The Geometry of Ciliary Dynamics

TL;DR

This paper develops a continuum model of ciliary material incorporating key constraints, revealing a fundamental coupling of shear and twist in ciliary motion that enhances understanding of how cilia convert shear stress into movement.

Contribution

It introduces a novel continuum model of cilia that integrates inextensibility, incompressibility, and shear constraints, leading to a new coupling of shear and twist in ciliary dynamics.

Findings

Standard ciliary models are extended with an additional shear-twist coupling term.

The model explains how shear stress is converted into motility without shape evolution.

Provides a theoretical framework linking microscopic shear stresses to macroscopic ciliary motion.

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.