A study of helical and planar waves on sea urchin sperm flagella, with a theory of how they are generated

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.

Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.

Colloidal Active Matter Mimics the Behavior of Biological Microorganisms-An Overview

This article provides a review of the recent development of biomimicking behaviors in active colloids. While the behavior of biological microswimmers is undoubtedly influenced by physics, it is frequently guided and manipulated by active sensing processes. Understanding the respective influences of the surrounding environment can help to engineering the desired response also in artificial swimmers. More often than not, the achievement of biomimicking behavior requires the understanding of both biological and artificial microswimmers swimming mechanisms and the parameters inducing mechanosensory responses. The comparison of both classes of microswimmers provides with analogies in their dependence on fuels, interaction with boundaries and stimuli induced motion, or taxis.

MODELING OF FLAGELLUM BEHAVIOR AND TWO-DIMENSIONAL SPERM CELL MOTILITY WITHIN THE CONTEXT OF FLUID–SOLID INTERACTIONS

In this study, the flagellar motility of a swimmer microorganism as a model of a human sperm cell, inside a two-dimensional channel as a model of the female reproductive tract containing a viscous fluid, is numerically investigated. The Navier–Stokes equations governing the fluid are coupled with the equations governing the models flagellum via applying a fluid–solid interaction approach and then solved using the finite element method. To stimulate the flagellum to move, a prescribed sinusoidal waveform is applied to it. The strain induced by this waveform along the flagellum initiates a continuous interaction between the flagellum and the fluid. The simulations are validated using data available in the literature. A very good agreement is seen between them. The results show that by decreasing the Young modulus of the flagellum as well as increasing the fluid viscosity, the swimming velocity of the model significantly decreases. It is found that for lower Young modulus of the flagellum, the effect of the fluid viscosity on the flagellar deformation is stronger. It is also found that for higher amplitude of the waveform applied to stimulate the flagellum, both the swimming velocity of the model and the average work rate are greater. Moreover, it is found that in a channel with a smaller height, the model swims at a higher speed and with a higher average work rate.

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.

Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signalling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the 3D motion of the flagellum in a viscous Newtonian fluid with the evolving calcium concentration. The flagellum is modelled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a 1D reaction-diffusion model on a moving domain, the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

IRONSperm: Sperm-templated soft magnetic microrobots

We develop biohybrid magnetic microrobots by electrostatic self-assembly of nonmotile sperm cells and magnetic nanoparticles. Incorporating a biological entity into microrobots entails many functional advantages beyond shape templating, such as the facile uptake of chemotherapeutic agents to achieve targeted drug delivery. We present a single-step electrostatic self-assembly technique to fabricate IRONSperms, soft magnetic microswimmers that emulate the motion of motile sperm cells. Our experiments and theoretical predictions show that the swimming speed of IRONSperms exceeds 0.2 body length/s (6.8 ± 4.1 µm/s) at an actuation frequency of 8 Hz and precision angle of 45°. We demonstrate that the nanoparticle coating increases the acoustic impedance of the sperm cells and enables localization of clusters of IRONSperm using ultrasound feedback. We also confirm the biocompatibility and drug loading ability of these microrobots, and their promise as biocompatible, controllable, and detectable biohybrid tools for in vivo targeted therapy.

Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering

Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.

Flagellar ultrastructure suppresses buckling instabilities and enables mammalian sperm navigation in high-viscosity media

Eukaryotic flagellar swimming is driven by a slender motile unit, the axoneme, which possesses an internal structure that is essentially conserved in a tremendous diversity of sperm. Mammalian sperm, however, which are internal fertilizers, also exhibit distinctive accessory structures that further dress the axoneme and alter its mechanical response. This raises the following two fundamental questions. What is the functional significance of these structures? How do they affect the flagellar waveform and ultimately cell swimming? Hence we build on previous work to develop a mathematical mechanical model of a virtual human sperm to examine the impact of mammalian sperm accessory structures on flagellar dynamics and motility. Our findings demonstrate that the accessory structures reinforce the flagellum, preventing waveform compression and symmetry-breaking buckling instabilities when the viscosity of the surrounding medium is increased. This is in agreement with previous observations of internal and external fertilizers, such as human and sea urchin spermatozoa. In turn, possession of accessory structures entails that the progressive motion during a flagellar beat cycle can be enhanced as viscosity is increased within physiological bounds. Hence the flagella of internal fertilizers, complete with accessory structures, are predicted to be advantageous in viscous physiological media compared with watery media for the fundamental role of delivering a genetic payload to the egg.

