Team:Peking/Modeling/Ring/Simulation

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Revision as of 04:28, 24 October 2012

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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

Parameter	Value	Unit	Description	Source
a_G	2	10^-6M/min	GFP production rate constant	[1]
a_C	2	10^-6M/min	CI production rate constant	[1]
a_L1	1	10^-6M/min	LacI production rate constant	[1]
a_L2	1	10^-6M/min	LacIM1 production rate constant	[1]
b_C	8.x10^-3	10^-6M	Binding strength of CI on LacI operator	[1]
b_L	8.x10^-1	10^-6M	Binding strength of LacI or LacIM1 on GFP operator	[1]
b_R	1.x10^-2	10^-6M	Binding strength of Luminesensor on corresponding operator
r_G	6.92x10^-2	min^-1	GFP dissociation rate constant	[1]
r_C	6.92x10^-2	min^-1	CI dissociation rate constant	[1]
r_L	2.31x10^-2	min^-1	LacI and LacIM1 dissociation rate constant	[1]
r_R	2.31x10^-2	min^-1	Luminesensor dissociation rate constant
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 result is 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
Reduce responsing time	k₃	rate constant of monomer LexA releasing from specific binding site
Enhance contrast	K₂	Vivid association equilibrium constant	More dimerization provides more binding opportunity
Enhance contrast	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

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   </div>
   <p>
-From the Figure 1 above, we discovered that the activation and decay of <i>Luminesensor</i> 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 <i>Luminesensor</i> does not totally dimerized.
+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.
   </p>
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   <h3 id="title2">Parameter Analysis</h3>
   <p>
-After modeling the prototype <i>Luminesensor</i>, 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 <i>Luminesensor</i>.
+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.
   </p>
   <table style="width:600px;"><tr>