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Mathematical Model

Fig. 1: Genetic flip-flop

Let us pose:

The genetic circuit in Figure 1 can be modeled with the following equations:

Where:

In the model we distinguish between LacI protein binded to repressor IPTG () and protein free ().

Since and considering the law of mass action we can write .

Knowing that

and the law of mass action

is possible write

where we can replace

represents the entry of IPTG inside the cell. The same thing can be done even for LexA obtaining

where

represents the UV radiation.

Placing:

The dimensionless equations are:

Hypothesizing: to be under conditions of equilibrium;

all the entries are void (

);

the affinity of the repressor for the operator site is high,

for as we have been defined it will surely be smaller of one so

;

the cooperativity is the same both for the LacI and for TetR and it is worth 2; the equations become:

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