Mechano-Turing patterning and self-organisation of the human sperm beating in 3D: observation and theory

Elastohydrodynamic equations have been applied under a hierarchy of approximations to describe the dynamics of the human sperm flagellum, one of many examples in biology of an interaction between inextensible filaments and inertialess fluids. Recent high-speed 3D imaging has shown the beating of the flagellum to be asymmetric. Previous models have assumed symmetrical planar beating, now realised to be an illusion of 2D microscopy manifested by the rotation of the sperm as it moves. The ability of the sperm to reach and fertilize the egg rests on its ability to move through the viscous cervical mucus. Further research into what characterises successful motion will contribute in the design of soft matter artificial swimmers, and with our understanding and potential to intervene in problems of male fertility.

This research will aim to accurately model the motion of the human sperm in 3D by viewing it as a self-organised spatiotemporal Turing pattern, with reaction kinetics, diffusion, and mechanical forces all playing a role. Situated within the context of higher order reaction-diffusion systems (which describe self-organisation in superconductors, water waves and biochemical systems among others) research on this problem will have a wide appeal.