Table 2.

Mean and standard deviations of parameter values. For given oscillation frequencies ω∕2π, which were determined from the power spectrum [Fig. 3B] the stiffness per unit length K and the friction per unit length λ were used as fit parameters. The amplitude of basal sliding $\mid {\tilde{\Delta }}_0\mid$ and therefore the values of the basal stiffness and friction k_s and γ_s were inferred from the best fits. The normalized mean squared distance between experimental and theoretical curves, as defined in the Materials and Methods section, is denoted by Q. The number n of sperm for each condition is indicated. The values obtained by averaging over all experimental conditions are summarized in the bottom two rows. The fit parameters presented here were obtained from the dimensionless fit parameters using estimated values for the diameter of the axoneme, a=185 nm, its bending rigidity κ=1.7×10⁻²¹ N m², friction coefficient per unit length ξ_⊥, and flagellar length L=58.3 μm. Using a distance of 4 μm between the flagellum and the cover slip, we estimated ξ_⊥=3.4×10⁻³ N s∕m² for the experiments with clamped and pivoting head (observed at 22 °C) and ξ_⊥=2.5×10⁻³ N s∕m² for the swimming sperm (observed at 36 °C). The length L does not include the length d=5.5 μm between the head center and the beginning of the flagellum. The estimation of parameters is discussed in Appendix C.

	K$\left(\frac{\mathrm{kN}}{{\mathrm{m}}^2}\right)$	λ$\left(\frac{\mathrm{N}\bullet \mathrm{s}}{{\mathrm{m}}^2}\right)$	ks$\left(\frac{\mathrm{mN}}{\mathrm{m}}\right)$	γs$\left(\frac{\mathrm{mN}\bullet \mathrm{s}}{\mathrm{m}}\right)$	$\mid {\tilde{\Delta }}_0\mid$ (nm)	ω∕2π (Hz)	Q
Clamped head (n=6)
Mean	−1.62	−7.6	94.8	0.274	170	20.6	0.977
s.d.	0.04	0.1	2.6	0.006	18	1.2	0.005
Pivoting head (n=5)
Mean	−1.48	−7.9	88.6	0.299	145	20.0	0.958
s.d.	0.13	0.7	9.8	0.041	34	4.2	0.033
Planar swimming (n=7)
Mean	−1.63	−5.3	96.2	0.201	162	31.3	0.953
s.d.	0.06	0.1	3.3	0.008	17	1.9	0.019
All (n=18)
Mean	−1.58	−6.8	93.6	0.253	160	24.6	0.962
s.d.	0.10	1.3	6.3	0.048	24	6.0	0.023