Flagellar Bending Waves Research Articles

Reconstruction of the three-dimensional beat pattern underlying swimming behaviors of sperm

The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior.Graphic abstract

Micromotor-mediated sperm constrictions for improved swimming performance

Sperm-driven micromotors, consisting of a single sperm cell captured in a microcap, utilize the strong propulsion generated by the flagellar beat of motile spermatozoa for locomotion. It enables the movement of such micromotors in biological media, while being steered remotely by means of an external magnetic field. The substantial decrease in swimming speed, caused by the additional hydrodynamic load of the microcap, limits the applicability of sperm-based micromotors. Therefore, to improve the performance of such micromotors, we first investigate the effects of additional cargo on the flagellar beat of spermatozoa. We designed two different kinds of microcaps, which each result in different load responses of the flagellar beat. As an additional design feature, we constrain rotational degrees of freedom of the cell’s motion by modifying the inner cavity of the cap. Particularly, cell rolling is substantially reduced by tightly locking the sperm head inside the microcap. Likewise, cell yawing is decreased by aligning the micromotors under an external static magnetic field. The observed differences in swimming speed of different micromotors are not so much a direct consequence of hydrodynamic effects, but rather stem from changes in flagellar bending waves, hence are an indirect effect. Our work serves as proof-of-principle that the optimal design of microcaps is key for the development of efficient sperm-driven micromotors.Graphic

The counterbend dynamics of cross-linked filament bundles and flagella

Cross-linked filament bundles, such as in cilia and flagella, are ubiquitous in biology. They are considered in textbooks as simple filaments with larger stiffness. Recent observations of flagellar counterbend, however, show that induction of curvature in one section of a passive flagellum instigates a compensatory counter-curvature elsewhere, exposing the intricate role of the diminutive cross-linking proteins at large scales. We show that this effect, a material property of the cross-linking mechanics, modifies the bundle dynamics and induces a bimodal L2 - L3 length-dependent material response that departs from the Euler-Bernoulli theory. Hence, the use of simpler theories to analyse experiments can result in paradoxical interpretations. Remarkably, the counterbend dynamics instigates counter-waves in opposition to driven oscillations in distant parts of the bundle, with potential impact on the regulation of flagellar bending waves. These results have a range of physical and biological applications, including the empirical disentanglement of material quantities via counterbend dynamics.

Active phase and amplitude fluctuations of flagellar beating.

The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit-cycle reconstruction. We report a quality factor of flagellar oscillations Q = 38.0 ± 16.7 (mean ± s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems.

Cyclic nucleotide-gated channels on the flagellum control Ca2+ entry into sperm.

Cyclic nucleotide-gated (CNG) channels are key elements of cGMP- and cAMP-signaling pathways in vertebrate photoreceptor cells and in olfactory sensory neurons, respectively. These channels form heterooligomeric complexes composed of at least two distinct subunits (alpha and beta). The alpha subunit of cone photoreceptors is also present in mammalian sperm. Here we identify one short and several long less abundant transcripts of beta subunits in testis. The alpha and beta subunits are expressed in a characteristic temporal and spatial pattern in sperm and precursor cells. In mature sperm, the alpha subunit is observed along the entire flagellum, whereas the short beta subunit is restricted to the principal piece of the flagellum. These findings suggest that different forms of CNG channels coexist in the flagellum. Confocal microscopy in conjunction with the Ca2+ indicator Fluo-3 shows that the CNG channels serve as a Ca2+ entry pathway that responds more sensitively to cGMP than to cAMP. Assuming that CNG channel subtypes differ in their Ca2+ permeability, dissimilar localization of alpha and beta subunits may give rise to a pattern of Ca2+ microdomains along the flagellum, thereby providing the structural basis for control of flagellar bending waves.

