Direct measurement of the passive stiffness of rat sperm and implications to the mechanism of the calcium response

Glass microprobes were used to measure the stiffness of the flagella of Triton X-100-extracted rat sperm models. The sperm models were treated with 50 microM sodium vanadate and 0.1 mM Mg-ATP to evaluate the stiffness of the passive flagellar structure without the influence of the dynein motor proteins. The passive stiffness was determined to be 4.6 (+/- 1.1) x 10(-19) N x m(2). Rat sperm models exposed to greater than 10(-5) M calcium ions exhibit a strong bend in the basal 40 microm of the flagellum, resulting in a fishhook-like appearance. The torque required to bend a passive rat sperm flagellum into the fishhook-like configuration was determined. The result was compared to the previously published measurement of the torque required to straighten the flagella of rat sperm in the Ca(2+)-induced fishhook configuration [Moritz et al., 2001: Cell Motil. Cytoskeleton 49:33-40]. The torque required to induce a fishhook in a passive flagellum was 2.7 (+/- 0.7) x 10(-14) N x m and the torque to straighten an active Ca(2+)-induced fishhook was 2.6 (+/- 1.4) x 10(-14) N x m. These values are identical within the limit of error of the measurement technique. This finding suggests that the fishhook configuration observed in the Ca(2+) response of rat sperm is the result of a Newtonian equilibrium, where active torque produced by dynein is counterbalanced by an equal and opposite passive torque that results from bending the flagellum. Consistent with this mechanism, the Ca(2+)-induced fishhook configuration is progressively relaxed by incremental increases in sodium vanadate concentration. This supports an active role of the dynein motors in producing the torque for the response. When rat sperm respond to Ca(2+), the bend in the flagellum always forms in the direction opposite the curvature of the asymmetric sperm head. Based on this polarity, the bending torque for the Ca(2+) response must result from the action of the dyneins on outer doublets 1 through 4.     

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.     

Elastic Properties of the Sea Urchin Sperm Flagellum

The theory of flexural vibrations in thin rods, applied to the movement of flagella, has been extended to include an investigation of the influence of the boundary conditions on the theoretical waveforms. It was found that for flagella which are flexible enough, the flexibility can be estimated solely from the wavelength of the wave traveling in it. This can be expected to hold for those flagella which do not possess a fibrous sheath. The bending moment in flagella in which the ampitude of the wave is maintained as the wave travels distally is almost completely produced by active contractile elements. This means that the active bending moment can be estimated from the radius of curvature of the flagellum and the stiffness. The above findings were applied to the case of the sea urchin sperm flagellum. One finds that the stiffness of the flagellum is caused mainly by the nine longitudinal fibers which must have a Young's modulus of slightly less than 10⁸dyne/cm². The longitudinal fibers need to develop a tension of 1.6 × 10⁸dyne/cm² to account for the bending moment in the flagellum. These two figures are in line with those found for muscle fibers.     

Calcium regulation of flagellar curvature and swimming pattern in triton X-100--extracted rat sperm

Free Ca2+ changes the curvature of epididymal rat sperm flagella in demembranated sperm models. The radius of curvature of the flagellar midpiece region was measured and found to be a continuous function of the free Ca2+ concentration. Below 10(-7) M free Ca2+, the sperm flagella assumed a pronounced curvature in the same direction as the sperm head. The curvature reversed direction at 2.5 x 10(-6) M Ca2+ to assume a tight, hook-like bend at concentrations of 10(-5) to 10(-4) M free Ca2+. Sodium vanadate at 2 x 10(-6) M blocked flagellar motility, but did not inhibit the Ca2+-mediated change in curvature. Nickel ion at 0.2 mM and cadmium ion at 1 microM interfered with the transition and induced the low Ca2+ configuration of the flagellum. The forces that maintain the Ca2+-dependent curvature are locally produced, as dissection of the flagella into segments did not significantly alter the curvature of the excised portions. Irrespective of the induced pattern of curvature, the sperm exhibited coordinated, repetitive flagellar beating in the presence of ATP and cAMP. At 0.3 mM ATP the flagellar waves propagated along the principal piece while the level of free Ca2+ controlled the overall curvature. When Ca2+-treated sperm models with hooked midpieces were subjected to higher concentrations of ATP (1-5 mM), some cells exhibited a pattern of movement similar to hyperactivated motility in capacitated live sperm. This type of motility involved repetitive reversals of the Ca2+-induced bend in the midpiece, as well as waves propagated along the principal piece. The free Ca2+ available to the flagellum therefore appeared to modify both the pattern of motility and the flagellar curvature.     

