An integrated chemomechanical model of sperm locomotion reveals two fundamental swimming modes

Mammalian sperm cells achieve locomotion by the spontaneous periodic oscillation of their flagellum. Dynein motors inside the flagellum consume energy from ATP to exert active sliding forces between microtubule doublets, thus creating bending waves along the flagellum and enabling the sperm cell to swim in a viscous medium. Using a sliding-control model of the axoneme that captures the coupling of motor kinetics with elastic deformations, we develop a chemomechanical model of a freely swimming sperm cell that accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. The model is shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Remarkably, we find that the swimming velocity does not vary monotonically with motor activity, but instead displays two local maxima corresponding to distinct modes of swimming.