Revision as of 21:01, 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 in MATLAB with equations listed as below:



We applied the inverse square law to describe the light intensity distribution on the plate according to different radius, with a central intensity I0 in a region of r=1mm. Here, parameters are:

aG210-6M/minGFP production rate constant[1]
aC210-6M/minCI production rate constant[1]
aL1110-6M/minLacI production rate constant[1]
aL2110-6M/minLacIM1 production rate constant[1]
bC8.x10-310-6MBinding strength of CI on LacI operator[1]
bL8.x10-110-6MBinding strength of LacI or LacIM1 on GFP operator[1]
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[1]
rL2.31x10-2min-1LacI and LacIM1 dissociation rate constant[1]
I01000AUMaximum light intensity in the middle of the plate
k50010-6MLuminesensor activation rate under light
K10000AULight sensitivity of Luminesensor activation

The simulation results in static state are 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 & 2 above, we discover that, with wildtype parameters, ring-like pattern is formed based on sender-receiver communication through bio-luminescence.

Parameter Analysis

After modeling the ring-like pattern formation with wildtype parameters, we attempted to optimize it in a rational way. We have tuned the parameters both up and down, one by one, and finally discovered five parameters which predominantly influence the expression intensity, ring radius, and band width of pattern formation.

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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