Tokyo/Works/Formulation

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Revision as of 10:31, 25 October 2007

Works top　　0.Hybrid promoter　　1.Formulation　　2.Assay1　　3.Simulation　　4.Assay2　　5.Future works

Step1　　Step2　　Step3　　Step4　　Step5

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. 　⇒ see more

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. 　⇒ see more

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.

Figure 5.2.A 　t=0.2(min)

Figure 5.2.C 　 t=30(min)　　success!! coexistence

Click!! movie here!!

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