From short-time molecular dynamics to long-time stochastic dynamics of proteins

Abstract

To extend the time scales of descriptions of protein dynamics, beyond those accessible by the molecular dynamics method, theories of stochastic processes are utilized for both short- and long-time dynamics. A first step is the bridging from short-time fluctuations in conformational states to transitions between conformational states. Stochastic short-time dynamics of a reaction coordinate of a conformational transition is deduced starting from the classical equations of motion of a molecular system. The coupling strength between the reaction coordinate and the bath, that remaining degrees of freedom constitute, is determined by an analysis of the short-time fluctuations in molecular dynamics trajectories. An effective potential energy function of the reaction coordinate is obtained by an energy minimization method. The required transition rates are determined from the nonstationary solutions of the Fokker–Planck equation for Brownian motion. As a first application of this approach, dihedral transitions in the sidechain of an aromatic amino acid residue in an α-helix are studied. The rate constants of elementary conformational transitions constitute the basic parameters of a stochastic model of protein conformational relaxation dynamics. This model is useful for descriptions of the coupling between protein conformational dynamics and reactions involved in the functions of proteins.