Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells

Flocking behavior is observed in biological systems from the cellular to super-organismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. Remarkably, these cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase exhibits anisotropic giant number fluctuations and possesses transverse density fluctuation correlations consistent with the Toner-Tu theory of the polar fluid phase, despite the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. In addition to these flow-induced flocking states, we also find a self-organized global vortex state of the sperm cells. We simulate this system, modeling the sperm as persistently turning active particles. Although the model does not reproduce the vortex state, it exhibits a polar-disorder phase boundary as a function of cell density and persistence time that is predictive of the experimental phase boundary. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.