Team:Peking/Modeling/Ring/Simulation

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(Difference between revisions)
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     <td>Parameter</td><td>Value</td><td>Unit</td><td>Description</td><td>Source</td>
     <td>Parameter</td><td>Value</td><td>Unit</td><td>Description</td><td>Source</td>
   </tr><tr>
   </tr><tr>
-
     <td>a<sub>G</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>vivid decay rate constant</td><td></td>
+
     <td>a<sub>G</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>GFP production rate constant</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>a<sub>C</sub></td><td>2</td><td>10<sup>-6</sup>M/min</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>
+
     <td>a<sub>C</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>CI production 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>
   </tr><tr>
-
     <td>a<sub>L1</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>monomer LexA releasing rate constant from specific binding site</td><td></td>
+
     <td>a<sub>L1</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacI production rate constant</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>a<sub>L2</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>binded monomer LexA dissociation rate constant</td><td></td>
+
     <td>a<sub>L2</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacIM1 production rate constant</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>b<sub>C</sub></td><td>8.x10<sup>-3</sup></td><td>10<sup>-6</sup>M</td><td>dimered LexA releasing rate constant from specific binding site</td><td></td>
+
     <td>b<sub>C</sub></td><td>8.x10<sup>-3</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of CI on LacI operator</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>b<sub>L</sub></td><td>8.x10<sup>-1</sup></td><td>10<sup>-6</sup>M</td><td>equilibrium excitation constant on dark</td><td></td>
+
     <td>b<sub>L</sub></td><td>8.x10<sup>-1</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of LacI or LacIM1 on GFP operator</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>b<sub>R</sub></td><td>1.x10<sup>-2</sup></td><td>10<sup>-6</sup>M</td><td>equilibrium excitation constant on light</td><td></td>
+
     <td>b<sub>R</sub></td><td>1.x10<sup>-2</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of <i>Luminesensor</i> on corresponding operator</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>r<sub>G</sub></td><td>6.92x10<sup>-2</sup></td><td>min<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>
+
     <td>r<sub>G</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>GFP dissociation rate 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>
   </tr><tr>
-
     <td>r<sub>C</sub></td><td>6.92x10<sup>-2</sup></td><td>min<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>
+
     <td>r<sub>C</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>CI dissociation rate constant</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>
   </tr><tr>
-
     <td>r<sub>L</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>binded monomer LexA association equilibrium constant</td><td>Thermal Principle</td>
+
     <td>r<sub>L</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>LacI and LacIM1 dissociation rate constant</td><td>Thermal Principle</td>
   </tr><tr>
   </tr><tr>
-
     <td>r<sub>R</sub></td><td>2.31x10<sup>-2</sup></td><td>min<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>
+
     <td>r<sub>R</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td><i>Luminesensor</i> dissociation rate 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>
   </tr><tr>
-
     <td>I<sub>0</sub></td><td>1000</td><td>AU</td><td>initial concentration of <i>Luminesensor</i> in ground state</td><td></td>
+
     <td>I<sub>0</sub></td><td>1000</td><td>AU</td><td>Maximum light intensity in the middle of the plate </td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>k</td><td>500</td><td>10<sub>-6</sub>M</td><td>initial concentration of <i>Luminesensor</i> in active state</td><td></td>
+
     <td>k</td><td>500</td><td>10<sup>-6</sup>M</td><td><i>Luminesensor</i> activation rate under light</td><td></td>
   </tr><tr>
   </tr><tr>
-
     <td>K</td><td>10000</td><td>AU</td><td>initial concentration of dimered <i>Luminesensor</i></td><td></td>
+
     <td>K</td><td>10000</td><td>AU</td><td>light sensitivity of <i>Luminesensor</i> activation </td><td></td>
   </tr>
   </tr>
   </table>
   </table>

Revision as of 04:07, 24 October 2012

ODE Model

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

Formulae


Formulae

And parameters as

ParameterValueUnitDescriptionSource
aG210-6M/minGFP production rate constant
aC210-6M/minCI production rate constant[3]
aL1110-6M/minLacI production rate constant
aL2110-6M/minLacIM1 production rate constant
bC8.x10-310-6MBinding strength of CI on LacI operator
bL8.x10-110-6MBinding strength of LacI or LacIM1 on GFP operator
bR1.x10-210-6MBinding strength of Luminesensor on corresponding operator
rG6.92x10-2min-1GFP dissociation rate constant[1]
rC6.92x10-2min-1CI dissociation rate constant[2]
rL2.31x10-2min-1LacI and LacIM1 dissociation rate constantThermal Principle
rR2.31x10-2min-1Luminesensor dissociation rate constant[2]
I01000AUMaximum light intensity in the middle of the plate
k50010-6MLuminesensor activation rate under light
K10000AUlight sensitivity of Luminesensor activation

The simulation result is shown below:

Simulation Result

Figure 1. ODE Simulation in a plate of the ring-like pattern formation.

Simulation Result

Figure 2. ODE Simulation for the radial expression amplitude of the ring-like pattern formation.

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.

Parameter Analysis

After modeling the prototype Luminesensor, we attempted to optimize it in a rational way. We have tuned the parameters both up and down, one by one, and finally discovered four parameters which predominantly influence the performance of the Luminesensor.

Function Parameter Description Remark
Reduce responsing time k1Vivid lighting decay rate constantMainly on process from Light to Dark
k3rate constant of monomer LexA releasing from specific binding site
Enhance contrast K2Vivid association equilibrium constantMore dimerization provides more binding opportunity
K5dimered LexA binding equilibrium constantMore binding affinity

Reference

  • 1. Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. Nature, vol.434: 1130: 1134
  • Totop Totop