Fish sperm motility analysis: the central role of the flagellum

Motility analysis of spermatozoa relies on the investigation of either head trajectories or flagellum characteristics. Those two sets of parameters are far from being independent, the flagellum playing the role of motor, whereas the head plays a passive role of cargo. Therefore, quantitative descriptions of head trajectories represent a simplification of the complex pattern of whole sperm cell motion, resulting from the waves developed by the flagellum. The flagellum itself responds to a large variety of signals that precisely control its axoneme to allow activation, acceleration, slowing down or reorientation of the whole spermatozoon. Thus, it is obvious that analysis of flagellum characteristics provides information on the original source of movement and orientation of the sperm cell and presents additional parameters that enrich the panoply of quantitative descriptors of sperm motility. In this review, we briefly describe the methodologies used to obtain good-quality images of fish spermatozoa (head and especially flagellum) while they move fast and the methods developed for their analysis. The paper also aims to establish a link between classical analyses by computer-aided sperm analysis (CASA) and the descriptors generated by fish sperm flagellum analysis, and emphasises the information to be gained regarding motility performance from flagellum motion data.

Controllable switching between planar and helical flagellar swimming of a soft robotic sperm

Sperm cells undergo a wide variety of swimming patterns by a beating flagellum to maintain high speed regardless of the rheological and physical properties of the background fluid. In this work, we develop and control a soft robotic sperm that undergoes controllable switching between swimming modes like biological sperm cells. The soft robotic sperm consists of a magnetic head and an ultra-thin flexible flagellum, and is actuated using external magnetic fields. We observe that out-of-plane wobbling of the head results in helical wave propagation along the flagellum, whereas in-plane wobbling achieves planar wave propagation. Our theoretical predictions and experimental results show the ability of the soft robotic sperm to change its swimming speed by tuning the beating frequency of its flagellum and the propulsion pattern. The average speed of the soft robotic sperm increases by factors of 2 and 1.2 in fluids with viscosity of 1 Pa.s and 5 Pa.s at relatively low actuation frequencies, respectively, when they switch between planar to helical flagellar propulsion.

Load response of shape-changing microswimmers scales with their swimming efficiency

External forces acting on a microswimmer can feed back on its self-propulsion mechanism. We discuss this load response for a generic microswimmer that swims by cyclic shape changes. We show that the change in cycle frequency is proportional to the Lighthill efficiency of self-propulsion. As a specific example, we consider Najafi's three-sphere swimmer. The force-velocity relation of a microswimmer implies a correction for a formal superposition principle for active and passive motion.

Forward and inverse problems in the mechanics of soft filaments

Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

Radial Spokes-A Snapshot of the Motility Regulation, Assembly, and Evolution of Cilia and Flagella

Propulsive forces generated by cilia and flagella are used in events that are critical for the thriving of diverse eukaryotic organisms in their environments. Despite distinctive strokes and regulations, the majority of them adopt the 9+2 axoneme that is believed to exist in the last eukaryotic common ancestor. Only a few outliers have opted for a simpler format that forsakes the signature radial spokes and the central pair apparatus, although both are unnecessary for force generation or rhythmicity. Extensive evidence has shown that they operate as an integral system for motility control. Recent studies have made remarkable progress on the radial spoke. This review will trace how the new structural, compositional, and evolutional insights pose significant implications on flagella biology and, conversely, ciliopathy.

Fluid flow and sperm guidance: a simulation study of hydrodynamic sperm rheotaxis

How does a sperm find its way? The study of guidance cues has fascinated sperm biologists and in particular the prospect of rheotaxis, that is a fluid flow orienting the direction of sperm swimming, has been the subject of extensive recent study, as readily motivated by the prospect that such guidance may be active in the mammalian female reproductive tract. For instance, it has been hypothesized that helical sperm flagellar beating is necessary for such guidance, whereas there is an extensive diversity of flagellar beating patterns, with planar sperm beating readily observed in human cells for example. In particular, such cells will not be guided by fluid flow according to hypothesized mechanisms for rheotaxis presented thus far. Here, using simulation methods, we investigate rheotaxis for a wide range of flagellar beat patterns. Providing the virtual sperm firstly does not possess a tightly circling trajectory in the absence of a background flow and secondly, remains within a region of low shear to prevent being washed away by the background flow, rheotaxis is generally observed with the sperm swimming into the flow together with a possible transverse velocity. Tight circling sperm motility, as observed in select hyperactivated sperm and CatSper mutants, is predicted to disrupt the rheotactic response, whereas confinement to low shear regions generally requires boundary accumulation, thus introducing subtleties in the relationship between rheotactic behaviours and the flagellar waveform and sperm characteristics. Nonetheless, such predictions suggest such rheotactic guidance may be more common and robust than previously thought, and we document simple criteria for the presence of rheotaxis that are consistent with our simulations and understanding, as well as reported observations to date.

Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells

Rheotaxis, the directed response to fluid velocity gradients, has been shown to facilitate stable upstream swimming of mammalian sperm cells along solid surfaces, suggesting a robust physical mechanism for long-distance navigation during fertilization. However, the dynamics by which a human sperm orients itself relative to an ambient flow is poorly understood. Here, we combine microfluidic experiments with mathematical modeling and 3D flagellar beat reconstruction to quantify the response of individual sperm cells in time-varying flow fields. Single-cell tracking reveals two kinematically distinct swimming states that entail opposite turning behaviors under flow reversal. We constrain an effective 2D model for the turning dynamics through systematic large-scale parameter scans, and find good quantitative agreement with experiments at different shear rates and viscosities. Using a 3D reconstruction algorithm to identify the flagellar beat patterns causing left or right turning, we present comprehensive 3D data demonstrating the rolling dynamics of freely swimming sperm cells around their longitudinal axis. Contrary to current beliefs, this 3D analysis uncovers ambidextrous flagellar waveforms and shows that the cell's turning direction is not defined by the rolling direction. Instead, the different rheotactic turning behaviors are linked to a broken mirror symmetry in the midpiece section, likely arising from a buckling instability. These results challenge current theoretical models of sperm locomotion.

Two-dimensional slither swimming of sperm within a micrometre of a surface

Sperm motion near surfaces plays a crucial role in fertilization, but the nature of this motion has not been resolved. Using total internal reflection fluorescence microscopy, we selectively imaged motile human and bull sperm located within one micron of a surface, revealing a distinct two-dimensional (2D) ‘slither' swimming mode whereby the full cell length (50–80 μm) is confined within 1 μm of a surface. This behaviour is distinct from bulk and near-wall swimming modes where the flagellar wave is helical and the head continuously rotates. The slither mode is intermittent (∼1 s, ∼70 μm), and in human sperm, is observed only for viscosities over 20 mPa·s. Bull sperm are slower in this surface-confined swimming mode, owing to a decrease in their flagellar wave amplitude. In contrast, human sperm are ∼50% faster—suggesting a strategy that is well suited to the highly viscous and confined lumen within the human fallopian tube.

Sperm motion near surfaces plays a key role in fertilization, but a description of how this motion differs from bulk swimming is lacking. Here, Nosrati et al. visualize sperm swimming within 1 μm of a glass surface and describe a ‘slither' swimming mode which differs from bulk helical swimming, and increases the velocity of human sperm.

Motility initiation of sterlet sturgeon (Acipenser ruthenus) spermatozoa: Describing the propagation of the first flagellar waves

In the present study, for the first time in fish spermatozoa, we describe the precise chronology of motility initiation of sterlet (sturgeon) sperm from completely immotile flagella to regular full wave propagation. The successive activation steps were investigated by high-speed video microscopy, using specific experimental situation, where sperm motility initiation was delayed in time up to several seconds (10 ± 2.68 seconds). Starting from fully immotile, the flagellum shows some trembling for a brief period, soon followed by appearance of the first real bend (so-called "principal bend") with a large wave amplitude 4.28 ± 0.65 μm, then by the "reverse bend," the latter presenting a lower (P < 0.05) wave amplitude (1.14 ± 0.32 μm). This couple of first bends formed at the basal region begins to propagate toward the flagellar tip but gradually fades when reaching the midflagellum, wherein consequently the sperm cell remains nonprogressive. This behavior repeats several times until a stage where the amplitude of the reverse bend gradually reaches a value similar that of the principal bend: The larger amplitude of this couple of bends finally leads to sustain a real "takeoff" of the sperm cell characterized by a full flagellar wave propagation generating an active forward displacement similar to that occurring during regular steady state motility (several seconds after activation). Starting from the earliest stages of motility initiation, the wave propagation along the flagellum and formation of new waves proceeded in a helical manner leading to a 3-dimensional rotation of the whole spermatozoon. Eventually, we estimated that the time period needed from the activation signal (contact with fresh water) to full wave propagation ranges from 0.4 to 1.2 seconds.

A fully three-dimensional model of the interaction of driven elastic filaments in a Stokes flow with applications to sperm motility

In many animals, sperm flagella exhibit primarily planar waveforms. An isolated sperm with a planar flagellar beat in a three-dimensional unbounded fluid domain would remain in a plane. However, because sperm must navigate through complex, three-dimensional confined spaces along with other sperm, forces that bend or move the flagellum out of its current beat plane develop. Here we present an extension of previous models of an elastic sperm flagellar filament whose shape change is driven by the pursuit of a preferred curvature wave. In particular, we extend the energy of the generalized elastica to include a term that penalizes out-of-plane motion. We are now able to study the interaction of free-swimmers in a 3D Stokes flow that do not start out beating in the same plane. We demonstrate the three-dimensional nature of swimming behavior as neighboring sperm swim close to each other and affect each others' trajectories via fluid-structure coupling.

