BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany and Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany.
J Chem Phys. 2013 Nov 7;139(17):175104. doi: 10.1063/1.4827497.
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
非运动性分子马达必须协同工作才能产生可观的力或运动水平。例如，在骨骼肌中，数百个肌球蛋白 II 分子在粗丝中协同作用。相比之下，在非肌肉细胞中，只有数十个非肌肉肌球蛋白 II 马达组成的小团体参与了重要的细胞过程，如运输、形状变化或机械感应。在这里，我们引入了一个详细且可分析的模型来描述这种重要情况。我们使用肌球蛋白 II 马达循环的三态交联模型，并利用快速动力冲程动力学的假设以及等效状态下马达之间的等效负载分配，将随机反应网络简化为结合和解离动力学的一步主方程（平行簇模型），并推导出集合运动的规则。我们发现，对于恒定的外部负载，集合动力学强烈受到肌球蛋白 II 捕获键特性的影响，这导致负载下结合的马达比例增加，从而即使在小集合中也能实现牢固的附着。这种对负载的适应导致了由 Hill 关系描述的凹力-速度关系。对于线性弹簧提供的外部负载，肌球蛋白 II 集合会动态调整自己以达到等长状态，具有恒定的平均位置和负载。集合的动力学现在主要由马达在不同结合状态之间的分布决定。随着外部弹簧刚度的增加，会出现一个急剧的转变，超过这个转变肌球蛋白 II 就无法再进行动力冲程。从预动力冲程状态缓慢解联可以保护集合体免受脱离。
