Sperm chemotaxis in marine species is optimal at physiological flow rates according theory of filament surfing
Fig 3
Comparison to experiment at moderate shear rates and short exposure time.
Fertilization probability Pfert(α) that an egg becomes fertilized as function of external shear rate α from previous experiments with red abalone H. rufescens gametes in a Taylor-Couette chamber (filled gray triangles: with chemotaxis, open gray triangles: inhibited chemotaxis; for α = 0 s−1 a different experimental protocol was used) [20] and our corresponding simulations (filled blue circles: with chemotaxis, open blue circles: without chemotaxis, mean ± SD). We find reasonable agreement using a single fit parameter, fertilizability pf ≈ 60%, which characterizes the fraction of sperm-egg encounters that result in successful fertilization, see Eq (5). From the experimental protocol, we estimate a background concentration cbg ∼ 4 nM of chemoattractant. While our theory of filament surfing does not directly apply due to this high background concentration, a near-field estimate (red line) yields a similar decay of fertilization probability as function of shear rate α. The single fit parameter of the theory, jout = 4.8 ⋅ 103 m−2s−1, is again consistent with the limit jout = ρegg vh/4 = 7.5 ⋅ 103 m−2s−1 of a ballistic swimmer with random initial conditions (note the the higher value of jout compared to Fig 2 due to higher egg density). For simplicity, simulations do not account for co-rotation of sperm cells, see Fig A in S1 Text for results with co-rotation.