Synchronization between beating cilia.

A novel quantitative parameter is proposed to define and measure the degree of synchronization between two small ciliary areas. These areas can be close to or far from one another. The Pearson correlation factor is used to define the degree of synchronization by a single number. This approach is based on a computerized, dual photoelectric method which simulataneously measures the scattered light from two small areas on the ciliary epithelium or its tissue culture. The measurements were performed on tissue culture from frog's palate epithelium. It was found that: (a) the degree of synchronization decreases, as a function of distance; (b) the correlation is fairly high even at relatively large separations, when measured on the same patch; (c) on a given patch the synchronization factor is independent of the direction of the metachronal wave; (d) close disconnected ciliary cells exhibit fairly high correlation; (e) disconnected randomly choosen ciliary cells at relatively large separation distances exhibit relatively low correlation, smaller by a factor of 2 than the correlation factor at the same distances when measured along the metachronal wave; (f) the average frequencies' ratio and the metachronal wavelength can be used as first-order indicators of ciliary synchronization; (g) there is a spread of metachronal wavelengths even over a single well-organized patch.     

Direct measurement of the velocity of the metachronal wave in beating cilia

Recently a computerized electro-optical method was developed which enables one to simultaneously measure the frequency and the wavelength of the metachronal waves in beating cilia. The method is based on measurement of scattered light from two areas at a given distance apart. The distance between measured areas can be varied from zero to hundreds of microns. The relative ease of the measurement and data analysis of this method enable one to create large statistical ensembles in order to obtain reliable averages. In this work we show that in addition to the previously mentioned parameters this system can measure directly the velocity of the metachronal wave. It was found that the average velocity in the tissue culture from frog's palate epithelium at room temperature is approximately 270 micron/sec, about twice the average particle velocity at the frog's palate.     

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.     

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.     

An Outer Arm Dynein Conformational Switch Is Required for Metachronal Synchrony of Motile Cilia in Planaria

Motile cilia mediate the flow of mucus and other fluids across the surface of specialized epithelia in metazoans. Efficient clearance of peri-ciliary fluids depends on the precise coordination of ciliary beating to produce metachronal waves. The role of individual dynein motors and the mechanical feedback mechanisms required for this process are not well understood. Here we used the ciliated epithelium of the planarian Schmidtea mediterranea to dissect the role of outer arm dynein motors in the metachronal synchrony of motile cilia. We demonstrate that animals that completely lack outer dynein arms display a significant decline in beat frequency and an inability of cilia to coordinate their oscillations and form metachronal waves. Furthermore, lack of a key mechanosensitive regulatory component (LC1) yields a similar phenotype even though outer arms still assemble in the axoneme. The lack of metachrony was not due simply to a decrease in ciliary beat frequency, as reducing this parameter by altering medium viscosity did not affect ciliary coordination. In addition, we did not observe a significant temporal variability in the beat cycle of impaired cilia. We propose that this conformational switch provides a mechanical feedback system within outer arm dynein that is necessary to entrain metachronal synchrony.     

STUDIES ON CILIA : The Fixation of the Metachronal Wave

Upon excision into spring water, the lateral cilia of the gill of the freshwater mussel Elliptio complanatus (Solander) stop beating, but 0.04 M potassium ion can activate the gill so that these cilia again beat with metachronal rhythm. One per cent osmium tetroxide quickly pipetted onto a fully activated gill fixes the lateral cilia in a pattern that preserves the form and arrangement of the metachronal wave, and permits the cilia to be studied with the electron microscope in all stages of their beat cycle. Changes are seen in the fixed active preparation that are not present in the inactive control, i.e., in the packing of the cilia, the position of the axis of the ciliary cross-section, and the diameter of the ring of peripheral filaments. Analysis of these parameters may lead to new correlations between ciliary fine structure and function.     

