$p$-Adic Models for Ultrametric Diffusion in Conformational Dynamics of Macromolecules

It is shown that $p$-adic models of ultrametric diffusion can be used for describing the conformational dynamics of macromolecules and the chemical kinetics associated with macromolecular dynamics. The approach considered in this paper is based on the application of a hierarchical approximation to the description of dynamics on multidimensional strongly rugged energy landscapes and to the $p$-adic description of the dynamics of macromolecules in terms of transitions between basins of states. It is shown that ultrametric models allow one to describe the characteristic types of relaxation in macromolecular systems, namely, the Kohlrausch law, the power decay law, and the logarithmic decay law, within a unified approach. A $p$-adic model of ultrametric diffusion with reaction sink is constructed and analyzed. This model is applied to the description of the kinetics of CO rebinding to myoglobin. Agreement between theoretical results and experimentally observed features of the rebinding kinetics is demonstrated.