Team:Peking/Modeling/Ring/Simulation

From 2012.igem.org

(Difference between revisions)

Revision as of 04:11, 24 October 2012

Home
Team
Project
Data Page
Modeling
Human Practice
Safety

- Data Page
- Judging Criteria

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 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	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

@@ Line 27: / Line 27: @@
      <td>Parameter</td><td>Value</td><td>Unit</td><td>Description</td><td>Source</td>
     </tr><tr>
-     <td>a<sub>G</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>GFP production rate constant</td><td></td>
+     <td>a<sub>G</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>GFP production rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>a<sub>C</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>CI production rate constant</td><td><a href="#ref3" title="Zoltowski, B.D., Vaccaro, B., and Crane, B.R. (2009). Mechanism-based tuning of a LOV domain photoreceptor. Nat. Chem. Biol. 5: 827: 834">[3]</a></td>
+     <td>a<sub>C</sub></td><td>2</td><td>10<sup>-6</sup>M/min</td><td>CI production rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>a<sub>L1</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacI production rate constant</td><td></td>
+     <td>a<sub>L1</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacI production rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>a<sub>L2</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacIM1 production rate constant</td><td></td>
+     <td>a<sub>L2</sub></td><td>1</td><td>10<sup>-6</sup>M/min</td><td>LacIM1 production rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>b<sub>C</sub></td><td>8.x10<sup>-3</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of CI on LacI operator</td><td></td>
+     <td>b<sub>C</sub></td><td>8.x10<sup>-3</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of CI on LacI operator</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>b<sub>L</sub></td><td>8.x10<sup>-1</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of LacI or LacIM1 on GFP operator</td><td></td>
+     <td>b<sub>L</sub></td><td>8.x10<sup>-1</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of LacI or LacIM1 on GFP operator</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
      <td>b<sub>R</sub></td><td>1.x10<sup>-2</sup></td><td>10<sup>-6</sup>M</td><td>Binding strength of <i>Luminesensor</i> on corresponding operator</td><td></td>
     </tr><tr>
-     <td>r<sub>G</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>GFP dissociation rate constant</td><td><a href="#ref1" title="Zoltowski, B.D., Crane, B.R.(2008). Light Activation of the LOV Protein Vivid Generates a Rapidly Exchanging Dimer.Biochemistry, 47: 7012: 7019 ">[1]</a></td>
+     <td>r<sub>G</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>GFP dissociation rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>r<sub>C</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>CI dissociation rate constant</td><td><a href="#ref2" title="2. Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of speciﬁc DNA in tightening protein-protein interactions. J. Biol. Chem., 275: 4708: 4712">[2]</a></td>
+     <td>r<sub>C</sub></td><td>6.92x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>CI dissociation rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>r<sub>L</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>LacI and LacIM1 dissociation rate constant</td><td>Thermal Principle</td>
+     <td>r<sub>L</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td>LacI and LacIM1 dissociation rate constant</td><td><a href="#ref1" title="Subhayu Basu et al.(2005), A synthetic multicellular system for programmed pattern formation. <i>Nature</i>, vol.434: 1130: 1134">[1]</a></td>
     </tr><tr>
-     <td>r<sub>R</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td><i>Luminesensor</i> dissociation rate constant</td><td><a href="#ref2" title="Mohana-Borges, R., Pacheco, A.B., Sousa, F.J., Foguel, D., Almeida, D.F., and Silva, J.L. (2000). LexA repressor forms stable dimers in solution. The role of speciﬁc DNA in tightening protein-protein interactions. J. Biol. Chem., 275: 4708: 4712">[2]</a></td>
+     <td>r<sub>R</sub></td><td>2.31x10<sup>-2</sup></td><td>min<sup>-1</sup></td><td><i>Luminesensor</i> dissociation rate constant</td><td></td>
     </tr><tr>
      <td>I<sub>0</sub></td><td>1000</td><td>AU</td><td>Maximum light intensity in the middle of the plate </td><td></td>