Rotating the plane of imposed vibration can rotate the plane of flagellar beating in sea-urchin sperm without twisting the axoneme

When the head of a sea-urchin sperm is held in the tip of a micropipette and vibrated laterally, the flagellum beats in phase with the imposed vibration. Rotation of the plane of pipette vibration around the head axis induces a corresponding rotation of the plane of beating, in both live and reactivated sperm. Detailed analysis of the waveforms occurring at different stages of this rotation shows that the characteristic asymmetry of the flagellar bending waves rotates along with the plane of beat. The positions of small polystyrene beads attached as markers on the axonemes of demembranated sperm flagella appear unaffected by the rotation of the beat plane and asymmetry. The imposed rotation of the waveform is thus the result of a rotation of the coordinated pattern of sliding among the doublet tubules of the axoneme, and is not accompanied by a twisting of the whole axonemal structure. These data indicate that neither the plane of flagellar beat nor the direction of beat asymmetry is tightly dependent upon a structural or chemical specialization of particular members of the nine outer doublet microtubules, but that both are the result of some regulatory structure that can be forced to rotate relative to the outer structure of the axoneme.

Calcium sensors in sea urchin sperm flagella

The asymmetry of ATP-reactivated flagellar bending waves of Triton-demembrated sea urchin spermatozoa has been measured over a range of free Ca2+ ion concentrations from 10(-9) to 10(-4) M. Detailed examination of the gradual response of asymmetry to Ca2+ ion concentration over this wide range indicates the presence of two Ca2+ sensors. A high-affinity sensor operates at Ca2+ concentrations near 10(-7.5) M. A lower-affinity sensor operates at Ca2+ concentrations above 10(-6) M, in the typical range for calmodulin-mediated responses. Incubation of demembranated sperm flagella at high Ca2+ concentrations to release calmodulin is required to enable these Ca2+ responses to be observed. This treatment also causes a decrease in the apparent affinity of the flagella for calmodulin, as determined by measuring the increase in asymmetry in response to addition of exogenous calmodulin at low Ca2+ concentration.

Flagellar oscillation: new vibes from beads

The oscillatory mechanism of eukaryotic flagella and cilia remains one of the mysteries of cell biology. It has been difficult to dissect the oscillation functionally when its coupling to the bending of the flagellum has been required to provide a read-out of the functioning of the oscillator. A way around this difficulty is now provided by work from several laboratories, involving the attachment of submicrometer diameter beads to microtubules as indicators of dynein-driven movement of microtubules. No one considers the flagellar oscillator to be a purely biochemical oscillator, since its frequency, and other properties of flagellar bending waves, can be significantly altered by external mechanical influences (reviewed by Brokaw, 1989a). Flagella can be described as highpowered mechanochemical oscillators that operate at the subcellular level. The oscillatory mechanism of the dynein-microtubule system in flagella is therefore comparable to that of the myosin-actin system of insect fibrillar flight muscle (Pringle, 1957). However, flagella oscillate at frequencies ranging from less than 1 cycle per second to more than 100 cycles per second, with microtubule sliding amplitudes of 100 nm or more, while fibrillar muscles oscillate at frequencies up to 1000 cycles per second, but with local amplitudes usually of the order of 10 nm.

External mechanical control of the timing of bend initiation in sea urchin sperm flagella.

The movement parameters of a sea urchin sperm flagellum can be manipulated mechanically by applying various modes of periodic vibrations to the sperm head held by suction in the tip of a micropipette. The beat frequency of the flagellum readily synchronizes with the frequency of the externally imposed lateral vibration, and the plane of flagellar bending waves adapts itself to the plane of the pipette vibration (Gibbons et al., J. Cell Biol. 101:270a, 1985; Nature 325: 351-352, 1987). In this study, we observed the particular effects of external asymmetric forces on flagellar beating parameters by vibrating the micropipette holding the sperm head in a transverse sawtooth-like motion composed of a rapid effective stroke and a slower recovery stroke, while keeping the vibration frequency constant. The results demonstrate that the timing of bend initiation within the flagellar beat cycle can be controlled mechanically by changing the time point within the vibration cycle at which the micropipette changes its direction of motion. A switch in the sidedness of the asymmetric movement of the micropipette produces dramatic changes in the profiles of bend growth in the basal 5 microns of the flagellum but has almost no effect on the asymmetry or other parameters of bending in the mid- and distal regions of the flagellum. Our results suggest that elastic strain within the basal region of the flagellar structure may play a more significant role in the process of bend initiation than has been realized heretofore.

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.