Insights into the mechanism of ADP action on flagellar motility derived from studies on bull sperm

Adenosine diphosphate (ADP) is known to have interesting effects on flagellar motility. Permeabilized and reactivated bull sperm exhibit a marked reduction in beating frequency and a greatly increased beat amplitude in the presence of 1-4 mM ADP. In this study we examined the force production of sperm reactivated with 0.1 mM ATP with and without 1 mM ADP and found that there is little or no resulting change in the stalling force produced by a bull sperm flagella in response to ADP. Because bull sperm bend to a higher curvature after ADP treatment we explored the possibility that ADP-treated sperm flagella are more flexible. We measured the stiffness of 50 μM sodium vanadate treated bull sperm in the presence of 4 mM ADP, but found no change in the passive flagellar stiffness. When we analyzed the torque that develops in ADP-treated sperm at the point of beat reversal we found that the torque developed by the flagellum is significantly increased. Our torque estimates also allow us to calculate the transverse force (t-force) acting on the flagellum at the point of beat direction reversal. We find that the t-force at the switch-point of the beat is increased significantly in the ADP treated condition, averaging 0.7 ± 0.29 nN/μm in 0.1 mM ATP and increasing to 2.9 ± 1.2 nN/μm in 0.1 mM ATP plus 4 mM ADP. This suggests that ADP is exerting its effect on the beat by increasing the tenacity of dynein attachment at the B-subtubule. This could be a direct result of a regulatory effect of ADP on the binding affinity of dynein for the B-subtubule of the outer doublets. This result could also help to explain a number of previous experimental observations, as discussed.     

Differentiation Within the Bacterial Flagellum and Isolation of the Proximal Hook

Purified and crude flagellar isolates from cells of Bacillus pumilus NRS 236 were treated with acid, alcohol, acid-alcohol, or heat, and were examined electron microscopically in negatively stained and shadow-cast preparations. Under certain conditions, each of these agents causes the flagella to break between the proximal hooks and the spiral filaments. In such preparations, filaments are seen in various stages of disintegration, whereas hooks of fairly constant length retain their integrity and morphological identity. When crude isolates of flagella are treated under these conditions, the hooks remain attached to membrane fragments or bear basal material. These findings substantiate previous structural observations that led to the view that the proximal hook is a distinct part of the bacterial flagellum and further confirm that the hook is tightly associated with basal material and the cytoplasmic membrane. It appears that the hook is a polarly oriented structure, and that the interactions between the hook and the basal material or the cytoplasmic membrane are different from those between the hook and the filamentous portion of the organelle. Moreover, both types of interaction apparently differ still from those by which the flagellin subunits are held together in the flagellar filament. Hooks were isolated by exploiting the differences in relative stability shown by the various morphological regions of the bacterial flagellum.     