Intensification of ciliary motility by extracellular ATP

Ciliary metachronism and motility were examined optically in tissue cultures from frog palate epithelium as a function of extracellular ATP concentration in the range of 10(-7)-10(-3) M. The main findings were: a) upon addition of ATP the metachronal wavelength increased by a factor of up to 2. b) the velocity of the metachronal wave increased by a factor of up to 5. c) the frequency of ciliary beating increased by a factor of up to 2-3, the increase being temperature insensitive in the range of 15 degrees C-25 degrees C. d) the area under the 1-second FFT spectrum decreased by a factor of up to 2.5. e) the energy of the metachronal wave is increased by a factor of up to 9.5. f) all the spectrum parameters are subject to influence by ATP, as also by ADP and AMP. However, there are pronounced differences in the various responses to them. Based on these findings, physical aspects of the rate increase of particle transport caused by addition of extracellular ATP are explained. A plausible overall chemical mechanism causing pronounced changes in ciliary motility is discussed.     

An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel

The propulsion mechanics of cilia-induced flow is studied through a mathematical model. The problem of two-dimensional motion of a power law fluid inside a channel with ciliated walls is considered. The characteristics of ciliary systems are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Solutions for the longitudinal, transverse, and resultant velocities are obtained. The pressure gradient and volume flow rate for different values of the power law index are also calculated. The flow properties for the power law fluid are determined as a function of the cilia and metachronal wave velocity. The viscous and power law fluid are compared and discussed graphically.     

Urceolaria mitra (von Seib) Epizoic on Polycelis tenuis (IJIMA) an SEM Study.

Dense populations of Urceolaria mitra (Cilophora, Peritrichid) were observed on the surface of the planarian Polycelis tenuis (Platyhelminthes Turbellaria). Although the epizoite was primarily confined to the anterior dorsal surface of the planarian, heavily infested individuals had peritrichs attached to the posterior, lateral and ciliated ventral surfaces. Unique profiles of the skeletal ring (aboral disc) in relation to the host surface showed that some local erosion of planarian epithelium occurs. Outer and inner rows of cilia extended anti-clockwise around the peristomal disc. The cilia ran for one and one-eighth turns around the disc and overlapped in the form of a spiral when the protist was extended and feeding. The cilia appeared to beat in metachronal rhythm and exhibited a wavelength and amplitude of approximately 10μm. Regular striations having a periodicity of 1μm were observed in the periostimal membrane. A posterior or basal circlet of locomotor cilia was also observed and freeze fracture revealed an internal arrangement of microvilli, cilia and reticular membranes.     

Ciliary feeding structures and particle capture mechanism in the freshwater bryozoan Plumatella repens (Phylactolaemata)

Abstract. In contrast to marine bryozoans, the lophophore structure and the ciliary filter‐feeding mechanism in freshwater bryozoans have so far been only poorly described. Specimens of the phylactolaemate bryozoan Plumatella repens were studied to clarify the tentacular ciliary structures and the particle capture mechanism. Scanning electron microscopy revealed that the tentacles of the lophophore have a frontal band of densely packed cilia, and on each side a zigzag row of laterofrontal cilia and a band of lateral cilia. Phalloidin‐linked fluorescent dye showed no sign of muscular tissue within the tentacles. Video microscopy was used to describe basic characteristics of particle capture. Suspended particles in the incoming water flow, set up by the lateral ‘pump’ cilia on the tentacles, approach the tentacles with a velocity of 1–2 mm s^‐1. Near the tentacles, the particles are stopped by the stiff sensory laterofrontal cilia acting as a mechanical sieve, as previously seen in marine bryozoans. The particle capture mechanism suggested is based on the assumed ability of the sensory stiff laterofrontal cilia to be triggered by the deflection caused by the drag force of the through‐flowing water on a captured food particle. Thus, when a particle is stopped by the laterofrontal cilia, the otherwise stiff cilia are presumably triggered to make an inward flick which brings the restrained particle back into the downward directed main current, possibly to be captured again further down in the lophophore before being carried to the mouth via the food groove. No tentacle flicks and no transport of captured particles on the frontal side of the tentacles were observed. The velocity of the metachronal wave of the water‐pumping lateral cilia was measured to be ～0.2 mm s^‐1, the wavelength was ～7 μm, and hence the ciliary beat frequency estimated to be ～30 Hz (～20 °C). The filter feeding process in P. repens reported here resembles the ciliary sieving process described for marine bryozoans in recent years, although no tentacle flicks were observed in P. repens. The phylogenetic position of the phylactolaemates is discussed in the light of these findings.     

