Studies on the eel sperm flagellum. 2. The kinematics of normal motility

The sperm flagellum of Anguilla anguilla lacks outer dynein arms, radial spokes and central structures. Its characteristic motion has been obtained by studying cells swimming perpendicularly against, but not adhering to, the coverslip. The flagellum generates a sinistrally helical wave of rising, then falling, amplitude. The frequency of the wave, which can exceed 70 Hz, is inversely related to its maximum amplitude. As a reaction to the torque, the entire cell rolls (spins) in the opposite direction to that taken by points on the flagellum in the generation of the sinistral wave. However, because the head (which contributes on opposing torque) is asymmetrical, the axis of this counter-rotation is displaced laterally from the axis of the flagellar rotation. As a result, the flagellum precesses around the progression axis, with each point on the flagellum travelling along a special flagelloid curve, specified by the ratios of the two frequencies and the two radii for the circular motions. The instantaneous flagellar waveform (the flagelloid wave) is thus derived as a succession of phase-shifted points on the series of flagelloid curves along the axis of the cell's rotation. This adds complexity to the underlying, rather simple, helical geometry. Calculations suggest that the forward swimming speed of the sperm is greatly aided by the orientation and shape of the sperm head. The movement of latex beads was observed around sperm swimming against the coverslip and around sperm swimming freely. Bulk, vortical flows of fluid were seen in the former case and net lateral displacements in the latter; this is in accordance with hydrodynamic theory for low Reynolds number systems.