Team:Peking/Modeling/Luminesensor/Simulation

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  <h3 id="title1">ODE model</h3>
  <h3 id="title1">ODE model</h3>
  <p>
  <p>
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According to the previous network and ODE model, we listed all the differential equations (<a href="/Team:Peking/Modeling/Appendix/ODE">detail here</a>) and simulated this system with MATLAB. We specifically watched three expressions to understand the mechanism for <i>Luminesensor</i>.
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According to the previous network and ODE model, we listed all the differential equations <!--(<a href="/Team:Peking/Modeling/Appendix/ODE">detail here</a>)--> and simulated this system with MATLAB with equations listed as
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</p>
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<div class="floatC">
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  <img src="" alt="Formulae"/>
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</div>
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<p>
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And parameters as
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</p>
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<div class="floatC">
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  <table>
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  <tr>
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    <td>Parameter</td><td>Value</td><td>Unit</td><td>Description</td><td>Source</td>
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  </tr><tr>
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    <td>k<sub>1</sub></td><td>3.x10<sup>-4</sup></td><td>s<sup>-1</sup></td><td>vivid decay rate constant</td><td></td>
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  </tr><tr>
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    <td>k<sub>2</sub></td><td>5.6x10<sup>-5</sup></td><td>s<sup>-1</sup></td><td>vivid dissociation rate constant</td><td><a href="#ref3" title="Mechanism-based tuning of a LOV domain photoreceptor, Brian D. Zoltowski, etc. NATURE CHEMICAL BIOLOGY">[3]</a></td>
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  </tr><tr>
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    <td>k<sub>3</sub></td><td>8.x10<sup>-4</sup></td><td>s<sup>-1</sup></td><td>monomer LexA releasing rate constant from specific binding site</td><td></td>
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  </tr><tr>
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    <td>k<sub>4</sub></td><td>1.x10<sup>-3</sup></td><td>s<sup>-1</sup></td><td>binded monomer LexA dissociation rate constant</td><td></td>
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  </tr><tr>
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    <td>k<sub>5</sub></td><td>1.x10<sup>-4</sup></td><td>s<sup>-1</sup></td><td>dimered LexA releasing rate constant from specific binding site</td><td></td>
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  </tr><tr>
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    <td>K<sub>1</sub>(Dark)</td><td>0</td><td>1</td><td>equilibrium excitation constant on dark</td><td></td>
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  </tr><tr>
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    <td>K<sub>1</sub>(Light)</td><td>1.x10<sup>+3</sup></td><td>1</td><td>equilibrium excitation constant on light</td><td></td>
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  </tr><tr>
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    <td>K<sub>2</sub></td><td>7.7x10<sup>-5</sup></td><td>(n mol/L)<sup>-1</sup></td><td>vivid association equilibrium constant</td><td><a href="#ref4" title="Protein Vivid Generates a Rapidly Exchanging Dimer, Brian D. Zoltowski, etc. BIOCHEMISTRY">[4]</a></td>
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  </tr><tr>
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    <td>K<sub>3</sub></td><td>1.x10<sup>-3</sup></td><td>(n mol/L)<sup>-1</sup></td><td>monomer LexA binding equilibrium constant with specific binding site</td><td><a href="#ref2" title="LexA Repressor Forms Stable Dimers in Solution, R.Mohana-Borges, etc. THE JOURNAL OF BIOLOGICAL CHEMISTRY">[2]</a></td>
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  </tr><tr>
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    <td>K<sub>4</sub></td><td>K<sub>2</sub>xK<sub>5</sub>/K<sub>3</sub></td><td>(n mol/L)<sup>-1</sup></td><td>binded monomer LexA association equilibrium constant</td><td>Thermal Principle</td>
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  </tr><tr>
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    <td>K<sub>5</sub></td><td>1.</td><td>(n mol/L)<sup>-1</sup></td><td>dimered LexA binding equilibrium constant</td><td><a href="#ref2" title="LexA Repressor Forms Stable Dimers in Solution, R.Mohana-Borges, etc. THE JOURNAL OF BIOLOGICAL CHEMISTRY">[2]</a></td>
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  </tr><tr>
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    <td>[L<sub>G</sub>]<sub>0</sub></td><td>1000</td><td>n mol/L</td><td>initial concentration of Luminesensor in ground state</td><td></td>
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  </tr><tr>
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    <td>[L<sub>A</sub>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of Luminesensor in active state</td><td></td>
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  </tr><tr>
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    <td>[L<sub>A</sub><sup>2</sup>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of dimered Luminesensor</td><td></td>
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  </tr><tr>
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    <td>[D<sub>L</sub>]<sub>0</sub></td><td>100</td><td>n mol/L</td><td>initial concentration of free specific binding site on DNA</td><td>high-copy plasmid</td>
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  </tr><tr>
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    <td>[L<sub>G</sub>D<sub>L</sub>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of dimered Luminesensor binded Luminesensor in ground state</td><td></td>
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  </tr><tr>
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    <td>[L<sub>A</sub>D<sub>L</sub>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of dimered Luminesensor binded Luminesensor in active state</td><td></td>
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  </tr><tr>
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    <td>[L<sub>A</sub><sup>2</sup>D<sub>L</sub>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of binded and dimered Luminesensor</td><td></td>
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  </tr>
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  </table>
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</div>
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<p>
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We specifically watched three expressions to understand the mechanism for <i>Luminesensor</i>.
  </p>
  </p>
  <table style="width:600px;"><tr>
  <table style="width:600px;"><tr>
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  <h3 id="title3">Stochastic Simulation</h3>
  <h3 id="title3">Stochastic Simulation</h3>
  <p>
  <p>
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In order to check the working stability of Luminesensor, we simulated this reaction network with a <a href="/Team:Peking/Modeling/Appendix/Stochastic">stochastic model</a>. By estimating the volume of a cell, we converted the concentration of a component into the number of molecules by 1 n mol/L : 1. The result are shown below:
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In order to check the working stability of Luminesensor, we simulated this reaction network with a <!--<a href="/Team:Peking/Modeling/Appendix/Stochastic">-->stochastic model<!--</a>-->. By estimating the volume of a cell, we converted the concentration of a component into the number of molecules by 1 n mol/L : 1. The result are shown below:
  <p>
  <p>
  <div class="floatC">
  <div class="floatC">

