Designing metachronal waves of cilia

TL;DR

This paper develops a theoretical framework linking individual cilia dynamics to collective metachronal wave patterns, validated by simulations, advancing understanding of ciliary coordination in active matter systems.

Contribution

It introduces a systematic coarse-graining approach to predict ciliary wave properties from single cilium dynamics and array geometry.

Findings

Analytical criteria for stable wave frequency and wavevector

Quantitative agreement between simulations and theory

Insights into how individual cilia influence collective behavior

Abstract

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse-graining. We uncover the criteria that control the selection of frequency and wavevector of stable metchacronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of single cilia, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units, and as such exemplifies a bottom-up study of a rich active matter system.