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We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle's velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis-Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.

A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system