From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions

TL;DR

This paper uses detailed simulations to connect individual flagellum dynamics of sperm cells with their collective behaviors, revealing how variations influence aggregation and turbulence-like motion.

Contribution

It introduces a comprehensive mathematical model that resolves flagellum dynamics and explores the impact of individual variability on collective sperm motion.

Findings

Hydrodynamic interactions drive aggregation and swirling behaviors.

Flows at flagellum undulation scales significantly contribute to fluid energy.

Variation in individual dynamics determines collective state.

Abstract

Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and propulsion mechanisms. Even for sperm cells, which have a stereotyped shape consisting of a cell body connected to a flexible flagellum, a wide range of collective dynamics is observed spanning from the formation of tightly packed groups to the display of larger-scale, turbulence-like motion. Using a detailed mathematical model that resolves flagellum dynamics, we perform simulations of sperm suspensions containing up to 1000 cells and explore the connection between individual and collective dynamics. We find that depending on the level of variation in individual dynamics from one swimmer to another, the sperm exhibit either a strong tendency to aggregate, or the suspension exhibits large-scale swirling. Hydrodynamic interactions govern the formation and evolution of both states. In addition, a quantitative analysis of the states reveals that the flows generated at the time-scale of flagellum undulations contribute significantly to the overall energy in the surrounding fluid, highlighting the importance of resolving these flows.