Master Equation Approach to Molecular Motor’s Directed Motion

The master equation approach based on the periodic one-dimensional three-state hopping model is developed to study the molecular motor’s directed motion. An explicit solution P_x(t) is obtained for the probability distribution as a function of the time for any initial distribution P_x(0) with all the transients included. We introduce d_j to represent the sub-step lengths, which can reflect how the external load affects the individual rate via load distribution factors θ_j⁺ and θ_j^-. A wide variety of molecular motor behaviour under external load f can readily be obtained by the unequal-distance transition model with load-dependent transition rates. By comparison with the experiments, namely of the drift velocity v and the randomness parameter r versus adenosine triphosphate concentration and external load f, it is shown that the model presented here can rather satisfactorily explain the available data.