The mechanics of cilia and flagella: What we know and what we need to know.

In this review, we provide a condensed overview of what is currently known about the mechanical functioning of the flagellar/ciliary axoneme. We also present a list of 10 specific areas where our current knowledge is incomplete and explain the benefits of further experimental investigation. Many of the physical parameters of the axoneme and its component parts have not been determined. This limits our ability to understand how the axoneme structure contributes to its functioning in several regards. It restricts our ability to understand how the mechanics of the structure contribute to the regulation of motor function. It also confines our ability to understand the three-dimensional workings of the axoneme and how various beating modes are accomplished. Lastly, it prevents accurate computational modeling of the axoneme in three-dimensions.

The many modes of flagellar and ciliary beating: Insights from a physical analysis.

The mechanism that allows the axoneme of eukaryotic cilia and flagella to produce both helical and planar beating is an enduring puzzle. The nine outer doublets of eukaryotic cilia and flagella are arranged in a circle. Therefore, each doublet pair with its associated dynein motors, should produce torque to bend the flagellum in a different direction. Sequential activation of each doublet pair should, therefore result in a helical bending wave. In reality, most cilia and flagella have a well-defined bending plane and many exhibit an almost perfectly flat (planar) beating pattern. In this analysis we examine the physics that governs flagellar bending, and arrive at two distinct possibilities that could explain the mechanism of planar beating. Of these, the mechanism with the best observational support is that the flagellum behaves as two ribbons of doublets interacting with a central partition. We also examine the physics of torsion in flagella and conclude that torsion could play a role in transitioning from a planar to a helical beating modality in long flagella. Lastly, we suggest some tests that would provide theoretical and/or experimental evaluation of our proposals.

Functional anatomy of the mammalian sperm flagellum.

The eukaryotic flagellum is the organelle responsible for the propulsion of the male gamete in most animals. Without exception, sperm of all mammalian species use a flagellum for swimming. The mammalian sperm has a centrally located 9 + 2 arrangement of microtubule doublets and hundreds of accessory proteins that together constitute an axoneme. However, they also possess several characteristic peri-axonemal structures that make the mammalian sperm tail function differently. These modifications include nine outer dense fibers (ODFs) that are paired with the nine outer microtubule doublets of the axoneme, and are anchored in a structure called the connecting piece located at the base. The presence of the ODFs and connecting piece, and the absence of a basal body, dictate that physical forces generated by the dynein motors are transmitted to the base of the flagellum through the ODFs. Mammalian sperm flagella also possess a mitochondrial and a fibrous sheath that encircle most of the axoneme. These sheaths and the ODFs add mechanical rigidity to the flagellum creating the functional effect of increasing bend wavelength, which requires the entrainment of more dynein motors in the production of a single wave. The sheaths also act as a retinaculum and maintain the integrity of the central axoneme when large bending torques are generated by dynein. Large torque production is crucial to the process of hyperactivation and the unique motility transitions associated with effective fertilizing capacity. Consequently, these specialized anatomical features are essential for the effective interaction of sperm with the female reproductive tract and ovum. © 2016 Wiley Periodicals, Inc.

Mechanics of the eukaryotic flagellar axoneme: Evidence for structural distortion during bending.

The sliding doublet mechanism is the established explanation that allows us to understand the process of ciliary and flagellar bending. In this study, we apply the principles of the sliding doublet mechanism to analyze the mechanics of the counterbend phenomenon in sea urchin sperm flagella. When a passive, vanadate-treated, flagellum is forced into a bend with a glass microprobe, the portion of the flagellum distal to the probe exhibits a bend of opposite curvature (counterbend) to the imposed bend. This phenomenon was shown to be caused by the induction of inter-doublet shear and is dependent on the presence of an inter-doublet shear resistance. Here we report that in sea urchin flagella there is systematically less shear induced in the distal flagellum than is predicted by the sliding doublet mechanism, if we follow the assumption that the diameter of the flagellum is uniform. To account for the reduced shear that is observed, the likeliest and most direct interpretation is that the portion of the axoneme that is forced to bend undergoes substantial compression of the axoneme in the bending plane. A compression of 30-50 nm would be sufficient to account for the shear reduction from a bend of 2 radians. A compression of this magnitude would require considerable flexibility in the axoneme structure. This would necessitate that the radial spokes and/or the central pair apparatus are easily compressed by transverse stress. © 2016 Wiley Periodicals, Inc.

