An Integrated Mechanochemical Model of Sperm Locomotion

Mammalian sperm cells manage locomotion by the movement of their flagella. 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. Recently, a model has been proposed for the planar nonlinear beating of the flagellum under clamped and hinged boundary conditions, where spontaneous oscillations emerged from the coupling of dynein motor kinetics with deformations. In a new framework combining slender-body theory and the boundary element method, we extend this model to study the free swimming of sperm cells with arbitrary head shapes, considering the effects of non-local hydrodynamic interactions between 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