The Geometry of Ciliary Dynamics

Abstract

Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (1) one-dimensional inextensibility of filaments, (2) three-dimensional incompressibility, and (3) shear strain only along filaments. This hypothetical ciliary material combines one- and three-dimensional properties in a way that makes it a natural and flexible model for how real cilia convert nanoscopic shear stress into motility on a much larger scale. Without reference to the evolving shape of the cilium, conventional continuum mechanics applied to this hypothetical material leads to the standard model of ciliary dynamics, but with one additional term, required by constraints (2) and (3) above, a model-independent coupling of shear and twist in general ciliary motion.