Revision as of 03:30, 24 October 2012 by Shrine (Talk | contribs)

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:



And parameters as

aG3.x10-4s-1vivid decay rate constant
aC5.6x10-5s-1vivid dissociation rate constant[3]
aL18.x10-4s-1monomer LexA releasing rate constant from specific binding site
aL21.x10-3s-1binded monomer LexA dissociation rate constant
bC1.x10-4s-1dimered LexA releasing rate constant from specific binding site
bL(Dark)01equilibrium excitation constant on dark
bR(Light)1.x10+31equilibrium excitation constant on light
rG7.7x10-5(n mol/L)-1vivid association equilibrium constant[1]
rC1.x10-3(n mol/L)-1monomer LexA binding equilibrium constant with specific binding site[2]
rLK2xK5/K3(n mol/L)-1binded monomer LexA association equilibrium constantThermal Principle
rR1.(n mol/L)-1dimered LexA binding equilibrium constant[2]
I01000n mol/Linitial concentration of Luminesensor in ground state
k0n mol/Linitial concentration of Luminesensor in active state
K0n mol/Linitial concentration of 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


  • 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
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