The geometric clutch at 20: stripping gears or gaining traction?

It has been 20 years since the geometric clutch (GC) hypothesis was first proposed. The core principle of the GC mechanism is fairly simple. When the axoneme of a eukaryotic flagellum is bent, mechanical stress generates forces transverse to the outer doublets (t-forces). These t-forces can push doublets closer together or pry them apart. The GC hypothesis asserts that changes in the inter-doublet spacing caused by t-forces are responsible for the activation and deactivation of the dynein motors, that creates the beat cycle. A series of computer models utilizing the clutch mechanism has shown that it can simulate ciliary and flagellar beating. The objective of the present review is to assess where things stand with the GC hypothesis in the clarifying light of new information. There is considerable new evidence to support the hypothesis. However, it is also clear that it is necessary to modify some of the original conceptions of the hypothesis so that it can be consistent with the results of recent experimental and ultrastructural studies. In particular, dynein deactivation by t-forces must be able to occur with dyneins that remain attached to the B-subtubule of the adjacent doublet.

Ultrastructural evidence that motility changes caused by variations in ATP, Mg2+ , and ADP correlate to conformational changes in reactivated bull sperm axonemes.

We report the results of an ultrastructural study of Triton X-100-extracted, Mg-adenosine triphosphate (ATP)-reactivated bull sperm. We utilized a rapid fixation method to look for differences in the flagellar apparatus that correlate to the state of motility of reactivated sperm models. In a companion article, we examined the motility characteristics induced in bull sperm models by varying the concentration ratio of ATP and Mg(2+) and the stabilizing effect of adenosine diphosphate (ADP) on coordinated beating. Based on the results of that report, we selected four dissimilar states that appeared to represent extremes. One reactivation condition produces vigorous motility similar to live sperm, another produces large amplitude, low frequency beating while the remaining two conditions produce small amplitude vibrations of the flagellum with little coordinated beating. Morphometric analysis of transmission electron micrographs of sperm from these four treatment conditions revealed statistically significant differences between the samples in regard to axoneme diameter, inter-microtubule doublet spacing, and outer dense fiber (ODF) spacing. Our results show that Mg(2+) decreases the axoneme diameter and reduces interdoublet spacing, while ATP, uncomplexed with Mg(2+) , had the opposite effect. We also provide supporting evidence that this may be due to Mg(2+) increasing, and ATP decreasing, the interdoublet adhesion of dynein. We also found that 4 mM ADP significantly increases the separation between the ODFs and the space between the ODFs and the central axoneme within the middle piece. We present a hypothetical explanation that is consistent with our results to explain how ATP, ADP, and Mg(2+) act to regulate the beat cycle. © 2014 Wiley Periodicals, Inc.

The physiological role of ADP and Mg2+ in maintaining a stable beat cycle in bull sperm.

Sperm flagella derive their motive power from the motor protein dynein. In this study, we show that maintenance of the flagellar beat cycle in detergent-extracted bull sperm models is highly dependent on the ratio of Mg(2+) to adenosine triphosphate (ATP). An excess of either ATP un-complexed with Mg(2+) , or an excess of Mg(2+) without an equivalent concentration of ATP, results in the loss of beat amplitude and a reduced curvature development in the beat cycle. In addition, we find that adenosine diphosphate (ADP) can stabilize the beat cycle and permit rhythmic beating across a broader range of ATP and Mg(2+) concentrations. We provide evidence that suggests that when ATP is un-complexed with Mg(2+) , it disrupts the beat cycle by reducing dynein adhesion and thereby, reduces the transmission of dynein-generated force between the doublets. Excess Mg(2+) does not act by the same mechanism and induces a condition where the flagellum is more resistant to bending. This is consistent with the idea that high Mg(2+) stabilizes rigor bridges, and ATP reduces the microtubule binding affinity of dynein. Our results may explain how intact sperm are able to sustain coordinated flagellar beating under a wide range of metabolic conditions, as intact sperm produce ADP in direct proportion to their consumption of ATP.

