A MARKOVIAN MODEL FOR COOPERATIVE INTERACTIONS IN PROTEINS

A stochastic model for cooperative interactions in proteins is propose d. The description is based on the theory of Markov's chains and of bi rth-and-death processes. Even if the model depends only on two paramet ers: the mean probability p and the coupling capacity Delta p, it pres ents a surprising wealth of qualitative behaviors when the two paramet ers are varied. In particular we provide numerical evidence of change of concavity of the stationary distribution at a critical value of the coupling capacity Delta p. The main mathematical feature is that the probability of creating a new chemical bond depends on the total numbe r of bonds already present in the system. In this sense, we speak of a cooperative behavior.