### Jihun Han

Courant Institute of Mathematical Sciences

New York University

October 4, 2016

Spontaneous Oscillation and Fluid-Structure Interaction of Cilia

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 three-dimensional 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 three dimensional 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 dynamical law we contrived, 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 dynamical instability of a symmetrical steady state in which the cilium is straight and 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 well-coordinated wave motion in which multiple cilia in an array organize their beating to pump fluid, in particular, by breaking phase synchronization.