Tangling of tethered swimmers: interactions between two nematodes

The tangling of two tethered microswimming worms serving as the ends of "active strings" is investigated experimentally and modeled analytically. C. elegans nematodes of similar size are caught by their tails using micropipettes and left to swim and interact at different separations over long times. The worms are found to tangle in a reproducible and statistically predictable manner, which is modeled based on the relative motion of the worm heads. Our results provide insight into the intricate tangling interactions present in active biological systems.

Rheotaxis facilitates upstream navigation of mammalian sperm cells

A major puzzle in biology is how mammalian sperm maintain the correct swimming direction during various phases of the sexual reproduction process. Whilst chemotaxis may dominate near the ovum, it is unclear which cues guide spermatozoa on their long journey towards the egg. Hypothesized mechanisms range from peristaltic pumping to temperature sensing and response to fluid flow variations (rheotaxis), but little is known quantitatively about them. We report the first quantitative study of mammalian sperm rheotaxis, using microfluidic devices to investigate systematically swimming of human and bull sperm over a range of physiologically relevant shear rates and viscosities. Our measurements show that the interplay of fluid shear, steric surface-interactions, and chirality of the flagellar beat leads to stable upstream spiralling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilisation. A minimal mathematical model is presented that accounts quantitatively for the experimental observations.DOI: http://dx.doi.org/10.7554/eLife.02403.001.

Ultrastructure of the sperm axoneme and molecular analysis of axonemal dynein in Ephemeroptera (Insecta)

The Ephemeroptera sperm axoneme is devoid of outer dynein arms (ODA) and exhibits a pronounced modification of the central pair complex (CPC), which is substituted by the central sheath (CS): a tubular element of unknown molecular composition. We performed a detailed ultrastructural analysis of sperm axonemes in the genera Cloeon and Ecdyonurus using quick-freeze, deep-etch electron microscopy, showing that the loss of the conventional CPC is not only concomitant with the loss of ODA, but also with a substantial modification in the longitudinal distribution of both radial spokes (RS) and inner dynein arms (IDA). Such structures are no longer distributed following the alternation of different repeats as in the 9 + 2 axoneme, but instead share a 32 nm longitudinal repeat: a multiple of the 8 nm repeat observed along the CS wall. Differently from the conventional CPC, the CS and the surrounding RS possess a ninefold symmetry, coherently with the three-dimensional pattern of motility observed in Cloeon free spermatozoa. Biochemical analyses revealed that ultrastructural modifications are concomitant with a reduced complexity of the IDA heavy chain complement. We propose that these structural and molecular modifications might be related to the relief from the evolutionary constraints imposed by the CPC on the basal 9 + 9 + 2 axoneme and could also represent the minimal set compatible with flagellar beating and progressive motility mechanically regulated as suggested by the geometric clutch hypothesis. © 2014 Wiley Periodicals, Inc.

The conserved ciliary protein Bug22 controls planar beating of Chlamydomonas flagella

Eukaryotic flagella and cilia can exhibit planar and non-planar beating, and the mechanism controlling these beating patterns is not well understood. Chlamydomonas reinhardtii flagella beat in approximately the same plane with either an asymmetric ciliary-type or symmetric flagellar-type waveform. Each B-tubule of the number 1, 5 and 6 doublets of the flagellar axoneme possesses a beak-like structure. The number 5 and 6 beak structures are implicated in conversion of ciliary motion into flagellar motion. Here, we show that in a null mutant of Bug22, the asymmetric ciliary waveform is converted into a three-dimensional (non-planar) symmetric flagellar waveform. Bug22 is localized to approximately the proximal half to two-thirds of the flagellum, similar to localization of beak-like structures. However, as shown by immunogold labeling, Bug22 associates with axonemal microtubules without apparent preference for any particular doublets. Interestingly, bug22 mutants lack all beak-like structures. We propose that one function of Bug22 is to regulate the anchoring of the beak-like structures to the doublet microtubules and confine flagellar beating to a plane.

High-speed holographic microscopy of malaria parasites reveals ambidextrous flagellar waveforms

Axonemes form the core of eukaryotic flagella and cilia, performing tasks ranging from transporting fluid in developing embryos to the propulsion of sperm. Despite their abundance across the eukaryotic domain, the mechanisms that regulate the beating action of axonemes remain unknown. The flagellar waveforms are 3D in general, but current understanding of how axoneme components interact stems from 2D data; comprehensive measurements of flagellar shape are beyond conventional microscopy. Moreover, current flagellar model systems (e.g., sea urchin, human sperm) contain accessory structures that impose mechanical constraints on movement, obscuring the "native" axoneme behavior. We address both problems by developing a high-speed holographic imaging scheme and applying it to the (male) microgametes of malaria (Plasmodium) parasites. These isolated flagella are a unique, mathematically tractable model system for the physics of microswimmers. We reveal the 3D flagellar waveforms of these microorganisms and map the differential shear between microtubules in their axonemes. Furthermore, we overturn claims that chirality in the structure of the axoneme governs the beat pattern [Hirokawa N, et al. (2009) Ann Rev Fluid Mech 41:53-72], because microgametes display a left- or right-handed character on alternate beats. This breaks the link between structural chirality in the axoneme and larger scale symmetry breaking (e.g., in developing embryos), leading us to conclude that accessory structures play a critical role in shaping the flagellar beat.

