Complex flagellar motions and swimming patterns of the flagellates Paraphysomonas vestita and Pteridomonas danica

Most flagellates with hispid flagella, that is, flagella with rigid filamentous hairs (mastigonemes), swim in the direction of the flagellar wave propagation with an anterior position of the flagellum. Previous analysis was based on planar wave propagation showing that the mastigonemes pull fluid along the flagellar axis. In the present study, we investigate the flagellar motions and swimming patterns for two flagellates with hispid flagella: Paraphysomonas vestita and Pteridomonas danica. Studies were carried out using normal and high-speed video recording, and particles were added to visualize flow around cells generating feeding currents. When swimming or generating flow, P. vestita was able to pull fluid normal to, and not just along, the flagellum, implying the use of the mastigonemes in an as yet un-described way. When the flagellum made contact with food particles, it changed the flagellar waveform so that the particle was fanned towards the ingestion area, suggesting mechano-sensitivity of the mastigonemes. Pteridomonas danica was capable of more complex swimming than previously described for flagellated protists. This was associated with control of the flagellar beat as well as an ability to bend the plane of the flagellar waveform.     

Analysis of the flagellar bending waves of ejaculated ram sperm

The variability of flagellar movement, illustrated by the highly heterogeneous nature of the ejaculated sperm population of the ram, was analyzed by the use of a stroboscopic technique and an adapted microphotographic 24 X 36 camera system. The multiple-moving-exposures (MME) records give very distinct successive sequences of the flagellar beats and are particularly suitable for the analysis of bend development and propagation along the tail. With this technique, the parameters of the flagellar bending waves of ejaculated ram sperm have been determined. Most of the sperm have planar flagellar beatings; few are rolling under the conditions of observation. The trajectories of the gametes are mostly linear; nevertheless, some have circular paths. The analysis of bending has been focused on two examples for which the difference in the progressiveness ratio was maximum. The circular pathways for ram spermatozoa are linked to an asymmetry between principal and reverse bend probably induced by differences in wave propagation evidenced along the flagellum. A typical sperm flagellar movement may be related either to the conditions of the observations or to some differences in the maturation process of the sperm.     

Functional state of the axonemal dyneins during flagellar bend propagation

When mouse spermatozoa swim in media of high viscosity, additional waves of bending are superimposed on the primary traveling wave. The additional (secondary) waves are relatively small in scale and high in frequency. They originate in the proximal part of the interbend regions. The initiation of secondary bending happens only in distal parts of the flagellum. The secondary waves propagate along the interbends and then tend to die out as they encounter the next-most-distal bend of the primary wave, if that bend exceeds a certain angle. The principal bends of the primary wave, being of greater angle than the reverse bends, strongly resist invasion by the secondary waves; when a principal bend of the primary wave propagates off the flagellar tip, the secondary wave behind it suddenly increases in amplitude. We claim that the functional state of the dynein motors in relation to the primary wave can be deduced from their availability for recruitment into secondary wave activity. Therefore, only the dyneins in bends are committed functionally to the maintenance and propagation of the flagellar wave; dyneins in interbend regions are not functionally committed in this way. We equate functional commitment with tension-generating activity, although we argue that the regions of dynein thus engaged nevertheless permit sliding displacements between the doublets.     

Decrease of internal free calcium and human sperm movement

In order to elucidate the effects of calcium on the movement of human spermatozoa, studies were conducted using motile cells selected by swim-up migration at 37 degrees C in 5% CO2 in air in a synthetic BWW medium containing 1.7 x 10(-3) M CaCl2 or BWW without added calcium (BWW-Ca). Preliminary experiments have confirmed that the addition of EGTA (5 x 10(-3); 10(-2) M) to BWW medium decreased the intracellular calcium concentration ((Ca++)i) of spermatozoa, as measured in cells loaded with a fluorescent Ca++ indicator, Quin-2. Concomitant measurements of (Ca++)i and sperm movement (analysed by videomicrography at 200 f/s at room temperature) were carried out on Quin-2 loaded cells incubated in BWW-Ca medium plus EGTA (10(-5) M; 10(-4) M; 10(-3) M). Under these conditions a decrease in (Ca++)i was observed and associated with a decrease in mean amplitude of lateral head displacement (ALH). Analysis using an automatic analyser (Hamilton Thorn at 37 degrees C) confirmed these results: the percentage of spermatozoa swimming with ALH greater than or equal to 6 microns is decreased when the external free calcium in BWW-Ca is decreased by the addition of 10(-5) M, 10(-4) M, or 10(-3) M EGTA. Flagellar analysis of the sperm population characterized by ALH greater than or equal to 6 microns showed a large proximal curvature of the tail associated with a low propagation wave velocity and a low beat frequency as compared to the spermatozoa with ALH less than 6 microns with similar progressive velocities. These characteristics result in a high flagellar beat efficiency (in terms of head displacement per beat). The disappearance of this pattern of movement when intracellular calcium is lowered indicates that calcium plays a complex role in the relationship between curvature and wave propagation. The ability of spermatozoa to modulate their movement in response to an alteration in the intracellular calcium level confirms the role of calcium in controlling flagellar movement in intact cells.     