Sperm competition and the evolution of the sperm hook in house mice

Sperm morphology varies considerably both between and within species. The sperm of many muroid rodents bear an apical hook at the proximal end of the head. The curvature of the sperm hook varies greatly across species, however the adaptive significance of the sperm hook is currently not known. In wood mice the apical hooks intertwine to form sperm ‘trains’, which exhibit faster swimming velocities than single cells. Thus, it has been suggested that if sperm ‘trains’ were advantageous in a competitive situation, then the apical sperm hook might be an evolutionary product of selection via sperm competition. A comparative study of rodent species provided support for the hypothesis, and showed that species with higher levels of sperm competition had more reflected sperm hooks. Here, we tested this hypothesis at the intraspecific level. We quantified sperm hook morphology from seven house mouse populations, and found that interpopulation variation in hook curvature was not explained by variation in sperm competition risk. Furthermore, observations of ejaculated sperm revealed that sperm groups are not a common characteristic of mouse ejaculates. We suggest that selection for sperm attachment to the oviduct epithelium, and thus better retainment of sperm fertilizing potential, may provide a more general explanation of the evolutionary relationship between sperm competition risk and the curvature of the sperm hook among rodents, and provide a phylogenetic comparison among rodent species that supports our hypothesis.     

Changes in the curvature of sperm apical hooks in murine rodents

Sperm apical hooks in murine rodents play an important role in sperm competition. Apical hooks are more curved and longer in species with relatively larger testes, that is in species with a higher risk of sperm competition. The sperm can form aggregations, ‘trains’, that can move faster than individual sperm, thus reaching the egg earlier as was observed in Apodemus sylvaticus. The apical hook plays an important role for train formation. This study focuses on the changes in the curvature of sperm apical hooks during the final stages of spermiogenesis and stages before fertilization (sperm-life span). Apical hook curvatures of field mice (A. agrarius and A. sylvaticus) vary significantly between dormant and active sperm. In contrast, there are no significant differences among the stages in the eastern house mouse. Since there are high ranges of angle values in all stages, the mean angles of apical hook curvature are not appropriate for evaluating risk of sperm competiton. The ranges of angle values point to a level of flexibility of the apical hooks. The lengths of sperm hooks in individual species do not change during particular stages. The length and flexibility of the sperm apical hooks are important for the formation of sperm aggregations, thus these sperm characters indicate the risk of sperm competition and the sperm strategies in murine rodents.     

Digitized precision measurements of the movements of sea urchin sperm flagella.

High speed cinemicrographs were made of sea urchin sperm at temperatures varying from 22 to 6 degrees C. Apparatus, combining a television camera and a video digitizer, was constructed to scan individual flagellar images and to digitize the flagellar waveforms. With appropriate smoothing and averaging procedures, the rough data were condensed by a microcomputer into the coordinates of 20 points along a flagellum, spaced 2 microns apart. The curvature of the flagellum at these points was also computed. The coordinates of the flagellar positions were obtained to an accuracy of approximately +/- 0.1 micron, flagellar curvature to an accuracy of approximately +/- 50 cm-1. At all temperatures the amplitude of the flagella was found to vary with time in a purely sinusoidal fashion to within +/- 2%. The local curvature of the flagella had basically a purely sinusoidal time course to within +/- 50 cm-1, but a varying amount of asymmetry was present in the distal and the proximal ends of the flagella. This asymmetry in the curvature was related to the radius of the circular path of the sperm. The flagellar waveforms can probably be summarized in simple algebraic functions.     

Length Control of the Flagellar Hook in a Temperature-Sensitive flgE Mutant of Salmonella enterica Serovar Typhimurium

The flagellar hook is a short, curved, extracellular structure located between the basal body and the filament. The hook is composed of the FlgE protein. In this study, we analyzed flagellum assembly in a temperature-sensitive flgE mutant of Salmonella enterica serovar Typhimurium. When the mutant cells were grown at 30°C, they produced flagella of a normal length (71% of the population) and short hooks without filaments (26%). At 37°C, 70% of the basal bodies lacked hooks, and intact flagella made up only 6% of the population. Mutant cells secreted monomeric FlgE in abundance at 37°C, suggesting that the mutant FlgE protein might be defective in polymerization at higher temperatures. The average length of the hooks in intact filaments was 55 nm, whereas after acid treatment, it was 45 nm. SDS-PAGE analysis of the hook-basal body showed that HAP1 was missing in the mutant but not in the wild type. We concluded that hook length in the mutant is controlled in the same way as in the wild type, but the hook appeared short after acid treatment due to the lack of HAP1. We also learned that the true length of the hook is possibly 45 nm, not 55 nm, as has been believed.     

