Measurement of the force produced by an intact bull sperm flagellum in isometric arrest and estimation of the dynein stall force

The force generated by a detergent-extracted reactivated bull sperm flagellum during an isometric stall was measured with a force-calibrated glass microprobe. The average isometric stall force from 48 individual measurements was 2.5 +/- 0.7 x 10(-5) dyne (2.5 +/- 0.7 x 10(-10) N). The force measurements were obtained by positioning a calibrated microprobe in the beat path of sperm cells that were stuck by their heads to a glass microscope slide. The average position of the contact point of the flagellum with the probe was 15 microm from the head-tail junction. This average lever arm length multiplied by the measured force yields an estimate of the active bending moment (torque) of 3.9 x 10(-8) dyne x cm (3.9 x 10(-15) N x m). The force was sustained and was for the most part uniform, despite the fact that the flagellum beyond the point of contact with the probe usually continued beating. It appears that the dynein motors in the basal portion of the flagellum continue to pull in an isometric stall for as long as the motion of the flagellum is blocked. If dynein motors in the flagellum distal to the contact point with the probe were contributing force to the displacement of the probe, then the flagellar segment immediately past the point of contact would have to show a net curvature in the direction of the probe displacement. No such curvature bias was observed in the R-bend arrests, and only a small positive curvature bias was measured in the P-bend arrests. Our analysis of the data suggests that more than 90% of the sustained force component is generated by the part of the flagellum between the probe and the flagellar base. Based on this premise, the isometric stall force per dynein head is estimated to be 5.0 x 10(-7) dyne (5 pN). This equals approximately 1.0 x 10(-6) dyne (10 pN) per intact dynein arm. These values are close to the isometric stall force of isolated dynein. This suggests that all of the dynein heads between the base and the probe, on the active side of the axoneme, are contributing to the force exerted against the probe.     

Progression of flagellar stages during artificially delayed motility initiation in sea urchin sperm

Transition from immotile to motile flagella may involve a series of states, in which some of regulatory mechanisms underlying normal flagellar movement are working with others being still suppressed. To address ourselves to the study of starting transients of flagella, we analyzed flagellar movement of sea urchin sperm whose motility initiation had been retarded in an experimental solution, so that we could capture the instance at which individual spermatozoa began their flagellar beating. Initially straight and immotile flagella began to shiver at low amplitude, then propagated exclusively the principal bend (P bend), and finally started stable flagellar beating. The site of generation of the P bend in the P-bend propagating stage varied in position in the basal region up to 10 microm from the base, indicating that the ability of autonomous bend generation is not exclusively possessed by the very basal region but can be unmasked throughout a wider region when the reverse bend (R bend) is suppressed. The rate of change in the shear angle, the curvature of the R bend and the frequency and regularity of beating substantially increased upon transition from P-bend propagating to full-beating, while the propagation velocity of bends remained unchanged. These findings indicate that artificially delayed motility initiation may accompany sequential modification of the motile system and that mechanisms underlying flagellar motility can be analyzed separately under experimentally retarded conditions.     

The Bacillus subtilis catabolite control protein CcpA exerts all its regulatory functions by DNA-binding

Swimming speed (v) and flagellar-bundle rotation rate (f) of Salmonella typhimurium, which has peritrichous flagella, were simultaneously measured by laser dark-field microscopy (LDM). Clear periodic changes in the LDM signals from a rotating bundle indicated in-phase rotation of the flagella in the bundle. A roughly linear relation between v and f was observed, though the data points were widely distributed. The ratio of v to f (v-f ratio), which indicates the propulsive distance during one flagellar rotation, was 0.27 microm (11% of the flagellar pitch) on average. The experimental v-f ratio was twice as large as the calculated one on the assumption that a cell had a single flagellum. A flagellar bundle was considered to propel a cell more efficiently than a single flagellum.     

The effect of sulfhydryl oxidation on the morphology of immature hamster epididymal spermatozoa induced to acquire motility in vitro