Kinematics of human spermatozoa

A microcinematographic (50 f/s) study was performed on motile human spermatozoa. Eighty percent were found to have a linear trajectory and a pseudo-sinusoidal head displacement pattern. Throughout their progression, the spermatozoa periodically rotated on their longitudinal axis at a frequency equal to that of flagellar wave formation. These waves were found always to begin on the same side of the cell and to propagate in the flattened plane of the head until the moment of rotation. At this time the wave had reached a point near the middle of the flagellum. Beyond this point, the flagellum moves out of the plane of the head. Different variables used to characterize the movement of spermatozoa included the velocity of progression, amplitude and velocity of head displacement, frequency of rotation, wave amplitude, and propagation velocity of the flagellar wave. Among these variables, it was the propagation velocity of the wave that was found to be best correlated with the velocity of spermatozoan progression. This flagellar wave exhibited two stages, one of initiation and one of propagation.     

Comparative analysis of movement characteristics of lancelet and fish spermatozoa having different morphologies

The movement characteristics of the sperm and their flagella obtained from a lancelet and 35 species from almost all orders of fishes were examined using high-speed video microscopy. The aim was to clarify the relationship between the motility parameters of the spermatozoa having different morphologies and how these motility parameters affect the swimming speed of the spermatozoa. The motility parameters representing the flagellar waveform, the wavelength, and the amplitude were neither very different between the spermatozoa of the different species nor related to the swimming speed. In contrast, the beat frequency was remarkably changed in the different spermatozoa and was proportional to the swimming speed. The maximum shear angle of the flagellar wave, which is directly related to the maximum sliding displacement between the doublet microtubules, remained nearly constant while the beat frequency varied widely; therefore, the spermatozoa beat in the constant sliding displacement mode. An analysis of the relationship between swimming speed and flagellar length revealed that short flagella were at a disadvantage in developing swimming speed; however, so were extra-long flagella. The ratio of the swimming speed to the wave velocity calculated from the wavelength and the beat frequency depended on the distance from the glass surface. The swimming speeds calculated using the original resistive-force theory were greater than the measured values. To rationalize the measured values, the ratio between the normal and tangential drag coefficient in the resistive-force theory was corrected; namely, 1.99 at 1 μm and 1.63 at 3 μm from the glass surface.     

A new automated method of image analysis: comparison of ciliary and flagellar beats

A new automated method of image analysis of sperm flagellar (human) and cilia (Dunaliella) bends is developed. This method permits an automatic determination of the line characterizing the flagellum. Two dynamic parameters are measured: the wave propagation velocity and the wave curvature radius. The data reveal similar patterns in the propagation of the principal and reverse waves between flagelated and ciliated cells. Conversely, differences are seen in principal wave curvature due perhaps to the presence of periaxonemal structures in the flagellum, absent in cilium. The identical patterns of reverse wave curvaturei in both systems may be linked to axonemal limitations.     

The equation of motion for sperm flagella.

The equation of motion for sperm flagella, in which the elastic bending moment and the active contractile moment are balanced by the moment from the viscous resistance of the surrounding fluid, is solved for a wave solution that superimposes partial solutions. Substitution of the expression for the wave solution into the equation leads to an expression for the active contractile moment. This active moment can be decomposed into two parts. The first part describes an active moment that travels over the flagellum with the mechanical flagellar wave, the second part represents a moment in phase over the entire length of the flagellum, which decreases linearly towards the distal tip. The linear synchronous moment, to which an amount of traveling moment has been added as a perturbation, leads to wave solutions that closely resemble flagellar waves. Properties such as wavelength and wave amplitudes and also the shape of the waves in sea urchin sperm flagella at different frequencies are accurately described by the theory. The change in wave shape in sea urchin sperm flagella at raised viscosity is predicted well by the theory. The different wave properties caused in bull sperm flagella by different boundary conditions at the proximal junction are explained. When only a traveling active moment is present in a flagellum, the wave solutions describe waves of a small wave length in a long flagellum. Some properties of the wave motion of sperm flagella are derived from the theory and verified experimentally.     

