Team:Peking/Modeling/Ring/Simulation

From 2012.igem.org

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The simulation result is shown below:
The simulation result is shown below:
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  <h3 id="title2">Parameter Analysis</h3>
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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:
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After modeling the prototype <i>Luminesensor</i>, 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 <i>Luminesensor</i>.
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  <img src="/wiki/images/c/c3/Peking2012_sto_YL.png" alt="Simulation Result" style="width:600px;"/>
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Figure 2. Stochastic Simulation Result of Prototype <i>Luminesensor</i>.
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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.
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  <td>Function</td>
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  <td>Parameter</td>
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  <td rowspan="2">Reduce responsing time</td>
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  <td>k<sub>1</sub></td><td>Vivid lighting decay rate constant</td><td>Mainly on process from Light to Dark</td>
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  <td>k<sub>3</sub></td><td>rate constant of monomer LexA releasing from specific binding site</td><td></td>
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  <td rowspan="2">Enhance contrast</td>
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  <td>K<sub>2</sub></td><td>Vivid association equilibrium constant</td><td>More dimerization provides more binding opportunity</td>
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  <td>K<sub>5</sub></td><td>dimered LexA binding equilibrium constant</td><td>More binding affinity</td>
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<h3 id="title3">Simulation for GFP Expression <br />Regulated by the <i>Luminesensor</i></h3>
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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.
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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.
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  <h3 id="title4">Reference</h3>
  <h3 id="title4">Reference</h3>

Revision as of 02:53, 23 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
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

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. 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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