Doing more with less: the flagellar end piece enhances the propulsive effectiveness of human spermatozoa

Abstract

Spermatozoa self-propel by propagating bending waves along a predominantly active elastic flagellum. The organized structure of the "9 + 2" axoneme is lost in the most-distal few microns of the flagellum, and therefore this region is unlikely to have the ability to generate active bending; as such it has been largely neglected in biophysical studies. Through elastohydrodynamic modeling of human-like sperm we show that an inactive distal region confers significant advantages, both in propulsive thrust and swimming efficiency, when compared with a fully active flagellum of the same total length. The beneficial effect of the inactive end piece on these statistics can be as small as a few percent but can be above 430%. The optimal inactive length, between 2-18% of the total length, depends on both wavenumber and viscous-elastic ratio, and therefore is likely to vary in different species. Potential implications in evolutionary biology and clinical assessment are discussed.

arXiv commentTo Appear, Physical Review Fluids. 25 pages, 14 figures

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• Well-posedness and applications of classical elastohydrodynamics for a swimming filament
• Regularised non-uniform segments and efficient no-slip elastohydrodynamics
• Minimal design of a synthetic cilium