Elastohydrodynamic mechanisms govern beat pattern transitions in eukaryotic flagella

Eukaryotic cilia and flagella exhibit complex beating patterns that vary depending on environmental conditions such as fluid viscosity ¹ . These transitions are thought to arise from changes in the internal forcing provided by the axoneme, although the mechanism remains unclear ^2,3 . We demonstrate with simulations of Kirchhoff rods driven internally by active bending moments that a single elastohydrodynamic instability universally explains transitions between planar, quasiplanar, helical, and complex beating patterns due to changes in either the internal forcing, flagellar stiffness and length, or due to changes in the hydrodynamic resistance, either due to the viscosity of the ambient medium or the presence of a plane wall. The beat patterns and transitions are comparable to those exhibited by bull sperm and sea urchin sperm in our experiments and elsewhere ^3–5 . Our results point to a general model that can describe flagellar and ciliary beating across all species. We further show that internal dynein forces can be estimated by comparing simulation results with experimental observations of transitional viscosities. This can potentially lead to diagnostic assays to measure the health of sperm cells based on their beating pattern.