Team:Peking/Modeling/Luminesensor/Simulation

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<div class="PKU_context floatR first">
<div class="PKU_context floatR first">
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  <h3 id="title1">ODE model</h3>
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  <h3 id="title1">ODE Model</h3>
  <p>
  <p>
-
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>.
+
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 below:
  </p>
  </p>
-
  <table><tr>
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  <div class="floatC">
 +
  <img src="/wiki/images/5/5f/Peking2012_Formula000.png" alt="Formulae" style="width:500px;"/>
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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">
 +
  <table>
 +
  <tr>
 +
    <td>Parameter</td><td>Value</td><td>Unit</td><td>Description</td><td>Source</td>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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="Zoltowski, B.D., Vaccaro, B., and Crane, B.R. (2009). Mechanism-based tuning of a LOV domain photoreceptor. Nat. Chem. Biol. 5: 827: 834">[3]</a></td>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <td>K<sub>1</sub>(Dark)</td><td>0</td><td>1</td><td>equilibrium excitation constant on dark</td><td></td>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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="#ref1" title="Zoltowski, B.D., Crane, B.R.(2008). Light Activation of the LOV Protein Vivid Generates a Rapidly Exchanging Dimer.Biochemistry, 47: 7012: 7019 ">[1]</a></td>
 +
  </tr><tr>
 +
    <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="2. Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of specific DNA in tightening protein-protein interactions. J. Biol. Chem., 275: 4708: 4712">[2]</a></td>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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="Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of specific DNA in tightening protein-protein interactions. J. Biol. Chem., 275: 4708: 4712">[2]</a></td>
 +
  </tr><tr>
 +
    <td>[L<sub>G</sub>]<sub>0</sub></td><td>1000</td><td>n mol/L</td><td>initial concentration of <i>Luminesensor</i> in ground state</td><td></td>
 +
  </tr><tr>
 +
    <td>[L<sub>A</sub>]<sub>0</sub></td><td>0</td><td>n mol/L</td><td>initial concentration of <i>Luminesensor</i> in active state</td><td></td>
 +
  </tr><tr>
 +
    <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 <i>Luminesensor</i></td><td></td>
 +
  </tr><tr>
 +
    <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>
 +
  </tr><tr>
 +
    <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 <i>Luminesensor</i> binded <i>Luminesensor</i> in ground state</td><td></td>
 +
  </tr><tr>
 +
    <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 <i>Luminesensor</i> binded <i>Luminesensor</i> in active state</td><td></td>
 +
  </tr><tr>
 +
    <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 <i>Luminesensor</i></td><td></td>
 +
  </tr>
 +
  </table>
 +
</div>
