Revision as of 23:02, 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 several parameters which predominantly influence the expression intensity, ring radius, and band width of pattern formation.

Parameter Function Description Remark
aG/rGIf increasing, the expression intensity will be amplified, but the ring radius and the band width will not change. Related to the production and dissociation of GFPThe production rate of GFP is easily tuned.
aC/(bC*rC)If increasing, the expression intensity will increase, but the ring radius will decease and the band width will not change. Related to the production and dissociation of CIThe production rate of CI is easily tuned
(k*I0)/(bR*K)If increasing, the ring radius and the band width will increase, leaving the expression amplitude unchanged. Related to the light intensity emitted by sender cells and the activation rate, light sensitivity, and binding efficiency of Luminesensor. Light intensity could be tuned, although the effect may noe be obvious experimentally.
LacI and LacIM1 related parametersTend to influence all three criteria.Related to the production and dissociation rate and binding efficiency of LacI and LaciM1. Tuning is not useful to guide to make a better pattern.


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