Tokyo/Formulation/3.AHL-experssing model

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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● 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