Three-dimensional mechanics of eukaryotic flagella.

Equations are derived that account for the contribution of internal structure of cilia and flagella to motion in three dimensions according to a sliding filament model of the motile system. It is shown that for reasonable amounts of bending and twisting, the bending properties of an axoneme can be described by a linear elastic bending resistance, and approximate values for the bending and twisting resistances are computed. Expressions for the shear moments contributed by purely elastic or pinned links between filaments are also derived. It is shown that within the confines of a strict sliding filament model such internal structures cannot by themselves produce twist. Thus planar bending will occur if the internal shear force lies in a plane. Application of an external force, however, will in general produce twisting. Computer simulations of flagellar shape in response to a constant external force applied to the distal end of the axoneme are presented. It is shown that a small amount of twist may arise because of acylindrical bend resistance. Large twists, however, result when the external force is applied to an axoneme with internal shear resistant links.