Regulations of microtubule sliding by Ca2+ and cAMP and their roles in forming flagellar waveforms

The function of Ca(2+) and cAMP in extruding doublet microtubules from sea urchin sperm axoneme and generating flagellar waves was investigated in order to clarify the regulatory mechanism of microtubule sliding and the formation mechanism of beating patterns of cilia and flagella. Almost all potentially asymmetric spermatozoa that were demembranated with Triton in the absence of Ca(2+) and reactivated with MgATP(2-) (Gibbons, B.H. and Gibbons, I.R. (1980). J. Cell Biol., 84: 13-27), beat with planar waves closely resembling those of the intact spermatozoa, whereas potentially symmetric spermatozoa, in which axonemal calmodulin was removed by detergent extraction in the presence of millimolar Ca(2+) (Brokaw, C.J. and Nagayama, S.M. (1985). J. Cell Biol., 100: 1875-1883), beat with three-dimensional waves if they were reactivated with low MgATP(2-). At a high MgATP(2-), almost all demembranated spermatozoa beat with planar waves. cAMP enhanced the three-dimensionality of the flagellar waves at a low Ca(2+). These changes in the flagellar waves were caused by different regulations of the microtubule sliding by calcium, cAMP, and MgATP(2-).

High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories

Dynamic tracking of human sperms across a large volume is a challenging task. To provide a high-throughput solution to this important need, here we describe a lensfree on-chip imaging technique that can track the three-dimensional (3D) trajectories of > 1,500 individual human sperms within an observation volume of approximately 8-17 mm(3). This computational imaging platform relies on holographic lensfree shadows of sperms that are simultaneously acquired at two different wavelengths, emanating from two partially-coherent sources that are placed at 45° with respect to each other. This multiangle and multicolor illumination scheme permits us to dynamically track the 3D motion of human sperms across a field-of-view of > 17 mm(2) and depth-of-field of approximately 0.5-1 mm with submicron positioning accuracy. The large statistics provided by this lensfree imaging platform revealed that only approximately 4-5% of the motile human sperms swim along well-defined helices and that this percentage can be significantly suppressed under seminal plasma. Furthermore, among these observed helical human sperms, a significant majority (approximately 90%) preferred right-handed helices over left-handed ones, with a helix radius of approximately 0.5-3 μm, a helical rotation speed of approximately 3-20 rotations/s and a linear speed of approximately 20-100 μm/s. This high-throughput 3D imaging platform could in general be quite valuable for observing the statistical swimming patterns of various other microorganisms, leading to new insights in their 3D motion and the underlying biophysics.

The structural heterogeneity of radial spokes in cilia and flagella is conserved

Radial spokes (RSs) are ubiquitous components of motile cilia and flagella and play an essential role in transmitting signals that regulate the activity of the dynein motors, and thus ciliary and flagellar motility. In some organisms, the 96 nm axonemal repeat unit contains only a pair of spokes, RS1 and RS2, while most organisms have spoke triplets with an additional spoke RS3. The spoke pairs in Chlamydomonas flagella have been well characterized, while spoke triplets have received less attention. Here, we used cryoelectron tomography and subtomogram averaging to visualize the three-dimensional structure of spoke triplets in Strongylocentrotus purpuratus (sea urchin) sperm flagella in unprecedented detail. Only small differences were observed between RS1 and RS2, but the structure of RS3 was surprisingly unique and structurally different from the other two spokes. We observed novel doublet specific features that connect RS2, RS3, and the nexin-dynein regulatory complex, three key ciliary and flagellar structures. The distribution of these doublet specific structures suggests that they could be important for establishing the asymmetry of dynein activity required for the oscillatory movement of cilia and flagella. Surprisingly, a comparison with other organisms demonstrated both that this considerable RS heterogeneity is conserved and that organisms with RS pairs contain the basal part of RS3. This conserved RS heterogeneity may also reflect functional differences between the spokes and their involvement in regulating ciliary and flagellar motility.

A novel motility pattern in quail spermatozoa with implications for the mechanism of flagellar beating

BACKGROUND INFORMATION

The spermatozoon of the quail (Coturnix coturnix L., var japonica) has a '9+2' flagellum that is unusually long. When it moves in a viscous medium, near to the coverslip, it develops a meander waveform. Because of the high viscosity, the meander bends are static in relation to the field of view; bend propagation is therefore manifest as the forward movement of the flagellum through the meander shape. At the same time, the origin of the oscillation typically shifts proximally in a stepwise fashion. These movements have been analysed in the hope of contributing to the resolution of problems in flagellar mechanics.

