Tokyo/Formulation/3.AHL-experssing model

From 2007.igem.org

Revision as of 02:47, 27 October 2007

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

Step1   Step2   Step3　　

Step.3 Single cell model with hybrid promoter and cell-produced AHL

The differential equaitons of the system considering AHL produced by E.coli themselves were given as

Ex 3-1

Table 3

These equations were normalized as follows:

Ex 3-2

In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as

Ex 3-3

By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as

Ex 3-4

Therefore, the phase plane of this system can be plotted as Fig.3.1.A-D and the number of equilibrium points were decided by the value of the parameters:

Figure 3.1.A

Figure 3.1.B

Figure 3.1.C

Figure 3.1.D

Comparison between Fig3.1.A and B indicated that Hill coefficients are critical parameters even in the cell-produced AHL model. In the case of N2=1, N3=1, and λ=3, the phase plane was monostable. In contrast, in the case of N2=2, N3=2, and λ=3, the phase plane was bistable.
In the cases of λ=1 (Fig.3.1.C and D), the system can not take bistability even if the values of Hill coefficients are changed. For the implementation of the circuit in a cell, the parameter λ should be controlled by changing the RBSs and/or promoter sequences of LuxR.

Step.3 >> Formulation top