The exact mechanism to orchestrate the action of hundreds of dynein motor proteins to generate wave-like ciliary beating remains puzzling and has fascinated many scientists. We present a 3D model of a cilium and the simulation of its beating in a fluid environment. The model cilium obeys a simple geometric constraint that arises naturally from the microscopic structure of a real cilium. This constraint allows us to determine the whole 3D structure at any instant in terms of the configuration of a single space curve. The tensions of active links, which model the dynein motor proteins, follow a postulated dynamical law, and together with the passive elasticity of microtubules, this dynamical law is responsible for the ciliary motions. In particular, our postulated tension dynamics lead to the instability of a symmetrical steady state, in which the cilium is straight and its active links are under equal tensions. The result of this instability is a stable, wave-like, limit cycle oscillation. We have also investigated the fluid-structure interaction of cilia using the immersed boundary (IB) method. In this setting, we see not only coordination within a single cilium but also, coordinated motion, in which multiple cilia in an array organize their beating to pump fluid, in particular by breaking phase synchronization.
Keywords: Hopf bifurcation; fluid transport; motile cilia; phase desynchronization; symmetry breaking.