Team:Bologna/Modeling

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Revision as of 08:43, 24 October 2008

Logo1a.gifTestata dx.jpg
HOME TEAM PROJECT MODELING WET-LAB SOFTWARE SUBMITTED PARTS BIOSAFETY AND PROTOCOLS


Contents

Mathematical Model of the Flip-Flop genetic circuit


Model definition


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

Figure 1: Scheme of the genetic Flip-Flop

The circuit behaviour can be modeled by the following equations:

Equa1.jpg

Symbols and parameters are defined in Table 1:

Tab.jpg
  • 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 F001.jpg and protein free F002.jpg.

Since F003.jpg and considering the law of mass action F004.jpg we can write:


F005new.jpg


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Adimensional equations


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


Equa2new.jpg

where:


F006.jpg
F007.jpg



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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:

Equa3new.jpg

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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