Flagellar energetics from high-resolution imaging of beating patterns in tethered mouse sperm

While much is known about the microstructure of sperm flagella, the mechanisms behind the generation of flagellar beating patterns by the axoneme are still not fully understood. We demonstrate a technique for investigating the energetics of flagella or cilia. We record the planar beating of tethered wildtype and Crisp2-knockout mouse sperm at high-speed and high-resolution and extract centerlines using digital image processing techniques. We accurately reconstruct beating waveforms using a Chebyshev-polynomial based Proper Orthogonal Decomposition of the centerline tangent-angle profiles. External hydrodynamic forces and the internal resistance from the passive flagellar material are calculated from the observed kinematics of the beating patterns using a Soft, Internally-Driven Kirchhoff-Rod (SIDKR) model. Energy conservation is employed to further compute the flagellar energetics. We thus obtain the distribution of mechanical power exerted by the dynein motors without any further assumptions about mechanisms regulating axonemal function. We find that, in both the mouse genotypes studied, a large proportion of the mechanical power exerted by the dynein motors is dissipated internally, within the passive structures of the flagellum and by the motors themselves. This internal dissipation is considerably greater than the hydrodynamic dissipation in the aqueous medium outside. The net power input from the dynein motors in sperm from Crisp2-knockout mice is significantly smaller than in corresponding wildtype samples. The reduced power is correlated with slower beating and smaller amplitudes. These measurements of flagellar energetics indicate that the ion-channel regulating cysteine-rich secretory proteins (CRISPs) may also be involved in regulating mammalian sperm motility.