Immotile spermatozoa from the caput epididymidis become progressively motile when incubated in medium containing theophylline, seminal plasma, and albumin. We previously reported that under these incubation conditions the spermatozoa induced to acquire motility exhibited a marked flagellar angularity, with the sperm head or midpiece bent 90-180 degrees towards the tail. In addition, we demonstrated that sperm flagellar bending did not occur when the sulfhydryl oxidant diamide was added to the motility induction medium. In the present study, we examined further the effect of sulfhydryl oxidation on the morphology and sulfhydryl content of immature caput spermatozoa induced to acquire motility in vitro. We found that flagellar bending was prevented and sperm flagellar straightness was maintained in a dose-dependent manner by diamide. Moreover, flow cytometric analysis of caput sperm sulfhydryls using the sulfhydryl reagent monobromobimane (mBBr) revealed that 1) diamide oxidizes caput sperm sulfhydryls, and 2) less than 15% of the total reactive sperm sulfhydryls were oxidized at diamide concentrations capable of preventing sperm angulation. Sodium tetrathionate (NaTT), another sulfhydryl oxidant, and hamster cauda epididymal fluid (CEF) containing sulfhydryl oxidase enzyme activity also maintained flagellar straightness in induced caput spermatozoa and oxidized sperm sulfhydryls. The flagellar straightness in caput spermatozoa treated with sulfhydryl oxidants, however, was temporary; with extended incubation, diamide- or CEF-treated spermatozoa exhibited flagellar bending. Additional studies showed that the flagellar straightness observed in sulfhydryl-oxidized spermatozoa was sustained when nitrofurantoin, an inhibitor of glutathione reductase, was included in the induction medium. Flow cytometric analysis of nitrofurantoin-treated spermatozoa showed that nitrofurantoin maintained the sperm disulfides formed by diamide and prevented the reduction of sperm disulfides back to sulfhydryls. Taken together, these studies demonstrate the significance of sulfhydryl oxidation in maintaining the morphology of immature caput epididymal spermatozoa induced to acquire motility in vitro and suggest that sulfhydryl oxidation may be important in the development of motility during sperm epididymal maturation in vivo.     

Roles of cAMP in regulating microtubule sliding and flagellar bending in demembranated hamster spermatozoa

To understand the mechanism regulating spermatozoa motility, it is important to investigate the mechanism regulating the conversion of microtubule sliding into flagellar bending. Therefore, we analyzed microtubule sliding and its conversion into flagellar bending using a demembranated spermatozoa model in which microtubule sliding and flagellar bending could be analyzed separately by treating the demembranated spermatozoa with and without dithiothreitol, respectively. Using this model, we examined the roles of cAMP and its target molecules in regulating flagellar bending and microtubule sliding. Although flagellar bending did not occur in the absence of cAMP, microtubule extrusion occurred without it, suggesting that cAMP is necessary for the conversion of microtubule sliding into flagellar bending, but not for microtubule sliding itself. The target of cAMP for regulating flagellar bending was not cAMP-dependent protein kinase (PKA), since flagellar bending was still observed in the spermatozoa treated with a PKA-specific inhibitor. Alternatively, the Epac/Rap pathway may be the target. Epac2 and Rap2 were detected in hamster spermatozoa using immunoblotting. Since Rap2 is a GTPase, we investigated the flagellar bending of demembranated spermatozoa treated with GTPgammaS. The treatment markedly increased the beat frequency and bending rate. These results suggest that cAMP activates the Epac/Rap pathway to regulate the conversion of microtubule sliding into flagellar bending.     

Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory.

This paper investigates the accuracy of the resistive-force theory (Gray and Hancock method) which is commonly used for hydrodynamic analysis of swimming flagella. We made a comparison between the forces, bending moments, and shear moments calculated by resistive-force theory and by the more accurate slender-body theory for large-amplitude, planar wave forms computed for a flagellar model. By making an upward empirical adjustment, by about 35%, of the classical drag coefficient values used in the resistive-force theory calculations, we obtained good agreement between the distributions of the forces and moments along the length of the flagellum predicted by the two methods when the flagellum has no cell body attached. After this adjustment, we found the rate of energy expenditure calculated by the two methods for the few typical test cases to be almost identical. The resistive-force theory is thus completely satisfactory for use in analysis of mechanisms for the control of flagellar bending, at the current level of sophistication of this analysis. We also examined the effects of the presence of a cell body attached to one end of the flagellum, which modifies the flow field experienced by the flagellum. This interaction, which is not considered in resistive-force theory, is probably insignificant for small cell bodies, such as the heads of simple spermatozoa, but for larger cell bodies, or cell bodies that have large-amplitude motions transverse to the swimming direction, use of slender-body theory is required for accurate analysis.     

