Cooperation of Sperm in Two Dimensions: Synchronization, Attraction and Aggregation through Hydrodynamic Interactions

TL;DR

This study uses simulations to explore how sperm interact hydrodynamically in two dimensions, revealing synchronization and attraction effects that lead to swarm formation depending on beating frequency differences.

Contribution

It introduces a particle-based simulation approach to analyze sperm cooperation via hydrodynamics, highlighting synchronization and attraction mechanisms in 2D environments.

Findings

Hydrodynamic interactions cause sperm synchronization.

Sperm exhibit attraction leading to clustering.

Swarm behavior depends on beating frequency distribution.

Abstract

Sperm swimming at low Reynolds number have strong hydrodynamic interactions when their concentration is high in vivo or near substrates in vitro. The beating tails not only propel the sperm through a fluid, but also create flow fields through which sperm interact with each other. We study the hydrodynamic interaction and cooperation of sperm embedded in a two-dimensional fluid by using a particle-based mesoscopic simulation method, multi-particle collision dynamics (MPC). We analyze the sperm behavior by investigating the relationship between the beating-phase difference and the relative sperm position, as well as the energy consumption. Two effects of hydrodynamic interaction are found, synchronization and attraction. With these hydrodynamic effects, a multi-sperm system shows swarm behavior with a power-law dependence of the average cluster size on the width of the distribution of beating frequencies.