Regulation of sperm flagellar motility by calcium and cAMP-dependent phosphorylation.

There is substantial evidence that cAMP-dependent phosphorylation is involved in the activation of motility of spermatozoa as they are released from storage in the male reproductive tract. This evidence includes observations that in vivo activation of motility can be inhibited by protein kinase inhibitors, can be reversed by protein phosphatase treatment of demembranated spermatozoa, and is associated with phosphorylation of sperm proteins, and observations that spermatozoa that have not been activated in vivo can be activated in vitro by cAMP-dependent phosphorylation. Activation in vivo can often be triggered by conditions that increase intracellular pH, but the relevance of this to in vivo activation under natural conditions and the steps between pH increase and cAMP increase have not been fully established. The relationships between changes in the protein substrates for cAMP-dependent phosphorylation and changes in axonemal function are still unknown. Sperm chemotaxis to egg secretions is widespread; in the sea urchin Arbacia, the egg jelly peptide resact has been identified as a chemoattractant. Response to chemoattractants involves changes in asymmetry of flagellar bending waves, and similar changes in asymmetry can be produced in vitro by increases in [Ca++]. Temporal changes in resact receptor occupancy might lead to transient changes in intracellular [Ca++] and the asymmetry of flagellar bending, but many links in this hypothetical sequence remain to be established. Both of these signalling systems offer immediate opportunities for investigations of biochemical pathways leading to easily assayable biological responses. However, complications resulting from interactions between these two systems need to be considered.

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.

Future directions for studies of mechanisms for generating flagellar bending waves.

Future directions for studies of mechanisms for generating flagellar bending waves.

Computer simulation of bend propagation by axoplasmic microtubules

The generation of bending waves by microtubules in squid nerve axoplasm has been modelled using appropriately modified versions of computer programs developed previously for simulation of flagellar bending waves. The results confirm that a constant longitudinal force directed along the axis of the microtubule is sufficient to cause the generation of regular oscillations and propagated bending waves when the forward gliding movement of the microtubule is obstructed. No control mechanism is required to modulate the active force-generating system. In order to obtain bending waves similar to those observed experimentally, it was necessary to use a model for the force-generating system in which the active force decreases with increasing sliding velocity. If the elastic bending resistance of axoplasmic microtubules is similar to that of microtubules in sperm terminal filaments, the longitudinal force per unit length generated by the axoplasmic microtubules must be of the same order of magnitude as the force generated by dynein arms along the doublet microtubules of eukaryotic flagella.

Calcium‐induced change in form of demembranated sea urchin sperm flagella immobilized by vanadate

AbstractIncreased Ca2+ concentration causes a reversible increase in asymmetry of the flagellar bending waves of “potentially symmetric” demembranated sea urchin spermatozoa. When these flagella are immobilized with 5 μM vanadate, increased Ca2+ concentration causes a reversible increase in the total bend angle between the tip and the base of the immobilized flagella. These effects of Ca2+, and the movement which can be activated by CaATP2−, can be inhibited by vanadate, but in both cases, high concentrations of vanadate, of the order of 100 μM, are required. These observations suggest that ATP, possibly in the form of CaATP2−, is required for the Ca2+‐induced change in shape of the flagella, but other observations suggest that the magnitudes of asymmetry and total bend angle are more closely related to Ca2+ concentration than to CaATP2− concentration.

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.

The effect of antidynein 1 serum on the movement of reactivated sea urchin sperm.

Rabbit antiserum prepared against an ATPase-containing tryptic fragment of dynein by Ogawa and Mohri (J. Biol. Chem. 250: 6476-6483) specifically inhibited the ATPase activity of dynein 1 and not that of dynein 2. Varying amounts of this antidynein 1 serum were added to demembranated sperm while they were swimming in reactivating solution containing 1 mM ATP. The sperm continued to form regularly propagated flagellar bending waves, but the beat frequency decreased gradually with time, the greater part of the change occurring in the first 15 min. The beat frequency after 1 h was a function of the amount of antiserum used, and could be as low as 1 Hz. The waveforms of the treated sperm resembled those of normal reactivated sperm except that the bend angles of both the principal and reverse bends were larger in the proximal portion of flagellum. The ATPase activity and corresponding beat frequency of sperm which had been pretreated with varying amounts of antidynein 1 serum for 15 min at 0 degrees C and then diluted were both decreased as a function of the amount of antiserum added, the ATPase activity of homogenized, nonmotile sperm also decreased upon pretreatment with antiserum, but the percentage decrease was less than for motile sperm. For moderate to low concentrations of antiserum, the rates of reaction with motile and with rigor sperm were almost identical. The overall results suggest that antidynein 1 inhibits the functioning of the dynein arms, probably by blocking the ATPase sites of the dynein 1.

