Analytical theory of the stochastic dynamics of the power stroke in nonprocessive motor proteins

Statistical distributions of the structural states of individual molecules of nonprocessive motor complexes such as actomyosins are examined theoretically by considering a two-state stochastic model coupled by chemical reactions along the reaction coordinate representing the internal conformational states of the motor. The use of a conformational reaction coordinate allows for the approximation of taking the rate constants as local in their dependence on the reaction coordinate, and yields a simple analytic solution of the stationary states. The approximation is also tested against numerical solutions with a nonlocal form of rate constants. The theory is well-suited for computational treatments based on atomic structures of protein constituents using free energy molecular dynamics simulations. With empirical sets of free energy functions, stationary distributions of forces exerted by a motor head compare well with known experimental data.