Quantile regression estimates of animal population trends

Ecologists often estimate population trends of animals in time series of counts using linear regression to estimate parameters in a linear transformation of multiplicative growth models, where logarithms of rates of change in counts in time intervals are used as response variables. We present quantile regression estimates for the median (0.50) and interquartile (0.25, 0.75) relationships as an alternative to mean regression estimates for common density-dependent and density-independent population growth models. We demonstrate that the quantile regression estimates are more robust to outliers and require fewer distributional assumptions than conventional mean regression estimates and can provide information on heterogeneous rates of change ignored by mean regression. We provide quantile regression trend estimates for 2 populations of greater sage-grouse (Centrocercus urophasianus) in Wyoming, USA, and for the Crawford population of Gunnison sage-grouse (Centrocercus minimus) in southwestern Colorado, USA. Our selected Gompertz models of density dependence for both populations of greater sage-grouse had smaller negative estimates of density-dependence terms and less variation in corresponding predicted growth rates (λ) for quantile than mean regression models. In contrast, our selected Gompertz models of density dependence with piecewise linear effects of years for the Crawford population of Gunnison sage-grouse had predicted changes in λ across years from quantile regressions that varied more than those from mean regression because of heterogeneity in estimated λs that were both less and greater than mean estimates. Our results add to literature establishing that quantile regression provides better behaved estimates than mean regression when there are outlying growth rates, including those induced by adjustments for zeros in the time series of counts. The 0.25 and 0.75 quantiles bracketing the median provide robust estimates of population changes (λ) for the central 50% of time series data and provide a 50% prediction interval for a single new prediction without making parametric distributional assumptions or assuming homogeneous λs. Compared to mean estimates, our quantile regression trend estimates for greater sage-grouse indicated less variation in density-dependent λs by minimizing sensitivity to outlying values, and for Gunnison sage-grouse indicated greater variation in density-dependent λs associated with heterogeneity among quantiles.     

Peptide-induced hyperactivation-like vigorous flagellar movement in starfish sperm

Asterosap, a sperm-activating peptide (SAP) from the starfish egg jelly coat, is diffusible and controls a cGMP-signalling pathway in starfish sperm in the same manner as resact, a potent chemoattracting SAP in sea urchins. This fact suggests that asterosap may serve as a chemoattractant like resact at concentrations with appropriate gradients. Since asterosap is one of three egg jelly components, which in concert induce the acrosome reaction, it is still worthwhile to evaluate how asterosap modulates sperm motility prior to this reaction. We analysed the flagellar movement of sperm of the starfish Aphelasterias japonica in artificial seawater (ASW) containing the asterosap isoform P15 at 1 micromol l(-1). We found that sperm swim straighter with more symmetrical flagellar movement in P15 than in ASW, but without any significant difference in the flagellar beat frequency and the swimming velocity. The flagellar movement is, however, dramatically different between sperm firmly attached to the solid surface by the head in P15 and those attached in ASW: in P15 the flagellum bends to a greater extent, with higher curvature and with higher shear angle up to a right angle to the flagellar wave axis, and beats at an increased frequency. The vigorous flagellar movement of sperm, which can be activated when sperm are placed in high-load circumstances just as entering into a jelly layer, may increase propulsive forces and hydrodynamic resistances, allowing sperm to undergo the acrosome reaction as effectively as possible.     

Form and Function of the Dinoflagellate Transverse Flagellum1

A reexamination of the dinoflagellate transverse flagellum in relation to swimming in more than 50 species, using a television recording system, has revealed the following new facts: the flagellar beat always proceeds counterclockwise when seen from the cell apex; the cell always rotates in the direction of the flagellar beat, and fluid is propelled in the opposite direction. These observations can be explained by the actions of flagellar mastigonemes not included in previous models. The shape of the flagellar wave is not isotropic. New explanations are offered for other morphological features of the cell as they relate to swimming.     

Computer simulation of flagellar movement. VI. Simple curvature-controlled models are incompletely specified.

