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.     

A selective effect of Ni2+ on wave initiation in bull sperm flagella

Bull sperm that are extracted with 0.1% Triton X-100 and restored to motility with Mg2+-ATP lose coordination and stop swimming in the presence of 0.5 mM NiSO4. Although spontaneous coordination of flagellar waves is lost after exposure to Ni2+, other functions of the flagellum remain intact. The capacity for wave propagation along the flagellum is maintained together with the capacity for microtubular sliding. Wave motility can be restored to Ni2+-inhibited sperm by inducing a permanent bend onto the flagellum by micromanipulation. In the absence of such intervention, the loss of wave coordination is complete and irreversible. Ni2+-inhibited demembranated cells that are kept active by maintaining a bend in the flagellum exhibit a normal beat frequency. Both intact and demembranated sperm can retain spontaneous wave production at considerably slower rates of motion than Ni2+-inhibited cells. Short segments from the distal tip of the flagellum contain only the 9 + 2 microtubular axoneme. These short segments are able to propagate imposed bends even in the presence of Ni2+. In addition to wave propagation Ni2+-treated sperm can be shown to exhibit a normal sliding tubule phenomenon by direct assay. Although Ni2+-treated cells have a functional sliding tubule mechanism, and consequently the axoneme can propagate bends, it appears that these retained functions are not sufficient to cause spontaneous bend initiation. Our findings show that bend initiation is inhibited by Ni2+, and therefore is an independent process separate from the sliding tubule mechanism responsible for wave propagation.     

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.     

Basal sliding and the mechanics of oscillation in a mammalian sperm flagellum

The mechanism of oscillation in cilia and flagella has been a long-standing mystery. This article raises the possibility of a mechanical explanation based on new findings relating to where in the flagellum microtubule sliding can occur--and where it cannot occur. All theoretical analyses of flagellar bending have until now made the assumption that sliding displacements at the base of the flagellum cannot occur. One consequence of this has been the need to accept that sliding must be transmitted through propagating bends, an idea that has been tolerated even though it becomes paradoxical if bends are the result of resistance to sliding. Our observations, of spermatozoa from the chinchilla, have led us to a contradictory view. We have shown directly, by light microscopy and by two methods of electron microscopy, that basal sliding does occur. Also, evidence from video microscopy indicates that a propagating bend cannot transmit sliding through it. We have analyzed a movement pattern in which the beat frequency increases fourfold in a phasic manner. Our analysis of this suggests that new bends terminate when no further sliding is possible. At this point the bend direction immediately reverses. That is, the flagellar beat frequency increases when there is a limitation to sliding. One can see directly the alternation in basal sliding direction under these circumstances. This suggests a mechanism for the initiation of a new bend in the opposite direction to the bend just completed: we propose that the initiating trigger is the reversal of elastic deformations at the base, which reverses the direction of interdoublet sliding.     

Microtubule sliding in swimming sperm flagella: direct and indirect measurements on sea urchin and tunicate spermatozoa [published erratum appears in J Cell Biol 1991 Nov;115(4):1204]

Direct measurements of microtubule sliding in the flagella of actively swimming, demembranated, spermatozoa have been made using submicron diameter gold beads as markers on the exposed outer doublet microtubules. With spermatozoa of the tunicate, Ciona, these measurements confirm values of sliding calculated indirectly by measuring angles relative to the axis of the sperm head. Both methods of measurement show a nonuniform amplitude of oscillatory sliding along the length of the flagellum, providing direct evidence that "oscillatory synchronous sliding" can be occurring in the flagellum, in addition to the metachronous sliding that is necessary to propagate a bending wave. Propagation of constant amplitude bends is not accomplished by propagation of a wave of oscillatory sliding of constant amplitude, and therefore appears to require a mechanism for monitoring and controlling the bend angle as bends propagate. With sea urchin spermatozoa, the direct measurements of sliding do not agree with the values calculated by measuring angles relative to the head axis. The oscillation in angular orientation of the sea urchin sperm head as it swims appears to be accommodated by flexure at the head-flagellum junction and does not correspond to oscillation in orientation of the basal end of the flagellum. Consequently, indirect calculations of sliding based on angles measured relative to the longitudinal axis of the sperm head can be seriously inaccurate in this species.     

Computer simulation of flagellar movement. VI. Simple curvature-controlled models are incompletely specified.

