Difference between revisions of "Team:NTNU Trondheim/Modeling"

 
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</div>
 
</div>
  
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<div class="highlightBox">
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<div class="panel panel-default">
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<h4>Note</h4>
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  <!-- Default panel contents -->
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<p>In order to be considered for the <a href="https://2015.igem.org/Judging/Awards#SpecialPrizes">Best Model award</a>, you must fill out this page.</p>
+
  <div class="panel-heading">Modeling</div>
 +
 
 +
  <!-- List group -->
 +
  <ul class="list-group">
 +
    <li class="list-group-item"><a href="https://2015.igem.org/Team:NTNU_Trondheim/Modeling#mcherry">Glucose-mCherry response</a></li>
 +
<li class="list-group-item"><a href="https://2015.igem.org/Team:NTNU_Trondheim/Modeling#brixells"><i>Brixells modeling</i></a></li>
 +
  </ul>
 +
</div>
 
</div>
 
</div>
  
 +
 +
<div class="alert alert-warning" role="alert">
 +
This page contains mathematical equations using MathML. Most browsers support it (Safari, Firefox, etc.) but Chrome and IE do not. If you are using Chrome or IE, please consider viewing this page in an alternative browser.
 +
</div>
 +
<p>
 +
The pathway triggering the expression of mCherry upon reception of Glucose is shown in <b>Figure 1</b>.
 +
</p>
 +
 +
<h3 id="mcherry">Glucose-mCherry response</h3>
  
  
 
<figure>
 
<figure>
 
   <img class="img-responsive" style="max-width:650px" src="https://static.igem.org/mediawiki/2015/0/06/NTNU_Trondheim_modeling_pathway.png">
 
   <img class="img-responsive" style="max-width:650px" src="https://static.igem.org/mediawiki/2015/0/06/NTNU_Trondheim_modeling_pathway.png">
−
   <figcaption><b>Figure 2.</b> Biological molecules involved in the <i>P. Putida</i> signaling pathway for expressing mCherry.</figcaption>
+
   <figcaption><b>Figure 1.</b> Biological molecules involved in the <i>P. Putida</i> signaling pathway for expressing mCherry.</figcaption>
 
