Flagellar Bending Waves Research Articles

Contractile Mechanisms in Flagella

The elastic theory of flexural waves in thin rods accurately predicts the velocity of flagellar bending waves over a wide range of viscosities. This shows that flagella behave as a purely mechanical system for the transmission of these waves. An evaluation of the total bending moment reveals that this moment occurs in phase over the entire length of a flagellum. From this it is concluded that each contractile fiber in the flagella is activated simultaneously over its whole length. The magnitude of the bending moment decreases linearly along the flagellum. This is most easily explained by a sliding filament hypothesis in flagella with the elementary 9 + 2 fibers. The expression found for the bending moment explains logically that the wave velocity in flagella is determined by their mechanical properties and the outside viscosity only.

Effects of increased viscosity on the movements of some invertebrate spermatozoa.

ABSTRACT Two distinctly different patterns of sperm movement in response to increased viscosity have been found, which appear to be variations in the behaviour of a common mechanism for generating and controlling flagellar bending waves. One type of pattern is found with the normal movements of spermatozoa of Ciona and Lytechinus, and with glycerinated Lytechinus spermatozoa when their movements are reactivated at high (2 mM) ATP concentrations. The radius of curvature of the bends on the flagellum, and the viscous bending moment, remain relatively constant, while the propagation velocity, wave amplitude, and energy expenditure decrease with increasing viscosity. The second pattern of response is found with the normal movements of spermatozoa of Chaetopterus, with Lytechinus spermatozoa when the beat frequency is reduced by the presence of an inhibitor, thiourea, and with glycerinated Lytechinus spermatozoa when their movements are reactivated at low (0·2 mM) ATP concentrations. The decrease in propagation velocity with increasing viscosity is accompanied by substantial reductions in the radius of curvature, and the wave amplitude is not greatly decreased. This response involves an increase in viscous bending moment and energy expenditure as the rate of bending decreases, and may resemble the increased force and work outputs obtainable from muscle at reduced shortening velocities. This type of response is obtained under conditions where the initial beat frequency and energy expenditure are relatively low, and may not be possible when the initial level of energy expenditure is higher. Although each species shows a unique pattern of changes in frequency and wavelength with increasing viscosity, the relationship between bend propagation velocity and viscosity has nearly the same form in each case, indicating that the velocity of bend propagation is relatively independent of the magnitude of the bend. This result is consistent with at least one proposed mechanism for bend propagation. On the basis of this mechanism, the results suggest that the rate of bending is independent of the magnitude of the bend and inversely proportional to the square root of the viscosity. In some cases, the wavelength and other wave parameters are adjusted so that a constant proportionality between viscous and elastic bending moments will be maintained as the viscosity is increased. This proportionality will also be maintained during the passive propagation of bending waves along an inert flagellum, and for an active flagellum it implies that the wave parameters are adjusted so that energy stored in elastic bending of the flagellum could be efficiently used to effect unbending, without indicating how this adjustment is accomplished. Other cases, in which the proportionality between viscous and elastic bending moments is not maintained, may represent cases where the flagellum is not operating efficiently. Under certain conditions the normal nearly planar bending waves of Ciona spermatozoa are replaced by helical bending waves.

Bending Waves of the Posterior Flagellum of Ceratium

Flagellar bending waves, as shown by multiple-flash photomicrographs of the posterior flagellum of Ceratium, are not sine waves. The bent regions are circular arcs; these regions are separated by short segments without bending.