A Model Describing Bending in Flagella

In Part I of this paper, we present a modelto account for the force generationproducing bending, and the formation of awaveform in sperm flagella. The model isbased on the observation that dimers, andhence microtubules, possess dipole moments.The electric field these dipoles produce isthe source for storing mechanical work indynein arms. The mechanical work is thenreleased and act on the doublets to producea distally directed force with the resultthat bending occurs. The model described isconsistent with experimental observationsreported in the literature. The flexuralrigidity of a dynein arm is alsocalculated. In Part II of this paper, theconsequences of the bending mechanism arediscussed. It is shown that the sum offorces from dynein arms acting distallyalong doublet microtubules in a flagellumis essentially zero when all dyneins areattached thus resulting in the rigor state.The waveform in a flagellum occurs if oneof the sets of bending moments is zero,that is, a row of dyneins are detached oversome distance along the flagellum. Thedirection of the bend in the waveform isdetermined by which set of dynein arms aredetached with respect to the verticalmedian plane of the flagellum. Thepropagation of a bending wave is the resultof a moving region in which alternate sidesfrom the vertical median plane haveinactive dynein arms. The processes bywhich this moving region occurs and therelationship of the above results to thepropulsion of the flagellum are notconsidered.     

Polarity and asymmetry in the arrangement of dynein and related structures in the Chlamydomonas axoneme

Understanding the molecular architecture of the flagellum is crucial to elucidate the bending mechanism produced by this complex organelle. The current known structure of the flagellum has not yet been fully correlated with the complex composition and localization of flagellar components. Using cryoelectron tomography and subtomogram averaging while distinguishing each one of the nine outer doublet microtubules, we systematically collected and reconstructed the three-dimensional structures in different regions of the Chlamydomonas flagellum. We visualized the radial and longitudinal differences in the flagellum. One doublet showed a distinct structure, whereas the other eight were similar but not identical to each other. In the proximal region, some dyneins were missing or replaced by minor dyneins, and outer-inner arm dynein links were variable among different microtubule doublets. These findings shed light on the intricate organization of Chlamydomonas flagella, provide clues to the mechanism that produces asymmetric flagellar beating, and pose a new challenge for the functional study of the flagella.     

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.     

Structural and Functional Characterization of Paramecium Dynein: Initial Studies

ABSTRACT Dynein arms and isolated dynein from Paramecium tetraurelia ciliary axonemes are comparable in structure, direction of force generation, and microtubule translocation ability to other dyneins. In situ arms have dimensions and substructure similar to those of Tetrahymena. Based on spoke arrangement in intact axonemes, arms translocate axonemal microtubules in sliding such that active dynein arms are (-) end directed motors and the doublet to which the body and cape of the arms binds (N) translocates the adjacent doublet (N+1) upward. After salt extraction, based on ATPase activity, paramecium dynein is found as a 22S and a 14S species. the 22S dynein is a three-headed molecule that has unfolded from the in situ dimensions; the 14S dynein is single headed. Both dyneins can be photocleaved by UV light (350 nm) in the presence of Mg^2-, ATP and vanadate; the photocleavage pattern of 22S dynein differs from that seen with Tetrahymena. Both isolated dyneins translocate taxol-stabilized, bovine brain microtubules in vitro. Under standard conditions, 22S dynein, like comparable dyneins from other organisms, translocates at velocities that are about three times faster than 14S dynein.     

Structural and functional characterization of paramecium dynein: initial studies.

Dynein arms and isolated dynein from Paramecium tetraurelia ciliary axonemes are comparable in structure, direction of force generation, and microtubule translocation ability to other dyneins. In situ arms have dimensions and substructure similar to those of Tetrahymena. Based on spoke arrangement in intact axonemes, arms translocate axonemal microtubules in sliding such that active dynein arms are (-) end directed motors and the doublet to which the body and cape of the arms binds (N) translocates the adjacent doublet (N + 1) tipward. After salt extraction, based on ATPase activity, paramecium dynein is found as a 22S and a 14S species. The 22S dynein is a three-headed molecule that has unfolded from the in situ dimensions; the 14S dynein is single headed. Both dyneins can be photocleaved by UV light (350 nm) in the presence of Mg2+, ATP and vanadate; the photocleavage pattern of 22S dynein differs from that seen with Tetrahymena. Both isolated dyneins translocate taxol-stabilized, bovine brain microtubules in vitro. Under standard conditions, 22S dynein, like comparable dyneins from other organisms, translocates at velocities that are about three times faster than 14S dynein.     

On the contribution of moment-bearing links to bending and twisting in a three-dimensional sliding filament model

Previously (Hines, M., and J.J. Blum 1983, Biophys. J., 41:67-79), a method was developed that allowed one to compute curvature and twist for a three-dimensional sliding filament model. In that formalism it was difficult to specify the shear and bending moments arising from moment-bearing interfilament links such as fixed 5-6 bridges or dyneins. Euler's equation offers a straightforward method for computing these bending and shear moments when the potential energy stored in the links as a function of axonemal shape is specified. We used this approach to examine the effect of 5-6 bridges on curvature and twist for several distributions of internal shear moments. Twist changes the angle that a link makes with a doublet and thus in some circumstances may reduce the potential energy stored in those links. Twist is a second-order effect proportional to the square of the distance between an outer doublet and the neutral axis. Fixed links will not generate twist if they are symmetrically located around the axoneme.     

A model of flagellar movement based on cooperative dynamics of dynein-tubulin cross-bridges

A theoretical model based on molecular mechanisms of both dynein cross-bridges and radial spokes is used to study bend propagation by eukaryotic flagella. Though nine outer doublets are arranged within an axoneme, a simplified model with four doublets is constructed on the assumption that cross-bridges between two of the four doublets are opposed to those between the other two, corresponding to the geometric array of cross-bridges on the 6-9 and the 1-4 doublets in the axoneme. We also assume that external viscosity is zero, whereas internal viscosity is non-zero in order to reduce numerical complexity. For demonstrating flagellar movement, computer simulations are available by dividing a long flagellum into many straight segments. Considering the fact that dynein cross-bridge spacing is almost equal to attachment site spacing, we may use a localized cross-bridge distribution along attachment sites in each straight segment. Dynamics of cross-bridges are determined by a three-state model, and effects of radial spokes are represented by a periodic mechanical potential whose periodicity is considered to be a stroke distance of the radial spoke. First of all, we examine the model of a short segment to know basic properties of the system. Changing parameters relating to "activation" of cross-bridges, our model demonstrates various phenomena; for example "excitable properties with threshold phenomena" and "limit cycle oscillation". Here, "activation" and "inactivation" (i.e. switching mechanisms) between a pair of oppositely-directed cross-bridges are essential for generation of excitable or oscillatory properties. Next, the model for a flagellar segment is incorporated into a flagellum with a whole length to show bending movement. When excitable properties of cross-bridges, not oscillatory properties, are provided along the length of the flagellum and elastic links between filaments are presented at the base, then our model can demonstrate self-organization of bending waves as well as wave propagation without special feedback control by the curvature of the flagellum. Here, "cooperative interaction" between adjacent short segments, based on "cooperative dynamics" of cross-bridges, is important for wave propagation.     

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.     

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.     

A Computational Model of Dynein Activation Patterns that Can Explain Nodal Cilia Rotation

Normal left-right patterning in vertebrates depends on the rotational movement of nodal cilia. In order to produce this ciliary motion, the activity of axonemal dyneins must be tightly regulated in a temporal and spatial manner; the specific activation pattern of the dynein motors in the nodal cilia has not been reported. Contemporary imaging techniques cannot directly assess dynein activity in a living cilium. In this study, we establish a three-dimensional model to mimic the ciliary ultrastructure and assume that the activation of dynein proteins is related to the interdoublet distance. By employing finite-element analysis and grid deformation techniques, we simulate the mechanical function of dyneins by pairs of point loads, investigate the time-variant interdoublet distance, and simulate the dynein-triggered ciliary motion. The computational results indicate that, to produce the rotational movement of nodal cilia, the dynein activity is transferred clockwise (looking from the tip) between the nine doublet microtubules, and along each microtubule, the dynein activation should occur faster at the basal region and slower when it is close to the ciliary tip. Moreover, the time cost by all the dyneins along one microtubule to be activated can be used to deduce the dynein activation pattern; it implies that, as an alternative method, measuring this time can indirectly reveal the dynein activity. The proposed protein-structure model can simulate the ciliary motion triggered by various dynein activation patterns explicitly and may contribute to furthering the studies on axonemal dynein activity.     

Direction of force generated by the inner row of dynein arms on flagellar microtubules

Our goal was to determine the direction of force generation of the inner dynein arms in flagellar axonemes. We developed an efficient means of extracting the outer row of dynein arms in demembranated sperm tail axonemes, leaving the inner row of dynein arms structurally and functionally intact. Sperm tail axonemes depleted of outer arms beat at half the beat frequency of sperm tails with intact arms over a wide range of ATP concentrations. The isolated, outer arm-depleted axonemes were induced to undergo microtubule sliding in the presence of ATP and trypsin. Electron microscopic analysis of the relative direction of microtubule sliding (see Sale, W. S. and P. Satir, 1977, Proc. Natl. Acad. Sci. USA, 74:2045-2049) revealed that the doublet microtubule with the row of inner dynein arms, doublet N, always moved by sliding toward the proximal end of the axoneme relative to doublet N + 1. Therefore, the inner arms generate force such that doublet N pushes doublet N + 1 tipward. This is the same direction of microtubule sliding induced by ATP and trypsin in axonemes having both inner and outer dynein arms. The implications of this result for the mechanism of ciliary bending and utility in functional definition of cytoplasmic dyneins are 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.     

On the contribution of dynein-like activity to twisting in a three-dimensional sliding filament model.

It has been shown (Hines, M., and J. J. Blum, Biophys.J., 1984, 46:559-565) that passive moment-bearing links do not contribute appreciable twist resistance to an axoneme nor do they cause appreciable twisting in response to internal shear forces. We now examine the contribution of active moment-bearing links such as dynein arms to the generation of twist within an axoneme. The dynein model used causes distal sliding of the adjacent doublet by a force dependent on the angle of attachment of the arms. Attachment of the arms occurs at a specified angle relative to the angle of minimum potential energy. The steady state shape consistent with the forces applied by the attached dyneins is computed. It is shown that the twist generated in an active region is counterclockwise as viewed from tip to base and therefore accumulates at the end of the axoneme. For realistic forces and twist resistances, cumulative twist should not exceed a few degrees.     

Bending patterns of ATP-reactivated sea urchin sperm flagella following high salt extraction for removal of outer dynein arms

Two procedures were used for extraction of demembranated sea urchin sperm flagella with increased KCl concentrations, to remove outer dynein arms. Extraction with 0.55 M KCl in the Triton-demembranation solution produced a rapid fall in average sliding velocity to 50% of its unextracted value, with extensive changes in bending behavior of the distal half of the flagellum. Extraction with 0.42 M KCl following demembranation and activation by incubation with cAMP produced a more gradual fall in sliding velocity, reaching 50% of the unextracted value after 180 sec extraction. This procedure produced somewhat more normal bending patterns. In both cases, the bending pattern of the basal region of the flagellum is altered very little by extraction, in agreement with data from Chlamydomonas mutant flagella deficient in outer arm dyneins.     

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.     

Clockwise translocation of microtubules by flagellar inner-arm dyneins in vitro

Cilia and flagella are equipped with multiple species of dyneins that have diverse motor properties. To assess the properties of various axonemal dyneins of Chlamydomonas, in vitro microtubule translocation by isolated dyneins was examined with and without flow of the medium. With one inner-arm dynein species, dynein c, most microtubules became aligned parallel to the flow and translocated downstream after the onset of flow. When the flow was stopped, the gliding direction was gradually randomized. In contrast, with inner-arm dyneins d and g, microtubules tended to translocate at a shallow right angle to the flow. When the flow was stopped, each microtubule turned to the right, making a curved track. The clockwise translocation was not accompanied by lateral displacement, indicating that these dyneins generate torque that bends the microtubule. The torque generated by these dyneins in the axoneme may modulate the relative orientation between adjacent doublet microtubules and lead to more efficient functioning of total dyneins.     

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.     

Keeping an eye on I1: I1 dynein as a model for flagellar dynein assembly and regulation

Among the major challenges in understanding ciliary and flagellar motility is to determine how the dynein motors are assembled and localized and how dynein-driven outer doublet microtubule sliding is controlled. Diverse studies, particularly in Chlamydomonas, have determined that the inner arm dynein I1 is targeted to a unique structural position and is critical for regulating the microtubule sliding required for normal ciliary/flagellar bending. As described in this review, I1 dynein offers additional opportunities to determine the principles of assembly and targeting of dyneins to cellular locations and for studying the mechanisms that regulate dynein activity and control of motility by phosphorylation.     

Dynein heavy chain isoforms and axonemal motility

The translocation of dynein along microtubules is the basis for a wide variety of essential cellular movements. Dynein was first discovered in the ciliary axoneme, where it causes the directed sliding between outer doublet microtubules that underlies ciliary bending. The initiation and propagation of ciliary bends are produced by a precisely located array of different dyneins containing eight or more different dynein heavy chain isoforms. The detailed clarification of the structural and functional diversity of axonemal dynein heavy chains will not only provide the key to understanding how cilia function, but also give insights applicable to the study of non-axonemal microtubule motors.     

Regulation of outer-arm-dynein activity by phosphorylation and control of ciliary beat frequency

Summary Ciliary beating is empowered by a mechanochemical enzyme, dynein, which appears as two rows of projections on doublet microtubules. While inner-arm dyneins modulate beat form, outer-arm dynein empowers ciliary beat and sets beat frequency. Beat frequency is controlled via phosphorylation of outer-arm dynein. UsingParamecium tetraurelia as model system, we have previously identified a regulatory light chain of outer-arm dynein (22S dynein), M_r29 (p29), whose phosphorylation is cAMP-dependent. The phosphorylation state of the p29 in 22 S dynein determines in vitro microtubule translocation velocity. Although in vitro phosphorylation of p29 takes place in a short time, the percent change ist significantly less than the percent change in dynein activation, or in ciliary beat frequency. A potential mechanism that explains how a few activated dyneins can change ciliary beating is discussed.