Hydrodynamic synchronisation in strong confinement
arXiv:2104.10111 · doi:10.1103/PhysRevE.103.022403
Abstract
Cellular appendages conferring motility, such as flagella or cilia, are known to synchronise their periodic beats. The origin of synchronisation is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing. To help uncover the physical mechanism for hydrodynamic synchronisation most essential overall in biology, we theoretically investigate the effect of strong confinement on the effectiveness of hydrodynamic synchronisation. We use minimal models where appendages are modelled as rigid spheres forced to move along circular trajectories near a rigid surface. Strong confinement is modelled by adding a second nearby surface, parallel to the first one, where the distance between the surfaces is much smaller than the typical distance between the cilia. We calculate separately the impact of confinement on the synchronisation dynamics of the elastic compliance and the force modulation mechanisms and compare our results to the case with no confinement. Applying our results to the biologically-relevant situation of nodal cilia, we show that force modulation is a mechanism that leads to phase-locked states under strong confinement that are very similar to those without confinement as a difference with the elastic compliance mechanism. Our results point therefore to the robustness of force modulation for synchronisation, an important feature for biological dynamics that suggests it could be the most essential physical mechanism overall in arrays of nodal cilia. We further examine the distinct situation of primary cilia and show in that case that the difference in robustness of the mechanisms is not as pronounced but still favours the force modulation.
References in corpus (10)
- Physical Aspects of Axonemal Beating and Swimming
- Hydrodynamic flow patterns and synchronization of beating cilia
- Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia
- Coordinated Beating of Algal Flagella is Mediated by Basal Coupling
- Generic Conditions for Hydrodynamic Synchronization
- Synchronization of rotating helices by hydrodynamic interactions
- Metachronal wave and hydrodynamic interaction for deterministic switching rowers
- Minimal Model for Hydrodynamic Synchronization
- Hydrodynamic synchronization of spontaneously beating filaments
- Confinement enhances the diversity of microbial flow fields