Ciliary beating in three dimensions: Steps of a quantitative description

We document a novel approach for quantitative assessment of ciliary activity, exemplified in rapid three-dimensional cyclic motion of the frontal cirri of Stylonychia. Cells held under voltage-clamp control are stimulated by step pulses to elicit reproducible hyperpolarization- or depolarization-induced ciliary motor responses. High-speed video recording at 200 fields per second is used for imaging ciliary organelles of the same cell in two perspectives: the axial view and, following cell rotation by 90 degrees, the lateral view. From video sequences of typically 1 s, the contours of the cirral images are determined and digitized. Computer programs are established to (1) reduce an observed image to a "ciliary axis", (2) sort series of axes by template to generate an averaged ciliary cycle in 2D-projection, and (3) to associate the generalized axial and lateral 2D-images for generation of a sequence of three-dimensional images, which quantitatively represent the cycle in space and time. The method allows us to produce predetermined perspectives of images selected from the ciliary cycle, and to generate stereo views for graphical representation of ciliary motion. The approach includes a potential for extraction of the complete microtubular sliding program of a cilium under reproducible electric stimulation of the ciliary membrane.     

The Positioning of Ciliary Organelles in Hypotrich Ciliates*†

It is commonly observed in hypotrichs that new ciliary rudiments arise directly from or in close juxtaposition to certain pre-existing ciliary elements. Oral primordia often are initiated near specific cirri, cirral rudiments frequently arise as a result of the disaggregation of certain old cirri, and new dorsal ciliature is formed within pre-existing ciliary rows. In the first 2 situations it has been demonstrated experimentally that neither the old ciliature in question nor the specific cortical site marked by that ciliature is essential for the appearance of the new cirral rudiment. The experimental analysis done thus far suggests that the positions of oral and cirral primordia are determined by interacting gradients established in relation to certain reference points. The nature of the reference points is not fully elucidated; in some cases at least these points appear to be more closely related to topographic features of the cell than to specific pre-existing cortical structures. In the dorsal ciliary rows of Euplotes new ciliary units are formed usually and perhaps invariably in close proximity to old ones, and are generally oriented along the axis of the pre-existing row. The result is a tendency to perpetuate the preexisting row number across cell generations. Changes in row number, however, can occur as a result of occasional formation of new units at right angles to the row, a process that is much enhanced in certain homozygous segregants (basal body deficient). The optimal row number (stability range) as well as the number of ciliary units are under genic control. In addition, the spatial pattern of distribution of ciliary units among rows is invariant in all of the material examined. This pattern is presumed to result from an underlying field whose geometry is independent of both the number of units and the number of rows.     

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

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

Simulations of three-dimensional ciliary beats and cilia interactions.

A new set of equations describing the time evolution of torsion and curvature for an inextensible curve is developed. Combined with our recently developed Slender Body Theory approach to such problems, these equations were applied to simulate three-dimensional ciliary beats, while allowing for cilia interactions. The computer animation technique, which was originally designed to display two-dimensional beats, has been enhanced to accommodate the new three-dimensional results.     

Mean curvature motion facilitates the segmentation and surface visualization of electron tomograms

Three-dimensional visualization of biological samples is essential for understanding their architecture and function. However, it is often challenging due to the macromolecular crowdedness of the samples and low signal-to-noise ratio of the cryo-electron tomograms. Denoising and segmentation techniques address this challenge by increasing the signal-to-noise ratio and by simplifying the data in images. Here, mean curvature motion is presented as a method that can be applied to segmentation results, created either manually or automatically, to significantly improve both the visual quality and downstream computational handling. Mean curvature motion is a process based on nonlinear anisotropic diffusion that smooths along edges and causes high-curvature features, such as noise, to disappear. In combination with level-set methods for image erosion and dilation, the application of mean curvature motion to electron tomograms and segmentations removes sharp edges or spikes in the visualized surfaces, produces an improved surface quality, and improves overall visualization and interpretation of the three-dimensional images.     

