Wave-like beating of eukaryotic cilia and flagella—threadlike protrusions found in many cells and microorganisms—is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending. Here we show that in the presence of myosin motors, polymerizing actin filaments self-assemble into polar bundles that exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin-bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin bundle shape, providing a feedback mechanism between the myosin activity and filament deformations for the self-organization of large motor filament assemblies.

真核纤毛和鞭毛的波状跳动（在许多细胞和微生物中发现的线状突起）是生物学中自发机械振荡的典型例子。这种类型的自组织活性物质提出了分子运动活动和细胞骨架丝弯曲之间的协调机制的问题。在这里，我们表明，在肌球蛋白马达存在的情况下，聚合肌动蛋白丝自组装成极性束，表现出波状跳动。重要的是，肌丝跳动与肌球蛋白密度波相关，肌球蛋白密度波的频率是肌动蛋白弯曲波频率的两倍。基于运动与细丝结合和运动活动的曲率控制的理论描述解释了我们在高内摩擦状态下的观察结果。总的来说，我们的结果表明，肌球蛋白与肌动蛋白的结合取决于肌动蛋白束的形状，为大型运动丝组件的自组织提供了肌球蛋白活性和丝变形之间的反馈机制。