Hydrodynamic calculations on the movements of cilia and flagella. II. Opalina.

Two different theoretical models are used to represent the propulsive mechanisms of Opalina. One model uses the concept of an envelope over all the cilia, while the other considers an array of elongated rods, similar to the model used in part 1. The envelope model shows a correlation between the motion of the cilium tip and the type of metachronism exhibited by the organism but under-predicts the velocities of propulsion. Calculations of the velocity profile, force and bending moment are carried out on the three-dimensional beat of a cilium of Opalina ranarum using the cilia sublayer model. The mean velocity profile is found to be twisted in form: in a clockwise direction at the top of the cilia sublayer relative to the effective stroke. Calculations of the force and rate of working emphasize the approximately equal duration of the effective and recovery strokes. Overall the sublayer model is found to be a more informative and useful approach than the envelope model which is limited to small amplitude motions.     

The Contractile Mechanism in Cilia

A detailed analysis is made of the motion and the forces in the cilium of Sabellaria over the complete cycle. The results indicate that the stiffness of the cilium is directly related to the moments produced by the internal contractile elements. A sliding filament model is developed to generate the complete cycle of motion. The activation of the force-producing elements, the peripheral fibers, occurs over their entire length at once during the effective stroke. In the recovery stroke the sliding of peripheral fibers relative to each other produces activation. The peripheral fibers contribute to the stiffness of the cilium in the sliding filament model only when they are not free to slide because of cross-linkage. The model describes successfully the motion of a variety of types of cilia.     

Laser-induced spreading arrest of Mytilus gill cilia

Using a "slit camera" recording technique, we have examined the effects of local laser irradiation of cilia of the gill epithelium of Mytilus edulis. The laser produces a lesion which interrupts epithelial integrity. In artificial sea water that contains high K+ or is effectively Ca++ free, metachronism of the lateral cilia continues to either side of the lesion with only minor perturbations in frequency synchronization and wave velocity, such as would be expected if metachronal wave coordination is mechanical. However, in normal sea water and other appropriate ionic conditions (i.e., where Ca++ concentration is elevated), in addition to local damage, the laser induces distinct arrest responses of the lateral cilia. Arrest is not mechanically coordinated, since cilia stop in sequence depending on stroke position as well as distance from the lesion. The velocity of arrest under standard conditions is about 3 mm/s, several orders of magnitude faster than spreading velocities associated with diffusion of materials from the injured region. Two responses can be distinguished on the basis of the kinetics of recovery of the arrested regions. These are (a) a nondecremental response that resembles spontaneous ciliary stoppage in the gills, and (b) a decremental response, where arrest nearer the stimulus point is much longer lasting. The slower recovery is often periodic, with a step size approximating lateral cell length. Arrest responses with altered kinetics also occur in laterofrontal cilia. The responses of Mytilus lateral cilia resemble the spreading ciliary arrest seen in Elliptio and arrest induced by electrical and other stimuli, and the decremental response may depend upon electrotonic spread of potential change produced at the stimulus site. If this were coupled to transient changes in Ca++ permeability of the cell membrane, a local rise in Ca++ concentration might inhibit ciliary beat at a sensitive point in the stroke cycle to produce the observed arrest.     

Effect of vanadate on gill cilia: Switching mechanism in ciliary beat

Lateral (L) cilia of freshwater mussel (Margaritana margaritifera and Elliptio complanatus) gills can be arrested in one of two unique positions. When treated with 12.5 mM CaCl₂ and 10^?5 M A23187 they arrest in a “hands up” position, ie, pointing frontally. When treated with approximately 10 mM vanadate (V) they arrest in a “hands down” position, ie, pointing abfrontally. L-cilia treated with 12.5 mM CaCl₂ and 1 mM NaN₃ also arrest in a “hands down” position; substitution of 20 mM KC1 and 1 mM NaN₃ causes cilia to move rapidly and simultaneously to a “hands up” position. The observations suggest that there are two switching mechanisms for activation of active sliding in ciliary beat one at the end of the recovery stroke and the other at the end of the effective stroke; the first is inhibited by calcium and the second by vanadate or azide. This is consistent with a model of ciliary beating where microtubule doublet numbers 1, 2, 3, and 4 are active during the effective stroke while microtubule doublets numbers 6, 7, 8, and 9 are passive, and the converse occurs during the recovery stroke.     

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.     

