Research Projects

Motile cilia are hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments can coordinate their beating phases to generate metachronal waves (MWs) that drive long-range fluid transport and locomotion. Understanding the emergence and properties of MWs in ciliary arrays is a multiscale problem central to biology, transport phenomena, nonequilibrium physics, and biomedical applications. Prior modeling and simulations in 1D and 2D idealized lattices have shown that fluid-mediated long-range interactions can form and maintain such waves. However, most ciliated organisms are diffeomorphic to a sphere. Recent experiments in such ciliates reveal a rich array of exotic collective behaviors and fluid flows intrinsically tied to their topology. Much of these dynamics remain poorly understood. In this work, we will develop coarse-grained continuum models for ciliary beds and combine large-scale computations in curved geometries to study the interplay of topology, hydrodynamics, and synchronization in ciliary carpets. Our primary focus will be a continuum model that coarse-grains the dynamics of cilia as an active traction layer on the fluid, incorporating a two-way coupling between synchronization and fluid flows. Here, the active stress and collective flows depend on the synchronization state of the cilia, while each cilium’s beating phase, in turn, evolves in response to these emergent flows. We will solve the governing Stokes equations on 2-spheres using a boundary element method. This framework will provide an analytical handle to study the stability of disordered and ordered states of ciliary coordination. Our simulations will reveal how topological defects on spherical surfaces spontaneously emerge, coordinating flows and synchronization patterns. We will also illustrate how spherical ciliates can control microscopic ciliary actuation to alter synchronization patterns and, in turn, their swimming gaits to respond to external cues. Finally, to complement these models, we will use direct numerical simulations of active filaments anchored on a sphere. Using slender body theory and fast kernel summation techniques, these fluid-structure-interaction simulations will elucidate how mechanochemical feedback within each cilium responds to hydrodynamic interactions and topology. The work will significantly advance our understanding of coupled cilia in multicellular life at the scale of a whole organism. Our results may inform the design of microswimmers and control strategies of coral ciliates with potential implications for ocean conservation efforts. Beyond the biological significance, this work opens a new realm in nonequilibrium physics, involving hydrodynamic phase synchronization of active particles. The development of models and state-of-the-art computational tools will find applications in a range of problems in fluid mechanics and soft matter.