the line will overlap. The signal of GFP isn’t changing.

Conclusion:

Assume that we want to make a difference in our system, the amount of arabinose shouldn’t be too large, and the interval should be too large either. Because pBAD system is very sensitive to arabinose, a trivial change can result in drastic impact. And we found out that the system would reach equilibrium at approximately 60 mins. So we learned that the kill switch would be activated after 1 hour. So the sampling point interval can be roughly 1 hour.

Reference:

1. Ben-Samoun, K., Leblon, G., & Reyes, O. (1999). Positively regulated expression of the Escherichia coli araBAD promoter in Corynebacterium glutamicum. FEMS microbiology letters, 174(1), 125-130.
2. Guzman, L.-M., Belin, D., Carson, M. J., & Beckwith, J. (1995). Tight regulation, modulation, and high-level expression by vectors containing the arabinose PBAD promoter. Journal of bacteriology, 177(14), 4121-4130.
3. https://2015.igem.org/Team:Oxford/Modeling