Ciliary behavior of a negatively phototactic Chlamydomonas reinhardtii

With an instrument that can record the motion of both cilia of the unicellular alga Chlamydomonas reinhardtii for many hours, the behavioral differences of its two cilia have been studied to determine their specific role in phototaxis. The organism was held on a fixed micropipette with the plane of ciliary beating rotated into the imaging plane of a quadrant photodetector. The responses to square-wave light patterns of a wide range of temporal frequencies were used to characterize the responses of each cilium. Eighty-one cells were examined showing an unexpectedly diverse range of responses. Plausible common signals for the linear and nonlinear signals from the cell body are suggested. Three independent ciliary measures--the beat frequency, stroke velocity, and phasing of the two cilia--have been identified. The cell body communicates to the cilia the direction of phototaxis the cell desires to go, the absolute light intensity, and the appropriate graded transient response for tracking the light source. The complexity revealed by each measure of the ciliary response indicates many independent variables are involved in the net phototactic response. In spite of their morphological similarity, the two cilia of Chlamydomonas respond uniquely. Probably the signals from the cell body fan out to independent pathways in the cilia. Each cilium modifies the input in its own way. The change in the pattern of the effective and recovery strokes of each cilium associated with negative phototaxis has been demonstrated and its involvement in phototactic turning is described.     

On metachronism in ciliary systems: a model describing the dependence of the metachronal wave properties on the intrinsic ciliary parameters

A mathematical model is proposed to explain the dependence of the direction and the length of the metachronal wave on parameters that characterize the ciliary beat, the dimensions of the cilia, and the geometry of their arrangement on the ciliated surface. The metachronal wave is decomposed into two mutually perpendicular components, which are chosen in such a way that the direction of one of them is in the direction of the effective stroke. The magnitudes of the two components are determined by using the concept of the time of delay between adjacent cilia. The properties of the metachronal wave are then calculated as a function of the ciliary parameters. The results obtained with the present model predict that the direction of the wave propagation is strongly dependent on the type of metachronism in the direction of the effective stoke and the polarization in time and in space of the ciliary beat. The metachronal wavelength is found to depend on four parameters: the ciliary length, the angle of the arc projected on the cell surface by the ciliary tip during the recovery stroke, the degree of asymmetry of ciliary beat, and the portion of the cycle occupied by the pause. The metachronal wavelength is also found to be only weakly dependent on the ciliary frequency. At this stage there exists relatively little experimental information with which to characterize fully the metachronal properties of ciliary systems. Even when only partial information exists, the model allows prediction, to within a certain range, of the direction of the wave propagation. It also suggests a possible mechanism for the influence of changes in environmental conditions on wave direction and wavelength. In several cases in which full information does exist, good agreement between the experimental findings and the predictions of the model is found. According to this model it will be worthwhile to invest more effort in measuring the time and space polarization of ciliary beating and times of delay between cilia.     

THE METACHRONAL WAVE OF LATERAL CILIA OF MYTILUS EDULIS

The form of beat of cilia and the structure of the metachronal wave on the lateral gill epithelium of Mytulus edulis have been studied on living material by interference-contrast microscopy and stroboscopic illumination, and compared with the same features in rapid-fixed preparations studied by light microscopy and with the scanning electron microscope. The most striking finding is that the beat of the cilia is not planar, as previously assumed, but involves a sideways movement in the recovery stroke Previous reports on nonplanar ciliary beating from protozoan examples describe a planar effective stroke and a counterclockwise rotation in the recovery stroke; in this molluscan example there is a clockwise rotation in the recovery stroke The lateral inclination of the cilia in the recovery stroke is in the same direction as the propagation of the waves, and the orientation of cilia in the recovery stroke is thought to determine whether the waves move to the left or right of the direction of the effective stroke     

Control of ciliary beat frequency in the gill of Mytilus--II. Effects of saponin and Brij-58 on the lateral cilia

The effects of saponin and Brij-58 on the beat activation of the lateral cilia on the gill of Mytilus edulis were investigated. The ciliary activation by 5-hydroxytryptamine (5HT) decreased as the saponin-induced permeabilization progressed, increasing the reactivation of the ciliary beat by extracellularly applied ATP (1 mM). The cilia were activated by 5HT even after the treatment with saponin (0.01 and 0.02% w/v) or Brij-58 (0.07%) rendered the preparation capable of the reactivation by ATP. The saponin treatment itself stimulated the beat of the cilia. Theophylline (1 mM) augmented the saponin-induced activation of the cilia.     