RESULTS

(1) Meander waves originate from spontaneous sigmoid bend complexes. (2) On a given flagellum, fully developed meander bends are uniform in their large angle, curvature and propagation speed; interbends can vary in length and shape. (3) No intra-axonemal sliding is transmitted through formed bends; sliding related to new bends is accommodated proximally. (4) Sliding reversal is initiated at a threshold shear angle of approx. 1 rad. (5) The arc wavespeed is the product of the arc wavelength and the beat frequency. (6) Physical obstruction to bend development causes a pause in the oscillation. (7) New bend initiation can thus be dissociated from bend propagation on the distal flagellum. (8) The steps in the forward advance of the oscillation site occur during the early phase of bend growth.

CONCLUSIONS

(1) The main conclusion is that, in meander waves, the mechanical basis of the oscillation appears to be that the propulsive thrust arising from bend propagation acts as a bending stress to trigger sliding reversal, thus perpetuating the rhythmic beating. (2) Oscillations can originate at any position, provided the position is distal to a location where doublet sliding is restrained. (3) Meander waves are an example of new bend development without 'paradoxical' classes of sliding.

Tubulin-dynein system in flagellar and ciliary movement

Eukaryotic flagella and cilia have attracted the attention of many researchers over the last century, since they are highly arranged organelles and show sophisticated bending movements. Two important cytoskeletal and motor proteins, tubulin and dynein, were first found and described in flagella and cilia. Half a century has passed since the discovery of these two proteins, and much information has been accumulated on their molecular structures and their roles in the mechanism of microtubule sliding, as well as on the architecture, the mechanism of bending movement and the regulation and signal transduction in flagella and cilia. Historical background and the recent advance in this field are described.

Mechanical constraint converts planar waves into helices on tunicate and sea urchin sperm flagella

The change in the flagellar waves of spermatozoa from a tunicate and sea urchins was examined using high-speed video microscopy to clarify the regulation of localized sliding between doublet microtubules in the axoneme. When the tunicate Ciona spermatozoa attached to a coverslip surface by their heads in seawater or they moved in seawater with increased viscosity, the planar waves of the sperm flagella were converted into left-handed helical waves. On the other hand, conversion of the planar waves into helical waves in the sea urchin Hemicentrotus spermatozoa was not seen in seawater with an increased viscosity as well as in ordinary seawater. However, the sea urchin Clypeaster spermatozoa showed the conversion, albeit infrequently, when they thrust their heads into seawater with an increased viscosity. The chirality of the helical waves of the Clypeaster spermatozoa was right-handed. When Ciona spermatozoa swam freely near a glass surface, they moved in relatively large circular paths (yawing motion). There was no difference in the proportion of spermatozoa yawing in either a clockwise or counterclockwise direction when viewed from above, which was also different from that of the sea urchin spermatozoa. These observations suggest that the planar waves generally observed on the sperm flagella are mechanically regulated, although their stability must depend on the Ca(2+) concentration in the cell. Furthermore, the chirality of the helical waves may be determined by the intracellular Ca(2+) concentration and changed by transmitting the localized active sliding between the doublet microtubules around the axoneme in an alternative direction.

Motility activation and metabolism characteristics of spermatozoa of the black-lip-pearl oyster Pinctada margaritifera var: cumingii (Jameson, 1901)

Motility of Pinctada margaritifera (Linnaeus, 1758); var: cumingii (Jameson, 1901) (P. margaritifera) spermatozoa collected from gonads are not immediately activated at spawning in seawater (SW) but motility occurs when spermatozoa are transferred into alkaline seawater (pH ranging from 9.0 to 11.4). This motility-activating effect of alkaline pH is reversed when pH is shifted back to more acidic values. In both cases, activity of sperm (% motile cells) increases gradually after alkaline pH activation then lasts for several minutes. The characteristics of these fully motile spermatozoa are described in details at the level of flagella: the wave amplitude and wave-length range 5 to 6 μm and 15 μm respectively, while the flagellar beat frequency is approximately 49 Hz. The velocity of sperm displacement is from 220 to 230 μm/sec. The general swimming pattern is almost circular: the head trajectories describe portions of circles intercalated with small linear segments. Spermatozoa saved in natural seawater at 4°C retain potent motility for several days and can be subsequently activated by alkaline seawater. Respiration and ATP concentration were measured in 3 conditions: regular seawater (pH 7.8), artificial diluent (pH 8.2), and alkaline Tris-buffered seawater (pH 10.5). Results show that sperm respiration rates are higher whereas ATP levels are lower in the latter two media.

Ultrastructure of cilia and flagella - back to the future!

