An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating

We present a fluid-mechanical model of an individual cilium which incorporates discrete representations of the dynein arms, the passive elastic structure of the axoneme including the microtubules and nexin links. This model, based upon the immersed boundary method (Peskin, 1977), couples the internal force generation of the molecular motors through the passive elastic structure with the external fluid mechanics governed by the Navier-Stokes equations. Detailed geometric information is available, such as the spacing and shear between the microtubules, the local curvature of individual microtubules and the stretching of the nexin links. In addition, the explicit representation of the dynein motors allows us the flexibility to incorporate a variety of activation theories. In this article, we choose a simple activation theory so that the ciliary beat is not present, but is an emergent property of the interacting components of the coupled fluid-axoneme system. We present numerical results from computer simulations of sliding disintegration and ciliary beating with several different viscosities.