Computer simulation is used to examine a simple flagellar model that will initiate and propagate bending waves in the absence of viscous resistances. The model contains only an elastic bending resistance and an active sliding mechanism that generates reduced active shear moment with increasing sliding velocity. Oscillation results from a distributed control mechanism that reverses the direction of operation of the active sliding mechanism when the curvature reaches critical magnitudes in either direction. Bend propagation by curvature-controlled flagellar models therefore does not require interaction with the viscous resistance of an external fluid. An analytical examination of moment balance during bend propagation by this model yields a solution curve giving values of frequency and wavelength that satisfy the moment balance equation and give uniform bend propagation, suggesting that the model is underdetermined. At 0 viscosity, the boundary condition of 0 shear rate at the basal end of the flagellum during the development of new bends selects the particular solution that is obtained by computer simulations. Therefore, the details of the pattern of bend initiation at the basal end of a flagellum can be of major significance in determining the properties of propagated bending waves in the distal portion of a flagellum. At high values of external viscosity, the model oscillates at frequencies and wavelengths that give approximately integral numbers of waves on the flagellum. These operating points are selected because they facilitate the balance of bending moments at the ends of the model, where the external viscous moment approaches 0. These mode preferences can be overridden by forcing the model to operate at a predetermined frequency. The strong mode preferences shown by curvature-controlled flagellar models, in contrast to the weak or absent mode preferences shown by real flagella, therefore do not demonstrate the inapplicability of the moment-balance approach to real flagella. Instead, they indicate a need to specify additional properties of real flagella that are responsible for selecting particular operating points.     

Induction of beating by imposed bending or mechanical pulse in demembranated, motionless sea urchin sperm flagella at very low ATP concentrations

A basic feature of the movement of eukaryotic flagella is oscillation. Although flagellar oscillation is thought to be regulated by a self-regulatory feedback system including the mechanical signal of bending itself, the mechanism regulating the dynein motile activity to produce oscillation is not well understood. To elucidate the mechanism, we developed a new experimental system which allowed us to analyze the conditions necessary for the induction of oscillation. When a mechanical signal of bending or a pulse was applied by micromanipulation to a demembranated motionless sea urchin sperm flagellar axoneme at very low ATP concentrations (1-3 microM), a localized pair of bends was induced. The bend formation was often followed by further responses including propagation of the distal bend of paired bends, growth and propagation of the paired bends, and cyclical beating. The beating was induced at 2.0 microM or higher concentrations of ATP, but appeared even at 1.5 microM ATP if a few muM of ADP was also present. When the proximal half of a flagellum was attached to a microneedle, beating could not be induced in the distal free region at 2 microM ATP. These results suggest that mechanical signal is involved in the mechanism regulating the motile activity of dynein to produce oscillation. Our results also showed that the presence of a small amount of ADP and the axial difference along the flagellum are factors essential for the induction of flagellar oscillation.     

Starting transients in sea urchin sperm flagella

Live sea urchin spermatozoa were rendered immotile by lowered pH; Triton-extracted spermatozoa were rendered immotile by either lowered pH or by deprivation of ATP. The spermatozoa began to beat after an increase in pH or as ATP was supplied, and the first bends were recorded on ciné film. Triton-extracted spermatozoa deprived of ATP retained a partially formed basal bend which could be either principal or reverse, and which resumed its development and propagation as ATP was supplied. Both live and tritonated flagella straightened at low pH. As the pH was increased, a series of principal bends formed near the base and propagated to the tip. Reverse bends began to develop as the pH continued to increase. The principal and reverse bends thus exhibited different sensitivities to pH, which suggests differences in the mechanisms that produce them. Straight flagella began to move by synchronous sliding all along the flagellum, thus forming principal bends. Flagella that contained a basal bend began to move by primarily metachonous sliding within that bend.     

Evidence for a sliding-resistance at the tip of the trypanosome flagellum

Motility in trypanosomes is achieved through the undulating behaviour of a single "9 + 2" flagellum; normally the flagellar waves begin at the flagellar tip and propagate towards the base. For flagella in general, however, propagation is from base-to-tip and it is believed that bend formation, and sustained regular oscillation, depend upon a localised resistance to inter-doublet sliding - which is normally conferred by structures at the flagellar base, typically the basal body. We therefore predicted that in trypanosomes there must be a resistive structure at the flagellar tip. Electron micrographs of Crithidia deanei, Herpetomonas megaseliae, Trypanosoma brucei and Leishmania major have confirmed that such attachments are present. Thus, it can be assumed that in trypanosomes microtubule sliding at the flagellar tip is resisted sufficiently to permit bend formation.     