Theoretical analysis of twist/bend ratio and mechanical moduli of bacterial flagellar hook and filament

Certain motile bacteria employ rotating flagella for propulsion. The relative flexibility of two key components of the flagellum, filament and hook, is partially responsible for the mechanistic workings of this motor. A new computational method, the quantized elastic deformational model, was employed in this article to calculate the dimensionless twist/bend ratio (EI/GJ) of the filament and hook, providing a quantitative means to compare their relative stiffness. Both ratios were much <1.0, an average of 0.0440 for the filament and 0.0512 for the hook, indicating that within each structure bending is favored over twisting. These two ratios, along with previous experimental measurements, allowed us to propose a theoretical Young's modulus (E) between 10(6) and 10(7) dyn/cm(2) for the hook. This value is orders of magnitude smaller than experimentally determined Young's moduli of the filament, hence in agreement with empirical evidence linking compliance in the flagellum mainly to the hook.     

Flagellar hook and basal complex of Caulobacter crescentus.

Intact bacterial flagella possessing a membrane-free hook and basal complex were purified from Caulobacter crescentus CB15, as well as from mutants which synthesize incomplete flagella. The basal body consisted of five rings mounted on a rod. Two rings were in the hook-proximal upper set, and three rings (two narrow and one wide) were in the lower set. The diameters of the two upper rings differed, being 32 and 21 nm, respectively. The lower rings were all approximately 21 nm in diameter, although they varied significantly in width. During the normal course of the C. crescentus cell cycle, the polar flagellum with hook and rod was shed into the culture medium without the basal rings. Similarly, hooks with attached rods were shed from nonflagellate mutants, and these structures also lacked the basal rings. The hook structure was purified from nonflagellated mutants and found to be composed of a 70,000-molecular-weight protein component.     

Inhibition and relaxation of sea urchin sperm flagella by vanadate

Direct measurements of the stiffness (elastic bending resistance) of demembranated sera urchin sperm flagella were made in the presence of MgATP2- and vanadate. Under these conditions, the flagellum is in a relaxed state, with a stiffness of approximately 0.9 x 10(-21) N m2, which is approximately 5% of the stiffness obtained in the rigor state in the absence of MgATP2-. MgADP- dose not substitute for MgATP2- in producing relaxed state. A progressive inhibition of movement is observed after addition of MgATP2- to flagella preincubated with vanadate, in which new bend generation, propagation, and relaxation by straightening are distinguished, depending on the ratio of MgATP2- and vanadate. At appropriate concentrations of vanadate, increase of the velocity of bend propagation is observed at a very low concentration of MgATP2- that is not enough to induce spontaneous beating. Vanadate enhances competitive inhibition of beat frequency by MgADP- but not by ADP3-, ATP4-, or Pi. These observations, and the uncompetitive inhibition of beat frequency by vanadate, indicate that vanadate can only bind to dynein-nucleotide complexes induced by MgATP2- and MgADP-. The state accessible by MgATP2- binding must be a state in which the cross-bridges are detached and the flagellum is relaxed. The state accessible by MgADP- binding must be a cross-bridged state. Bound vanadate prevents the transition between these two states. Inhibition and relaxation by banadate in the presence of MgATP2- results from the specific affinity of vanadate for a state in which nucleotide is bound, rather than a specific affinity for the deteched state.     

Movement of sea urchin sperm flagella

The motion of the sea urchin sperm flagellum was analyzed from high-speed cinemicrographs. At all locations on the flagellum the transversal motion and the curvature were found to vary sinusoidally in time. The curvatures of the flagella increase strongly near the proximal junction. Two sperm are described in transient from rest to normal motion. The full wave motion developed in both sperm within 40 ms.     