</figure>
 
</figure>
  
 +
<p>Using the generalized mass action equations and the pathway shown in the figure above, we can write the kinetics of the systems in the following form, the results are shown in <b>Figure 2</b>:</p>
 +
 +
<span id="Object1"> <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
      <mtable>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi mathvariant="italic">KGN</mi>
 +
                <mi>i</mi>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi>c</mi>
 +
            </msub>
 +
            </mrow>
 +
            <mrow>
 +
            <mrow>
 +
              <mo fence="true" stretchy="false">(</mo>
 +
              <mrow>
 +
              <mrow>
 +
                <msub>
 +
                <mi mathvariant="italic">GLC</mi>
 +
                <mi>e</mi>
 +
                </msub>
 +
                <mo stretchy="false">−</mo>
 +
                <msub>
 +
                <mi mathvariant="italic">KGN</mi>
 +
                <mi>i</mi>
 +
                </msub>
 +
              </mrow>
 +
              </mrow>
 +
              <mo fence="true" stretchy="false">)</mo>
 +
            </mrow>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
            </mrow>
 +
            <msubsup>
 +
            <mi mathvariant="italic">KGN</mi>
 +
            <mi>i</mi>
 +
            <mn>2</mn>
 +
            </msubsup>
 +
            <mrow>
 +
            <msup>
 +
              <mi mathvariant="italic"> PtxS </mi>
 +
              <mn>2</mn>
 +
            </msup>
 +
            <mo stretchy="false">+</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi>C</mi>
 +
            <mn>1</mn>
 +
            </msub>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi>C</mi>
 +
                <mn>1</mn>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi mathvariant="italic">KGN</mi>
 +
            <mi>i</mi>
 +
            </msub>
 +
            <mrow>
 +
            <mi mathvariant="italic"> PtxS </mi>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi>C</mi>
 +
            <mn>1</mn>
 +
            </msub>
 +
            <msub>
 +
            <mi>k</mi>
 +
            <mn>2</mn>
 +
            </msub>
 +
            <mi mathvariant="italic">PGad</mi>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi>C</mi>
 +
                <mn>2</mn>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>2</mn>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi>C</mi>
 +
            <mn>1</mn>
 +
            </msub>
 +
            <mrow>
 +
            <mi mathvariant="italic">PGad</mi>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>2</mn>
 +
            </msub>
 +
            </mrow>
 +
            <mrow>
 +
            <msub>
 +
              <mi>C</mi>
 +
              <mn>2</mn>
 +
            </msub>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi mathvariant="italic">tr</mi>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi>C</mi>
 +
            <mn>2</mn>
 +
            </msub>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi mathvariant="italic">KGN</mi>
 +
                <mn>2</mn>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <mrow>
 +
              <msub>
 +
              <mi>k</mi>
 +
              <mi mathvariant="italic">PtxS</mi>
 +
              </msub>
 +
              <mo stretchy="false">−</mo>
 +
              <mn>2</mn>
 +
            </mrow>
 +
            </mrow>
 +
            <msub>
 +
            <mi>C</mi>
 +
            <mn>1</mn>
 +
            </msub>
 +
            <msub>
 +
              <mi>-2C</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi mathvariant="italic">mCherry</mi>
 +
                <mi>i</mi>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi mathvariant="italic">tr</mi>
 +
            </msub>
 +
            </mrow>
 +
            <mrow>
 +
            <msub>
 +
              <mi>C</mi>
 +
              <mn>2</mn>
 +
            </msub>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi>m</mi>
 +
            </msub>
 +
            </mrow>
 +
            <mrow>
 +
            <msub>
 +
              <mi mathvariant="italic">mCherry</mi>
 +
              <mi>i</mi>
 +
            </msub>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi>d</mi>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi mathvariant="italic">mCherry</mi>
 +
            <mi>i</mi>
 +
            </msub>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        <mtr>
 +
          <mtd>
 +
          <mrow>
 +
            <mrow>
 +
            <mfrac>
 +
              <mrow>
 +
              <mi>d</mi>
 +
              <msub>
 +
                <mi mathvariant="italic">mCherry</mi>
 +
                <mi>m</mi>
 +
              </msub>
 +
              </mrow>
 +
              <mi mathvariant="italic">dt</mi>
 +
            </mfrac>
 +
            <mo stretchy="false">=</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi>m</mi>
 +
            </msub>
 +
            </mrow>
 +
            <mrow>
 +
            <msub>
 +
              <mi>G</mi>
 +
              <mi>i</mi>
 +
            </msub>
 +
            <mo stretchy="false">−</mo>
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mi>d</mi>
 +
            </msub>
 +
            </mrow>
 +
            <msub>
 +
            <mi mathvariant="italic">mCherry</mi>
 +
            <mi>m</mi>
 +
            </msub>
 +
          </mrow>
 +
          </mtd>
 +
        </mtr>
 +
        </mtable>
 +
      </math>
 +
 +
 +
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">              <msub>
 +
                <mi mathvariant="italic">KGN</mi>
 +
                <mi>i</mi>
 +
              </msub></math> is the internal ketogluconate concentration,  <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">                  <msub>
 +
                <mi mathvariant="italic">GLC</mi>
 +
                <mi>e</mi>
 +
                </msub></math> is the external glucose concentration,                <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">  <mi mathvariant="italic"> PtxS </mi></math> is the population of free PtxS,  <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">        <msub>
 +
            <mi>C</mi>
 +
            <mn>1</mn>
 +
            </msub></math> is the KGN-PtXs dimer, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">        <msub>
 +
            <mi>C</mi>
 +
            <mn>2</mn>
 +
            </msub></math> is the complex that involves the dimer bound to the promoter sequence, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">            <mi mathvariant="italic">PGad</mi></math> is the Gad promoter concentration,<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">              <msub>
 +
              <mi mathvariant="italic">mCherry</mi>
 +
              <mi>i</mi>
 +
            </msub></math> is the immature mCherry, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">              <msub>
 +
              <mi mathvariant="italic">mCherry</mi>
 +
              <mi>m</mi>
 +
            </msub></math> is mature mCherry. The rate constants are described below in <b>Table 1</b>.
 +
 +
<div class="panel panel-default" style="max-width:600px">
 +
      <!-- Default panel contents -->
 +
      <div class="panel-heading">Table 1 - System parameters</div>
 +
 +
      <!-- Table -->
 +
      <table class="table">
 +
        <thead>
 +
          <tr>
 +
            <th>Description</th>
 +
            <th>Symbol</th>
 +
            <th>Value</th>
 +
          </tr>
 +
        </thead>
 +
        <tbody>
 +
            <tr>
 +
              <th scope="row">Glucose diffusion rate</th>
 +
              <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
 +
                <msub>
 +
                <mi>k</mi>
 +
                <mn>e</mn>
 +
                </msub>
 +
 +
 +
  </math> </td>
 +
              <td>10 mmol/g/h [1]</td>
 +
            </tr>
 +
 +
          <tr>
 +
            <th scope="row">C<sub>1</sub> formation/dissociation rate</th>
 +
            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>1</mn>
 +
            </msub>
 +
 +
 +
</math> </td>
 +
            <td>50/h (approximation)</td>
 +
          </tr>
 +
 +
          <tr>
 +
            <th scope="row">C<sub>2</sub> formation/dissociation rate</th>
 +
              <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>2</mn>
 +
            </msub>
 +
 +
            </math></td>
 +
            <td>500/h (approximation)</td>
 +
           
