Master equation approach for a cross-bridge power-stroke model with a finite number of motors

摘要

The cross-bridge power-stroke model has been widely used to describe the motion of large motor assembliesnconnected to a common rigid filament. In this paper, we go beyond the original velocity-ensemble approachnand propose a master equation approach to account for the cooperative motion of a finite number of motorsnbased on the cross-bridge model. By studying the force-velocity relationship for motors with strain-independentndetachment rate, we show the convergence of our approach to the velocity-ensemble approach in the limit of largenmotor numbers. In the case that the detachment rate of motors is strain dependent, based on two assumptionsnfor the strain distribution among motors, we show the occurrence of the bimodal distribution of the number ofnmotors bound to the filament. This provides a new perspective to look at the instability of a multimotor system,nwhich is essential for all the experimentally observed complex motions displayed by a group of motors, such asnhysteresis, bidirectional motion, and spontaneous oscillation. By comparing the velocities calculated using thentwo assumptions with the stochastic simulation, it suggests that the coupling between motors via the commonnconnection to the filament might facilitate the fast movement of filaments at small loading forces.