The mechanism that allows the axoneme of eukaryotic cilia and flagella to produce both helical and planar beating is an enduring puzzle. The nine outer doublets of eukaryotic cilia and flagella are arranged in a circle. Therefore, each doublet pair with its associated dynein motors, should produce torque to bend the flagellum in a different direction. Sequential activation of each doublet pair should, therefore result in a helical bending wave. In reality, most cilia and flagella have a well‐defined bending plane and many exhibit an almost perfectly flat (planar) beating pattern. In this analysis we examine the physics that governs flagellar bending, and arrive at two distinct possibilities that could explain the mechanism of planar beating. Of these, the mechanism with the best observational support is that the flagellum behaves as two ribbons of doublets interacting with a central partition. We also examine the physics of torsion in flagella and conclude that torsion could play a role in transitioning from a planar to a helical beating modality in long flagella. Lastly, we suggest some tests that would provide theoretical and/or experimental evaluation of our proposals.

中文翻译：

---

鞭毛和纤毛跳动的多种模式：来自物理分析的见解

允许真核纤毛和鞭毛的轴丝产生螺旋和平面跳动的机制是一个持久的难题。真核纤毛和鞭毛的九个外部双联体排列成一个圆圈。因此，每个双峰对及其相关的动力蛋白电机应产生扭矩以使鞭毛向不同方向弯曲。因此，每个双峰对的顺序激活应该导致螺旋弯曲波。实际上，大多数纤毛和鞭毛都有明确的弯曲平面，并且许多都表现出几乎完全平坦（平面）的跳动模式。在这项分析中，我们研究了控制鞭毛弯曲的物理学，并得出了两种不同的可能性，可以解释平面跳动的机制。这些，具有最佳观察支持的机制是鞭毛表现为两条双峰带与中央隔板相互作用。我们还研究了鞭毛扭转的物理特性，并得出结论，扭转可能在长鞭毛从平面到螺旋跳动方式的转变中发挥作用。最后，我们建议进行一些测试，这些测试将为我们的建议提供理论和/或实验评估。