Eukaryotic cilia and flagella perform motility and sensory functions which are essential for cell survival in protozoans, and to organism development and homoeostasis in metazoans. Their ultrastructure has been studied from the early beginnings of electron microscopy, and these studies continue to contribute to much of our understanding about ciliary biology. In the light of the progress made in the visualization of cellular structures over the last decade, we revisit the ultrastructure of cilia and flagella. We briefly describe the typical features of a 9+2 axoneme before focusing extensively on the transition zone, the ciliary necklace, the singlet zone, the ciliary cap and the ciliary crown. We discuss how the singlet zone is linked to sensory and/or motile function, the contribution of the ciliary crown to ovocyte and mucosal propulsion, and the relationship between the ciliary cap and microtubule growth and shortening, and its relation to ciliary beat. We further examine the involvement of the transition zone/the ciliary necklace in axonemal stabilization, autotomy and as a diffusion barrier.

Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions

The spermatozoon must find its female gamete partner and deliver its genetic material to generate a new individual. This requires that the spermatozoon be motile and endowed with sophisticated swimming strategies to locate the oocyte. A common strategy is chemotaxis, in which spermatozoa detect and follow a gradient of chemical signals released by the egg and its associated structures. Decoding the female gamete’s positional information is a process that spermatozoa undergo in a three-dimensional (3D) space; however, due to their speed and small size, this process has been studied almost exclusively in spermatozoa restricted to swimming in two dimensions (2D). This review examines the relationship between the mechanics of sperm propulsion and the physiological function of these cells in 3D. It also considers whether it is possible to derive all the 3D sperm swimming characteristics by extrapolating from 2D measurements. It is concluded that full insight into flagellar beat dynamics, swimming paths and chemotaxis under physiological conditions will eventually require quantitative imaging of flagellar form, ion flux changes, cell trajectories and modelling of free-swimming spermatozoa in 3D.

Swimming of Xenopus laevis sperm exhibits multiple gears and its duration is extended by egg jelly constituents

The motility of Xenopus sperm is initiated by the osmotic shock experienced when these cells are ejaculated into low-salinity pond water. Motility is brief and is required for the sperm to penetrate the jelly layers and fertilize the egg. In this study we demonstrate that extracts of egg jelly contain factors that extend the period of sperm motility as well as providing a chemoattractant activity as previously reported. Both activities are partially dependent on extracellular calcium. Time-lapse and video microscopy show that after activation of motility the number of motile sperm decreases rapidly, with a half-time of about 2 min. Addition of 10% v/v egg jelly extract ("egg water") increased the number of motile sperm 2-fold over controls at 20 s and about 4- to 10-fold over controls at 10 min after initiation of motility. Extension of motility lifetime was not mediated by a nonspecific protein or by allurin, the egg-water protein that has chemoattractant activity. The helical path of Xenopus sperm exhibited tight coupling between rotational and forward velocities in egg jelly, but coupling changed rapidly from moment to moment in low-salinity buffer. Our observations suggest that jelly-derived factors regulate both the longevity and directionality of sperm propulsion.

Drosophila sperm motility in the reproductive tract

Motile cilia and flagella exhibit many waveforms as outputs of dynein activation sequences on the highly conserved axoneme. Motility change of sperm in the reproductive tract is difficult to study and remains an important area of investigation. Sperm typically execute a sinusoidal waveform. Increased viscosity in the medium induces somewhat unusual arc-line and helical waveforms in some sperm. However, whether the latter two waveforms occur in vivo is not known. Using green fluorescence protein imaging, we show that Drosophila sperm in the uterus move in circular foci via arc-line waves, predominantly in a tail-leading orientation. From the uterus, a small fraction of the sperm enters the seminal receptacle (SR) in parallel formations. After sperm storage and coincident with fertilization of the egg, the sperm exit the SR via head-leading helical waves. Consistent with the observed bidirectional movements, the sperm show the ability to propagate both base-to-tip and tip-to-base flagellar waves. Numerous studies have shown that sperm motility is regulated by intraflagellar calcium concentrations; in particular, the Pkd2 calcium channel has been shown to affect sperm storage. Our analyses here suggest that Pkd2 is required for the sperm to adopt the correct waveform and movement orientation during SR entry. A working model for the sperm's SR entry movement is proposed.

The dynein regulatory complex is the nexin link and a major regulatory node in cilia and flagella

Elegant cryoelectron tomography reveals that the nexin link between microtubule doublets in 9 + 2 axonemal structures, critical for their ability to bend, is the dynein regulatory complex.

Cilia and flagella are highly conserved microtubule (MT)-based organelles with motile and sensory functions, and ciliary defects have been linked to several human diseases. The 9 + 2 structure of motile axonemes contains nine MT doublets interconnected by nexin links, which surround a central pair of singlet MTs. Motility is generated by the orchestrated activity of thousands of dynein motors, which drive interdoublet sliding. A key regulator of motor activity is the dynein regulatory complex (DRC), but detailed structural information is lacking. Using cryoelectron tomography of wild-type and mutant axonemes from Chlamydomonas reinhardtii, we visualized the DRC in situ at molecular resolution. We present the three-dimensional structure of the DRC, including a model for its subunit organization and intermolecular connections that establish the DRC as a major regulatory node. We further demonstrate that the DRC is the nexin link, which is thought to be critical for the generation of axonemal bending.

