# Team:Peking/Modeling/Ring/Simulation

(Difference between revisions)
 Revision as of 04:28, 24 October 2012 (view source)Shrine (Talk | contribs)← Older edit Revision as of 20:59, 24 October 2012 (view source)Shrine (Talk | contribs) Newer edit → Line 10: Line 10:

ODE Model

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: + 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:

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- And parameters as + 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:

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rL2.31x10-2min-1LacI and LacIM1 dissociation rate constant[1] rL2.31x10-2min-1LacI and LacIM1 dissociation rate constant[1]
rR2.31x10-2min-1Luminesensor dissociation rate constant
I01000AUMaximum light intensity in the middle of the plate I01000AUMaximum light intensity in the middle of the plate
- - Line 58: Line 56:

- The simulation result is shown below: + The simulation results in static state are shown below:

## Revision as of 20:59, 24 October 2012

### 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:

 Parameter Value Unit Description Source aG 2 10-6M/min GFP production rate constant [1] aC 2 10-6M/min CI production rate constant [1] aL1 1 10-6M/min LacI production rate constant [1] aL2 1 10-6M/min LacIM1 production rate constant [1] bC 8.x10-3 10-6M Binding strength of CI on LacI operator [1] bL 8.x10-1 10-6M Binding strength of LacI or LacIM1 on GFP operator [1] bR 1.x10-2 10-6M Binding strength of Luminesensor on corresponding operator rG 6.92x10-2 min-1 GFP dissociation rate constant [1] rC 6.92x10-2 min-1 CI dissociation rate constant [1] rL 2.31x10-2 min-1 LacI and LacIM1 dissociation rate constant [1] I0 1000 AU Maximum light intensity in the middle of the plate k 500 10-6M Luminesensor activation rate under light K 10000 AU light sensitivity of Luminesensor activation

The simulation results in static state are shown below:

Figure 1. ODE Simulation in a plate of the ring-like pattern formation.

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 k1 Vivid lighting decay rate constant Mainly on process from Light to Dark k3 rate constant of monomer LexA releasing from specific binding site Enhance contrast K2 Vivid association equilibrium constant More dimerization provides more binding opportunity K5 dimered LexA binding equilibrium constant More binding affinity

### Reference

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