The forces applied by cilia depend linearly on their frequency due to constant geometry of the effective stroke

Mucus propelling cilia are excitable by many stimulants, and have been shown to increase their beating frequency up to threefold, by physiological extracellular stimulants, such as adenosine-triphosphate, acetylcholine, and others. This is thought to represent the evolutionary adaptation of mucociliary systems to the need of rapid and efficient cleansing the airways of foreign particles. However, the mucus transport velocity depends not only on the beat frequency of the cilia, but on their beat pattern as well, especially in the case of mucus bearing cilia that beat in a complex, three-dimensional fashion. In this study, we directly measured the force applied by live ciliary tissues with an atomic force microscope, and found that it increases linearly with the beating frequency. This implies that the arc swept by the cilia during their effective stroke remains unchanged during frequency increase, thus leading to a linear dependence of transport velocity on the beat frequency. Combining the atomic force microscope measurements with optical measurements, we have indications that the recovery stroke is performed on a less inclined plane, leading to an effective shortening of the overall path traveled by the cilia tip during this nontransporting phase of their beat pattern. This effect is observed to be independent of the type of stimulant (temperature or chemical), chemical (adenosine-triphosphate or acetylcholine), or concentration (1 μM-100 μM), indicating that this behavior may result from internal details of the cilium mechanical structure.     

Hydrodynamic calculations on the movements of cilia and flagella I. Paramecium

Calculations of the velocity profile, force, moment and bending moment using a theoretical model are carried out for the three-dimensional “conical-helical” beat of a cilium of Paramecium multimicro-nucleatum. The mean velocity profile obtained by numerical computation is found to be twisted in form: it is inclined at a slight angle to the effective stroke at the top of the cilia sublayer, but twists around with the recovery stroke in the lower part of the sublayer. The force and moment are larger during the fast effective stroke, but over a complete cycle their contributions are approximately zero. Calculations on the bending moments reveals that they are larger during the recovery stage of the beating cycle.     

A numerical study of muco-ciliary transport under the condition of diseased cilia

Structural and functional disorders of pulmonary cilia may result from genetic disorders and acquired insults. A two-dimensional numerical model based on the immersed boundary method coupled with the projection method is used to study the flow physics of muco-ciliary transport of the human respiratory tract under various abnormalities of cilia. The effects of the cilia beat pattern (CBP), ciliary length, immotile cilia, beating amplitude and uncoordinated beating of cilia are investigated. As expected, the mucus velocity decreases as the beating amplitude reduces. The windscreen wiper motion and rigid planar motion, which are two abnormal CBPs owing to genetic disorders, greatly reduce or almost stop the mucus transport. If the ciliary length varies from its standard length, the mucus velocity would decrease. The mucus velocity decreases rather linearly if the number of uniformly distributed immotile cilia increases. The numerical results show that the mucus velocity would be further reduced marginally when the uniformly distributed immotile cilia are rearranged as a cluster of immotile cilia. Furthermore, if half of the cilia are immotile and uniformly distributed and motile cilia beat at reduced amplitude, the incoordination between the active motile cilia would not significantly affect the mucus velocity.     

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.     

Membrane control of ciliary movement in ciliates

Ciliary movement is generated in the axoneme by the unidirectional sliding of the outer doublets of microtubules produced by the adenosine triphosphate (ATP)-energized dynein arms. It is composed of an effective stroke phase and a passive recovery stroke phase. Two parameters are modulated to determine swimming characteristics of the cell (speed and direction): beat frequency; direction of the effective stroke. They are linked to the internal Ca++ level and to the membrane potential. The membrane governs the internal Ca++ level by regulating Ca++ influx and efflux. It contains voltage-sensitive Ca++ channels through which a passive Ca++ influx, driven by the electrochemical gradient, occurs during step depolarization. The rise of the Ca++ level, up to 6.10-7M triggers ciliary reversal and enhances beat frequency. Ca+ is extruded from cilia by active transport. Ca++ also activates a multistep enzymatic process, the first component of which is a membrane calmodulin-dependent guanylate cyclase. cGMP interacts with Ca++ to modulate the parameters of the ciliary beat. The phosphorylation-dephosphorylation cycle of axoneme and membrane proteins seems to play a major role in controlling ciliary movement. Hyperpolarization of the membrane enhances beat frequency by an unknown mechanism. It could be a modification of the ratio of axonemal bound Ca++ and Mg++, or activation by cyclic adenosine monophosphate (cAMP) produced by a membrane adenylate cyclase. The ciliary membrane behaves as a receptor able to detect modifications of external parameters, and as a transductor transmitting the detected signal by a second or third messengers toward the interior of the cilia. These messengers. acting at different levels, modulate the parameters of the mechanism that generates ciliary movement.     

