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.

Keywords

• cilium
• flagellum
• synchronization
• hydrodynamic interaction
• low Reynolds number
• 87.16.Qp