Oscillatory Active Brownian Motion: A Minimal Model for Sperm Dynamics

Abstract

Active biological microswimmers typically combine persistent self-propulsion with cyclic motion generated by flagellar or ciliary beating. However, standard active Brownian motion (ABM) does not explicitly account for these intrinsic oscillations. This limitation is particularly relevant for sperm cells, whose transport depends not only on directional persistence and stochastic reorientation but also on periodic head motion. Here we introduce oscillatory active Brownian motion (OABM), a minimal extension of ABM in which the swimmer orientation undergoes directional diffusion while being modulated by a periodic angular drive. The model yields analytical expressions for experimentally relevant observables, including the time-averaged mean-squared displacement, velocity autocorrelation function, and transverse excursion amplitude. A central prediction is a crossover between two ballistic regimes: short-time motion governed by the swimming velocity and an intermediate regime with a reduced, oscillation-averaged effective velocity determined by the angular beat amplitude. Using trajectories of human sperm, we infer model parameters from standard motility measures. The model quantitatively reproduces both single-cell trajectories and population-level dynamics under control conditions and following induction of hyperactivation. Overall, OABM provides a compact active-matter framework that links measurable flagellar kinematics to coarse-grained transport, enabling a description of sperm motility across different physiological states.