The effects of Ca2+ and ADP on dynein switching during the beat cycle of reactivated bull sperm models.

Calcium regulation of flagellar motility is the basis for chemotaxis, phototaxis, and hyperactivation responses in eukaryotic flagellates and spermatozoa. Ca2+ is the internal messenger for these responses, but the coupling between Ca2+ and the motor mechanism that generates the flagellar beat is incompletely understood. We examined the effects of Ca2+ on the flagellar curvature at the switch-points of the beat cycle in bull sperm. The sperm were detergent extracted and reactivated with 0.1 mM adenosine triphosphate (ATP). With their heads immobilized and their tails beating freely it is possible to calculate the bending torque and the transverse force acting on the flagellum at the switch-points. An increase in the free Ca2+ concentration (pCa 8 to pCa 4) significantly decreased the development of torque and t-force in the principal bending direction, while having negligible effect on the reverse bend. The action of Ca2+ was more pronounced when the sperm were also treated with 4 mM adenosine diphosphate (ADP); it was sufficient to change the direction of bending that reaches the greater curvature. We also observed that the curvature of the distal half of the flagellum became locked in one direction in the presence of Ca2+ . This indicates that a subset of the dynein becomes continuously activated by Ca2+ and fails to switch with the beat cycle. Our evidence suggests this subset of dyneins is localized to doublets #1-4 of the axoneme.

The calcium response of mouse sperm flagella: role of calcium ions in the regulation of dynein activity.

Triton X-100-extracted mouse sperm treated with 0.1 mM ATP and 1.0 mM Ca(2+) exhibit an extremely coiled configuration that has been previously described as a curlicue. Sperm in the curlicue configuration exhibit a monotonically curved flagellum where the shear angle of the flagellum can reach a value as high as 14 radians at the flagellar tip. We utilized this strong reaction to Ca(2+) to elucidate the mechanism of the calcium response. The disintegration of the axoneme was facilitated by the use of an extraction procedure that removed the mitochondrial sheath without eliminating the calcium response. The order of emergence of the doublet microtubule outer dense fiber complexes was observed in the presence and absence of added Ca(2+). The identity of the emergent elements was confirmed by transmission electron microscopy. Ca(2+) altered the order of emergence of internal axoneme elements to favor the appearance of the elements of the 9-1-2 side of the axoneme. These elements are propelled baseward by the action of dyneins on doublets 1 and 2. It was also possible to establish that the motive force for maintaining the curlicue configuration is dynein-based. The curlicues were relaxed by inhibition with 50 µM NaVO(3) and were reestablished by disinhibiting the vanadate with 2.5 mM catechol.

Flagellar and ciliary beating: the proven and the possible.

The working mechanism of the eukaryotic flagellar axoneme remains one of nature's most enduring puzzles. The basic mechanical operation of the axoneme is now a story that is fairly complete; however, the mechanism for coordinating the action of the dynein motor proteins to produce beating is still controversial. Although a full grasp of the dynein switching mechanism remains elusive, recent experimental reports provide new insights that might finally disclose the secrets of the beating mechanism: the special role of the inner dynein arms, especially dynein I1 and the dynein regulatory complex, the importance of the dynein microtubule-binding affinity at the stalk, and the role of bending in the selection of the active dynein group have all been implicated by major new evidence. This Commentary considers this new evidence in the context of various hypotheses of how axonemal dynein coordination might work.

Functional deficiencies and a reduced response to calcium in the flagellum of mouse sperm lacking SPAG16L.

The Spag16L gene codes for a protein that is localized to the central apparatus which is essential for normal sperm motility and male fertility. Sperm from mice homozygous for a targeted deletion of the Spag16L gene were examined to assess their flagellar motor functions compared with age- and strain-matched control sperm. Sperm were also demembranated with Triton X-100 and examined for their ability to respond to free calcium, as well as for their ability to undergo microtubule sliding driven by dynein action. In addition, the passive flagella, inhibited by sodium metavanadate to disable the dyneins, were examined for mechanical abnormalities. Live Spag16L-null sperm exhibited much less bending of the flagellum during the beat. The amount of microtubule sliding in the R-bend direction of the beat was selectively restricted, which suggests that there is limited activation of the dyneins on one side of the axoneme in the live cells. This is corroborated by the results on detergent-extracted sperm models. The flagellar response to calcium is greatly reduced. The calcium response requires the activation of the dyneins on outer doublets 1, 2, 3, and 4. These are the same dyneins required for R-bend formation. In axonemes prepared to disintegrate by microtubule sliding, we observed little or no extrusion of doublets 1 and 2, consistent with a reduced activity of their dyneins. This deficit in motor function, and an increased rigidity of the midpiece region which we detected in the passive flagella, together can explain the observed motility characteristics of the Spag16L-null sperm.

