Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

¹ Institut Curie

^* To whom correspondence should be addressed. E-mail: boris.guirao{at}m4x.org.

Submitted on March 11, 2006
Revised on May 1, 2006
Accepted on 27 November 2006

	Abstract

Cells or bacteria carrying cilia on their surface show many striking features : alignment of cilia in an array, two-phase asymmetric beating for each cilium and existence of metachronal coordination with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors, to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronal coordination arises as a consequence of the internal mechanism of the cilia and their hydrodynamic couplings, with a wavelength comparable to that found in experiments. It allows the cilia to start beating at a lower ATP threshold and at a higher frequency than for a single cilium. It also leads to a rather stationary flow, which might be its major advantage.

Key Words: beating, cilia, coordination, hydrodynamic interactions, metachronal waves, symmetry breaking