Synchronization in cilia carpets and the Kuramoto model with local coupling: breakup of global synchronization in the presence of noise

Abstract

Carpets of actively bending cilia represent a paradigmatic example of self-organized synchronization of noisy biological oscillators, characterized by traveling waves of cilia phase. We present a multi-scale model of a cilia carpet, which comprises realistic hydrodynamic interactions between cilia computed for a chiral cilia beat pattern from unicellular Paramecium and active noise of the cilia beat. We demonstrate an abrupt loss of global synchronization beyond a characteristic noise strength. We characterize stochastic transitions between synchronized and disordered dynamics, which generalizes the notion of phase slips in pairs of coupled noisy phase oscillators. Our theoretical work establishes a link between the two-dimensional Kuramoto model of phase oscillators with mirror-symmetric oscillator coupling and detailed models of biological oscillators with asymmetric, chiral interactions.

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

“…Noise excites these Goldstone modes, which rules out global order in infinite systems. Based on the observed divergence of relaxation times, we expect a similar behavior for metachronal synchronization in cilia carpets in the presence of noise [52]. The non-equilibrium dynamics in cilia carpets is thus different from other non-equilibrium dynamical models such as the Toner-Tu model of flocking birds [53]: in that two-dimensional model, global order is possible, because the active motion of agents results in a continuous exchange of neighbors.…”