Phase Dependent Forcing and Synchronization in the three-sphere model of Chlamydomonas

TL;DR

This paper investigates how phase-dependent forcing influences synchronization in a hydrodynamic three-sphere model of Chlamydomonas, revealing that specific beat patterns are essential for stable synchronization.

Contribution

It demonstrates through numerical analysis that phase-dependent forcing is crucial for stable synchronization in the model, advancing understanding of flagellar coordination.

Findings

Phase-dependent forcing is necessary for stable synchronization.

The model's behavior depends on the shape of the driving force profile.

Synchronization stability varies with initial conditions and parameters.

Abstract

The green alga {\it Chlamydomonas} swims with synchronized beating of its two flagella, and is experimentally observed to exhibit run-and-tumble behaviour similar to bacteria. Recently we studied a simple hydrodynamic three-sphere model of {\it Chlamydomonas} with a phase dependent driving force which can produce run-and-tumble behaviour when intrinsic noise is added, due to the non-linear mechanics of the system. Here, we consider the noiseless case and explore numerically the parameter space in the driving force profiles, which determine whether or not the synchronized state evolves from a given initial condition, as well as the stability of the synchronized state. We find that phase dependent forcing, or a beat pattern, is necessary for stable synchronization in the geometry we work with.