Fluid viscoelasticity promotes collective swimming of sperm

From flocking birds to swarming insects, interactions of organisms large and small lead to the emergence of collective dynamics. Here, we report striking collective swimming of bovine sperm in dynamic clusters, enabled by the viscoelasticity of the fluid. Sperm oriented in the same direction within each cluster, and cluster size and cell-cell alignment strength increased with viscoelasticity of the fluid. In contrast, sperm swam randomly and individually in Newtonian (nonelastic) fluids of low and high viscosity. Analysis of the fluid motion surrounding individual swimming sperm indicated that sperm-fluid interaction was facilitated by the elastic component of the fluid. In humans, as well as cattle, sperm are naturally deposited at the entrance to the cervix and must swim through viscoelastic cervical mucus and other mucoid secretions to reach the site of fertilization. Collective swimming induced by elasticity may thus facilitate sperm migration and contribute to successful fertilization. We note that almost all biological fluids (e.g. mucus and blood) are viscoelastic in nature, and this finding highlights the importance of fluid elasticity in biological function.

A number of factors other than the elasticity of the medium could have contributed to the clustering observed, and we examine them here.
(1) Motility induced clustering. In a well-studied system, it was established that spherical colloids form clusters when chemical reactions cause them to propel themselves (1). Their movements result in coexistence between a solid phase (clustered with lattice structure) and a gas phase (dispersed).
Clusters formed through collisions, and it was demonstrated numerically that swimming pressure due to collisions caused by the propulsion alone result in clustering, even in the absence of other types of attraction between the self-propelled objects (2,3). In our experiments, if collision-induced swimming pressure were the dominant mechanism, we should have observed a high degree of sperm clustering in the viscous fluids as well as in the viscoelastic fluids, since collision probability enhancement would occur in both cases due to increased slithering of sperm The slight increase in correlation length in viscous solutions in contrast to that in the standard medium is likely to have contributed to increased slithering motility in the PVP solution. In standard medium, where rolling motion dominates, the sperm head is on average 5 µm from surfaces (4), while in viscous PVP solution, it is less than 1 µm from surfaces (5). This is because slithering motion keeps the head much closer to a surface. As a result, slithering sperm are likely to collide more often with other sperm than sperm in standard medium ( Figure 1A,B; and Video 1, 2).
(2) Shear thinning promotes aggregation of settling spheres. It has been proposed that the shearthinning property of viscoelastic fluids can create a corridor of fluid with lower viscosity for two settling spheres to aggregate together, since the settling spheres shear the fluid and therefore lower the viscosity (6). In that scenario, viscoelasticity allows settling spheres to generate larger flow fields.
Because we showed that the flow field generated by sperm in viscoelastic fluids was actually smaller than that in the standard medium, where no collective swimming was observed, this shear-thinning flow field enhancement is unlikely to be the dominant mechanism for the emergence of collective swimming.  (4) Collective swimming due to depletion interaction. Depletion interaction is an entropic force that results from the non-negligible sizes of the depletion molecules (polymers). Given that the radius of gyration scales as a square root of the polymer length, the radii of gyration of the PVP and SC-PAM are not orders of magnitude smaller than the LC-PAM, therefore offering relatively similar (at least similar orders of magnitude) exclusion zones (8). Because the difference in depletion interaction is not as drastically different between LC-PAM and PVP/SC-PAM, yet the amount of clustering is dramatically lower in PVP/SC-PAM, it is unlikely that the collective swimming is caused by depletion interaction.

Supplementary
Furthermore, we know that bovine sperm surfaces have a net negative charge (9), while the amine groups make PAM less negatively charged than PVP, making PAM less likely to be depleted from the zone close to sperm surface than PVP. Since the two polymers carry similar charges otherwise, depletion should be a stronger effect in PVP than in PAM; therefore, depletion is not a major contributor to the clustering of sperm.