A study of helical and planar waves on sea urchin sperm flagella, with a theory of how they are generated.

When the spermatozoon of Echinus esculentus swims in sea water containing methyl cellulose (viscosity 1.5--4 Pa s), its flagellum may generate either a helical or a planar waveform, each type being stable. The helical wave, which is dextral, is complicated by the concurrent passage of miniature waves along it. These miniature waves have a pulsatile origin in the neck region of the spermatozoon. Our videotape analysis indicates that there are two pulses of mechanical activity for each true cycle of the helical wave. (The true helical frequency was obtained from the apparent wave frequency and the roll frequency of the sperm head, the latter being detectable in some sperm when lit stroboscopically.) The planar wave has a meander shape. During the propagation of planar waves, the sliding displacements are adjustable in either direction; moribund flagella can undergo unrestricted sliding. The planar waves are, in fact, exactly planar only at interfaces. Otherwise, there tend to be torsions in the interbend segments between planar bends. Mechanical stimulation of the flagellum can cause a sudden transition from the helical to the planar waveform. To account for the two modes of beating, we advance the hypothesis that circumferential linkages yield beyond a threshold strain. Whether this yield point is exceeded, we suggest, depends upon the balance between the active shear force and the external viscosity (among other factors). We propose that a subthreshold force originates in one array and then triggers the other dynein arrays circumferentially, but unidirectionally, around the base of the flagellum; whereas a suprathreshold force provokes bi-directional circumferential triggering. These may be the two patterns of activation that result in helical and planar waveforms, respectively. The transition from helical to planar bending may result from an increment in the force produced by the dynein motors. The pulsatile origin of the helical wave resembles behaviour described previously for spermatozoa of Ciona intestinalis and of the quail Coturnix coturnix.