Ultrametric random walk and dynamics of protein molecules

This paper is a brief survey of applications of the $p$-adic equation of ultrametric random walk to the description of conformational dynamics of protein molecules. Two main experiments are considered that determine the properties of the fluctuation dynamic mobility of protein molecules from $300$ to $4$ K: the studies of the kinetics of CO binding to myoglobin and spectral diffusion in proteins. It is shown that an ultrametric description allows one to build a unified picture of the conformational mobility of a protein molecule in the whole range of the indicated temperatures and realize the fact that it varies in a self-similar way. This feature of protein molecules, which has remained hidden to date, significantly expands the idea of the structure of nanoscale systems related to the family of molecular machines.

Received in September 2013