Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model

Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for large-amplitude elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a 'high viscosity' parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5°-10°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.

The mechanics of hyperactivation in adhered human sperm

Hyperactivation is an important phenomenon exhibited by mammalian sperm during the process of acquiring fertilization capacity. The majority of studies have focused on incubation-induced hyperactivation in non-human species, which typically differ in size, shape, and are more homogeneous than human sperm. We develop an alternative approach via drug-induction, using high-speed imaging and analysis of same-cell changes in the flagellar movement of adhered cells. Following stimulation with 4-aminopyridine, approximately two-thirds (21 of 34) of the cells analysed exhibited a waveform with a single characteristic frequency; in all cases, the frequency was lower than before stimulation. The remaining cells (13 of 34) exhibited a more complex motility with multiple-frequency modes. The lowest mode in all cases was lower than the frequency prior to stimulation. Flagellar bending increased in all cells following stimulation and was significantly greater in the multiple-frequency responders. Despite the increased bending, time-averaged hydrodynamic power dissipation decreased significantly when assessed across all cells, the effect being significantly greater in the multiple-frequency responders than single frequency. These results reveal the heterogeneity of responses of human sperm to a hyperactivating stimulus, the methodology being potentially useful for assessing dynamic responses to stimuli in human sperm, and physiological selection of cells for assisted reproduction.

Comment on the article by J. Elgeti, U. B. Kaupp, and G. Gompper: hydrodynamics of sperm cells near surfaces

A recent study by Elgeti et al. used multiparticle collision dynamics to simulate a long-standing problem: the approach of sperm to surfaces, and subsequent accumulation. The authors highlight differences in their predictions with those of the earlier Stokes flow simulations of Smith et al. attributing the differences to methodological flaws in the earlier article. In this Comment, we discuss the criticisms leveled in detail, and review some recently published work that shows how species-specific details of cell morphology provides a more likely explanation for the differing predictions of the two studies. We also highlight experimental work that supports the study of Smith et al.

Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.