  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.
