The propulsion of mammalian spermatozoa during reproduction 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 active sliding forces between microtubule doublets, resulting in bending waves that propagate along the flagellum and enable locomotion of the cell through the viscous medium. In this work, we present a chemomechanical model of a freely swimming spermatozoon that uses a sliding-control model of the flagellar axoneme capturing the coupling of motor kinetics with elastic deformations and accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. Nonlinear simulations of the model equations are shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Our results demonstrate that the swimming velocity does not vary monotonically with dynein activity, but instead displays two local maxima corresponding to distinct modes of swimming, each characterized by qualitatively different waveforms and trajectories.

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.