A Markovian model for cooperative interactions in proteins

A stochastic model for cooperative interactions in proteins is proposed. The description is based on the theory of Markov's chains and of birth-and-death processes. Even if the model depends only on two parameters: the mean probability p and the coupling capacity Delta p, it presents a surprising wealth of qualitative behaviors when the two parameters 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 number of bonds already present in the system. In this sense, we speak of a cooperative behavior.