Computer simulation is used to examine a simple flagellar model that will initiate and propagate bending waves in the absence of viscous resistances. The model contains only an elastic bending resistance and an active sliding mechanism that generates reduced active shear moment with increasing sliding velocity. Oscillation results from a distributed control mechanism that reverses the direction of operation of the active sliding mechanism when the curvature reaches critical magnitudes in either direction. Bend propagation by curvature-controlled flagellar models therefore does not require interaction with the viscous resistance of an external fluid. An analytical examination of moment balance during bend propagation by this model yields a solution curve giving values of frequency and wavelength that satisfy the moment balance equation and give uniform bend propagation, suggesting that the model is underdetermined. At 0 viscosity, the boundary condition of 0 shear rate at the basal end of the flagellum during the development of new bends selects the particular solution that is obtained by computer simulations. Therefore, the details of the pattern of bend initiation at the basal end of a flagellum can be of major significance in determining the properties of propagated bending waves in the distal portion of a flagellum. At high values of external viscosity, the model oscillates at frequencies and wavelengths that give approximately integral numbers of waves on the flagellum. These operating points are selected because they facilitate the balance of bending moments at the ends of the model, where the external viscous moment approaches 0. These mode preferences can be overridden by forcing the model to operate at a predetermined frequency. The strong mode preferences shown by curvature-controlled flagellar models, in contrast to the weak or absent mode preferences shown by real flagella, therefore do not demonstrate the inapplicability of the moment-balance approach to real flagella. Instead, they indicate a need to specify additional properties of real flagella that are responsible for selecting particular operating points.     

Estimation of Precision in DLW Studies Using the Two-Point Methodology

Previous attempts to estimate precision of doubly labeled water (DLW) estimates of CO₂ production, using propagation of error analyses, have necessarily made simplifying assumptions which may compromise the resultant error estimate. Using an empirical iteration approach, error distributions for the DLW calculation were generated which overcome these problems. The error distribution for CO₂ estimates generated by DLW is symmetrical but not normal. The distribution is significantly truncated such that the 99% inclusion limits are 2.034 SD and not 2.58 SD. The precision error (99% CI for mean as percent of the mean) in DLW experiments, when using duplicate analyses, varies between approximately 3% and 47% depending on the ratio of the elimination constants of the two labels (k_o/k_d), experimental duration and initial isotope dose. The error could be improved by approximately 10 fold by increasing the number of replicates at all six isotope determinations from 2 to 5. Estimating precision in actual experiments can be made using the same empirical approach. The resultant estimates can be of extreme value in evaluating the role of precision as a factor influencing deviations during validation studies, and also for weighting mean estimates in applications of the technique. The deviations of DLW estimates from those made simultaneously by indirect calorimetry in a small mammal validation study were generally greater than the precision of the DLW estimates of CO₂ production. This may indicate there are more problems with the technique than precision alone.     

A selective effect of Ni2+ on wave initiation in bull sperm flagella

Bull sperm that are extracted with 0.1% Triton X-100 and restored to motility with Mg2+-ATP lose coordination and stop swimming in the presence of 0.5 mM NiSO4. Although spontaneous coordination of flagellar waves is lost after exposure to Ni2+, other functions of the flagellum remain intact. The capacity for wave propagation along the flagellum is maintained together with the capacity for microtubular sliding. Wave motility can be restored to Ni2+-inhibited sperm by inducing a permanent bend onto the flagellum by micromanipulation. In the absence of such intervention, the loss of wave coordination is complete and irreversible. Ni2+-inhibited demembranated cells that are kept active by maintaining a bend in the flagellum exhibit a normal beat frequency. Both intact and demembranated sperm can retain spontaneous wave production at considerably slower rates of motion than Ni2+-inhibited cells. Short segments from the distal tip of the flagellum contain only the 9 + 2 microtubular axoneme. These short segments are able to propagate imposed bends even in the presence of Ni2+. In addition to wave propagation Ni2+-treated sperm can be shown to exhibit a normal sliding tubule phenomenon by direct assay. Although Ni2+-treated cells have a functional sliding tubule mechanism, and consequently the axoneme can propagate bends, it appears that these retained functions are not sufficient to cause spontaneous bend initiation. Our findings show that bend initiation is inhibited by Ni2+, and therefore is an independent process separate from the sliding tubule mechanism responsible for wave propagation.     

