A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues

In this paper, a stochastic model for the cooperative relaxation of proteins, based on a hierarchic structure of the interactions between amino acids is proposed. It relies on the arbitrary splitting of interactions into two classes, strong and weak, and tests the preponderance of one class over the other. The presented model generalizes a first one valid for homogeneous interactions in the protein molecules previously studied by the authors. The time evolution of the system is studied as a function of five parameters, three of which are related to the cooperativity. Moreover, different approximations of the discrete system to a diffusion process, and to a Poisson process are considered, according to the magnitude of the parameters. A method for estimating the parameters from real data is proposed. Finally, numerical simulations and a comparison with the molecular dynamics of a real protein (Barnase) are reported.