Ma Rui, Li Ming, Ou-Yang Zhong-Can, Shu Yao-Gen
Institute for Advanced Study, Tsinghua University, Bejing, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052718. doi: 10.1103/PhysRevE.87.052718. Epub 2013 May 30.
The cross-bridge power-stroke model has been widely used to describe the motion of large motor assemblies connected to a common rigid filament. In this paper, we go beyond the original velocity-ensemble approach and propose a master equation approach to account for the cooperative motion of a finite number of motors based on the cross-bridge model. By studying the force-velocity relationship for motors with strain-independent detachment rate, we show the convergence of our approach to the velocity-ensemble approach in the limit of large motor numbers. In the case that the detachment rate of motors is strain dependent, based on two assumptions for the strain distribution among motors, we show the occurrence of the bimodal distribution of the number of motors bound to the filament. This provides a new perspective to look at the instability of a multimotor system, which is essential for all the experimentally observed complex motions displayed by a group of motors, such as hysteresis, bidirectional motion, and spontaneous oscillation. By comparing the velocities calculated using the two assumptions with the stochastic simulation, it suggests that the coupling between motors via the common connection to the filament might facilitate the fast movement of filaments at small loading forces.
横桥动力冲程模型已被广泛用于描述连接到共同刚性细丝的大型马达组件的运动。在本文中，我们超越了原始的速度系综方法，提出了一种主方程方法，以基于横桥模型来解释有限数量马达的协同运动。通过研究具有应变无关脱离速率的马达的力 - 速度关系，我们表明在马达数量很大的极限情况下，我们的方法收敛于速度系综方法。在马达的脱离速率与应变相关的情况下，基于关于马达之间应变分布的两个假设，我们展示了与细丝结合的马达数量的双峰分布的出现。这为观察多马达系统的不稳定性提供了一个新视角，而这种不稳定性对于一组马达所展示的所有实验观察到的复杂运动（如滞后、双向运动和自发振荡）至关重要。通过将使用这两个假设计算出的速度与随机模拟进行比较，这表明通过与细丝的共同连接，马达之间的耦合可能有助于细丝在小负载力下的快速移动。
