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 a 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.

Keywords

• synchronization
• cilia carpet
• metachronal wave
• multi-scale modeling
• local and global stability
• biological oscillator