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Chemomechanical model of sperm locomotion reveals two modes of swimming

Chenji Li1,*, Brato Chakrabarti2, Pedro Castilla1, Achal Mahajan1,†, and David Saintillan1,‡

  • 1Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA
  • 2Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA

  • *Present address: School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA.
  • †Present address: SI3 Computational Biology Hub, Altos Labs, Redwood City, California 94403, USA.
  • ‡dstn@ucsd.edu
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Phys. Rev. Fluids 8, 113102 – Published 15 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.113102

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 wave forms and trajectories. Our model also provides an estimate for the efficiency of swimming, which peaks at low sperm number.

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Phys. Rev. Fluids 8, 113102– Published 15 November, 2023
  • Received 14 October 2022
  • Accepted 20 September 2023
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