 +
<p>
 +
We specifically watched three expressions to understand the mechanism for <i>Luminesensor</i>.
 +
</p>
 +
<table style="width:600px;"><tr>
   <td style="text-align:center;">Expression</td>
   <td style="text-align:center;">Expression</td>
   <td style="text-align:center;">Description</td>
   <td style="text-align:center;">Description</td>
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  </tr><tr>
  </tr><tr>
   <td style="text-align:center;">r<sub>b</sub> = 1 - [D<sub>L</sub>]/[D<sub>T</sub>]</td>
   <td style="text-align:center;">r<sub>b</sub> = 1 - [D<sub>L</sub>]/[D<sub>T</sub>]</td>
-
   <td style="font-size:14px;width:220px;">This indicates the repressing degree.</td>
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   <td style="font-size:14px;width:250px;padding:5px;">This indicates the repressing degree.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">D<sub>T</sub> indicates the total specific binding sites, while the D<sub>L</sub> indicates the free ones among D<sub>T</sub>.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">D<sub>T</sub> indicates the total specific binding sites, while the D<sub>L</sub> indicates the free ones among D<sub>T</sub>.</td>
  </tr><tr>
  </tr><tr>
   <td style="text-align:center;">r<sub>d</sub> = 2[L<sub>A</sub><sup>2</sup>X]/[L<sub>T</sub>]</td>
   <td style="text-align:center;">r<sub>d</sub> = 2[L<sub>A</sub><sup>2</sup>X]/[L<sub>T</sub>]</td>
-
   <td style="font-size:14px;width:220px;">This indicates the dimerizing degree.</td>
+
   <td style="font-size:14px;width:250px;padding:5px;">This indicates the dimerizing degree.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">L<sub>T</sub> indicates the total <i>Luminesensor</i> molecules, and L<sub>A</sub><sup>2</sup>X indicates all dimered <i>Luminesensor</i> molecules, <i>i.e.</i> L<sub>A</sub><sup>2</sup> + L<sub>A</sub><sup>2</sup>D<sub>L</sub>.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">L<sub>T</sub> indicates the total <i>Luminesensor</i> molecules, and L<sub>A</sub><sup>2</sup>X indicates all dimered <i>Luminesensor</i> molecules, <i>i.e.</i> L<sub>A</sub><sup>2</sup> + L<sub>A</sub><sup>2</sup>D<sub>L</sub>.</td>
  </tr><tr>
  </tr><tr>
-
   <td style="text-align:center;">r<sub>a</sub> = ([L<sub>A</sub>X] + 2[L<sub>A</sub><sup>2</sup>X])/[L<sub>T</sub>]</td>
+
   <td style="text-align:center;">r<sub>a</sub> = <br /> (&#32;[L<sub>A</sub>X] + 2[L<sub>A</sub><sup>2</sup>X]&#32;)&#32;/[L<sub>T</sub>]</td>
-
   <td style="font-size:14px;width:220px;">This indicates the activating degree.</td>
+
   <td style="font-size:14px;width:250px;padding:5px;">This indicates the activating degree.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">L<sub>A</sub>X indicates all monomer <i>Luminesensor</i> molecules, <i>i.e.</i> L<sub>A</sub> + L<sub>A</sub>D<sub>L</sub>.</td>
   <td style="font-size:12px;width:200px;line-height:12px;">L<sub>A</sub>X indicates all monomer <i>Luminesensor</i> molecules, <i>i.e.</i> L<sub>A</sub> + L<sub>A</sub>D<sub>L</sub>.</td>
  </tr></table>
  </tr></table>
-
 