Revision as of 01:47, 25 September 2012

ODE model

According to the previous network and ODE model, we listed all the differential equations and simulated this system with MATLAB with equations listed as

Formulae

And parameters as

ParameterValueUnitDescriptionSource
k13.x10-4s-1vivid decay rate constant
k25.6x10-5s-1vivid dissociation rate constant[3]
k38.x10-4s-1monomer LexA releasing rate constant from specific binding site
k41.x10-3s-1binded monomer LexA dissociation rate constant
k51.x10-4s-1dimered LexA releasing rate constant from specific binding site
K1(Dark)01equilibrium excitation constant on dark
K1(Light)1.x10+31equilibrium excitation constant on light
K27.7x10-5(n mol/L)-1vivid association equilibrium constant[4]
K31.x10-3(n mol/L)-1monomer LexA binding equilibrium constant with specific binding site[2]
K4K2xK5/K3(n mol/L)-1binded monomer LexA association equilibrium constantThermal Principle
K51.(n mol/L)-1dimered LexA binding equilibrium constant[2]
[LG]01000n mol/Linitial concentration of Luminesensor in ground state
[LA]00n mol/Linitial concentration of Luminesensor in active state
[LA2]00n mol/Linitial concentration of dimered Luminesensor
[DL]0100n mol/Linitial concentration of free specific binding site on DNAhigh-copy plasmid
[LGDL]00n mol/Linitial concentration of dimered Luminesensor binded Luminesensor in ground state
[LADL]00n mol/Linitial concentration of dimered Luminesensor binded Luminesensor in active state
[LA2DL]00n mol/Linitial concentration of binded and dimered Luminesensor

We specifically watched three expressions to understand the mechanism for Luminesensor.

Expression Description Remark
rb = 1 - [DL]/[DT] This indicates the repressing degree. DT indicates the total specific binding sites, while the DL indicates the free ones among DT.
rd = 2[LA2X]/[LT] This indicates the dimerizing degree. LT indicates the total Luminesensor molecules, and LA2X indicates all dimered Luminesensor molecules, i.e. LA2 + LA2DL.
ra =
( [LAX] + 2[LA2X] ) /[LT]
This indicates the activating degree. LAX indicates all monomer Luminesensor molecules, i.e. LA + LADL.

The simulation result is shown below:

Simulation Result

Fig 2. ODE Simulation Result of the prototype Luminesensor.

From the figure above, we discovered that the activation and decay of Luminesensor are the pioneers of progress, and the activating rate is the most completely switched variable as lighting varies. The promoter sequences in the DNA are repressed even though the Luminesensor has not all dimered.

Stochastic Simulation

In order to check the working stability of Luminesensor, we simulated this reaction network with a stochastic model. By estimating the volume of a cell, we converted the concentration of a component into the number of molecules by 1 n mol/L : 1. The result are shown below:

Simulation Result

Fig 3. Stochastic Simulation Result of the prototype Luminesensor.

According to the figure above, the noise did not influence this system. Thus, the Luminesensor is expected to work theoretically. Besides, the average value of stochastic simulation is coupled with the result of ODE model, which in turn proves the self-consistency of our ODE model.

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