Measuring the Three-Dimensional Kinematics of a Free-Swimming Koi Carp by Video Tracking Method

A video tracking system for measuring three-dimensional kinematics of a free-swimming fish is presented. The tracking is accomplished by simultaneously taking images from the ventral view and the lateral view of the fish with two cameras mounted on two computer-controlled and mutually orthogonal translation stages. Compared to the previous system we reported, the time resolution is greatly improved. A koi carp is selected for the experiment. By processing the images caught by the video tracking system, the three-dimensional kinematics of the koi carp during a continuous swimming containing several moderate maneuvers are obtained. In particular, the pitching motion of fish body and the tail motion, including lateral excursion, variation in tail height and torsion, are revealed for burst-and-coast swimming and turning maneuver. The error analysis is also provided for the measurement results.     

The Structure and Morphogenesis of the Ventral Ciliature in Paraurostyla hymenophora*

SYNOPSIS. The structure and morphogenesis of the ventral ciliature of Paraurostyla hymenophora (Stokes) are described. The oral primordium apparently originates in association with transverse cirrus #6, from which it migrates anteriorly simultaneous with kinetosomal proliferation. The primordium eventually forms an elongate ciliary field from which the future opisthe's fronto-ventro-transverse (FVT) and undulating membrane primordial fields arise. Concomitantly, the future proter's FVT primordial field is initiated by the disaggregation of frontal cirri #4, #5, and #6. Primordia then develop simultaneously within marginal and ventral cirral rows by a disaggregation of cirri within the respective rows, and do not give rise to new cirri until the FVT fields complete segregation into discrete cirri. Near the completion of cirral production from the FVT primordia, each ventral cirral primordium (VCP) forms the 2 rightmost transverse cirri. Segregation of new cirri within the marginal cirral primordia and VCP then occurs, eventually replacing all old cirri within their respective marginal and ventral cirral rows. At the end of cortical morphogenesis, all old ciliary organelles, with the exception of the adoral zone of membranelles, are either reorganized or replaced. These results suggest an evolutionary affinity between the ventral and marginal cirral rows and raise questions about the control of the developmental competence of individual primordia.     

Curvature and torsion in growing actin networks

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque.     

Bending and twisting of an in vivo coronary artery at a bifurcation.

Dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer-tomographically reconstructed three-dimensional images of an in situ beating heart of an anesthetized dog. Wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion. For quantifying the local bending and twisting of the left coronary artery tree, the anatomic landmarks of the bifurcation points are selected as focussed locations. At these points, the space curves of the tree at different cardiac instants were first derived in parametric forms. Curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter. This analysis revealed that during the initial contraction of the heart wall, a 2% reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart. When the left ventricular chamber reached a maximum value, the radius of curvature was found to decrease at a rate of 2.3% ms-1. At the end of diastole, an increase in the radius of curvature at a rate of 5.7% ms-1 was observed. The twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from -0.62 to 0.63 degrees ms-1.     

Contractile events in the cilia of Paramecium, Opalina, Mytilus, and Phragmatopoma.

The motion of the abnormal cilia of Opalina and Mytilus can be described by the recently developed model for ciliary motion, provided the activation of the contractility during the effective stroke is reduced by three- to fivefold compared with that in the recovery stroke. The stiffness of the Mytilus cilium during the effective stroke is found several hundred times larger than that predicted by the model, however. The stiffness of the cilia of Paramecium, Opalina, Phragmatopoma, and of Mytilus in the recovery phase, is predicted approximately correctly by the model. The activation of contractility in Mytilus and Phragmatopoma cilia increases with the viscosity of the medium, as the velocity of the ciliary motion slows down. This leads to the equivalent of a force-velocity relation. The velocity of propagation of the bend in the cilia during the recovery stroke is shown to be dependent only on the elastic properties of the ciliary shaft, and to be independent of the contractile activiey.     

Cytogeometrical determination of ciliary pattern formation in the hypotrich ciliate Stylonychia mytilus: II. Stability and field regulation

The first regeneration sequence after folding of right fragments of Stylonychia mytilus results in formation of mirror-imaged incomplete doublets illustrating independent determination of polar and lateral axes. Analysis of the second morphogenetic sequence illustrates that the independent determination of polar and lateral axes is stable through a subsequent cellular reorganization and confirms that cytogeometry participates in determination of ciliary pattern. The morphogenetic inversion of cirral row primordia in this type of fragment is reflected in the structure of the individual cirri. These data not only extend and confirm our earlier study on this type of fragment, but also are consistent with the conclusion derived from data on a different type of mirror-imaged doublet, that global patterning and assembly of ciliature are independently determined.     