New evidence for a "biased baseline" mechanism for calcium-regulated asymmetry of flagellar bending

Time-averaged data covering six to ten beat cycles for ATP-reactivated spermatozoa of a sea urchin and Ciona, and from a uniflagellate mutant of Chlamydomonas, were analyzed to obtain parameters of oscillation and mean shear angle at each point along the flagellum. The mean shear angles usually show a sharp change near the base of the flagellum. This sharp basal change in angle is correlated with perceived asymmetry in the development times of principal and reverse bends when these bends are measured directly from the asymmetric bending patterns, without subtracting out the mean shear angle. The asymmetry in development times was previously considered to be evidence against a "biased baseline" mechanism for asymmetric bending waves, in which completely symmetric bending waves develop and propagate on a curved flagellum. Our analysis now shows that the asymmetry in development times can be fully explained by the presence of a sharp static bend near the base of the flagellum, which can confuse the determination of the times of initiation of new bends at the base of the flagellum. Our reinterpretation of these data removes previous objections to the "biased baseline" mechanism for the regulation of bending wave asymmetry by calcium, and supports other evidence favoring a biased baseline mechanism, rather than a "biased switching" mechanism.     

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.     

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.     

A new automated method of image analysis: comparison of ciliary and flagellar beats

A new automated method of image analysis of sperm flagellar (human) and cilia (Dunaliella) bends is developed. This method permits an automatic determination of the line characterizing the flagellum. Two dynamic parameters are measured: the wave propagation velocity and the wave curvature radius. The data reveal similar patterns in the propagation of the principal and reverse waves between flagelated and ciliated cells. Conversely, differences are seen in principal wave curvature due perhaps to the presence of periaxonemal structures in the flagellum, absent in cilium. The identical patterns of reverse wave curvaturei in both systems may be linked to axonemal limitations.     

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.     

Bending-wave propagation by microtubules and flagella

The movement of an elastic filament in a viscous medium can be computed from the fourth-order nonlinear partial differential equation obtained by balancing bending moments at all points along the length of the filament. These bending moments result from active forces, elastic resistance to bending, and viscous resistance to movement through the medium. I have studied numerical solutions obtained for two situations of biological interest: For the movement of individual microtubules, the active force is generated by interaction between the microtubule and the substratum over which it is moving, and is directed along the axis of the microtubule. The computations can reproduce the gliding movement of unrestrained microtubules, and also the periodic bending and bend propagation seen when the leading end of the microtubule is restrained. No modulation of active force is required to generate bending waves. For the movement of flagella, the active forces are generated internally as sliding forces between adjacent members of a cylinder of nine microtubular doublets. Without some additional control assumptions, the forces will be balanced and no bending moments will be generated. The problem faced by investigators of flagellar motility is to determine the control mechanisms that operate to make the system asymmetric, so that active bending moments are generated. Computations with models in which the curvature of the flagellum modulates the active-force generators have indicated that this control specification is sufficient to generate oscillation and bend propagation, but is insufficient to completely determine the movement.     

Thinking about flagellar oscillation

Bending of cilia and flagella results from sliding between the microtubular outer doublets, driven by dynein motor enzymes. This review reminds us that many questions remain to be answered before we can understand how dynein-driven sliding causes the oscillatory bending of cilia and flagella. Does oscillation require switching between two distinct, persistent modes of dynein activity? Only one mode, an active forward mode, has been characterized, but an alternative mode, either inactive or reverse, appears to be required. Does switching between modes use information from curvature, sliding direction, or both? Is there a mechanism for reciprocal inhibition? Can a localized capability for oscillatory sliding become self-organized to produce the metachronal phase differences required for bend propagation? Are interactions between adjacent dyneins important for regulation of oscillation and bend propagation? Cell Motil. Cytoskeleton 2008. (c) 2008 Wiley-Liss, Inc.     

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

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

Form of developing bends in reactivated sperm flagella.

1. Dark-field, multiple-exposure photographs of reactivated tritonated sea urchin sperm flagella swimming under a variety of conditions were analysed. 2. The length, radius and subtended angle of bends increased during bend development. The pattern of development was essentially the same under all conditions observed. 3. The angles of the two bends nearest the base tend to increase at the same rate, cancelling one another, so that the development of new bends causes little if any net microtubular sliding. 4. The direction of microtubular sliding within a bend is initially in the same direction as that within the preceding bend, and reverses as the bend develops.