Compliance of bacterial polyhooks measured with optical tweezers.

In earlier work, a single-beam gradient force optical trap ("optical tweezers") was used to measure the torsional compliance of flagella in wild-type cells of Escherichia coli that had been tethered to glass by a single flagellum. This compliance was nonlinear, exhibiting a torsionally soft phase up to 180 degrees, followed by a torsionally rigid phase for larger angles. Values for the torsional spring constant in the soft phase were substantially less than estimates based on the rigidity determined for isolated flagellar filaments. It was suggested that the soft phase might correspond to wind-up of the flagellar hook, and the rigid phase to wind-up of the stiffer filament. Here, we have measured the torsional compliance of flagella on cells of an E. coli strain that produces abnormally long hooks but no filaments. The small-angle compliance of these cells, as determined from the elastic rebound of the cell body after wind-up and release, was found to be the same as for wild-type cells. This confirms that the small-angle compliance of wild-type cells is dominated by the response of the hook. Hook flexibility is likely to play a useful role in stabilizing the flagellar bundle.     

Caulobacter flagellar organelle: synthesis, compartmentation, and assembly.

In Caulobacter crescentus biogenesis of the flagellar organelle occurs during one stage of its complex life cycle. Thus in synchronous cultures it is possible to assay the sequential synthesis and assembly of the flagellum and hook in vivo with a combination of biochemical and radioimmunological techniques. The periodicity of synthesis and the subcellular compartmentation of the basal hook and filament subunits were determined by radioimmune assay procedures. Unassembled 27,000-dalton (27K) flagellin was preferentially located in isolated membrane fractions, whereas the 25K flagellin was distributed between the membrane and cytoplasm. The synthesis of hook began before that of flagellin, although appreciable overlap of the two processes occurred. Initiation of filament assembly coincided with the association of newly synthesized hook and flagellin subunits. Caulobacter flagella are unusual in that they contain two different flagellin subunits. Data are presented which suggest that the ratio of the two flagellin subunits changes along the length of the filament. Only the newly synthesized 25K flagellin subunit is detected in filaments assembled during the swarmer cell stage. By monitoring the appearance of flagellar hooks in the culture medium, the time at which flagella are released was determined.     

Attachment and structural features of flagella of certain bacilli

Abram, Dinah (Purdue University, Lafayette, Ind.), A. E. Vatter, and Henry Koffler. Attachment and structural features of flagella of certain bacilli. J. Bacteriol. 91:2045-2068. 1966.-The attachment of flagella to cells of various mesophilic and thermophilic strains of Bacillus was studied electron microscopically. Studies of ghost cells and membrane fragments indicate that flagella are connected to the cytoplasmic membrane. Flagella removed from cells mechanically, during autolysis, or by phage lysis, have attached to the base of their proximal hooks material that is heterogeneous in character. In part, this material consists of cytoplasmic membrane; its varied shape appears to be caused by the folding of the membrane around the proximal end of the flagellum at the site of attachment. It is uncertain whether this material represents a real structure or an artifact. Highresolution microscopy reveals differences in the fine structure of intact flagella of the various strains studied. The proximal hook and the flagellar filament are distinct in morphology and fine structure. A specialized structure is associated with the hook of flagella of B. brevis and B. circulans. The filament of flagella of B. stearothermophilus 2184 has two regions that show marked differences in the manner in which the subunits appear to be organized. No correlation was found between the site of origin of flagella and the location of reduced tellurite when the reduction of potassium tellurite was used to indicate the loci of enzymatic respiratory activities.     

