A chemomechanical model of sperm locomotion reveals two modes of swimming

TL;DR

This paper introduces a comprehensive chemomechanical model of sperm motility that reveals two distinct swimming modes driven by internal dynein motor activity and elastic flagellar dynamics, with implications for understanding sperm efficiency and behavior.

Contribution

The study develops an integrated computational framework combining fluid mechanics and elastic deformation to simulate sperm locomotion, uncovering two different swimming modes linked to motor activity levels.

Findings

Swimming velocity exhibits two maxima at different dynein activity levels.

Distinct waveforms and trajectories characterize each swimming mode.

Swimming efficiency peaks at low sperm number.

Abstract

The propulsion of mammalian spermatozoa relies on the spontaneous periodic oscillation of their flagella. These oscillations are driven internally by the coordinated action of ATP-powered dynein motors that exert sliding forces between microtubule doublets, resulting in bending waves that propagate along the flagellum and enable locomotion. We present an integrated chemomechanical model of a freely swimming spermatozoon that uses a sliding-control model of the axoneme capturing the two-way feedback between motor kinetics and elastic deformations while accounting for detailed fluid mechanics around the moving cell. We develop a robust computational framework that solves a boundary integral equation for the passive sperm head alongside the slender-body equation for the deforming flagellum described as a geometrically nonlinear internally actuated Euler-Bernoulli beam, and captures full hydrodynamic interactions. Nonlinear simulations are shown to produce spontaneous oscillations with realistic beating patterns and trajectories, which we analyze as a function of sperm number and motor activity. Our results indicate that the swimming velocity does not vary monotonically with dynein activity, but instead displays two maxima corresponding to distinct modes of swimming, each characterized by qualitatively different waveforms and trajectories. Our model also provides an estimate for the efficiency of swimming, which peaks at low sperm number.