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arXiv 1808.01583physics.flu-dyn
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弹性微丝的不稳定性驱动振动

Instability-driven Oscillations of Elastic Microfilaments

Feng Ling, Hanliang Guo, Eva Kanso

摘要:

纤毛和鞭毛是高度保守的细长细胞器,它们表现出从非平面锥形运动到平面波浪状变形的各种节律性跳动模式。虽然它们的内部结构是由动力蛋白马达驱动的微管轴丝组成的,但负责这些跳动模式的机制仍然难以捉摸。现有的理论认为,动力蛋白的活动是动态调节,通过几何反馈从纤毛的机械变形的动力蛋白的力量。一个替代的,开环机制的基础上的“颤振”的不稳定性,最近被证明会导致平面振荡的弹性长丝下的追随者的力量。在这里,我们表明,在粘性流体中的弹性长丝,夹紧在一端,并通过外部分布的压缩轴向力的作用,表现出Hopf分叉,导致非平面自旋的屈曲长丝在锁定的曲率。我们还表明,存在第二个分歧,在较大的力值,诱导从非平面旋转平面波状振荡的过渡。我们阐明了这些不稳定性的性质,使用非线性数值分析,线性稳定性理论,低阶珠弹簧模型的组合。我们的研究结果表明,远离过渡阈值,这些跳动模式是强大的扰动的轴向力的分布和细丝配置。这些发现支持了这样的理论,即开环、不稳定驱动的机制可以解释持续的振荡以及在纤毛和鞭毛中观察到的各种周期性跳动模式。

英文摘要:

Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory, and low-order bead-spring models. Our results show that away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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