# In-phase and anti-phase flagellar synchronization by basal coupling

## TL;DR

This paper develops a comprehensive theory of flagellar synchronization in Chlamydomonas, showing how basal coupling and waveform compliance interact to produce in-phase synchronization, with predictions for controlling this process via fluid viscosity and flow.

## Contribution

It introduces a full hydrodynamic model that explains how basal coupling and waveform compliance combine to determine flagellar synchronization modes.

## Key findings

- Basal coupling and waveform compliance stabilize anti-phase synchronization individually.
- Their nonlinear interaction stabilizes in-phase synchronization as observed experimentally.
- Synchronization dynamics can be controlled by changing fluid viscosity or external flow.

## Abstract

We present a theory of flagellar synchronization in the green alga Chlamydomonas, using full treatment of flagellar hydrodynamics. We find that two recently proposed synchronization mechanisms, basal coupling and flagellar waveform compliance, stabilize anti-phase synchronization if operative in isolation. Their nonlinear superposition, however, stabilizes in-phase synchronization as observed in experiments. Our theory predicts different synchronization dynamics in fluids of increased viscosity or external flow, suggesting a non-invasive way to control synchronization by hydrodynamic coupling.