Motility of the microtubular axostyle in Pyrsonympha

The rhythmic movement of the microtubular axostyle in the termite flagellate, Pyrsonympha vertens, was analyzed with polarization and electron microscopy. The protozoan axostyle is birefringent as a result of the semi-crystalline alignment of approximately 2,000 microtubules. The birefringence of the organelle permits analysis of the beat pattern in vivo. Modifications of the beat pattern were achieved with visible and UV microbeam irradiation. The beating axostyle is helically twisted and has two principal movements, one resembling ciliary and the other flagellar beating. The anterior portion of the beating axostyle has effective and recovery phases with each beat thereby simulating the flexural motion of a beating cilium. Undulations develop from the flexural flipping motion of the anterior segment and travel along the axostyle like flagellar waves. The shape of the waves differs from that of flagellar waves, however, and are described as sawtooth waves. The propagating sawtooth waves contain a sharp bend, approximately 3 micron in length, made up of two opposing flexures followed by a straight helical segment approximately 23 micron long. The average wavelength is approximately 25 micron, and three to four sawtooth waves travel along the axostyle at one time. The bends are nearly planar and can travel in either direction along the axostyle with equal velocity. At temperatures between 5 degrees and 30 degrees C, one sees a proportionate increase or decrease in wave propagation velocity as the temperature is raised or lowered. Beating stops below 5 degrees C but will resume if the preparation is warmed. A microbeam of visible light shone on a small segment of the axostyle causes the typical sawtooth waves to transform into short sine-like waves that accumulate in the area irradiated. Waves entering the affected region appear to stimulate waves already accumulated there to move, and waves that emerge take on the normal sawtooth wave pattern. The effective wavelengths of visible light capable of modifying the wave pattern is in the blue region of the spectrum. The axostyle is severed when irradiated with an intense microbeam of UV light. Short segments of axostyle produced by severing it at two places with a UV microbeam can curl upon themselves into shapes resembling lockwashers. We propose that the sawtooth waves in the axostyle of P. vertens are generated by interrow cross-bridges which are active in the straight regions.     

Wave Propagation through a Viscous Incompressible Fluid Contained in an Initially Stressed Elastic Tube

To have a better understanding of the flow of blood in arteries a theoretical analysis of the pressure wave propagation through a viscous incompressible fluid contained in an initially stressed tube is considered. The fluid is assumed to be Newtonian. The tube is taken to be elastic and isotropic. The analysis is restricted to tubes with thin walls and to waves whose wavelengths are very large compared with the radius of the tube. It is further assumed that the amplitude of the pressure disturbance is sufficiently small so that nonlinear terms of the inertia of the fluid are negligible compared with linear ones. Both circumferential and longitudinal initial stresses are considered; however, their origins are not specified. Initial stresses enter equations as independent parameters. A frequency equation, which is quadratic in the square of the propagation velocity is obtained. Two out of four roots of this equation give the velocity of propagation of two distinct outgoing waves. The remaining two roots represent incoming waves corresponding to the first two waves. One of the waves propagates more slowly than the other. As the circumferential and/or longitudinal stress of the wall increases, the velocity of propagation and transmission per wavelength of the slower wave decreases. The response of the fast wave to a change in the initial stress is on the opposite direction.     

Reversible intracellular ATP changes in intact rat spermatozoa and effects on flagellar sperm movement.

The initiation of motility and modification of energy metabolism of rat caudal epididymal spermatozoa can be induced by dilution in a saline medium. We have investigated in these cells the relationships between the energy reserve (sperm ATP content measured by bioluminescence) and flagellar movement (high speed videomicrography, 200 frames/sec). A steady state was observed in sperm ATP content, progressive velocity (Vp) and flagellar beat frequency (F) with sperm dilution in a medium with glucose, lactate, pyruvate and acetate substrates after 30 minutes of incubation. Without these substrates, changes in metabolic pathways occurred immediately and initially disturbed the relationship between ATP levels and F, suggesting differences in motility initiation when energy is from an endogenous origin via mitochondrial oxidative phosphorylation. This "energy crisis" was reversed by the addition of substrates to the medium. The three-dimensional flagellar movement observed in the presence of substrates quickly became two-dimensional in their absence. The flagellar beat envelope became more splayed, the mean amplitude of lateral head displacement increased and F decreased. The resulting high flagellar beat efficiency can be compared to that observed during hyperactivation which is a physiological event related to a fall in intracellular ATP level. In both media, the displacement of the flagellum in relation to the wave axis varied sinusoidally. The sine period increased with time when the spermatozoa were incubated in the medium without substrates. These results suggest a gradual slowing-down of the velocity of wave formation in the proximal part of the flagellum.     

