In the same kind of idea than this question. Gene expression are regulated through complex interactions. The concentration of enhancers and repressors is an important aspect that dictate the level of expression of a given gene. These concentrations can take different value on a continuous scale.
Imagine a case where fitness is maximized when a given gene produce
n proteins per minute if the concentration of a given protein is greater than
x. If the concentration of the protein was to be lower than
x, then the gene should not be expressed (0 proteins per minute are produced). In such case, it would be great if a bunch of reactants were to be able to simulate a "switch function" that would switch from "NO EXPRESSION" to "EXPRESSION" at
It seems to me that such switch function should be very complicated to evolve. I would suspect that all chemical reactions, including the binding of enhancer to promoter region should follow the law of Michaelis-Menten and the Michaelis-Menten function is not at all switch function. So, I have been thinking about cooperative binding. Hill's equation describes a function that is effectively a switch function given that the hill coefficient is high enough. However, seeking a bit in the literature, it's seems that the Hill coefficient never really overpass 3 (or 5 for extreme estimates). A Hill coefficient of within this range gives a logistic function but still looks quite suboptimal compared to what a perfect switch function could do.
Are there switch functions in molecular genetics that could translate a concentration into a TRUE/FALSE signal? How well do they simulate the perfect switch function? Are they based on cooperative binding or on some other mechanism?
References for estimate of Hill coefficients: