Flagellate spermatozoa of Protura (Insecta,Apterygota) are motile

A new model of sperm axoneme with 16 + 0 doublets is described. The spermatozoon of Acerentulus confinis (Apterygota : Protura) has a short conical acrosome, a long helicoidal nucleus, well-developed centriolar adjunct material, and a long flagellum. Using fixation with a glutaraldehyde-tannic acid mixture, without osmium post-fixation, doublet protofilaments, inner dynein arms, radial spokes, nexin bridges, and Y-links of the sperm axoneme of A. confinis and Acerentomon italicum were clearly observed. Optical observation shows that the proturan flagellate spermatozoa are motile cells. The process involving the transformation of the spermatozoa from a coiled to an elongated swimming form was studied by scanning electron microscope. The findings confirmed that flagellar motility is due to the presence of a single dynein arm on doublets in spite of the unusual axonemal pattern.     

Effects of imposed bending on microtubule sliding in sperm flagella

The movement of eukaryotic flagella is characterized by its oscillatory nature. In sea urchin sperm, for example, planar bends are formed in alternating directions at the base of the flagellum and travel toward the tip as continuous waves. The bending is caused by the orchestrated activity of dynein arms to induce patterned sliding between doublet microtubules of the flagellar axoneme. Although the mechanism regulating the dynein activity is unknown, previous studies have suggested that the flagellar bending itself is important in the feedback mechanism responsible for the oscillatory bending. If so, experimentally bending the microtubules would be expected to affect the sliding activity of dynein. Here we report on experiments with bundles of doublets obtained by inducing sliding in elastase-treated axonemes. Our results show that bending not only "switches" the dynein activity on and off but also affects the microtubule sliding velocity, thus supporting the idea that bending is involved in the self-regulatory mechanism underlying flagellar oscillation.     

Are the local adjustments of the relative spatial frequencies of the dynein arms and the beta-tubulin monomers involved in the regulation of the "9+2" axoneme?

The “9+2” axoneme is a highly specific cylindrical machine whose periodic bending is due to the cumulative shear of its 9 outer doublets of microtubules. Because of the discrete architecture of the tubulin monomers and the active appendices that the outer doublets carry (dynein arms, nexin links and radial spokes), this movement corresponds to the relative shear of these topological verniers, whose characteristics depend on the geometry of the wave train. When an axonemal segment bends, this induces the compressed and dilated conformations of the tubulin monomers and, consequently, the modification of the spatial frequencies of the appendages that the outer doublets carry. From a dynamic point of view, the adjustments of the spatial frequencies of the elements of the two facing verniers that must interact create different longitudinal periodic patterns of distribution of the joint probability of the molecular interaction as a function of the location of the doublet pairs around the axonemal cylinder and their spatial orientation within the axonemal cylinder. During the shear, these patterns move along the outer doublet intervals at a speed that ranges from one to more than a thousand times that of sliding, in two opposite directions along the two opposite halves of the axoneme separated by the bending plane, respecting the polarity of the dynein arms within the axoneme. Consequently, these waves might be involved in the regulation of the alternating activity of the dynein arms along the flagellum, because they induce the necessary intermolecular dialog along the axoneme since they could be an element of the local dynamic stability/instability equilibrium of the axoneme. This complements the geometric clutch model [Lindemann, C., 1994. A “geometric clutch” hypothesis to explain oscillations of the axoneme of cilia and flagella. J. Theor. Biol. 168, 175-189].     

Flagellar motility contributes to cytokinesis in Trypanosoma brucei and is modulated by an evolutionarily conserved dynein regulatory system

