Flagellar Propulsion of Sperm Cells Against a Time-Periodic Interaction Force

Sperm cells undergo complex interactions with external environments, such
as a solid-boundary, fluid flow, as well as other cells before arriving at the
fertilization site. The interaction with the oviductal epithelium, as a site of
sperm storage, is one type of cell-to-cell interaction that serves as a selection
mechanism. Abnormal sperm cells with poor swimming performance,
the major cause of male infertility, are filtered out by this selection mechanism.
In this study, collinear bundles, consisting of two sperm cells, generate
propulsive thrusts along opposite directions and allow to observe the
influence of cell-to-cell interaction on flagellar wave-patterns. The developed
elasto-hydrodynamic model demonstrates that steric and adhesive forces
lead to highly symmetrical wave-pattern and reduce the bending amplitude
of the propagating wave. It is measured that the free cells exhibit a mean
flagellar curvature of 6.4 ± 3.5 rad mm-1 and a bending amplitude of 13.8 ±
2.8 rad mm-1. After forming the collinear bundle, the mean flagellar curvature
and bending amplitude are decreased to 1.8 ± 1.1 and 9.6 ± 1.4 rad mm-1,
respectively. This study presents consistent theoretical and experimental
results important for understanding the adaptive behavior of sperm cells to
the external time-periodic force encountered during sperm–egg interaction.