Mathematical tales of a sperm tail
Active cell motility via the controlled movement of a flagellum beating is among the phylogenetically oldest forms of motility, and has been retained in higher level organisms for spermatozoa transport. Despite this ubiquity and importance, the details of how the flagellar waveform emerges from the underlying mechanics and how the cell, or the environs, may control the beating pattern by regulating the flexible tail is far from fully understood. We demonstrate in this talk that mechanics and modelling can be utilised to interpret observations of flagellar dynamics, swimming trajectories, beating patterns, as well as unexpected phenomena associated with their complex material response. It also highlights that this is a fertile and challenging area of inter-disciplinary research for applied mathematicians and demonstrates the importance of future observational and theoretical studies in understanding the underlying mechanics of these motile cell appendages.