 +
          </tr>
 +
 
 +
 +
          <tr>
 +
            <th scope="row">PtxS production rate</th>
 +
            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>PtxS</mn>
 +
            </msub>
 +
 +
</math> </td>
 +
            <td>500 / h [2][3]</td>
 +
          </tr>
 +
 +
          <tr>
 +
            <th scope="row">Protein production rate</th>
 +
            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>tr</mn>
 +
            </msub>
 +
 +
</math> </td>
 +
            <td>100 / h (approximation)</td>
 +
          </tr>
 +
   
 +
          <tr>
 +
            <th scope="row">mCherry maturation rate</th>
 +
            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>m</mn>
 +
            </msub></math></td>
 +
            <td>2/h [4]</td>
 +
          </tr>
 +
     
 +
    <tr>
 +
      <th scope="row">mCherry degradation rate</th>
 +
      <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
 +
            <msub>
 +
              <mi>k</mi>
 +
              <mn>d</mn>
 +
            </msub>
 +
 +
 +
</math> </td>
 +
      <td> 40 / h [4]</td>
 +
    </tr>  
 +
 
 +
        </tbody>
 +
      </table>
 +
    </div>
 +
<figure>
 +
  <img class="img-responsive" src="https://static.igem.org/mediawiki/2015/e/e0/NTNU_Trondheim_model_Glucose-mCherry.png" alt="Glucose metabolism">
 +
  <figcaption>Figure 2- Glucose-mCherry response using the proposed model.</figcaption>
 +
</figure>
 +
 +
<h3 id="brixells">Brixells</h3>
 +
<p>The Brixells Modeling Tool</a>, has been created to assist <a href="https://2015.igem.org/Team:Warwick">Team Warwick</a> to predict the probability of bonding of 3D structures built with E. Coli expressing Zinc fingers and DNA strands. More details are available on the <a href="https://2015.igem.org/Team:NTNU_Trondheim/Collaborations">collaborations</a> page.</p>
 +
 +
<h3 id="conclusion">Conclusion</h3>
 +
<p>Modeling can be very useful to optimize the design of <i>P. Putida</i> as it is very sensitive to glucose toxicity. This framework can help in optimizing the lifetime of the glucose-sensing capsule and should be considered in the alginate formulation. This model is to be combined with a population level glucose toxicity model for agent-based modeling in BSim.</p>
 +
 +
 +
<h3>References</h3>
 +
[1] Rühl, Jana, Andreas Schmid, and Lars Mathias Blank. "Selected Pseudomonas putida strains able to grow in the presence of high butanol concentrations." Applied and environmental microbiology 75.13 (2009): 4653-4656.<br>
 +
[2] Colmer, J. A., and A. N. Hamood. "Characterization of ptxS, a Pseudomonas aeruginosa gene which interferes with the effect of the exotoxin A positive regulatory gene, ptxR." Molecular and General Genetics MGG 258.3 (1998): 250-259.<br>
 +
[3] Follonier, Stéphanie, Sven Panke, and Manfred Zinn. "A reduction in growth rate of Pseudomonas putida KT2442 counteracts productivity advances in medium-chain-length polyhydroxyalkanoate production from gluconate." Microb Cell Fact 10.1 (2011): 25.<br>
 +
[4] Piatkevich, Kiryl D., and Vladislav V. Verkhusha. "Guide to red fluorescent proteins and biosensors for flow cytometry." Methods in cell biology 102 (2011): 431.
 +
 +
<br>
 +
<br>
 
