Master Equation Approach to Molecular Motor's Directed Motion

摘要

@@ 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 Px ( t ) is obtained for the probability distribution as a function of the time for any initial distribution Px(0) with all the transients included. We introduce dj 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.