Collective effects in ciliar arrays.

Collective effects in one-dimensional ciliar arrays are studied analytically and numerically. A new phase oscillator description for ciliar motion is introduced which depends only on a single parameter. It allows the systematic study of hydrodynamic interactions between cilia exhibiting arbitrary beating patterns. It is shown that if the hydrodynamic interactions do not alter the beating pattern of the cilia no synchronization of ciliar motion occurs. This is in particular the case in arrays with low ciliar densities. But hydrodynamic interactions can lead to formation of a collective (metachronal) wave which is stable for periodic boundary conditions. In finite arrays free boundaries destroy this collective motion. The dispersion relation for metachronal waves is found to be non-universal, i.e., to depend crucially on the microscopic details of the ciliar beating pattern.