Tokyo/Formulation/3.AHL-experssing model

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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. So, 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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