Synchronization in cilia carpets: multiple metachronal waves are stable, but one wave dominates

TL;DR

This study models cilia carpets to understand how multiple wave modes coexist and compete, revealing that a single dominant wave emerges despite the presence of multiple stable modes, influenced by system size and disorder.

Contribution

We introduce a multi-scale Lagrangian Mechanics framework that predicts the stability and dominance of specific metachronal waves in cilia carpets, accounting for system size and disorder effects.

Findings

Multiple wave modes are stable in theory.

A single wave mode dominates in finite systems.

Relaxation times diverge with system size, preventing global order.

Abstract

Carpets of actively bending cilia represent arrays of biological oscillators that can exhibit self-organized metachronal synchronization in the form of traveling waves of cilia phase. This metachronal coordination supposedly enhances fluid transport by cilia carpets. Using a multi-scale model calibrated by an experimental cilia beat pattern, we predict multi-stability of wave modes. Yet, a single mode, corresponding to a 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. In finite systems, we characterize the synchronization transition as function of quenched frequency disorder, using generalized Kuramoto order parameters. Our framework termed Lagrangian Mechanics of Active Systems allows to predict the direction and stability of metachronal synchronization for given beat patterns.