Morphology and ultrastructure of Siberian sturgeon (Acipenser baerii) spermatozoa using scanning and transmission electron microscopy

BACKGROUND INFORMATION: Available data concerning the sperm morphology of teleost fishes demonstrate wide variation. In the present study, the spermatozoa of Siberian sturgeon (Acipenser baerii Brandt, 1869), a chondrostean fish, was investigated. In contrast with teleost fish, chondrostean spermatozoa have a head with a distinct acrosome, whereas other structures, such as a midpiece and a single flagellum, are present in spermatozoa of most species. RESULTS: The average length of the head including the acrosome and the midpiece was 7.01+/-0.83 microm. Ten posterolateral projections derived from the acrosome were present on a subacrosomal region, with mean lengths of 0.94+/-0.15 microm and widths of 0.93+/-0.11 microm. The nucleus consisted of electrodense homogeneous nuclear chromatin. Three intertwining endonuclear canals, bound by membranes, traversed the nucleus longitudinally from the acrosomal end to the basal nuclear fossa region. There were between three and six mitochondria, two types of centrioles (proximal and distal) in the midpiece and two vacuoles composed of lipid droplets. The flagellum (44.75+/-4.93 microm in length), originating from the centriolar apparatus, had a typical 9+2 eukaryotic flagellar organization. In addition, there was an extracellular cytoplasm canal between the cytoplasmic sheath and the flagellum. CONCLUSIONS: A principal components analysis explained the individual morphological variation fairly well. Of the total accumulated variance, 41.45% was accounted for by parameters related to the head and midpiece of the sperm and the length of the flagellum. Comparing the present study with previous studies of morphology of sturgeon spermatozoa, there were large inter- or intra-specific differences that could be valuable taxonomically.     

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.     

Movement of turritella spermatozoa: direction of propagation and chirality of flagellar bends.

The marine snail, Turritella communis, produces two types of spermatozoa, named apyrene and eupyrene. Eupyrene spermatozoa are usually paired, but unpaired ones are involved in fertilization. Movements of these spermatozoa were analyzed using a video camera with a high-speed shutter. The eupyrene spermatozoa usually swim with the head foremost but are able to swim flagellum foremost. A reversal of the direction of their swimming was found to be the result of a change in the direction of flagellar bend propagation, which changed with calcium concentration. Reversal of the direction of bend propagation was accompanied by a reversal of direction of the rotational movement of the spermatozoa around their long axis, suggesting that the bending waves keep the sense of their three-dimensional form. The swimming speed of apyrene spermatozoa in natural seawater was about one-eighth of that of the eupyrene ones and remained almost constant in highly viscous medium.The swimming speed of conjugated eupyrene spermatozoa was the same as that of unpaired spermatozoa over a wide viscosity range (<3,000 cP). No advantage of swimming by two spermatozoa could be detected in Turritella spermatozoa.     

Evolution of the flagellar waveform of ram spermatozoa in relation to the degree of epididymal maturation.

Motility and flagellar movement of ram spermatozoa along the epididymis were analysed in vitro. From the caput to the cauda of the epididymis, the percentage of motile and progressive spermatozoa increases. No flagellar bending was observed in spermatozoa from the testis or the epididymal anterior caput. When spermatozoa reached the distal caput of the epididymis, a static curvature, associated with an initiation of the flagellar beating, appeared on the flagella. This curvature normally disappeared during epididymal transit. Its disappearance was associated with an increase in the flagellar beat efficiency. Our results suggest that the initiation of motility is related to two mechanisms involving: (1) the presence of a transient static curvature, and (2) the establishment of a symmetric regular beating of the flagellum.     

Inhibition of tyrosine phosphorylation of sperm flagellar proteins,outer dense fiber protein‐2 and tektin‐2, is associated with impaired motility during capacitation of hamster spermatozoa

In mammals, acquisition of fertilization competence of spermatozoa is dependent on the phenomenon of sperm capacitation. One of the critical molecular events of sperm capacitation is protein tyrosine phosphorylation. In a previous study, we demonstrated that a specific epidermal growth factor receptor (EGFR)‐tyrosine kinase inhibitor, tyrphostin‐A47, inhibited hamster sperm capacitation, accompanied by a reduced sperm protein tyrosine phosphorylation. Interestingly, a high percentage of tyrphostin‐A47‐treated spermatozoa exhibited circular motility, which was associated with a distinct hypo‐tyrosine phosphorylation of flagellar proteins, predominantly of Mr 45,000–60,000. In this study, we provide evidence on the localization of capacitation‐associated tyrosine‐phosphorylated proteins to the nonmembranous, structural components of the sperm flagellum. Consistent with this, we show their ultrastructural localization in the outer dense fiber, axoneme, and fibrous sheath of spermatozoa. Among hypo‐tyrosine phosphorylated major proteins of tyrphostin‐A47‐treated spermatozoa, we identified the 45 kDa protein as outer dense fiber protein‐2 and the 51 kDa protein as tektin‐2, components of the sperm outer dense fiber and axoneme, respectively. This study shows functional association of hypo‐tyrosine‐phosphorylation status of outer dense fiber protein‐2 and tektin‐2 with impaired flagellar bending of spermatozoa, following inhibition of EGFR‐tyrosine kinase, thereby showing the critical importance of flagellar protein tyrosine phosphorylation during capacitation and hyperactivation of hamster spermatozoa. Mol. Reprod. Dev. 77: 182–193, 2010. © 2009 Wiley‐Liss, Inc.     

