Team:Peking/Modeling/Luminesensor/Simulation

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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:

And parameters as

Parameter	Value	Unit	Description	Source
k₁	3.x10^-4	s^-1	vivid decay rate constant
k₂	5.6x10^-5	s^-1	vivid dissociation rate constant	[3]
k₃	8.x10^-4	s^-1	monomer LexA releasing rate constant from specific binding site
k₄	1.x10^-3	s^-1	binded monomer LexA dissociation rate constant
k₅	1.x10^-4	s^-1	dimered LexA releasing rate constant from specific binding site
K₁(Dark)	0	1	equilibrium excitation constant on dark
K₁(Light)	1.x10⁺³	1	equilibrium excitation constant on light
K₂	7.7x10^-5	(n mol/L)^-1	vivid association equilibrium constant	[1]
K₃	1.x10^-3	(n mol/L)^-1	monomer LexA binding equilibrium constant with specific binding site	[2]
K₄	K₂xK₅/K₃	(n mol/L)^-1	binded monomer LexA association equilibrium constant	Thermal Principle
K₅	1.	(n mol/L)^-1	dimered LexA binding equilibrium constant	[2]
[L_G]₀	1000	n mol/L	initial concentration of Luminesensor in ground state
[L_A]₀	0	n mol/L	initial concentration of Luminesensor in active state
[L_A²]₀	0	n mol/L	initial concentration of dimered Luminesensor
[D_L]₀	100	n mol/L	initial concentration of free specific binding site on DNA	high-copy plasmid
[L_GD_L]₀	0	n mol/L	initial concentration of dimered Luminesensor binded Luminesensor in ground state
[L_AD_L]₀	0	n mol/L	initial concentration of dimered Luminesensor binded Luminesensor in active state
[L_A²D_L]₀	0	n mol/L	initial concentration of binded and dimered Luminesensor

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

Expression	Description	Remark
r_b = 1 - [D_L]/[D_T]	This indicates the repressing degree.	D_T indicates the total specific binding sites, while the D_L indicates the free ones among D_T.
r_d = 2[L_A²X]/[L_T]	This indicates the dimerizing degree.	L_T indicates the total Luminesensor molecules, and L_A²X indicates all dimered Luminesensor molecules, i.e. L_A² + L_A²D_L.
r_a = ( [L_AX] + 2[L_A²X] ) /[L_T]	This indicates the activating degree.	L_AX indicates all monomer Luminesensor molecules, i.e. L_A + L_AD_L.

The simulation result is shown below:

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:

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.

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

@@ Line 8: / Line 8: @@
 </script>
 <div class="PKU_context floatR first">
-  <h3 id="title1">ODE model</h3>
+  <h3 id="title1">ODE Model</h3>
   <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 with equations listed as
+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>
   <div class="floatC">
-   <img src="" alt="Formulae"/>
+   <img src="/wiki/images/5/5f/Peking2012_Formula000.png" alt="Formulae" style="width:500px;"/>
   </div>
   <p>
@@ Line 25: / Line 25: @@
      <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="Mechanism-based tuning of a LOV domain photoreceptor, Brian D. Zoltowski, etc. NATURE CHEMICAL BIOLOGY">[3]</a></td>
+     <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>
@@ Line 37: / Line 37: @@
      <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="#ref4" title="Protein Vivid Generates a Rapidly Exchanging Dimer, Brian D. Zoltowski, etc. BIOCHEMISTRY">[4]</a></td>
+     <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="LexA Repressor Forms Stable Dimers in Solution, R.Mohana-Borges, etc. THE JOURNAL OF BIOLOGICAL CHEMISTRY">[2]</a></td>
+     <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="LexA Repressor Forms Stable Dimers in Solution, R.Mohana-Borges, etc. THE JOURNAL OF BIOLOGICAL CHEMISTRY">[2]</a></td>
+     <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 Luminesensor in ground state</td><td></td>
+     <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 Luminesensor in active state</td><td></td>
+     <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 Luminesensor</td><td></td>
+     <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 Luminesensor binded Luminesensor in ground state</td><td></td>
+     <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 Luminesensor binded Luminesensor in active state</td><td></td>
+     <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 Luminesensor</td><td></td>
+     <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>
@@ Line 87: / Line 87: @@
    <img src="/wiki/images/7/71/Peking2012_ode_YL.png" alt="Simulation Result" style="width:600px;"/>
    <div>
-    <p class="description">
+    <p class="description" style="text-align:center;">
-Figure 2. ODE Simulation Result of the prototype Luminesensor.
+Figure 1. ODE Simulation Result of the prototype Luminesensor.
     </p>
    </div>
   </div>
   <p>
-From the figure above, we discovered that the activation and decay of <i>Luminesensor</i> 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 <i>Luminesensor</i> has not all dimered.
+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="title3">Stochastic Simulation</h3>
+  <h3 id="title2">Stochastic Simulation</h3>
   <p>
-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:
+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">
+    <p class="description" style="text-align:center;">
-Figure 3. Stochastic Simulation Result of the prototype Luminesensor.
+Figure 2. Stochastic Simulation Result of Prototype <i>Luminesensor</i>.
     </p>
    </div>
   </div>
   <p>
-According to the figure above, the noise did not influence this system. Thus, the <i>Luminesensor</i> 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.
+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 <i>Luminesensor</i></h3>
+  <h3 id="title3">Simulation for GFP Expression <br />Regulated by the <i>Luminesensor</i></h3>
   <p>
-In order to see whether our model is effective to present the downstream gene expression under the control of <i>Luminesensor</i>, we added transcription and translation process after the modeling of DNA binding process. In addition, we considered the delay of translation initiation time and the growth of cell. The simulation below represents the GFP expression of the cell regulated by <i>Luminesensor</i>. After a long time in the light condition, where the GFP expression is inhibited, from <i>t=0h</i>, the cells are moved into dark and begin to express GFP. The GFP expression level according to time is recorded.
+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="..." alt="Simulation Result" style="width:500px;"/>
+   <img src="/wiki/images/0/07/Wild_type.png" alt="Simulation Result" style="width:500px;"/>
    <div>
-    <p class="description">
+    <p class="description" style="text-align:center;">
-Figure 4. 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.
+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">
+. 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">
+. 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">
+. 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>
 </html>{{Template:Peking2012_Color_Epilogue}}