An electro-optic monitor of the behavior of Chlamydomonas reinhardtii cilia

The unicellular green alga Chlamydomonas reinhardtii steers through water with a pair of cilia (eukaryotic flagella). Long-term observation of the beating of its cilia with controlled stimulation is improving our understanding of how a cell responds to sensory inputs. Here we describe how to record ciliary motion continuously for long periods. We also report experiments on the network of intracellular signaling that connects the environment inputs with response outputs. Local spatial changes in ciliary response on the time scale of the underlying biochemical dynamics are observed. Near-infrared light monitors the cells held by a micropipette. This condition is tolerated well for hours, not interfering with ciliary beating or sensory transduction. A computer integrates the light stimulation of the eye of Chlamydomonas with the ciliary motion making possible long-term correlations. Measures of ciliary responses include the beating frequency, stroke velocity, and stroke duration of each cilium, and the relative phase of the cis and trans cilia. The stationarity and dependence of the system on light intensity was investigated. About 150,000,000 total beat cycles and up to 8 h on one cell have been recorded. Each beat cycle is resolved so that each asynchronous beat is detected. Responses extend only a few hundred milliseconds, but there is a persistence of momentary changes that last much longer. Interestingly, we see a response that is linear with absolute light intensity as well as different kinds of response that are clearly nonlinear, implying two signaling pathways from the cell body to the cilia.     

Control of ciliary beat frequency in the gill of Mytilus--I. Activation of the lateral cilia by cyclic AMP

The effect of cyclic AMP on the beat frequency of the lateral cilia on the gill of Mytilus edulis was investigated. Dibutyryl cyclic AMP (0.1 mM) weakly stimulated the cilia to beat. The activation was augmented by 1 mM theophylline. The cilia were hardly activated by cyclic AMP (0.1 mM) but a strong activation was observed when it was applied with saponin (0.0025-0.01% w/v) and theophylline (1 mM). The results suggest that cyclic AMP is involved in the mechanism of ciliary activation by 5-hydroxytryptamine.     

Ovum transport in the rat oviductal ampulla in the absence of muscle contractility

Ovum transport in mammalian oviducts involves two main effectors: ciliary motility and muscle contractility. To study the relative contribution of cilia to ovum transport in the rat, we blocked smooth muscle activity with isoproterenol, a beta-adrenergic agonist, and measured transport rates of surrogate ova in situ. Transport rates before isoproterenol administration were 0.04 mm/s in the cephalic ampulla and 0.03 mm/s in the caudal ampulla; rates were unchanged after administration of isoproterenol. To determine if isoproterenol affected ciliary activity, we measured ciliary beat frequency with laser-scattering spectroscopy over the effective isoproterenol dosage. Isoproterenol did not cause a significant change in ciliary beat frequency. Our results show that in the rat oviductal ampulla, ciliary motion is capable of transporting ova in the absence of muscle contractility.     

Ciliary specializations in branchial stigmatal cells of protochordates

Tissues from the pharynx of five representative species of the protochordates (subphylum Tunicata, the three classes Ascidiacea, Thaliacea and Appendicularia, and subphylum Cephalochordata) were examined in both thin sections and freeze-fracture replicas. In all species, the stigmatal cilia of the branchial chamber are neatly arranged and move continuously to propel sea-water in a fixed direction for respiration and feeding of the organism. A number of specializations are found in the basal region of these cilia and are represented by: a) bridges connecting axonemal doublets numbers 5 and 6; b) dense fibrous material linking the doublet microtubules of the axoneme to the ciliary membrane, sometimes in the shape of longitudinal strands or as clusters of filaments; c) intramembrane particles (IMPs) associated with the P-face of the membrane, often arranged in clusters evenly aligned along the ciliary shaft in relation to the underlying axonemal doublets. Ciliary specializations are distributed along the plane of the effective stroke of the beat in both the ascidian Botryllus schlosseri and in the thaliacean Pyrosoma atlanticum and the amphioxus Branchiostoma lanceolatum, whereas in the thaliacean Doliolum nationalis and the appendicularian Oikopleura dioica a more uniform distribution of these specializations all around the basal portion of the cilia is observed. Whatever the disposition of the ciliary specializations in all the examined species, they are always present at the base of the water-propelling cilia. Some morphological evidence suggests that these specializations play a mechanical function in tethering the ciliary membrane to the axoneme. We propose that they help maintain the orientation of the cilia during beating, enhance their stiffness and improve their efficiency.     

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.     

Ciliary motion modeling, and dynamic multicilia interactions

This paper presents a rigorous and accurate modeling tool for ciliary motion. The hydrodynamics analysis, originally suggested by Lighthill (1975), has been modified to remove computational problems. This approach is incorporated into a moment-balance model of ciliary motion in place of the previously used hydrodynamic analyses, known as Resistive Force Theory. The method is also developed to include the effect of a plane surface at the base of the cilium, and the effect of the flow fields produced by neighboring cilia. These extensions were not possible with previous work using the Resistive Force Theory hydrodynamics. Performing reliable simulations of a single cilium as well as modeling multicilia interactions is now possible. The result is a general method which could now be used for detailed modeling of the mechanisms for generating ciliary beat patterns and patterns of metachronal interactions in arrays of cilia. A computer animation technique was designed and applied to display the results.