Elastohydrodynamic phase-lock in two rotating cilia

Determination of left-right asymmetry of the body plan is achieved in the early embryo. At the 4-6 somite stage, a cavity structure, called a node, is observed in the ventral midline surface, in which hundreds of cilia rotate. Nodal cilia are typically tilted toward the posterior and rotate in the clockwise direction, resulting in the generation of leftward flow in the node. Such leftward flow acts as a trigger of left-specific gene expression, and fluid mechanics plays a role in left-right symmetry breaking. To understand the cilia-driven nodal flow, it is necessary to determine the hydrodynamic interactions among rotating cilia, as ciliary motions interact with each other through fluid motion. In this study, we numerically investigated the elastohydrodynamic synchronization of two rotating cilia, as well as the flow field. The ciliary motion was determined by the balance of cytoskeletal elastic force, motor protein-induced active force, and fluid viscous force. According to the geometric clutch hypothesis, the frequency of rotating cilia is controlled by the bending curvature. Owing to hydrodynamic interactions, bending deformations of two cilia become time-dependent, and the rotation is finally locked in anti-phase regardless of the relative position and initial phase difference. By locking in the reverse phase, the average propulsion flow rate becomes 2-3 times larger than in-phase beating. The results of this study form a basis for understanding cilium-driven nodal flow.