From 2007.igem.org

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

These equations were normalized as follows:

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

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

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

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 bistability. 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.