Maintenance of Constant Wave Parameters by Sperm Flagella at Reduced Frequencies of Beat

ABSTRACT Treatment of Ciona spermatozoa with low concentrations of Triton X-100 (less than 0·01 %) causes them to beat at lower than normal frequencies. The wavelength of the flagellar bending waves remains constant over the range from 10 to 40 Hz. There is a small increase in wavelength at lower frequencies; in the range of 1·5–6·2 Hz, the wavelength averaged 114% of the normal value for Ciona spermatozoa. The angle of bend of the bent regions of the flagellar bending waves remained constant within ± 10% over this range of frequencies. Decapitated sperm flagella from Lytechinus beat at a continually declining frequency as they exhaust their content of ATP. Both wavelength and bend angle retain normal values until the frequency falls below about 8 Hz. Both parameters increase at lower frequencies, with a sharp increase below 3 Hz. ATP-reactivated spermatozoa from Lytechinus show relatively small changes in wavelength and bend angle as the frequency is varied over the range from 5 to 25 Hz by varying the ATP concentration. Constancy of wavelength over a wide range of frequencies is consistent with the hypothesis that wavelength is determined by the relative values of viscous bending resistance within a flagellum and external viscosity. No satisfactory explanation is available at present for the constancy of bend angle over a wide range of frequencies nor for the changes in wave parameters which are observed at low frequencies.

The effect of partial extraction of dynein arms on the movement of reactivated sea-urchin sperm.

ABSTRACT Sea-urchin sperm were extracted with 0 · 5 M KC1 for 45 s at room temperature in the presence of Triton X-100, and then transferred to reactivating solution containing 1 mM ATP. The flagellar beat frequency of these KCl-extracted sperm (16 beats/s) was only about half that of control Triton-extracted sperm that had not been exposed to 0 · 5 M KC1 (31 beats/salthoughthe form of their bending waves was not significantly altered. Examination by electron microscopy showed that the extraction with 0 · 5 M KC1 removed the majority of the outer arms from the doublet tubules, leaving the inner arms apparently intact. By varying the duration of the KCl-extraction, it was shown that the rate of decrease in beat frequency paralleled the rate of disappearance of the arms. Prolonging the extraction time beyond 45 3 at room temperature, or 4 min at o°C, had little further effect on beat frequency. ATPase measurements suggested that 60—65 % of the dynein in the original axonemes had been solubilized when the extraction with KC1 was permitted to go to completion. These results indicate that the generation and propagation of flagellar bending waves of essentially typical form are not prevented by the removal of the outer row of dynein arms from the doublet tubules. In terms of the sliding filament model of flagellar bending, the results suggest that the rate of sliding between tubules under these conditions is proportional to the number of dynein arms present. The lack of significant change in wave form implies that the total amount of sliding that occurs during each bending cycle is not affected by the reduced number of dynein arms, but is regulated independently in some manner by the elastic forces generated by other structures in the bent axoneme.

Flagellar movement: a sliding filament model.

A sliding filament mechanism appears to provide the most satisfactory basis for a simple feedback mechanism for the control of bend propagation and bend initiation by flagella, and is supported by strong experimental evidence. A computer simulation of the movements of a flagellar model based on the sliding filament mechanism demonstrates that this mechanism offers a sufficient explanation for the automatic generation of flagellar bending waves. Further computer simulation studies may provide insight into questions such as the applicability of the sliding filament mechanism to the generation of the more complicated asymmetrical bending patterns of cilia, and the control of the bending pattern by interaction between several sliding filament systems within a flagellum.