Tokyo/Formulation/3.AHL-experssing model

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Works top　　0.Hybrid promoter　　1.Formulation　　2.Assay1　　3.Simulation

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, to take bistability the values of Hill coefficients were needed to be more than a certain value. Although the phase plane depended on the value of parameter λ,this value was controlled by changing the RBS of LuxR or the binding sequence of that.


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