Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

TL;DRAbstract

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps between arbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probability distribution as a function of the time and position for any initial distribution with all the transients included. Next, the transient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kinetic behaviors of a molecular motor under external load F.

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