Calcium-induced asymmetrical beating of triton-demembranated sea urchin sperm flagella

Asymmetrical bending waves can be obtained by reactivating demembranated sea urchin spermatozoa at high Ca2+ concentrations. Moving-film flash photography shows that asymmetrical flagellar bending waves are associated with premature termination of the growth of the bends in one direction (the reverse bends) while the bends in the opposite direction (the principal bends) grow for one full beat cycle, and with unequal rates of growth of principal and reverse bends. The relative proportions of these two components of asymmetry are highly variable. The increased angle in the principal bend is compensated by a decreased angle in the reverse bend, so that there is no change in mean bend angle; the wavelength and beat frequency are also independent of the degree of asymmetry. This new information is still insufficient to identify a particular mechanism for Ca2+-induced asymmetry. When a developing bend stops growing before initiation of growth of a new bend in the same direction, a modification of the sliding between tubules in the distal portion of the flagellum is required. This modification can be described as a superposition of synchronous sliding on the metachronous sliding associated with propagating bending waves. Synchronous sliding is particularly evident in highly asymmetrical flagella, but is probably not the cause of asymmetry. The control of metachronous sliding appears to be unaffected by the superposition of synchronous sliding.     

Topographical relationship between the axonemal arrangement and the bend direction in starfish sperm flagella

Since starfish spermatozoa have spherical heads, it is not easy to determine the topographical relationship of the axoneme to the directions of the flagellar bends, the principal, and the reverse bends as defined by Gibbons and Gibbons [J. Cell. Biol. 1972, 63:970-985]. The demembranated spermatozoa are known to take the quiescent "cane" shape with a sharp principal bend at the proximal region of the flagellum in the presence of high concentration of Ca2+. When such spermatozoa were placed on a grid for electron microscopy, fixed with osmic acid vapor, washed with distilled water, and negatively stained with uranyl acetate, the head of the spermatozoon was disrupted and dispersed disclosing the proximal centriole at the proximal end of the flagellum. The proximal centriole was always found on the concave side of the "cane"-shaped flagella. Electron microscopy of the serial thin sections of intact and demembranated spermatozoa revealed that the doublet microtubules numbers 5 and 6 were contained in the convex edge of the principal bend.     

Determination of the average shape of flagellar bends: a gradient curvature model

Data obtained by manual digitization of photographs of flagellar bending waves have been analyzed by determining size parameters for the bends by least-squares fitting of a model waveform. These parameters were then used to normalize the data so that the average shape of the bends could be determined. Best fits were obtained with a model waveform derived from the constant curvature waveforms used previously but with provision for a linear change in curvature across the central region of the bend-the gradient curvature model (GCM). The central regions of the GCM bending waves are separated by transition regions with length determined by a parameter called the truncation factor (FT). Fitting the GCM to sine-generated bending waves give optimal fit when FT = 0.34. Fitting the GCM to four different samples of flagellar bending waves gave best fits with values of FT ranging from 0.17 for ATP-reactivated Lytechinus spermatozoa beating at approximately 10 Hz to 0.32 for live spermatozoa of Arbacia. The difference between the Arbacia waveforms and a sine-generated waveform is therefore very small, but a sine-generated waveform lacks the degree of freedom represented by FT that is required to fit other waveforms optimally. The residual differences between the waveform data and optimal GCM waveforms were averaged and found to be small. In most cases, the curvature in the central region of the optimal GCM decreased in magnitude towards the tip of the flagellum; however, this slope was highly variable and sometimes positive. Significant variations in both this slope and FT were found in individual bends as they propagated along a flagellum.     

