Self-organization of spermatozoa via unsteady elastohydrodynamic interactions enhances their swimming speed and efficiency

Sperm bundling, swarming, and aggregation are observed in various species, suggesting that grouping enhances motility. In this study, we developed a numerical model of sperm computed by fluid-structure interactions between multiple flagella, showing that hydrodynamic interactions allow the sperm model to form polar orders, in which they swim alongside each other. The time required for order formation depends on the density n and is scaled by lnn/n. A wave propagation model controlled by the time derivative of flagellar curvature was introduced to represent flagellar synchronization via hydrodynamic interactions. The polar state results in hydrodynamic flagellar synchronization due to relatively long contact time, which increases swimming speed and flagellar beat speed by approximately 10% compared with no synchronization. During coordinated locomotion, the mechanical power performed by cells is similar to that in isolated systems, but grouping lowers the viscous resistance per cell and increases swimming speed by a factor of 2 compared to solitary swimming under high-density physiological conditions. Thus swimming efficiency increases with density (under physiological conditions, two- to fivefold times higher than in isolated systems). These numerical results show that, in the ordered state, sperm swim faster while expending less energy, suggesting that ordered swimming aids long-distance swimming from an energy perspective.