Sperm competition does not influence sperm hook morphology in selection lines of house mice

Sperm show a remarkable degree of variation in size, shape and complexity. Murine rodents exhibit a sperm head morphology that differs greatly from the ovoid shape that is characteristic of most mammals. These rodents have sperm that bear one or more apical hooks, the function of which is currently surrounded by much controversy. It has been suggested that the hook serves to facilitate the formation of sperm groups, which in some species exhibit relatively faster velocities than single cells and thus, may provide an advantage when ejaculates are competing for fertilisations. In support of this hypothesis, a comparative study reported a positive association between the strength of sperm competition (estimated from testes size) and the curvature of the sperm hook amongst 37 murine species. Here, we assessed whether sperm competition influences sperm hookedness at the intra-specific level. Following 16 generations of selection, we used geometric morphometry (GM) to describe sperm head morphology in selection lines of house mice evolving with (polygamous) and without (monogamous) sperm competition. Although the GM analysis returned two relative warps that described variation in the curvature of the sperm hook, we found no evidence of divergence between the selection lines. Thus, we can conclude that sperm competition does not influence the degree of sperm hookedness in house mice.     

Flagellar arrest behavior predicted by the Geometric Clutch model is confirmed experimentally by micromanipulation experiments on reactivated bull sperm.

The central tenet of the Geometric Clutch hypothesis of flagellar beating is that the internal force transverse to the outer doublets (t-force) mediates the initiation and termination of episodes of dynein engagement. Therefore, if the development of an adequate t-force is prevented, then the dynein-switching necessary to complete a cycle of beating should fail. The dominant component of the t-force is the product of the longitudinal force on each outer doublet multiplied by the local curvature of the flagellum. In the present study, two separate strategies, blocking and clipping, were employed to limit the development of the t-force in Triton X-100 extracted bull sperm models. The blocking strategy used a bent glass microprobe to restrict the flagellum during a beat, preventing the development of curvature in the basal portion of the flagellum. The clipping strategy was designed to shorten the flagellum by clipping off distal segments of the flagellum with a glass microprobe. This limits the number of dyneins that can contribute to bending and consequently reduces the longitudinal force on the doublets. The blocking and clipping strategies both produced an arrest of the beat cycle consistent with predictions based on the Geometric Clutch hypothesis. Direct comparison of experimentally produced arrest behavior to the behavior of the Geometric Clutch computer model of a bull sperm yielded similar arrest patterns. The computer model duplicated the observed behavior using reasonable values for dynein force and flagellar stiffness. The experimental data derived from both blocking and clipping experiments are fully compatible with the Geometric Clutch hypothesis.     

Antigenic variation of Campylobacter flagella.

Sodium dodecyl sulfate-polyacrylamide gel electrophoresis of flagella dissociated from strains of Campylobacter coli and Campylobacter jejuni belonging to the heat-labile serogroup LIO 8 showed that some strains were capable of producing flagellin subunits of two different molecular weights (MrS), 59,500 and 61,500. Immunoelectron microscopy of cultures of the type strain of this serogroup, C. coli VC167, showed the presence of two flagellum filaments of different antigenic specificity. Epitopes on the surface of one of these flagella bound antibodies in LIO 8 typing antiserum, and Western blotting (immunoblotting) and immunoprecipitation showed that the flagellum was composed of flagellin of Mr 61,500. The other flagellum antigenic type did not bind LIO 8 antibodies but did possess serospecific epitopes which bound a second polyclonal antiserum, LAH2. This second antigenic flagellum type was composed of the Mr 59,500 flagellin. Cells producing either of the flagellum antigenic types serotyped as LIO 8, indicating that flagella composed of the Mr 61,500 flagellin do not carry the serological determinants for this serogroup. The ability of C. coli VC167 to produce these flagella of different subunit MrS was shown to represent a bidirectional antigenic variation. When measured in culture medium, the phase 1-to-phase 2 transition occurred at a rate of approximately 2.0 x 10(-5) per cell per generation, and the phase 2-to-phase 1 transition occurred at a rate of 1.2 x 10(-6) per cell per generation.