Motile cilia hydrodynamics: Entrainment versus synchronization when coupling through flow

Coordinated motion of cilia is a fascinating and vital aspect of very diverse forms of eukaryotic life, enabling swimming and propulsion of fluid across cellular epithelia. There are many questions still unresolved, and broadly they fall into two classes. (i) The mechanism of how cilia physically transmit forces onto each other. It is not known for many systems if the forces are mainly of hydrodynamical origin, or if elastic forces within the cytoskeleton are important. (ii) In those systems where we know that forces are purely hydrodynamical, we do not have a framework for linking our understanding of how each cilium behaves in isolation to the collective properties of two or more cilia. In this work, we take biological data of cilia dynamics from a variety of organisms as an input for an analytical and numerical study. We calculate the relative importance of external flows versus internal cilia flows on cilia coupling. This study contributes to both the open questions outlined above: Firstly, we show that it is, in general, incorrect to infer cilium-cilium coupling strength on the basis of experiments with external flows, and secondly, we show a framework to recapitulate the dynamics of single cilia (the waveform) showing classes that correspond to biological systems with the same physiological activity (swimming by propulsion, versus forming collective waves).