The multiscale physics of cilia and flagella

Cilia and flagella are fundamental units of motion in cellular biology. These beating, hair-like organelles share a common basic structure but maintain widely varying functions in systems ranging from the isolated flagella of swimming algae to the dense ciliary carpets that pump fluid in the brains of mammals. Experiments and models have begun to elucidate the inner workings of single cilia as complex nonlinear oscillators, and the variety of hydrodynamical phenomena that result from beating dynamics. These results have shed light on complex locomotion strategies observed in single-celled microorganisms and collective phenomena observed in microbial suspensions. In animal systems, dense ciliary arrays exhibit a variety of emergent phenomena, including active filtration, noise robustness and metachronal waves. Surprising phenomena have been observed in neuronally controlled ciliary arrays, demonstrating the need for new physical models of cilia that include central control, defect dynamics and topology. We review the emergent physics of cilia across scales, starting from the microscale dynamics of single cilia, and then proceeding to microorganisms and animal systems. Cilia are hair-like organelles that enable cellular locomotion. This Review considers cilia from a dynamical systems perspective, discussing the nonlinear oscillations seen in the single cilia of microorganisms and the emergent topological phenomena seen in the ciliary arrays of animals. Key pointsThe complex beating dynamics of cilia can be modelled as noisy, nonlinear oscillations driven by coupled chemical, mechanical and hydrodynamical forces.Small numbers of coupled cilia can transiently synchronize and desynchronize in a manner analogous to that seen in classical studies of coupled oscillators.The synchronization dynamics of cilia may play a role in facilitating locomotion and navigation by single-celled microorganisms.Many animals have 'carpets' of densely packed cilia, which are used to pump mucous and other circulating fluids in the brain and lungs. The beating dynamics of these ciliary carpets exhibit physical phenomena that include travelling waves and topological defects.Neuronally controlled cilia in certain animal systems exhibit a rich, and understudied, set of dynamical phenomena, making their study a promising research direction.