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Latest revision as of 15:51, 2 October 2015

Modeling

Modeling

The pathway triggering the expression of mCherry upon reception of Glucose is shown in Figure 1.

Glucose-mCherry response

Figure 1. Biological molecules involved in the P. Putida signaling pathway for expressing mCherry.

Using the generalized mass action equations and the pathway shown in the figure above, we can write the kinetics of the systems in the following form, the results are shown in Figure 2:

d KGN i dt = k c ( GLC e − KGN i ) − k 1 KGN i 2 PtxS 2 + k 1 C 1 d C 1 dt = k 1 KGN i PtxS − k 1 C 1 k 2 PGad d C 2 dt = k 2 C 1 PGad − k 2 C 2 − k tr C 2 d KGN 2 dt = k PtxS − 2 C 1 -2C 1 d mCherry i dt = k tr C 2 − k m mCherry i − k d mCherry i d mCherry m dt = k m G i − k d mCherry m

where KGN i is the internal ketogluconate concentration, GLC e is the external glucose concentration, PtxS is the population of free PtxS, C 1 is the KGN-PtXs dimer, C 2 is the complex that involves the dimer bound to the promoter sequence, PGad is the Gad promoter concentration, mCherry i is the immature mCherry, and mCherry m is mature mCherry. The rate constants are described below in Table 1.

Table 1 - System parameters
Description Symbol Value
Glucose diffusion rate k e 10 mmol/g/h [1]
C1 formation/dissociation rate k 1 50/h (approximation)
C2 formation/dissociation rate k 2 500/h (approximation)
PtxS production rate k PtxS 500 / h [2][3]
Protein production rate k tr 100 / h (approximation)
mCherry maturation rate k m 2/h [4]
mCherry degradation rate k d 40 / h [4]
Glucose metabolism
Figure 2- Glucose-mCherry response using the proposed model.

Brixells

The Brixells Modeling Tool, has been created to assist Team Warwick to predict the probability of bonding of 3D structures built with E. Coli expressing Zinc fingers and DNA strands. More details are available on the collaborations page.

Conclusion

Modeling can be very useful to optimize the design of P. Putida as it is very sensitive to glucose toxicity. This framework can help in optimizing the lifetime of the glucose-sensing capsule and should be considered in the alginate formulation. This model is to be combined with a population level glucose toxicity model for agent-based modeling in BSim.

References

[1] Rühl, Jana, Andreas Schmid, and Lars Mathias Blank. "Selected Pseudomonas putida strains able to grow in the presence of high butanol concentrations." Applied and environmental microbiology 75.13 (2009): 4653-4656.
[2] Colmer, J. A., and A. N. Hamood. "Characterization of ptxS, a Pseudomonas aeruginosa gene which interferes with the effect of the exotoxin A positive regulatory gene, ptxR." Molecular and General Genetics MGG 258.3 (1998): 250-259.
[3] Follonier, Stéphanie, Sven Panke, and Manfred Zinn. "A reduction in growth rate of Pseudomonas putida KT2442 counteracts productivity advances in medium-chain-length polyhydroxyalkanoate production from gluconate." Microb Cell Fact 10.1 (2011): 25.
[4] Piatkevich, Kiryl D., and Vladislav V. Verkhusha. "Guide to red fluorescent proteins and biosensors for flow cytometry." Methods in cell biology 102 (2011): 431.

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