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Model-based analysis of the genetic Flip-Flop

Mathematical Model

Dimensional equations

The molecular circuit in Figure 1 works as a Flip-Flop (latch JK), which can switch between two different states according to the external stimuli (UVc and IPTG).

Figure 1: Scheme of the genetic Flip-Flop

The molecular circuit show two possible stable state: LacION and TetRON.

The circuit behaviour can be modeled by the following equations:

Symbols and parameters are defined in Table 1:

• A common motif in repressor proteins is the presence of a dimeric nucleotide binding site. In accordance to this general structure the cooperativity coefficients () were assumed equal to 2.

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:

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Adimensional equations

The equations (1.1) and (1.2) were modified to an adimensional form:

where:

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Equibrium conditions

At equilibrium and in absence of stimuli, the adimensional concentrations of LacI (i) and TetR (r) are related by the equation:

To obtain these equations the second term in equation (1.5)was ignored (). This is justified by the high binding constant of LexA for its operator, and the consequent low production of LacI (see Figure 1).

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Stability analysis

Assuming as starting condition the LacION state (Figure 1) its stability is guaranteed if the adimensional concentration of LacI is higher than 1 (Figure 2).
In the limit of (), equation (1.7) simplifies:

Experimental identification

The MAVs were identified comparing the experimental response of the genetic circuits in Figure

Numerical simulation

Bibliography

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