Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments
Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments
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DOI：
10.1103/physrevfluids.4.043102
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发表时间：
2019-04-02
影响因子：
2.7
通讯作者：
Saintillan, David
中科院分区：
文献类型：
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作者：
Chakrabarti, Brato;Saintillan, David
纤毛和鞭毛在自然界中普遍存在，并且已知通过执行振荡在细胞尺度上帮助运输和游泳。这些周期性波形的基础是被称为轴丝的细丝的核心内部结构，由一系列微管双峰、蛋白质连接体和动力蛋白马达组成。在ATP存在的情况下，分子马达的集体作用驱动内部滑动运动，这些滑动运动通过一种仍然难以捉摸的机制转化为自发振荡。最近提出了一种滑动控制轴丝反馈机制，并在小变形的限制下进行了探索，结果表明，通过动力蛋白动力学的机械调节，导致非线性振幅选择。在这里，我们建立在该模型，以获得一个更完整的一套平面非线性控制方程，保留所有的几何非线性，结合内在的生化噪声和帐户的远程，非局部流体动力学相互作用。对于一个固定的灯丝，电机活动驱动一个Hopf分岔导致行波解，从尖端传播到基地，与以前的弱非线性研究。非常值得注意的是，我们的研究结果表明，存在第二个过渡远离平衡，其中非线性引起波传播的方向反转，并产生各种波形，类似于游泳精子的跳动模式。我们进一步扩展的模型，占不对称的纤毛节拍，也允许广义的动力蛋白调节机制，可以定性地再现莱茵衣藻鞭毛动力学。在降维的精神，极限环表示得到各种波形和突出的生化噪声的作用。我们还分析了由细丝产生的速度场，并应用主成分分析来推导低阶流表示的基本斯托克斯奇点，可以用于构建最小模型的游泳微生物。
Cilia and flagella are ubiquitous in nature and are known to help in transport and swimming at the cellular scale by performing oscillations. Fundamental to these periodic waveforms is the core internal structure of the filaments known as the axoneme, consisting of an array of microtubule doublets, protein linkers, and dynein motors. In the presence of ATP, the collective action of the molecular motors drives internal sliding motions that are converted to spontaneous oscillations by a mechanism that still remains elusive. A sliding controlled axonemal feedback mechanism has recently been proposed and explored in the limit of small deformations, where it was shown to result in nonlinear amplitude selection through a mechanical regulation of dynein kinetics. Here, we build on that model to derive a more complete set of planar nonlinear governing equations that retains all the geometric nonlinearities, incorporates intrinsic biochemical noise and accounts for long-range, nonlocal hydrodynamic interactions. For a clamped filament, motor activity drives a Hopf bifurcation leading to traveling wave solutions that propagate from tip to base, in agreement with previous weakly nonlinear studies. Quite remarkably, our results demonstrate the existence of a second transition far from equilibrium, where nonlinearities cause a reversal in the direction of wave propagation and produce a variety of waveforms that resemble the beating patterns of swimming spermatozoa. We further extend the model to account for asymmetric ciliary beats and also allow for generalized dynein regulation mechanisms that can qualitatively reproduce Chlamydomonas reinhardtii flagellar dynamics. In the spirit of dimensional reduction, limit cycle representations are obtained for various waveforms and highlight the role of biochemical noise. We also analyze the velocity fields generated by the filaments and apply principal component analysis to derive low-order flow representations in terms of fundamental Stokes singularities that could be of use for constructing minimal models of swimming microorganisms.