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.
The 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.
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The authors thank G. Ramirez-San Juan, A. Mathijssen and the other members of the Prakash Lab for their helpful comments on the manuscript. W.G. was supported by the NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard University, NSF grant no. DMS-1764269, the Harvard FAS Quantitative Biology Initiative, the U. S. Department of Defense National Defense Science and Engineering Graduate (NDSEG) Fellowship Program and the National Geographic Society ‘Young Explorers’ program. M.S.B. thanks the NSF Graduate Research Fellowship Program and the Stanford Bio-X fellowship. M.P. thanks the NSF Careers Program, NSF ‘Center for Cellular Construction’ program (DBI-1548297), NIH Directors New Innovator Award, HHMI-Gates Faculty Fellows program, the W. M. Keck Foundation, the Gordon and Betty Moore Foundation and the Chan Zuckerberg Biohub Investigators program for supporting this work.
The authors declare no competing interests.
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A tube-shaped protein assembly found in the cytoplasm of many cells. Microtubules allow cells to maintain their shape and internal arrangements, and they can aggregate to form specialized structures, including cilia.
- Hopf bifurcations
A Hopf bifurcation is a phenomenon occurring in many nonlinear dynamical systems, in which a periodic orbit spontaneously appears or disappears as a control parameter is varied.
Commonly known as ‘globe algae’, these single-celled green algae form spherical colonies containing up to 50,000 cells.
A phenomenon in deforming elastic beams — and a deviation from classical Euler–Bernoulli beam theory — in which an applied curvature in one location induces a compensatory curvature elsewhere along the beam.
A navigation strategy employed by bacteria and other microorganisms, in which an organism follows nutrient gradients by intermittently switching between directional swimming and random reorientation.
- Reynolds numbers
Dimensionless quantity expressing the ratio of inertial to viscous forces in a fluid dynamics problem. Navigation and locomotion strategies are qualitatively different in the low-Reynolds-number (overdamped) regime and high-Reynolds-number (turbulent) regime.
Referring to a thin membrane of cells lining the ventricles of the brain and the central canal of the spinal cord. These cells play a central role in supporting neuronal function.
A phenomenon in the dynamics of spatially varying scalar fields, in which small-wavelength features are gradually consolidated into larger-wavelength patterns.
Travelling, bounded wave packets occurring in nonlinear media that propagate at fixed velocity.
- Lagrangian chaos
Chaotic motion of tracer particles in a fluid, which readily occurs in high-Reynolds-number flows (such as turbulence). Under certain conditions, it can also occur in the low-Reynolds-number flows produced by ciliated microorganisms.
An abstract coordinate system describing all possible forms or shapes of an organism, parameterized by a small number of independent variables.
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Gilpin, W., Bull, M.S. & Prakash, M. The multiscale physics of cilia and flagella. Nat Rev Phys 2, 74–88 (2020). https://doi.org/10.1038/s42254-019-0129-0
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