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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:
\partial x
where is the concentration of repressor 1,
is the concentration of repressor 2 and it depends on the concentration of inducer , is the effective rate of synthesis of repressor 1, is the effective rate of synthesis of repressor 2, is the cooperativity of repression of promoter 1, is the cooperativity of repression of promoter 2, η is the cooperativity of binding, is the dissociation constant of .
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|- | |align="center"| Team Example 2 |}
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.
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