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Team:Bologna/Modeling
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Mathematical Model
The behavior of this device and the conditions for bistability can be understood using the following dimensionless model for the network:
Where:
In the picture we can see the bond between ALFA, the rate of synthesis of repressor, and the INDUCTOR. In the first approximation we consider that ALFA is the same for the two repressors. For little value of ALFA we have a linear relation but when we increase ALFA we have a saturation and we have to increase the amount of INDUCTOR. Increasing the cooperativity of repression (beta and gamma) we have to grow the INDUCTOR to pass the transition (bifurcation) between bistability and monostability. Reducing the cooperativity of repression reduces the size of the bistable region.
Bibliography
Mads Kaern, William J. Blake, and J.J. Collins. The Engineering Of Gene Regulatory Networks. Annu.Rev.Biomed.Eng. 2003.5:179-206 Timothy S. Gardner, Charles R. Cantor & James J. Collins : Construction of a genetic toggle switch in Escherichia coli. Nature vol. 403 339-342