The flagellum of Trypanosoma brucei is a multifunctional organelle with critical roles in motility and other aspects of the trypanosome life cycle. Trypanin is a flagellar protein required for directional cell motility, but its molecular function is unknown. Recently, a trypanin homologue in Chlamydomonas reinhardtii was reported to be part of a dynein regulatory complex (DRC) that transmits regulatory signals from central pair microtubules and radial spokes to axonemal dynein. DRC genes were identified as extragenic suppressors of central pair and/or radial spoke mutations. We used RNA interference to ablate expression of radial spoke (RSP3) and central pair (PF16) components individually or in combination with trypanin. Both rsp3 and pf16 single knockdown mutants are immotile, with severely defective flagellar beat. In the case of rsp3, this loss of motility is correlated with the loss of radial spokes, while in the case of pf16 the loss of motility correlates with an aberrant orientation of the central pair microtubules within the axoneme. Genetic interaction between trypanin and PF16 is demonstrated by the finding that loss of trypanin suppresses the pf16 beat defect, indicating that the DRC represents an evolutionarily conserved strategy for dynein regulation. Surprisingly, we discovered that four independent mutants with an impaired flagellar beat all fail in the final stage of cytokinesis, indicating that flagellar motility is necessary for normal cell division in T. brucei. These findings present the first evidence that flagellar beating is important for cell division and open the opportunity to exploit enzymatic activities that drive flagellar beat as drug targets for the treatment of African sleeping sickness.     

Excitable dynein model with multiple active sites for large-amplitude oscillations and bend propagation in flagella

The formal excitable dynein model proposed by Murase et al. (1989, J. theor. Biol. 139, 413-430) is modified to produce large-amplitude oscillations and excitability. The present model assumes that (i) each dynein arm has multiple active sites, which are distributed along most of the 24-nm distance between adjacent B-subtubule attachment sites; and (ii) any given dynein molecule tends to produce force continuously during interdoublet sliding in one direction and to produce little force during sliding in the opposite direction. Since no sliding motion occurs without superthreshold perturbations in the form of the sliding displacement, this new model also possesses an excitable nature. Once passive elastic components (e.g. nexin links and radial spokes) are incorporated into this model, oscillations with large amplitudes result. To test the ability of the model for bend propagation without a curvature-control mechanism, forced oscillations are applied to the basal end of the flagellum by the sliding displacement. It is found that bend propagation can occur even in the absence of a curvature-control mechanism.     

Equations of Interdoublet Separation during Flagella Motion Reveal Mechanisms of Wave Propagation and Instability

The motion of flagella and cilia arises from the coordinated activity of dynein motor protein molecules arrayed along microtubule doublets that span the length of axoneme (the flagellar cytoskeleton). Dynein activity causes relative sliding between the doublets, which generates propulsive bending of the flagellum. The mechanism of dynein coordination remains incompletely understood, although it has been the focus of many studies, both theoretical and experimental. In one leading hypothesis, known as the geometric clutch (GC) model, local dynein activity is thought to be controlled by interdoublet separation. The GC model has been implemented as a numerical simulation in which the behavior of a discrete set of rigid links in viscous fluid, driven by active elements, was approximated using a simplified time-marching scheme. A continuum mechanical model and associated partial differential equations of the GC model have remained lacking. Such equations would provide insight into the underlying biophysics, enable mathematical analysis of the behavior, and facilitate rigorous comparison to other models. In this article, the equations of motion for the flagellum and its doublets are derived from mechanical equilibrium principles and simple constitutive models. These equations are analyzed to reveal mechanisms of wave propagation and instability in the GC model. With parameter values in the range expected for Chlamydomonas flagella, solutions to the fully nonlinear equations closely resemble observed waveforms. These results support the ability of the GC hypothesis to explain dynein coordination in flagella and provide a mathematical foundation for comparison to other leading models.     

Structural-functional relationships of the dynein,spokes, and central-pair projections predicted from an analysis of the forces acting within a flagellum

In the axoneme of eukaryotic flagella the dynein motor proteins form crossbridges between the outer doublet microtubules. These motor proteins generate force that accumulates as linear tension, or compression, on the doublets. When tension or compression is present on a curved microtubule, a force per unit length develops in the plane of bending and is transverse to the long axis of the microtubule. This transverse force (t-force) is evaluated here using available experimental evidence from sea urchin sperm and bull sperm. At or near the switch point for beat reversal, the t-force is in the range of 0.25-1.0 nN/ micro m, with 0.5 nN/ micro m the most likely value. This is the case in both beating and arrested bull sperm and in beating sea urchin sperm. The total force that can be generated (or resisted) by all the dyneins on one micron of outer doublet is also approximately 0.5 nN. The equivalence of the maximum dynein force/ micro m and t-force/ micro m at the switch point may have important consequences. Firstly, the t-force acting on the doublets near the switch point of the flagellar beat is sufficiently strong that it could terminate the action of the dyneins directly by strongly favoring the detached state and precipitating a cascade of detachment from the adjacent doublet. Secondly, after dynein release occurs, the radial spokes and central-pair apparatus are the structures that must carry the t-force. The spokes attached to the central-pair projections will bear most of the load. The central-pair projections are well-positioned for this role, and they are suitably configured to regulate the amount of axoneme distortion that occurs during switching. However, to fulfill this role without preventing flagellar bend formation, moveable attachments that behave like processive motor proteins must mediate the attachment between the spoke heads and the central-pair structure.     

Equations of Interdoublet Separation during Flagella Motion Reveal Mechanisms of Wave Propagation and Instability

The motion of flagella and cilia arises from the coordinated activity of dynein motor protein molecules arrayed along microtubule doublets that span the length of axoneme (the flagellar cytoskeleton). Dynein activity causes relative sliding between the doublets, which generates propulsive bending of the flagellum. The mechanism of dynein coordination remains incompletely understood, although it has been the focus of many studies, both theoretical and experimental. In one leading hypothesis, known as the geometric clutch (GC) model, local dynein activity is thought to be controlled by interdoublet separation. The GC model has been implemented as a numerical simulation in which the behavior of a discrete set of rigid links in viscous fluid, driven by active elements, was approximated using a simplified time-marching scheme. A continuum mechanical model and associated partial differential equations of the GC model have remained lacking. Such equations would provide insight into the underlying biophysics, enable mathematical analysis of the behavior, and facilitate rigorous comparison to other models. In this article, the equations of motion for the flagellum and its doublets are derived from mechanical equilibrium principles and simple constitutive models. These equations are analyzed to reveal mechanisms of wave propagation and instability in the GC model. With parameter values in the range expected for Chlamydomonas flagella, solutions to the fully nonlinear equations closely resemble observed waveforms. These results support the ability of the GC hypothesis to explain dynein coordination in flagella and provide a mathematical foundation for comparison to other leading models.     

Ultrastructure of the flagellar apparatus inPyramimonas octopus (Prasinophyceae)

Summary While green algae usually lack one of the outer dynein arms in the axoneme, flagella of the octoflagellated prasinophytePyramimonas octopus possess dynein arms on all peripheral doublets. The outer dynein arm on doublet no. 1 is modified, and additional structures are associated with doublets no. 2 and 6. The flagellar scales are asymmetrically arranged. Thus the two rows of thick flagellar hairscales are displaced towards doublet no. 6,i.e., in the direction of the effective stroke of each flagellum. The underlayer of small scales includes two nearly opposite double rows scales, arranged in the longitudinal direction of the flagellum. The hairscales emerge from these rows. The double rows are separated on one side by 9, on the other by 11 rows of helically arranged scales. The central pair of microtubules twists, but the axoneme itself (represented by the 9 peripheral doublets), does not seem to rotate. The flagella are arranged in two groups, showing modified 180° rotational symmetry. The effective strokes of the two central flagella are exactly opposite, while the other flagella beat in six intermediate directions.     

Bending of the “9+2” axoneme analyzed by the finite element method

Many data demonstrate that the regulation of the bending polarity of the “9+2” axoneme is supported by the curvature itself, making the internal constraints central in this process, adjusting either the physical characteristics of the machinery or the activity of the enzymes involved in different pathways. Among them, the very integrated Geometric Clutch model founds this regulation on the convenient adjustments of the probability of interaction between the dynein arms and the β-tubulin monomers of the outer doublet pairs on which they walk. Taking into consideration (i) the deviated bending of the outer doublets pairs (Cibert, C., Heck, J.-V., 2004. Cell Motil. Cytoskeleton 59, 153-168), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 μm long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, except that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.     

Evidence for axonemal distortion during the flagellar beat of Chlamydomonas

In order to understand the working mechanism that governs the flagellar beat it is essential to know if the axoneme undergoes distortion during the course of the beat cycle. The rapid fixation method employed by Mitchell was able to preserve the waveform of Chlamydomonas flagella much as it appears during normal flagellar beating [Mitchell, Cell Motil Cytoskeleton 2003;56:120-129]. This conservation of the waveform suggests that the stress responsible for the production of bending is also trapped by the fixation procedure. Longitudinal sections of these well-preserved flagella were used to document variations in the relative axonemal diameter. Sections aligned to the plane of bending, showing both the central pair microtubules and outer doublets, were examined for this purpose. Micrographs were selected that continuously showed both the outer doublets and the central pair from a straight region to a curved region of the flagellum. Axoneme diameters measured from these select micrographs showed an increase in relative diameter that averaged 39 nm greater at the crest of the bent region. This constituted a 24% increase in the axoneme diameter in the bends. The transverse stress acting across the axoneme during bending was calculated from the Geometric Clutch computer model for a simulated Chlamydomonas-like flagellar beat. If we assume that this is representative of the transverse stress acting in a real flagellum, then the Young's modulus of the intact axoneme is approximately 0.02 MPa. The possibility that the distortion of the axoneme during the beat could play a significant role in regulating dynein function is discussed.     

Testing the geometric clutch hypothesis

The Geometric Clutch hypothesis is based on the premise that transverse forces (t-forces) acting on the outer doublets of the eukaryotic axoneme coordinate the action of the dynein motors to produce flagellar and ciliary beating. T-forces result from tension and compression on the outer doublets when a bend is present on the flagellum or cilium. The t-force acts to pry the doublets apart in an active bend, and push the doublets together when the flagellum is passively bent and thus could engage and disengage the dynein motors. Computed simulations of this working mechanism have reproduced the beating pattern of simple cilia and flagella, and of mammalian sperm. Cilia-like beating, with a clearly defined effective and recovery stroke, can be generated using one uniformly applied switching algorithm. When the mechanical properties and dimensions appropriate to a specific flagellum are incorporated into the model the same algorithm can simulate a sea urchin or bull sperm-like beat. The computed model reproduces many of the observed behaviors of real flagella and cilia. The model can duplicate the results of outer arm extraction experiments in cilia and predicted two types of arrest behavior that were verified experimentally in bull sperm. It also successfully predicted the experimentally determined nexin elasticity. Calculations based on live and reactivated sea urchin and bull sperm yielded a value of 0.5 nN/microm for the t-force at the switch-point. This is a force sufficient to overcome the shearing force generated by all the dyneins on one micron of outer doublet. A t-force of this magnitude should produce substantial distortion of the axoneme at the switch-point, especially in spoke or spoke-head deficient motile flagella. This concrete and verifiable prediction is within the grasp of recent advances in imaging technology, specifically cryoelectron microscopy and atomic force microscopy.     

Building a radial spoke: flagellar radial spoke protein 3 (RSP3) is a dimer

Radial spokes are critical multisubunit structures required for normal ciliary and eukaryotic flagellar motility. Experimental evidence indicates the radial spokes are mechanochemical transducers that transmit signals from the central pair apparatus to the outer doublet microtubules for local control of dynein activity. Recently, progress has been made in identifying individual components of the radial spoke, yet little is known about how the radial spoke is assembled or how it performs in signal transduction. Here we focus on radial spoke protein 3 (RSP3), a highly conserved AKAP located at the base of the radial spoke stalk and required for radial spoke assembly on the doublet microtubules. Biochemical approaches were taken to further explore the functional role of RSP3 within the radial spoke structure and for control of motility. Chemical crosslinking, native gel electrophoresis, and epitope-tagged RSP3 proteins established that RSP3 forms a dimer. Analysis of truncated RSP3 proteins indicates the dimerization domain coincides with the previously characterized axoneme binding domain in the N-terminus. We propose a model in which each radial spoke structure is built on an RSP3 dimer, and indicating that each radial spoke can potentially localize multiple PKAs or AKAP-binding proteins in position to control dynein activity and flagellar motility.     

