Abstract

Motile cilia are hair-like extensions of biological cells that beat periodically like a whip. Collections of cilia on the surface of microorganisms or human airways beat in a coordinated fashion as a traveling wave—similar to a Mexican wave in a soccer stadium—to facilitate efficient fluid transport.

This emblematic example of synchronization of noisy biological oscillators attracted attention from physicists and mathematicians alike, yet some important questions remain open: How does the shape of the cilia beat determine the direction of metachronal waves? And what is the impact of active fluctuations?

Using a multi-scale modeling framework based on a measured cilia beat pattern, we predict that many waves are linearly stable to small perturbations, but a single dexioplectic wave has predominant basin-of-attraction. Similar to a “dynamic’’ Mermin-Wagner theorem, relaxation times diverge with system size, which rules out global order in infinite systems; instead, we observe local synchronization in the presence of active noise, providing an intriguing link to the statistical physics of the celebrated Kuramoto model.