A generic theory of metachronal waves

任何连续工作的机器都有一个明确的周期性工作循环。特别是，这包括分子尺度的机器，如分子马达，和细胞尺度的机器，如跳动的纤毛。通过机器的占空比的连续进展可以通过相变量来量化。我们建议补充活性流体的通用理论，这些理论已成功地用于描述细胞骨架的力学，通过这样的相变量生长组织和悬浮游动细菌。这将使我们能够研究在活性流体中的相位同步和相位波。这个项目的动机是几个生物学相关的过程，其中观察到相位同步和相位波。特别是，我们提出的理论发展将通知在跳动的纤毛异时波的研究。跳动的纤毛在许多生物过程中发挥着重要作用。例如，在人类肺部和大脑中泵送粘液。此外，它们参与了微生物的运动，如团藻或草履虫。在脊椎动物的发育过程中，它们参与打破生物体的左右对称。缺乏纤毛是导致人类多种疾病的原因。纤毛的主要任务之一是集体产生流体流动。在健康的生物体中，它们通过将其跳动模式同步为异时表面波来有效地完成这一任务。到目前为止，人们对这种同步是如何发生的还知之甚少。我们提出的活性流体的通用理论将采用我们在早期工作中提出的方法，将流动的活性力学结合起来。我们将扩展这个理论的相位变量，描述的相位跳动cilia的旋转。这个理论将允许研究的先决条件形成的异时波和异时波施加在周围的流体的力和扭矩，揭示的原则，流体运输纤毛地毯。

Any machine which performs work continuously has a well defined periodic duty cycle. In particular, this includes molecular scale machines such as molecular motors, and cellular scale machines such as beating cilia.The continuous progression through the duty cycle of a machine can be quantified by a phase variable.We propose to complement the generic theories for active fluids, which have been successfully used to describe the mechanics of the cell cytoskeleton, growing tissues and suspension of swimming bacteria by such a phase variable. This will enable us to study phase synchronization and traveling phase waves in active fluids.This project is motivated by several biologically relevant processes in which phase synchronization and phase waves are observed.In particular the theory we propose to develop will inform the study of metachronal waves in beating cilia.Beating cilia play an important role in many biological processes. Examples are the of pumping mucus in the human lungs and brains.Moreover, they are involved in the motility of microorganisms like {\it Volvox} or {\it Paramecium}.During the development of vertebrate organisms, they are involved in breaking the left-right symmetry of the organism. Deficient cilia are responsible for a large variety of human diseases.One of the main task of cilia is to collectively generate fluid flows.In healthy organisms they do so efficiently by synchronizing their beating patterns into metachronal surface waves. How this synchronization occurs is so far poorly understood. The generic theory for active fluids which we propose would incorporate the active mechanics of the flows, using the methods which we presented in our earlier work on active chiral fluids. We will expand this theory by a phase variable that describes the phase of rotation of the beating cilia.This theory would allow to study the prerequisites for the formation of metachronal waves and the forces and torques metachronal waves exert on the surrounding fluid, shedding light on the principles that underly fluid transport by ciliary carpets.