Detergent-extracted models for the study of cilia or flagella.

Methods for using non-ionic detergents to produce demembranated and reactivated cilia and flagella are described in detail. Demembranated and reactivated cell models are useful as a research tool for studying motility function in flagella and cilia. When the plasma membrane is removed, the factors regulating motility can be studied under standardized experimental conditions that otherwise would be impossible. Practical insight is provided to understand the important factors in producing stable reactivated models. In addition, several useful variations of the method are presented for different types of mammalian and non-mammalian flagellar and ciliary systems.

Mechanical properties of the passive sea urchin sperm flagellum.

In this study we used Triton X-100 extracted sea urchin spermatozoa to investigate the mechanical behavior of the basic 9+2 axoneme. The dynein motors were disabled by vanadate so that the flagellum is rendered a passive structure. We find that when a proximal portion of the flagellum is bent with a glass microprobe, the remainder of the flagellum distal to the probe exhibits a bend in the opposite direction (a counterbend). The counterbend can be understood from the prevailing sliding doublet model of axoneme mechanics, but does require the existence of elastic linkages between the outer doublets. Analysis of the shapes of counterbends provides a consensus value of 0.03-0.08/microm(2) for the ratio of the interdoublet shear resistance (E(S)) to the bending resistance (E(B)) and we find that the ratio E(S)/E(B) is relatively conserved for both passive flagella and transiently quiescent live flagella. This ratio expresses a fundamental mechanical property of the eukaryotic axoneme. It defines the contributions to total bending resistance derived from bending the microtubules and from stretching the interdoublet linkages, respectively. Using this ratio, and computer simulations of earlier experiments that measured the total stiffness of the flagellum, we obtain estimates of approximately 1 x 10(8) pN nm(2)/rad for E(B) and 6 pN/rad for E(S), assuming that both elasticities are linear. Our results indicate that the behavior of the flagellum is close to that predicted by a linear model for shear elasticity.

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 muM 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/microm in 0.1 mM ATP and increasing to 2.9 +/- 1.2 nN/microm 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.

The counterbend phenomenon in dynein-disabled rat sperm flagella and what it reveals about the interdoublet elasticity.

Rat sperm that have been rendered passive by disabling the dynein motors with 50 muM sodium metavanadate and 0.1 mM ATP exhibit an interesting response to imposed bending. When the proximal flagellum is bent with a microprobe, the portion of the flagellum distal to the probe contact point develops a bend in the direction opposite the imposed bend. This "counterbend" is not compatible with a simple elastic beam. It can be satisfactorily explained by the sliding tubule model of flagellar structure but only if there are permanent elastic connections between the outer doublets of the axoneme. The elastic component that contributes the bending torque for the counterbend does not reset to a new equilibrium position after an imposed bend but returns the flagellum to a nearly straight or slightly curved final position after release from the probe. This suggests it is based on fixed, rather than mobile, attachments. It is also disrupted by elastase or trypsin digestion, confirming that it is dependent on a protein linkage. Adopting the assumption that the elasticity is attributed to the nexin links that repeat at 96 nm intervals, we find an apparent elasticity for each link that ranges from 1.6 to 10 x 10(-5) N/m. However, the elasticity is nonlinear and does not follow Hooke's law but appears to decrease with increased stretch. In addition, the responsible elastic elements must be able to stretch to more than 10 times their resting length without breakage to account for the observed counterbend formation. Elasticity created by some type of protein unfolding may be the only viable explanation consistent with both the extreme capacity for extension and the nonlinear character of the restoring force that is observed.

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.