Revision as of 03:46, 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

aG210-6M/minvivid decay rate constant
aC210-6M/minvivid dissociation rate constant[3]
aL1110-6M/minmonomer LexA releasing rate constant from specific binding site
aL2110-6M/minbinded monomer LexA dissociation rate constant
bC8.x10-310-6Mdimered LexA releasing rate constant from specific binding site
bL8.x10-110-6Mequilibrium excitation constant on dark
bR1.x10-210-6Mequilibrium excitation constant on light
rG6.92x10-2min-1vivid association equilibrium constant[1]
rC6.92x10-2min-1monomer LexA binding equilibrium constant with specific binding site[2]
rL2.31x10-2min-1binded monomer LexA association equilibrium constantThermal Principle
rR2.31x10-2min-1dimered LexA binding equilibrium constant[2]
I01000AUinitial concentration of Luminesensor in ground state
k50010-6Minitial concentration of Luminesensor in active state
K10000AUinitial 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. Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. Nature, vol.434: 1130: 1134
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