+
<p>
-
 
+
The simulation result is shown below:
 +
</p>
 +
<div class="floatC">
 +
  <img src="/wiki/images/7/71/Peking2012_ode_YL.png" alt="Simulation Result" style="width:600px;"/>
 +
  <div>
 +
  <p class="description" style="text-align:center;">
 +
Figure 1. ODE Simulation Result of the prototype Luminesensor.
 +
  </p>
 +
  </div>
 +
</div>
 +
<p>
 +
From the Figure 1 above, we discovered that the activation and decay of <i>Luminesensor</i> are the key points of progress, and the activating rate is the most sensitive to light intensity. The promoter will be repressed even though the <i>Luminesensor</i> does not totally dimerized.
 +
</p>
 +
</div>
 +
<div class="PKU_context floatR">
 +
<h3 id="title2">Stochastic Simulation</h3>
 +
<p>
 +
In order to verify the robustness of <i>Luminesensor</i> function, 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 results are shown below:
 +
<p>
 +
<div class="floatC">
 +
  <img src="/wiki/images/c/c3/Peking2012_sto_YL.png" alt="Simulation Result" style="width:600px;"/>
 +
  <div>
 +
  <p class="description" style="text-align:center;">
 +
Figure 2. Stochastic Simulation Result of Prototype <i>Luminesensor</i>.
 +
  </p>
 +
  </div>
 +
</div>
 +
<p>
 +
According to Figure 2 above, noise does not influence this system. Thus the <i>Luminesensor</i> is expected to work theoretically. Besides, the average value of stochastic simulation is consistent with the result of ODE model, which in turn proves the self-consistency of our ODE model.
 +
</p>
 +
</div>
 +
<div class="PKU_context floatR">
 +
<h3 id="title3">Simulation for GFP Expression <br />Regulated by the <i>Luminesensor</i></h3>
 +
<p>
 +
In order to see whether our model is predictive for the downstream gene expression under control of the <i>Luminesensor</i>, transcription and translation process were incorporated into the modeling of DNA binding process. In addition, we considered the delay of translation initiation time and the growth of cell. The simulation below(Figure 3) represents the GFP expression regulated by the <i>Luminesensor</i>. After a long time in light condition, where GFP expression is inhibited, from <i>t=0h</i>, the cells are moved into dark and begin to express GFP. The GFP expression level varying with time was recorded in this simulation.
 +
</p>
 +
<div class="floatC">
 +
  <img src="/wiki/images/0/07/Wild_type.png" alt="Simulation Result" style="width:500px;"/>
 +
  <div>
 +
  <p class="description" style="text-align:center;">
 +
Figure 3. ODE Simulation Result is correspond to the experiment data of GFP expression level according to time from, which suggests that our model is effective to present the experiment situation.
 +
  </p>
 +
  </div>
 +
</div>
 +
</div>
 +
<div class="PKU_context floatR">
 +
<h3 id="title4">Reference</h3>
 +
<p></p>
 +
<ul class="refer"><li id="ref1">
 +
1. Zoltowski, B.D., Crane, B.R.(2008). Light Activation of the LOV Protein Vivid Generates a Rapidly Exchanging Dimer. <i>Biochemistry</i>, 47: 7012: 7019
 +
  </li><li id = "ref2">
 +
2. Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of specific DNA in tightening protein-protein interactions. <i>J. Biol. Chem.</i>, 275: 4708: 4712
 +
  </li><li id = "ref3">
 +
3. Zoltowski, B.D., Vaccaro, B., and Crane, B.R. (2009). Mechanism-based tuning of a LOV domain photoreceptor. <i>Nat. Chem. Biol.</i> 5: 827: 834
 +
</li></ul>
</div>
</div>
 +
</html>{{Template:Peking2012_Color_Epilogue}}

Latest revision as of 02:49, 27 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 below:

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[1]
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

Figure 1. ODE Simulation Result of the prototype Luminesensor.

From the Figure 1 above, we discovered that the activation and decay of Luminesensor are the key points of progress, and the activating rate is the most sensitive to light intensity. The promoter will be repressed even though the Luminesensor does not totally dimerized.

Stochastic Simulation

In order to verify the robustness of Luminesensor function, 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 results are shown below:

Simulation Result

Figure 2. Stochastic Simulation Result of Prototype Luminesensor.

According to Figure 2 above, noise does not influence this system. Thus the Luminesensor is expected to work theoretically. Besides, the average value of stochastic simulation is consistent with the result of ODE model, which in turn proves the self-consistency of our ODE model.

Simulation for GFP Expression
Regulated by the Luminesensor

In order to see whether our model is predictive for the downstream gene expression under control of the Luminesensor, transcription and translation process were incorporated into the modeling of DNA binding process. In addition, we considered the delay of translation initiation time and the growth of cell. The simulation below(Figure 3) represents the GFP expression regulated by the Luminesensor. After a long time in light condition, where GFP expression is inhibited, from t=0h, the cells are moved into dark and begin to express GFP. The GFP expression level varying with time was recorded in this simulation.

Simulation Result

Figure 3. ODE Simulation Result is correspond to the experiment data of GFP expression level according to time from, which suggests that our model is effective to present the experiment situation.

Reference

  • 1. Zoltowski, B.D., Crane, B.R.(2008). Light Activation of the LOV Protein Vivid Generates a Rapidly Exchanging Dimer. Biochemistry, 47: 7012: 7019
  • 2. Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of specific DNA in tightening protein-protein interactions. J. Biol. Chem., 275: 4708: 4712
  • 3. Zoltowski, B.D., Vaccaro, B., and Crane, B.R. (2009). Mechanism-based tuning of a LOV domain photoreceptor. Nat. Chem. Biol. 5: 827: 834
  • Totop Totop

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