Coordination of Dynein Motor Enzymes for Generation of 3-dimensional Flagellar Bending Waves

Eukaryotic flagella contain tens of thousands of dynein motor enzymes, arranged in regular arrays along the outer doublet microtubules of the axoneme-- the internal cytoskeleton of a flagellum or cilium. These dyneins produce longitudinal sliding between the doublet microtubules. They must interact cooperatively to generate the bending waves that are required for efficient propulsion of spermatozoa, or other situations. Sperm flagella can generate a variety of bending patterns, including nearly two dimensional patterns that can be approximated as planar bending waves and three-dimensional bending patterns that are approximately helical waves. In some situation, they can switch between these two types of bending [1,2]. Computer programs have been developed previously that can simulate planar flagellar bending waves, by assuming that bendin