$Volvox$鞭毛搏动的异时波及其流体动力学起源
Metachronal waves in the flagellar beating of $Volvox$ and their hydrodynamic origin
摘要：
真核生物的纤毛和鞭毛能够在大尺度上协调它们的跳动，通常以异时波的形式表现出集体动力学。这种行为的起源-可能受到机械相互作用和直接生物调节的影响-知之甚少，这在很大程度上是由于缺乏定量的实验研究。在这里，我们详细介绍了鞭毛协调的表面上的多细胞藻类$Volvox~carteri$，一个新兴的模式生物鞭毛动力学。我们的研究首次揭示，观察到的平均异时协调被周期性相位缺陷打断，在此期间，同步是部分的，仅限于特定的细胞群。流体动力学耦合振子的极小模型可以半定量地再现平均异时动力学的特征和缺陷的出现。我们系统地研究了模型的行为，通过评估改变固有转子特性的影响，包括振荡器刚度和内部驱动力的性质，以及它们的几何特性和空间布置。我们的研究结果表明，异时协调遵循从变形的振荡器的极限环引起的流体动力学应力，和缺陷的结果从足够陡峭的本地偏置振荡器的固有频率。此外，我们发现，在固有转子频率的随机变化增加了新兴异时波的平均属性的鲁棒性。
英文摘要：
Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour -- possibly influenced by both mechanical interactions and direct biological regulation -- is poorly understood, in large part due to lack of quantitative experimental studies. Here we characterise in detail flagellar coordination on the surface of the multicellular alga $Volvox~carteri$, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.
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