Method for Quantitative Study of Airway Functional Microanatomy Using Micro-Optical Coherence Tomography

We demonstrate the use of a high resolution form of optical coherence tomography, termed micro-OCT (μOCT), for investigating the functional microanatomy of airway epithelia. μOCT captures several key parameters governing the function of the airway surface (airway surface liquid depth, periciliary liquid depth, ciliary function including beat frequency, and mucociliary transport rate) from the same series of images and without exogenous particles or labels, enabling non-invasive study of dynamic phenomena. Additionally, the high resolution of μOCT reveals distinguishable phases of the ciliary stroke pattern and glandular extrusion. Images and functional measurements from primary human bronchial epithelial cell cultures and excised tissue are presented and compared with measurements using existing gold standard methods. Active secretion from mucus glands in tissue, a key parameter of epithelial function, was also observed and quantified.     

Ciliary function of the frog oro-pharyngeal epithelium

Summary The palate epithelium of the frog was examined by scanning electron microscopy, light microscopy and high speed cine micrography. The cilia remain stationary for much of the time in the end-of-effective stroke position. Each beat cycle begins with a forwardly-directed recovery stroke lasting about 60 ms, followed by an effective stroke towards the oesophagus lasting about 12 ms. Activity can often be correlated with the presence of mucus, which is carried as strands on the tips of the ciliary effective strokes whilst the recovery strokes move beneath the mucus. Coordination of ciliary activity was very variable; local antiplectic metachrony of the recovery strokes could almost always be seen, and on very active epithelia effective strokes were associated with approximately diaplectic waves (either to left or right), but any particular pattern of coordinated activity was transient and quickly transformed to another pattern. Beating and coordination of these short cilia were compared with those of cilia propelling water.     

Locally oscillatory motion of RNA helix derived from linear relationships of backbone torsion angles

A linear relationship in each of the torsion angle pairs, α-β, β-?, ?-ζ, and α-γ, has been found by applying a statistical method based on the concept of circular variates to backbone torsion angle data of helical in yeast tTNA^Phe. A series of helical dimer models generated with these relationships have been found to be stereochemically acceptable, and the models also indicate that the backbone unit in the RNA helix is geometrically capable of an oscillatory motion with the distance of about 3.4 Å between adjacent bases. The motion of the backbone unit is analogous to that of a helical spring. The adjacent bases, because of being attached to the backbone, oscillate in a manner similar to the oscillatory dimer model proposed by Davis and Tinoco [Davis, R. C. & Tinoco, I., Jr. (1968) Biopolymers 6 , 223–242]. Here, the oscillation of the backbone unit in the RNA helix is discussed in terms of two geometrical quantities: the torsion (τ) and curvature (κ) of the helix. On these lines, a stereochemical model of RNA strand separation is proposed.     

How Does Cilium Length Affect Beating?

The effects of cilium length on the dynamics of cilia motion were investigated by high-speed video microscopy of uniciliated mutants of the swimming alga, Chlamydomonas reinhardtii. Cells with short cilia were obtained by deciliating cells via pH shock and allowing cilia to reassemble for limited times. The frequency of cilia beating was estimated from the motion of the cell body and of the cilium. Key features of the ciliary waveform were quantified from polynomial curves fitted to the cilium in each image frame. Most notably, periodic beating did not emerge until the cilium reached a critical length between 2 and 4 μm. Surprisingly, in cells that exhibited periodic beating, the frequency of beating was similar for all lengths with only a slight decrease in frequency as length increased from 4 μm to the normal length of 10–12 μm. The waveform average curvature (rad/μm) was also conserved as the cilium grew. The mechanical metrics of ciliary propulsion (force, torque, and power) all increased in proportion to length. The mechanical efficiency of beating appeared to be maximal at the normal wild-type length of 10–12 μm. These quantitative features of ciliary behavior illuminate the biophysics of cilia motion and, in future studies, may help distinguish competing hypotheses of the underlying mechanism of oscillation.     

