Tokyo/Formulation/3.AHL-experssing model

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Revision as of 20:10, 26 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

Fig3.1.A and B indicated that in case of N2=1,N3=1,the phase plane was monostable and in case of N2=2,N3=2,the phase plane was bistable. So, the values of Hill coefficients were needed to be more than a certain value to take bistable. Fig.3.1.C and D represented the phase plane at λ=1. In this case, even if the values of Hill coefficients are changed, the system can’t take bistability. Although the phase plane depended on the value of parameter λ,this value can be controlled by changing the RBS of LuxR or the binding sequence of that.

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