The chimera state in colloidal phase oscillators with hydrodynamic interaction

Nonreciprocal interactions give rise to fast cilium synchronization in finite systems

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.

Changes in geometrical aspects of a simple model of cilia synchronization control the dynamical state, a possible mechanism for switching of swimming gaits in microswimmers

Active oscillators, with purely hydrodynamic coupling, are useful simple models to understand various aspects of motile cilia synchronization. Motile cilia are used by microorganisms to swim and to control the flow fields in their surroundings; the patterns observed in cilia carpets can be remarkably complex, and can be changed over time by the organism. It is often not known to what extent the coupling between cilia is due to just hydrodynamic forces, and neither is it known if it is biological or physical triggers that can change the dynamical collective state. Here we treat this question from a very simplified point of view. We describe three possible mechanisms that enable a switch in the dynamical state, in a simple scenario of a chain of oscillators. We find that shape-change provides the most consistent strategy to control collective dynamics, but also imposing small changes in frequency produces some unique stable states. Demonstrating these effects in the abstract minimal model proves that these could be possible explanations for gait switching seen in ciliated micro organisms like Paramecium and others. Microorganisms with many cilia could in principle be taking advantage of hydrodynamic coupling, to switch their swimming gait through either a shape change that manifests in decreased coupling between groups of cilia, or alterations to the beat style of a small subset of the cilia.

Entrainment of mammalian motile cilia in the brain with hydrodynamic forces

Motile cilia are widespread across the animal and plant kingdoms, displaying complex collective dynamics central to their physiology. Their coordination mechanism is not generally understood, with previous work mainly focusing on algae and protists. We study here the entrainment of cilia beat in multiciliated cells from brain ventricles. The response to controlled oscillatory external flows shows that flows at a similar frequency to the actively beating cilia can entrain cilia oscillations. We find that the hydrodynamic forces required for this entrainment strongly depend on the number of cilia per cell. Cells with few cilia (up to five) can be entrained at flows comparable to cilia-driven flows, in contrast with what was recently observed in Chlamydomonas Experimental trends are quantitatively described by a model that accounts for hydrodynamic screening of packed cilia and the chemomechanical energy efficiency of the flagellar beat. Simulations of a minimal model of cilia interacting hydrodynamically show the same trends observed in cilia.

Motile cilia hydrodynamics: entrainment versus synchronization when coupling through flow

Coordinated motion of cilia is a fascinating and vital aspect of very diverse forms of eukaryotic life, enabling swimming and propulsion of fluid across cellular epithelia. There are many questions still unresolved, and broadly they fall into two classes. (i) The mechanism of how cilia physically transmit forces onto each other. It is not known for many systems if the forces are mainly of hydrodynamical origin, or if elastic forces within the cytoskeleton are important. (ii) In those systems where we know that forces are purely hydrodynamical, we do not have a framework for linking our understanding of how each cilium behaves in isolation to the collective properties of two or more cilia. In this work, we take biological data of cilia dynamics from a variety of organisms as an input for an analytical and numerical study. We calculate the relative importance of external flows versus internal cilia flows on cilia coupling. This study contributes to both the open questions outlined above: firstly, we show that it is, in general, incorrect to infer cilium-cilium coupling strength on the basis of experiments with external flows, and secondly, we show a framework to recapitulate the dynamics of single cilia (the waveform) showing classes that correspond to biological systems with the same physiological activity (swimming by propulsion, versus forming collective waves). This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.