The physical consequences of sperm gigantism

Abstract: A male fruit fly produces $\sim$ 1.8 mm long sperm, thousands of which can be stored until mating in a $\sim$ 200 $\mu$m sac, the seminal vesicle (SV). While the evolutionary pressures driving such extreme sperm lengths have long been investigated, the physical consequences of their gigantism \textit{in vivo} are unstudied. Through high-resolution three-dimensional reconstructions of sperm morphologies and rapid live imaging, we discovered that stored sperm are organized into a dense and highly aligned state. We also found that the flagella exhibit system-wide collective `material’ flows, with persistent and slow-moving topological defects. Individual sperm, despite their extraordinary lengths, counter-propagate rapidly and smoothly through this flagellar material along director field lines. To rationalize these behaviors, we pose a conceptual model in which the motion of an individual sperm is topologically confined to a tube formed by its neighbors. Sperm propagate within these tubes by frictionally pushing off one another in opposite directions, through observed amplitude-constrained and internally driven flagellar bending waves. Building upon this conception, we formulate a continuum theory that produces the extensile material stresses that underlie an aligned flagellar material. Through experimental perturbations and simulations of active elastic filaments, we verify the model’s prediction that the sperm’s swimming speed depends on their local polarity. Numerical exploration of the continuum theory reproduces experimentally observed correlations and statistics. Our model also rationalizes the sperm’s \textit{in vivo} dynamics in the female, where the sperm are maintained in dedicated storage organs prior to fertilization. These findings suggest that active extensile stresses in the flagellar material maintain the sperm in an unentangled, hence functional state in both sexes, and establish giant sperm in their physiological habitat as a novel active matter system.

Recommended citation: Jasmin Imran Alsous, Brato Chakrabarti, Bryce Palmer, Michael J. Shelley. "The physical consequences of sperm gigantism." Submitted.