Hydrodynamic synchronization in strong confinement

Cellular appendages conferring motility, such as flagella or cilia, are known to synchronise their periodic beats. The origin of synchronisation is a combination long-range hydrodynamic interactions with physical mechanisms allowing the phases these biological oscillators evolve. Two have been identified by previous work, elastic compliance orbit oscillations driven phase-dependent forcing. To help uncover mechanism for most essential overall in biology, we theoretically investigate effect strong confinement on effectiveness synchronisation. We use minimal models where modelled rigid spheres forced move along circular trajectories near surface. Strong adding second nearby surface, parallel first one, distance between surfaces much smaller than typical cilia. calculate separately impact dynamics and force modulation compare our results case no confinement. Applying biologically-relevant situation nodal show that leads phase-locked states under very similar those without difference mechanism. Our point therefore robustness synchronisation, an important feature suggests it could be arrays further examine distinct primary cilia not pronounced but still favours modulation.