Regulation of flagellar motility by the conserved flagellar protein CG34110/Ccdc135/FAP50

Eukaryotic cilia and flagella are vital sensory and motile organelles. The calcium channel PKD2 mediates sensory perception on cilia and flagella, and defects in this can contribute to ciliopathic diseases. Signaling from Pkd2-dependent Ca2+ rise in the cilium to downstream effectors may require intermediary proteins that are largely unknown. To identify these proteins, we carried out genetic screens for mutations affecting Drosophila melanogaster sperm storage, a process mediated by Drosophila Pkd2. Here we show that a new mutation lost boys (lobo) encodes a conserved flagellar protein CG34110, which corresponds to vertebrate Ccdc135 (E = 6e-78) highly expressed in ciliated respiratory epithelia and sperm, and to FAP50 (E = 1e-28) in the Chlamydomonas reinhardtii flagellar proteome. CG34110 localizes along the fly sperm flagellum. FAP50 is tightly associated with the outer doublet microtubules of the axoneme and appears not to be a component of the central pair, radial spokes, dynein arms, or structures defined by the mbo waveform mutants. Phenotypic analyses indicate that both Pkd2 and lobo specifically affect sperm movement into the female storage receptacle. We hypothesize that the CG34110/Ccdc135/FAP50 family of conserved flagellar proteins functions within the axoneme to mediate Pkd2-dependent processes in the sperm flagellum and other motile cilia.     

Properties of an excitable dynein model for bend propagation in cilia and flagella

Murase & Shimizu (1986, J. theor. Biol. 119, 409) introduced an excitable dynein-microtubule system based on a three-state mechanochemical cycle of dynein to demonstrate bend propagation in the absence of a curvature control mechanism. To examine the essential behavior of this class of models in a viscous fluid, we have represented the force generated by the complex dynein mechanochemistry by a formal model consisting of "force" and "activation" functions vs. sliding distance. Since the model has excitable properties with threshold phenomena and hysteresis switching between two opposed subsystems, it closely resembles the more realistic dynein kinetic scheme in its overall properties but is specified by fewer parameters. This model displays both bend initiation and bend propagation when the filaments at the basal end are either fixed or free to slide. A passive region is necessary at one end of the axoneme in order to obtain stable wave propagation; bends propagate towards the end with the passive region. Stable bend propagation is highly sensitive to small perturbations in external force distribution.     

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.     

Heterogeneity of dynein structure implies coordinated suppression of dynein motor activity in the axoneme

Axonemal dyneins provide the driving force for flagellar/ciliary bending. Nucleotide-induced conformational changes of flagellar dynein have been found both in vitro and in situ by electron microscopy, and in situ studies demonstrated the coexistence of at least two conformations in axonemes in the presence of nucleotides (the apo and the nucleotide-bound forms). The distribution of the two forms suggested cooperativity between adjacent dyneins on axonemal microtubule doublets. Although the mechanism of such cooperativity is unknown it might be related to the mechanism of bending. To explore the mechanism by which structural heterogeneity of axonemal dyneins is induced by nucleotides, we used cilia from Tetrahymena thermophila to examine the structure of dyneins in a) the intact axoneme and b) microtubule doublets separated from the axoneme, both with and without additional pure microtubules. We also employed an ATPase assay on these specimens to investigate dynein activity functionally. Dyneins on separated doublets show more activation by nucleotides than those in the intact axoneme, both structurally and in the ATPase assay, and this is especially pronounced when the doublets are coupled with added microtubules, as expected. Paralleling the reduced ATPase activity in the intact axonemes, a lower proportion of these dyneins are in the nucleotide-bound form. This indicates a coordinated suppression of dynein activity in the axoneme, which could be the key for understanding the bending mechanism.     

