Revision as of 04:07, 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/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


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