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

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               <msub>
 
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               <mi>k</mi>
 
               <mi>k</mi>
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               <mi mathvariant="italic">Gad</mi>
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               <mi mathvariant="italic">PtsX</mi>
 
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               <mo stretchy="false">−</mo>
 
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             </msub></math> is mature mCherry. The rate constants are described below in <b>Table 1</b>.
 
             </msub></math> is mature mCherry. The rate constants are described below in <b>Table 1</b>.
  
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<div class="panel panel-default" style="max-width:600px">
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      <!-- Default panel contents -->
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      <div class="panel-heading">Table 1 - System parameters</div>
  
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      <!-- Table -->
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        <thead>
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          <tr>
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            <th>Description</th>
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            <th>Symbol</th>
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            <th>Value</th>
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          </tr>
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        </thead>
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        <tbody>
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          <tr>
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            <th scope="row">Glucose diffusion</th>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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</math> </td>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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        </math></td>
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          </tr>
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          <tr>
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            <th scope="row">C1 formation/dissociation rate</th>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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            <msub>
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              <mi>k</mi>
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              <mn>1</mn>
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        </math></td>
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          </tr>
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          <tr>
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            <th scope="row">PtxS production rate</th>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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            <msub>
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              <mi>k</mi>
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              <mn>PtxS</mn>
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            </msub>
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</math> </td>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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          </tr>
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          <tr>
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            <th scope="row">Protein production rate</th>
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            <msub>
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              <mi>k</mi>
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              <mn>tr</mn>
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          </math></td>
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          </tr>
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          <tr>
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            <th scope="row">mCherry maturation rate</th>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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            <msub>
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              <mi>k</mi>
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              <mn>m</mn>
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            </msub>
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</math> </td>
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            <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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          </math></td>
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          </tr>
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    <tr>
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      <th scope="row">mCherry degradation rate</th>
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      <td><math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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            <msub>
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              <mi>k</mi>
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              <mn>d</mn>
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            </msub>
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</math> </td>
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    </math></td>
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    </tr>  
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        </tbody>
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      </table>
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    </div>
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{{NTNU_Trondheim_End_Draft}}
 
{{NTNU_Trondheim_End_Draft}}

Revision as of 00:54, 19 September 2015

Modeling

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

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:

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 PtsX − 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
C1 formation/dissociation rate k 1 k 2
PtxS production rate k PtxS
Protein production rate k tr
mCherry maturation rate k m
mCherry degradation rate k d

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