Spontaneous phase coordination and fluid pumping in model ciliary carpets

TL;DR

This study combines simulations and continuum theory to show that large arrays of cilia naturally develop stable metachronal waves, which are crucial for effective fluid pumping in biological tissues.

Contribution

It introduces a new theoretical framework linking cilia coordination patterns to fluid flow, demonstrating the stability of metachronal waves in large ciliary carpets.

Findings

Metachronal waves are stable attractors in large ciliary arrays.

Isotropic and synchronized states are unstable in large cilia groups.

Wave characteristics depend on tissue and cilia properties.

Abstract

Ciliated tissues such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in-silico experiments with thousands of hydrodynamically-interacting cilia, and we develop a continuum theory in the limit of infinitely-many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure-to-function maps from cilium-level beat to tissue-level coordination and fluid pumping.