Asymmetry in cilia configuration induces hydrodynamic phase locking

Abstract

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

Interpreting the synchronisation of driven colloidal oscillators via the mean pair interaction

“…These model cilia are then used to investigate the synchronisation between pairs of cilia or small clusters of cilia, before building up to large arrays or chains of cilia [15,[17][18][19]. The more complex models often focus on specifics like the transport speed and energy efficiency [16,[20][21][22], or the effect of variations in the cilium themselves on coordination [23]. Alternatively the cilia can be highly simplified, in which case each cilium is usually represented by a bead or sphere [24][25][26].…”