Tokyo/Works/Formulation
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== [[Tokyo/Formulation/1.toggle model |Step1. toggle model]] == | == [[Tokyo/Formulation/1.toggle model |Step1. toggle model]] == | ||
<br>First, we saw the qualitative nature implied by simple dimentionless equations and found that the number of the stable points is one or two. Since our model must have A and B states, the number of its stable points should be two. | <br>First, we saw the qualitative nature implied by simple dimentionless equations and found that the number of the stable points is one or two. Since our model must have A and B states, the number of its stable points should be two. | ||
| - | <br>For the parameters required for this bistability, we have found that the production rates and Hill coefficients are critical. | + | <br>For the parameters required for this bistability, we have found that the production rates and Hill coefficients are critical.'''[[Tokyo/Formulation/1.toggle model | ⇒ see more]]''' |
| - | + | ||
<br> [[Image:expression1-2.jpg|200px]] | <br> [[Image:expression1-2.jpg|200px]] | ||
== [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2. toggle model with hybrid promoter ]] == | == [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2. toggle model with hybrid promoter ]] == | ||
| - | Factors of the hybrid promoter should be incorporated into the equations; that is, the term of the repression of toggle by LacI and that of the activation by AHL should be added. By these additions, the phase changes dependent on the amount of AHL. Lower concentration of AHL, monostable; while, higher one gives bistable. | + | Factors of the hybrid promoter should be incorporated into the equations; that is, the term of the repression of toggle by LacI and that of the activation by AHL should be added. By these additions, the phase changes dependent on the amount of AHL. Lower concentration of AHL, monostable; while, higher one gives bistable.'''[[Tokyo/Formulation/1.toggle model | ⇒ see more]]''' |
<br>[[Image:expression2-4.jpg|300px|]][[Image:AHLresponse2-2.jpg|300px|]] | <br>[[Image:expression2-4.jpg|300px|]][[Image:AHLresponse2-2.jpg|300px|]] | ||
Revision as of 10:28, 25 October 2007
Works top 0.Hybrid promoter 1.Formulation 2.Assay1 3.Simulation 4.Assay2 5.Future works
Step1. toggle model
First, we saw the qualitative nature implied by simple dimentionless equations and found that the number of the stable points is one or two. Since our model must have A and B states, the number of its stable points should be two.
For the parameters required for this bistability, we have found that the production rates and Hill coefficients are critical. ⇒ see more
Step2. toggle model with hybrid promoter
Factors of the hybrid promoter should be incorporated into the equations; that is, the term of the repression of toggle by LacI and that of the activation by AHL should be added. By these additions, the phase changes dependent on the amount of AHL. Lower concentration of AHL, monostable; while, higher one gives bistable. ⇒ see more
Step3. using cell-produced AHL
Now develop this system to the one with cell-produced AHL.
This time, the nullcrine is assymetric and the phaseplane is unconventionally shaped.
Here the new parameter λ is introduced whether monostalbe or bistable of the system depends on the velues of several parameters.
for more detail
Step4. population model
Here the concentration of AHL outside of the cells was assumed to be the same concentration of AHL inside the cell according to the description that AHL is freely permiable through cell membrane in the referenced articles.The phase plane analysis was made possible by focusing on an indivisual cell.The parameter N was assumed to be the number of the cells.
However, all the individuals behaved in the same way in this deterministic model. To see the bahavior of each individual cell, it is necessary to carry out stocastic simulation.
Step5. stochastic differential equation model with poisson random variables
we introduced the differential equations of step4 into Poisson random variables to simulate the stochastic model.
By using simulation with stochastic model, every cell can take different behavior.
A preview of the latter part of this Wiki:
With parameters from our wet experiments, we confirmed that our circuit with the new part can show “stable coexistence”see more リンク to simulation PAGE.
Click!! movie here!!
Before(Hybrid promoter) << Formulation >> Formulation Step.1 >>>> Next(Assay1)
