A generic theory of metachronal waves

任何连续做功的机器都有一个定义良好的周期性占空比。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，如拍打纤毛。通过机器占空比的连续进展可以用相位变量来量化。我们建议通过这样一个相变量来补充活性流体的一般理论，这些理论已经成功地用于描述细胞骨架、生长组织和游动细菌悬浮的力学。这将使我们能够研究活动流体中的相同步和行相波。这个项目的动机是几个生物学相关的过程中，相同步和相波被观察到。特别是，我们提出的理论将为搏动纤毛的超向波的研究提供信息。搏动纤毛在许多生物过程中起着重要的作用。例如将黏液泵入人体肺部和大脑。此外，它们还参与了像{\it Volvox}或{\it草履虫}这样的微生物的运动。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。纤毛不足是导致多种人类疾病的原因。纤毛的主要任务之一是共同产生流体流动。在健康的生物体中，它们通过将它们的跳动模式同步到超时空表面波来有效地做到这一点。到目前为止，人们对这种同步是如何发生的还知之甚少。我们提出的活动流体的一般理论将采用我们在早期关于活动手性流体的工作中提出的方法，将流动的活动力学纳入其中。我们将通过描述跳动纤毛旋转相位的相位变量来扩展这一理论。这一理论将有助于研究超向波形成的先决条件，以及超向波对周围流体施加的力和扭矩，从而揭示纤毛毯传输流体的原理。

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.