Collective Effects in Arrays of Cilia and Rotational Motors

Abstract

SummaryThe movement of cilia in arrays is very often coordinated. Neighboring cilia beat cooperatively in a synchronized fashion or they maintain a constant phase difference creating a metachronal wave. This collective ciliar motion is used by many microorganisms for swimming and feeding. There is also strong evidence that ciliar (nodal) flow plays an important role in the establishment of left and right in developing vertebrates. In this short review, we summarize current theoretical efforts in analyzing the influence of hydrodynamic interactions on collective effects in arrays of cilia. Analytical and numerical models for the beating of a single cilium are introduced and used to calculate the motion in the surrounding flow. In arrays, the velocity field induced by a cilium exerts forces on the neighboring cilia, giving rise to hydrodynamic interactions. The importance of these interactions for collective ciliar beating is analyzed in specific models and in a more general framework. We also discuss the influence of boundary conditions and the tilting of monocilia on the nodal flow. Finally, the importance of hydrodynamic interaction for collections of rotational motors are studied. We conclude with some examples of possible applications.