Figure 6.

Time evolution of the predicted force exerted by a spermatozoon and its angle towards the surface, for simulations with different flagellar waveforms, as depicted in figure 2b. (a) Results for a spermatozoon with a binding strength of K = 5 × 10⁵ and a waveform associated with a low-viscosity medium, respectively, a planar beat pattern, a helical beat pattern and a hyperactivated beat pattern (waveforms I, II, III of figure 2b). (b) Results for a spermatozoon with a beat pattern associated with a high-viscosity medium such as methylcellulose solution, waveform IV of figure 2b, and with two binding strengths, K = 1 × 10⁶ (escaper) and 1 × 10⁷ (adherer). (c) Results for a spermatozoon with a beat pattern associated with cumulus, waveform V of figure 2b, with two binding strengths, K = 3 × 10⁵ (escaper) and 1 × 10⁷ (adherer). The force perpendicular to the surface (left-hand column) is taken to be positive when the spermatozoon is repelled from the surface. In the central column, the magnitude of the surface interaction force parallel to the surface is presented. In the right-hand column, the angle between the surface and the spermatozoon is given, with positive values corresponding to the head of the spermatozoon oriented towards the wall.