Fig 1. Sperm chemotaxis in external flow.

(A) Simulated, three-dimensional concentration field c(r) of chemoattractant released from a freely-rotating, spherical egg (yellow sphere) suspended in unsteady shear flow as a model of small-scale turbulence. An exemplary simulated sperm cell (trajectory in red) finds the elongated concentration filament by chance and subsequently ‘surfs’ along the filament by chemotaxis. (B) Same as (A), but for the prototypical idealization of simple shear flow v_ext(r) = αy e_x accounting for convection and co-rotation by the external flow. We obtain a generic form of the concentration filament, Eq (1), and characterize surfing along the filament analytically as a damped oscillation. Parameters correspond to sea urchin A. punctuala, assuming continuous release of chemoattractant at constant rate $\dot{Q}=0.46\text{fmol}{\text{min}}^{-1}$ for an exposure time t_max = 6 min. Constant shear rate α = 0.17 s⁻¹ in (B), corresponding to root-mean-square shear rate of (A). Same color-code for concentration in (A) and (B), but different level sets. We use a generic theoretical description of helical sperm chemotaxis, see Methods and materials for details (helix radius r₀ = 7 μm not visible at length-scale of figure). Rotating views of the 3D images are provided as S1 and S2 Movies.