Control of synchronization in models of hydrodynamically coupled motile cilia

Abstract

In many organisms, multiple motile cilia coordinate their beating to facilitate swimming or driving of surface flows. Simple models are required to gain a quantitative understanding of how such coordination is achieved; there are two scales of phenomena, within and between cilia, and both host complex non-linear and non-thermal effects. We study here a model that is tractable analytically and can be realized by optical trapping colloidal particles: intra-cilia properties are coarse grained into the parameters chosen to drive particles around closed local orbits. Depending on these effective parameters a variety of phase-locked steady states can be achieved. We derive a theory that includes two mechanisms for synchronization: the flexibility of the motion along the predefined orbit and the modulation of the driving force. We show that modest tuning of the cilia beat properties, as could be achieved biologically, results in dramatic changes in the collective motion arising from hydrodynamic coupling.