The movement of spermatozoa with helical head: theoretical analysis and experimental results.

The present work is concerned with the study of the swimming of flagellated microscopic organisms with a helical head and a helical pattern of flagellar beating, such as Xenopus sperms. The theoretical approach is similar to that taken by Chang and Wu (1971) in the study of helical flagellar movement. The model used in the present study allows us to determine the velocity of propulsion (U) and the frequency of rotation of the sperm head (fh) as a function of the frequency of the wave of motion (ft) traveling along the tail. The results relative to the case of helical and planar flagellar waves are compared. Our main finding is that the helical shape of the head seems to increase the efficiency of propulsion of the spermatozoon when compared with the more commonly shaped spherical head. Experimentally measured values of fh versus U may be fitted by a linear plot whose slope is much higher than that corresponding to the case of planar flagellar beating. This fact is consistent with an effectively three-dimensional (nonplanar) movement of the flagellar tail. However, the results do not fit those predicted from a circular helix, suggesting that a different shape of the flagellar beating should be considered.     

Uncertainty in Calculations of Net Primary Production for Grasslands

Net primary production (NPP) is a fundamental characteristic of all ecosystems and foundational to understanding the fluxes of energy and nutrients. Because NPP cannot be measured directly, researchers use field-measured surrogates as input variables in various equations designed to estimate ‘true NPP’. This has led to considerable debate concerning which equations most accurately estimate ‘true NPP’. This debate has influenced efforts to assess NPP in grasslands, with researchers often advocating more complex equations to avoid underestimation. However, this approach ignores the increase in statistical error associated with NPP estimates as a greater number of parameters and more complex mathematical functions are introduced into the equation. Using published grassland data and Monte Carlo simulation techniques, we assessed the relative variability in NPP estimates obtained using six different NPP estimation equations that varied in both the number of parameters and intricacy of mathematical operations. Our results indicated that more complex equations may result in greater uncertainty without reducing the probability of underestimation. The amount of uncertainty associated with estimates of NPP was influenced by the number of parameters as well as the variability in the data and the nature of the mathematical operations. For example, due to greater variability in the field-measured belowground data than aboveground data, estimates of belowground NPP tended to have more uncertainty than estimates of aboveground NPP. An analysis in which the input data were standardized allowed us to isolate the details of the calculations from the variability in the data in assessing the propagation of uncertainty. This analysis made clear that equations with product terms have the potential to magnify the uncertainty of the inputs in the estimates of NPP although this relationship was complicated by interactions with data variability and number of parameters. Our results suggest that more complex NPP estimation equations can increase uncertainty without necessarily reducing risk of underestimation. Because estimates can never be tested by comparison to “true NPP”, we recommend that researchers include an assessment of propagation of statistical error when evaluating the ‘best’ estimation method.     

Evidence for functional differences between two flagellar dynein ATPases

Energy coupling in flagellar motility was investigated using demembranated, reactivated sea urchin spermatozoa (Arbacia punctulata). The ATP-dependence of ATPase activity was investigated for ATP concentrations ranging from 4 microM to 600 microM ATP. Using Eadie-Scatchard plot analysis, we identified two axonemal dynein ATPase activities. Their apparent Michaelis constants were calculated to be equal to 4 microM and 161 microM ATP, and they were referred to, respectively, as the high-affinity dynein ATPase (HADA) and the low-affinity dynein ATPase (LADA). Investigation of movement-coupled ATPase activity (difference between the ATPase activities of reactivated and broken, immotile spermatozoa) indicated that HADA and LADA were both 65% movement-coupled. The apparent Michaelis constants of movement-coupled HADA and LADA, 12 microM and 271 microM ATP, respectively, were two- to four-fold greater than the apparent Michaelis constants of movement-uncoupled HADA and LADA. The apparent Michaelis constants for force generation and beat frequency of reactivated spermatozoa were determined to be 24 microM and 290 microM ATP, respectively. These results raise the possibility that flagellar force generation is controlled primarily by movement-coupled HADA, and that flagellar beat frequency is controlled primarily by movement-coupled LADA. Thus, mechanochemical activity in flagellar motility may be divided between two enzymatically and functionally distinct classes of flagellar dyneins.