Trypanin, a component of the flagellar Dynein regulatory complex, is essential in bloodstream form African trypanosomes

The Trypanosoma brucei flagellum is a multifunctional organelle with critical roles in motility, cellular morphogenesis, and cell division. Although motility is thought to be important throughout the trypanosome lifecycle, most studies of flagellum structure and function have been restricted to the procyclic lifecycle stage, and our knowledge of the bloodstream form flagellum is limited. We have previously shown that trypanin functions as part of a flagellar dynein regulatory system that transmits regulatory signals from the central pair apparatus and radial spokes to axonemal dyneins. Here we investigate the requirement for this dynein regulatory system in bloodstream form trypanosomes. We demonstrate that trypanin is localized to the flagellum of bloodstream form trypanosomes, in a pattern identical to that seen in procyclic cells. Surprisingly, trypanin RNA interference is lethal in the bloodstream form. These knockdown mutants fail to initiate cytokinesis, but undergo multiple rounds of organelle replication, accumulating multiple flagella, nuclei, kinetoplasts, mitochondria, and flagellum attachment zone structures. These findings suggest that normal flagellar beat is essential in bloodstream form trypanosomes and underscore the emerging concept that there is a dichotomy between trypanosome lifecycle stages with respect to factors that contribute to cell division and cell morphogenesis. This is the first time that a defined dynein regulatory complex has been shown to be essential in any organism and implicates the dynein regulatory complex and other enzymatic regulators of flagellar motility as candidate drug targets for the treatment of African sleeping sickness.     

Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum

The axoneme "9 + 2" is basically a system constituted of a cylinder of 9 microtubule doublets surrounding a central pair of microtubules. These bi-tubular structures are considered as the support system of the active molecular complexes that generate and regulate the axonemal movement. Schoutens has calculated their moments of inertia [Schoutens, 1994: Journal of Theoretical Biology 171:163-177]. The results obtained allowed us to assume that these bi-tubular systems are endowed with dynamic properties that could be involved in the regulation of the axonemal machinery. For the first time, using the finite elements methods and the resistance of material principles, we have now calculated that the curvature of the axoneme induces the deviated-bending of the bi-tubular structures of the axoneme, because of their geometry only; they behave as beams in a framework. This approach is similar to the one used to measure the deflection of a single microtubule [Kasas et al., 2004: Chem Phys Chem 5:252-257]. These behaviors induce internal movement or constraints of either couples or triplets of doublets within the axonemal cylinder that could be directly involved in a constrained or a spontaneous "convergence/divergence" equilibrium of the cylindrical generatrices that they draw along the axonemal cylinder, which could apparently regulate the activity of the axonemal motors (the dynein arms). These results are discussed here, taking into consideration the dynamic propagation of the wave train along the flagellar axoneme, and the regulated balance between the activities of the two opposite sides of the axoneme during the beat. This study raises a few questions about the architecture-activity duo of the axonemal doublets.     

Direct measurement of inter-doublet elasticity in flagellar axonemes.

The outer doublet microtubules in ciliary and flagellar axonemes are presumed to be connected with each other by elastic links called the inter-doublet links or the nexin links, but it is not known whether there actually are such elastic links. In this study, to detect the elasticity of the putative inter-doublet links, shear force was applied to Chlamydomonas axonemes with a fine glass needle and the longitudinal elasticity was determined from the deflection of the needle. Wild-type axonemes underwent a high-frequency, nanometer-scale vibration in the presence of ATP. When longitudinal shear force was applied, the average position of the needle tip attached to the axoneme moved linearly with the force applied, yielding an estimate of spring constant of 2.0 (S.D.: 0.8) pN/nm for 1 microm of axoneme. This value did not change in the presence of vanadate, i.e., when dynein does not form strong cross bridges. In contrast, it was at least five times larger when ATP was absent, i.e., when dynein forms strong cross bridges. The measured elasticity did not significantly differ in various mutant axonemes lacking the central-pair microtubules, a subset of inner-arm dynein, outer-arm dynein, or the radial spokes, although it was somewhat smaller in the latter two mutants. It was also observed that the shear displacement in an axoneme in the presence of ATP often took place in a stepwise manner. This suggests that the inter-doublet links can reversibly detach from and reattach to the outer doublets in a cooperative manner. This study thus provides the first direct measure of the elasticity of inter-doublet links and also demonstrates its dynamic nature.