The Structure and Development of the Dorsal Bristle Complex of Oxytricha fallax and Stylonychia pustulata*

SYNOPSIS. Oxytricha fallax and Stylonychia pustulata possess 6 rows of dorsal bristle units. Each dorsal bristle unit consists of a pair of kinetosomes; the anterior kinetosome has a cilium and the posterior kinetosome a ciliary stub. The kinetosome pair, located at the bottom of a cortical pit surrounding the cilium and ciliary stub, is surrounded by an asymmetrical fibrillar mass. Future rows 1-4 are formed from 2 sets of primordia originating within mature dorsal rows 1-3. Rows 5 and 6 originate from the anterior regions of both right marginal cirral primordia. Old dorsal bristle units utilized in formation of primordia are presumably maintained in the new rows of the proter and opisthe; those outside the primordia are resorbed. The morphogenetic pattern of the Oxytrichidae is similar to those of the Urostylidae and Holostichidae, but quite different from that of the Euplotidae.     

Extraction of cilium beat parameters by the combined application of photoelectric measurements and computer simulation.

Photoelectric signals were created and used to investigate the features of the signals as a function of the ciliary beat parameters. Moreover, correlation between the simulated and the measured signals permitted measurement of the cilium beat parameters. The simulations of the signals were based on generation of a series of time-frozen top-view frames of an active ciliary area and determination of the amount of light passing through an observation area in each of these frames. All the factors that might contribute to the shape of the signals, namely, partial ciliary transmittance of light, three-dimensional ciliary beat (composed of recovery, effective, and pause parts), phase distribution on the ciliary surface, and the large number of cilia that contribute to the photoelectric signal, were taken into account in generation of the signals. Changes in the ciliary parameters influenced the shape of the photoelectric signals, and the different phases of the beat could not be directly and unequivocally identified in the signals. The degree of temporal asymmetry of the beat and the portion of the cycle occupied by the pause significantly influenced the shapes of both the lower and the upper parts of the signal and the slopes of the signal. Increases in the angle of the arc swept by the cilium during the effective stroke smoothed the signals and increased the duration of the upper part of the signal. The angle of the arc projected by the cilium onto the cell surface during the recovery stroke had minor effects on the signal's shape. Characteristics of the metachronal wave also influenced the signal's shape markedly. Decreases in ciliary spacing smoothed the signals, whereas ciliary length had a minor influence on the simulated photoelectric signals. Comparison of the simulated and the measured signals showed that the beat parameters of the best-fitting simulated signals converged to values that agree well with the accepted range of beat parameters in mucociliary systems.     

The use of correlated ultrastructural and morphogenetic characters in evolutionary taxonomy of hypotrich ciliates

A new morphogenetic criterion, the "unit of turn-over" emerges from the dynamic analysis of hypotrich morphogenesis. The unit corresponds to the set of morphogenetically interdependent somatic structures whose turn-over is correlated to nuclear modifications. Hypotrichs are seen to conform to one of two very general modes of turn-over of their ciliary structures during a variety of morphogenetic processes, one in which all somatic cilia and their infraciliature are replaced, and the other in which only the cirral structures (not the dorsal dikinetids) undergo replacement. A strong correlation is observed between the type of turn-over occurring and ultrastructural features of the corresponding species. From an evolutionary point of view, these data lead to a new subdivision of hypotrichs, into the Euhypotrichina and the Pseudohypotrichina.     

Functional architecture of the outer arm dynein conformational switch

Dynein light chain 1 (LC1/DNAL1) is one of the most highly conserved components of ciliary axonemal outer arm dyneins, and it associates with both a heavy chain motor unit and tubulin located within the A-tubule of the axonemal outer doublet microtubules. In a variety of model systems, lack of LC1 or expression of mutant forms leads to profound defects in ciliary motility, including the failure of the hydrodynamic coupling needed for ciliary metachronal synchrony, random stalling during the power/recovery stroke transition, an aberrant response to imposed viscous load, and in some cases partial failure of motor assembly. These phenotypes have led to the proposal that LC1 acts as part of a mechanical switch to control motor function in response to alterations in axonemal curvature. Here we have used NMR chemical shift mapping to define the regions perturbed by a series of mutations in the C-terminal domain that yield a range of phenotypic effects on motility. In addition, we have identified the subdomain of LC1 involved in binding microtubules and characterized the consequences of an Asn → Ser alteration within the terminal leucine-rich repeat that in humans causes primary ciliary dyskinesia. Together, these data define a series of functional subdomains within LC1 and allow us to propose a structural model for the organization of the dynein heavy chain-LC1-microtubule ternary complex that is required for the coordinated activity of dynein motors in cilia.