# Hydrodynamic synchronization of spontaneously beating filaments

## TL;DR

This study models how hydrodynamic interactions and biochemical feedback lead to synchronization of beating filaments like sperm and cilia, explaining experimental observations and the roles of waveform symmetry.

## Contribution

It introduces a geometric feedback model that captures elastohydrodynamic phase synchronization across various filament waveforms, including asymmetric and symmetric patterns.

## Key findings

- Both in-phase and anti-phase synchronization can occur in asymmetric beats.
- Symmetric waveforms tend to synchronize in-phase.
- Biochemical noise can cause phase slips in synchronization.

## Abstract

Using a geometric feedback model of the flagellar axoneme accounting for dynein motor kinetics, we study elastohydrodynamic phase synchronization in a pair of spontaneously beating filaments with waveforms ranging from sperm to cilia and Chlamydomonas. Our computations reveal that both in-phase and anti-phase synchrony can emerge for asymmetric beats while symmetric waveforms go in-phase, and elucidate the mechanism for phase slips due to biochemical noise. Model predictions agree with recent experiments and illuminate the crucial roles of hydrodynamics and mechanochemical feedback in synchronization.