Flagellar oscillation: a commentary on proposed mechanisms

Eukaryotic flagella and cilia have a remarkably uniform internal 'engine' known as the '9+2' axoneme. With few exceptions, the function of cilia and flagella is to beat rhythmically and set up relative motion between themselves and the liquid that surrounds them. The molecular basis of axonemal movement is understood in considerable detail, with the exception of the mechanism that provides its rhythmical or oscillatory quality. Some kind of repetitive 'switching' event is assumed to occur; there are several proposals regarding the nature of the 'switch' and how it might operate. Herein I first summarise all the factors known to influence the rate of the oscillation (the beating frequency). Many of these factors exert their effect through modulating the mean sliding velocity between the nine doublet microtubules of the axoneme, this velocity being the determinant of bend growth rate and bend propagation rate. Then I explain six proposed mechanisms for flagellar oscillation and review the evidence on which they are based. Finally, I attempt to derive an economical synthesis, drawing for preference on experimental research that has been minimally disruptive of the intricate structure of the axoneme. The 'provisional synthesis' is that flagellar oscillation emerges from an effect of passive sliding direction on the dynein arms. Sliding in one direction facilitates force-generating cycles and dynein-to-dynein synchronisation along a doublet; sliding in the other direction is inhibitory. The direction of the initial passive sliding normally oscillates because it is controlled hydrodynamically through the alternating direction of the propulsive thrust. However, in the absence of such regulation, there can be a perpetual, mechanical self-triggering through a reversal of sliding direction due to the recoil of elastic structures that deform as a response to the prior active sliding. This provisional synthesis may be a useful basis for further examination of the problem.

A study of synchronisation between the flagella of bull spermatozoa, with related observations

Flagellar synchronisation has been observed between bull spermatozoa as they swam in a viscous medium, confined to a glass surface. This process is of interest in understanding the regulation of flagellar oscillation in general. Exact and persisting synchrony between bull spermatozoa occurred only when the spermatozoan heads were tightly coupled mechanically. For these cells, viscous coupling between the flagella was not by itself sufficient to establish synchronisation. Immediately on synchronisation, with the spermatozoan heads superposed, the paired spermatozoa showed rises in conjoint beat frequency,wave velocity and swimming velocity, i.e. in nearly all cases, the new conjoint values were greater than those shown by either of the two singleton spermatozoa. In our interpretation of these results, we put forward hydrodynamic arguments for seeing the primary change as a rise in wave velocity, via a decreased viscous resistance to bend propagation. Mechanistically, the rise in beat frequency is mysterious unless, as we suggest, it is consequential to the rise in wave velocity, and mediated by an as-yet-unknown mechanical feedback process. The rise in swimming velocity is not surprising given the rise in wave velocity but there is evidence for an additional influence due to a subtle re-orientation of the conjoint spermatozoan heads, such that they experienced less frictional drag.

3D structure of eukaryotic flagella in a quiescent state revealed by cryo-electron tomography

We have used cryo-electron tomography to investigate the 3D structure and macromolecular organization of intact, frozen-hydrated sea urchin sperm flagella in a quiescent state. The tomographic reconstructions provide information at a resolution better than 6 nm about the in situ arrangements of macromolecules that are key for flagellar motility. We have visualized the heptameric rings of the motor domains in the outer dynein arm complex and determined that they lie parallel to the plane that contains the axes of neighboring flagellar microtubules. Both the material associated with the central pair of microtubules and the radial spokes display a plane of symmetry that helps to explain the planar beat pattern of these flagella. Cryo-electron tomography has proven to be a powerful technique for helping us understand the relationships between flagellar structure and function and the design of macromolecular machines in situ.

Nodal cilia dynamics and the specification of the left/right axis in early vertebrate embryo development

Nodal cilia dynamics is a key factor for left/right axis determination in mouse embryos through the induction of a leftward fluid flow. So far it has not been clearly established how such dynamics is able to induce the asymmetric leftward flow within the node. Herein we propose that an asymmetric two-phase nonplanar beating cilia dynamics that involves the bending of the ciliar axoneme is responsible for the leftward fluid flow. We support our proposal with a host of hydrodynamic arguments, in silico experiments and in vivo video microscopy data in wild-type embryos and inv mutants. Our phenomenological modeling approach underscores how the asymmetry and speed of the flow depends on different relevant parameters. In addition, we discuss how the combination of internal and external mechanisms might cause the two-phase beating cilia dynamics.

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.

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.