Motility of triton-demembranated sea urchin sperm flagella during digestion by trypsin

The survival curves for a population of reactivated spermatozoa exposed to digestion by trypsin indicate that a large number of trypsin-sensitive targets must be digested before the flagellum disintegrates. Changes in flagellar movement during trypsin digestion can be very small, especially when the spermatozoa are reactivated at 0.25 M KCl. They are not the changes which would be expected if elastic resistance of the trypsin-sensitive structures responsible for maintaining the integrity of the axoneme is a significant determinant of flagellar bend amplitude. By carrying out trypsin digestion under a variety of conditions, at least six distinct effects of trypsin digestion on parameters of flagellar movement have been detected. These include a gradual increase in the rate of sliding between tubules, gradual and abrupt changes in beat frequency accompanied by reciprocal decreases in bend angle, changes in the symmetry and planarity of bending, and selective interference with mechanisms for bend initiation and bend propagation.     

Computer simulation of flagellar movement VIII: coordination of dynein by local curvature control can generate helical bending waves

Computer simulations have been carried out with a model flagellum that can bend in three dimensions. A pattern of dynein activation in which regions of dynein activity propagate along each doublet, with a phase shift of approximately 1/9 wavelength between adjacent doublets, will produce a helical bending wave. This pattern can be termed "doublet metachronism." The simulations show that doublet metachronism can arise spontaneously in a model axoneme in which activation of dyneins is controlled locally by the curvature of each outer doublet microtubule. In this model, dyneins operate both as sensors of curvature and as motors. Doublet metachronism and the chirality of the resulting helical bending pattern are regulated by the angular difference between the direction of the moment and sliding produced by dyneins on a doublet and the direction of the controlling curvature for that doublet. A flagellum that is generating a helical bending wave experiences twisting moments when it moves against external viscous resistance. At high viscosities, helical bending will be significantly modified by twist unless the twist resistance is greater than previously estimated. Spontaneous doublet metachronism must be modified or overridden in order for a flagellum to generate the planar bending waves that are required for efficient propulsion of spermatozoa. Planar bending can be achieved with the three-dimensional flagellar model by appropriate specification of the direction of the controlling curvature for each doublet. However, experimental observations indicate that this "hard-wired" solution is not appropriate for real flagella.     

Polar flagellar motility of the Vibrionaceae.

Polar flagella of Vibrio species can rotate at speeds as high as 100,000 rpm and effectively propel the bacteria in liquid as fast as 60 microm/s. The sodium motive force powers rotation of the filament, which acts as a propeller. The filament is complex, composed of multiple subunits, and sheathed by an extension of the cell outer membrane. The regulatory circuitry controlling expression of the polar flagellar genes of members of the Vibrionaceae is different from the peritrichous system of enteric bacteria or the polar system of Caulobacter crescentus. The scheme of gene control is also pertinent to other members of the gamma purple bacteria, in particular to Pseudomonas species. This review uses the framework of the polar flagellar system of Vibrio parahaemolyticus to provide a synthesis of what is known about polar motility systems of the Vibrionaceae. In addition to its propulsive role, the single polar flagellum of V. parahaemolyticus is believed to act as a tactile sensor controlling surface-induced gene expression. Under conditions that impede rotation of the polar flagellum, an alternate, lateral flagellar motility system is induced that enables movement through viscous environments and over surfaces. Although the dual flagellar systems possess no shared structural components and although distinct type III secretion systems direct the simultaneous placement and assembly of polar and lateral organelles, movement is coordinated by shared chemotaxis machinery.     

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.     

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.     

Flagellar movement of human spermatozoa

Flagellar movement of human spermatozoa held by their heads with a micropipette was recorded by means of a video-strobe system. Spermatozoa were studied in normal Hanks' solution, Hanks' solution with increased viscosity, cervical mucus, and hyaluronic acid. When flagellar movement in normal Hanks' solution was observed from the direction parallel to the beating plane, segments of the flagellum in focus did not lie on a straight line but on two diverging dashed lines. The distance between the two dashed lines was about 20% of the bend amplitude in the major beating plane. These observations indicate that flagellar beating of human spermatozoa in normal Hanks' solution is not planar. In contrast, segments of the flagellum in focus lay on a straight line when the spermatozoa were observed in Hanks' solution with increased viscosity, cervical mucus, or hyaluronic acid. In normal Hanks' solution, free swimming spermatozoa rotated constantly around their longitudinal axes with a frequency similar to the beat frequency, whereas little or no rotation of spermatozoa occurred in Hanks' solution with increased viscosity, in cervical mucus, or in hyaluronic acid. We conclude that human spermatozoa in normal Hanks' solution beat with a conical helical waveform having an elliptical cross section, the semiaxes of which have a ratio of 0.2. The three-dimensional geometry of the flagellar movement is responsible for the rotation of the sperm around their longitudinal axes.