Synchronization in cilia carpets: multiple metachronal waves are stable, but one wave dominates

Abstract

Carpets of actively bending cilia represent arrays of biological oscillators that can exhibit self-organized metachronal synchronization in the form of traveling waves of cilia phase. This metachronal coordination supposedly enhances fluid transport by cilia carpets. Using a multi-scale model calibrated by an experimental cilia beat pattern, we predict multi-stability of wave modes. Yet, a single mode, corresponding to a dexioplectic wave, has predominant basin-of-attraction. Similar to a "dynamic" Mermin-Wagner theorem, relaxation times diverge with system size, which rules out global order in infinite systems. In finite systems, we characterize the synchronization transition as function of quenched frequency disorder, using generalized Kuramoto order parameters. Our framework termed Lagrangian Mechanics of Active Systems allows to predict the direction and stability of metachronal synchronization for given beat patterns.

arXiv comment16 pages, 7 color figures

References in corpus (22)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Hydrodynamic flow patterns and synchronization of beating cilia
• Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia
• Finding the ciliary beating pattern with optimal efficiency
• Coordinated Beating of Algal Flagella is Mediated by Basal Coupling
• Generic Conditions for Hydrodynamic Synchronization
• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• Active phase and amplitude fluctuations of flagellar beating
• Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
• Rhythmicity, Recurrence, and Recovery of Flagellar Beating
• Flagellar swimmers oscillate between pusher- and puller-type swimming
• The load-response of the flagellar beat
• The Size of the Sync Basin Revisited
• Mobility induces global synchronization of oscillators in periodic extended systems
• Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies
• In-phase and anti-phase flagellar synchronization by basal coupling
• Hydrodynamic synchronization of flagellar oscillators
• Multisynchrony in active microfilaments
• A three-sphere swimmer for flagellar synchronization
• Vortices and the entrainment transition in the 2D Kuramoto model
• Coarse-graining the dynamics of immersed and driven fiber assemblies
• Load response of shape-changing microswimmers scales with their energy efficiency

Cited by in corpus (5)

• A multiscale biophysical model gives quantized metachronal waves in a lattice of cilia
• Synchronization in cilia carpets and the Kuramoto model with local coupling: breakup of global synchronization in the presence of noise
• Synchronization in the presence of time delays and inertia: Stability criteria
• Periodic orbits in the Ott-Antonsen manifold
• Robust formation of metachronal waves in directional chains of phase oscillators