Flow in tubules due to ciliary activity

A simplified model for cilia-induced flows in tubules is presented. Each cilium is a long slender body which is constrained to move similar to its beat. An array of cilia is defined and coordinated in such a way as to represent the metachronal wave. The velocity field is represented by a distribution of viscous fluid singularities (Stokes flow) along the centerline of each slender body. The total mean velocity field due to all the cilia is obtained. It is found that backflow (reflux) can occur near the walls for cilia exhibiting antiplectic metachronism. Maximum flow rates are obtained for cilia whose length is 0.3 to 0.6 the radius of the tube.     

The role of cortical orientation in the control of the direction of ciliary beat in Paramecium

The swimming behavior of many ciliate protozoans depends on graded changes in the direction of the ciliary effective stroke in response to depolarizing stimuli (i.e., the avoiding reaction of Paramecium). We investigated the problem of whether the directional response of cilia with a variable plane of beat is related to the polarity of the cell as a whole or to the orientation of the cortical structures themselves. To do this, we used a stock of Paramecium aurelia with part of the cortex reversed 180 degrees. We determined the relation of the orientation of the kineties (ciliary rows) to the direction of beat in these mosaic paramecia by cinemicrography of particle movements near living cells and by scanning electron microscopy of instantaneously fixed material. We found that the cilia of the inverted rows always beat in the direction opposite to that of normally oriented cilia during both forward and backward swimming. In addition, metachronal waves of ciliary coordination were present on the inverted patch, travelling in the direction opposite to those on the normal cortex. The reference point for the directional response of Paramecium cilia to stimuli thus resides within the cilia or their immediate cortical surroundings.     

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.     

Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

Cells carrying cilia on their surface show many striking features: alignment of cilia in an array, two-phase asymmetric beating for each cilium, and existence of metachronal coordination with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronal coordination arises as a consequence of the internal mechanism of the cilia and their hydrodynamic couplings, with a wavelength comparable to that found in experiments. It allows the cilia to start beating at a lower adenosine-triphosphate threshold and at a higher frequency than for a single cilium. It also leads to a rather stationary flow, which might be its major advantage.     

Transitory behaviors in diffusively coupled nonlinear oscillators

We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant subspace, the all-synchronized state and one of the metachronal waves play an important role.     

STUDIES ON CILIA : III. Further Studies on the Cilium Tip and a "Sliding Filament" Model of Ciliary Motility

This study confirms and extends previous work on the lateral cilia of the fresh-water mussel, Elliptio complanatus, in support of a "sliding filament" mechanism of ciliary motility wherein peripheral filaments (microtubules) do not change length during beat (see Satir, 1967). Short sequences of serial sections of tips are examined in control (nonbeating) and activated (metachronal wave) preparations. Several different tip types, functional rather than morphogenetic variants, are demonstrated, but similarly bent cilia have similar tips. The peripheral filaments are composed of two subfibers: a and b. The bent regions of cilia are in the form of circular arcs, and apparent differences in subfiber-b length at the tip are those predicted solely by geometry of the stroke without the necessity of assuming filament contraction. Various subfibers b apparently move with respect to one another during beat, since small systematic variations in relative position can be detected from cilium to cilium. While subfiber-b lengths are uniform throughout, subfiber-a lengths are morphologically different for each filament: 8 and 3 are about 0.8 µ longer than 1, 4 and 5, but each unique length is independent of stroke position or tip type. Subfiber-a does not contract, nor does it move, e.g. slide, with respect to subfiber-b of the same doublet. The central pair of filaments extends to the tip of the cilium where its members fuse. Subunit assembly in ciliary microtubules is evidently precise. This may be of importance in establishing the relationships needed for mechanochemical interactions that produce sliding and beat.     

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     

Muco-ciliary transport in the lung

A two-layer Newtonian fluid model for muco-ciliary transport in the lung is developed where the viscosity of the upper mucous layer is very much greater than the viscosity of the lower periciliary layer. Theory is presented for both cases when the cilia penetrate, and do not penetrate, the very viscous mucous layer. Calculations suggest that, in normal circumstances, it is not essential for the cilia to penetrate the mucus to provide positive transport. However, it does suggest that there is a weak optimal penetration depth of the cilia of between 10-20% of the cilium length. In the case of high ciliary inactivity (e.g. 90% inactive), penetration of cilia into the mucus is essential for normal transport rates suggesting the mucociliary system may be deliberately overdesigned to cater for a whole range of pathological circumstances.