In-phase and anti-phase flagellar synchronization by waveform compliance and basal coupling

Abstract

We present a theory of flagellar synchronization in the green alga Chlamydomonas, using full treatment of flagellar hydrodynamics and measured beat patterns. We find that two recently proposed synchronization mechanisms, flagellar waveform compliance and basal coupling, stabilize anti-phase synchronization (AP) if operative in isolation. Their nonlinear superposition, however, can stabilize in-phase synchronization (IP) for suitable parameter choices, matching experimental observations. Our theory is based on a description of the flagellar beat as a limit-cycle oscillator, which was introduced and calibrated by experimental data in a recent letter (Klindt et al 2016 Phys. Rev. Lett. 117 258101). Using a minimal model of basal coupling, we identify regimes of IP, AP and even out-of-phase synchronization with spontaneous symmetry-breaking in this system of two identical coupled oscillators as a function of an effective strength of basal coupling. From our theory, we quantitatively predict different synchronization dynamics in fluids of increased viscosity or external flow, suggesting a non-invasive way to control synchronization by hydrodynamic coupling.