Ciliary Activity and the Origin of Metachrony in Paramecium: Effects of Increased Viscosity

The small dimensions of ciliary movement make viscosity of the medium a key factor in the hydrodynamic interaction of cilia. Because technical difficulties are encountered in direct observations of ciliary systems, little is known concerning the mechanisms by which the fluid medium actually influences the beat of cilia and metachronism. Gosselin (1958) observed in lateral cilia of mussel gills an increase in wave velocity when the viscosity was raised to 15 cP. Sleigh (1966), on the other hand, found that in increased viscosity Paramecium slowed down the frequency of the beat and the velocity of the metachronal wave and changed the metachronism from antiplectic to symplectic. Kuznicki, Jahn & Fonseca (1970) described an unpolarized^†, helicoidal travelling wave in the cilia of Paramecium swimming at normal and high viscosity. According to these authors metachrony is lost at the start of locomotion. The conclusions by Kuznicki et al. are not supported by my own observations made on swimming specimens at normal temperature and viscosity, which show a polarized beat in time and space and a dexioplectic metachrony (Machemer, 1972 a). Though it is widely accepted that metachronal patterns result from mechanical interactions of cilia, current hydrodynamic hypotheses (Gray, 1930; Machin, 1963; Jahn, 1964; Sleigh, 1966) do not explain certain systematic relations between ciliary activity and the parameters of metachronism. The present study was undertaken with the expectation that extensive variation of the viscosity of the medium would provide clues to the influence of this factor on the beating cilium and the coordination of movement in populations of cilia. The findings presented below have led to a working hypothesis of metachronal coordination which relates the parameters of this phenomenon to the spatio-temporal characteristics of the ciliary cycle.

Specimens of Paramecium multimicronucleatum, average length 251 µm (S.D. 18 µm, n = 43) were reared in straw infusion with added 9 mm CaCl₂ and 3 mm KC1, collected geotactically and washed twice in experimental solution of 9 mm CaCl₂ + 3 mm K.CI + 5 mm Tris-HCl buffer (pH 7·2). The viscosity of methyl cellulose solutions in the experimental medium was determined by a precision ball-viscosimeter and gauged to concentration and temperature.

A small amount of experimental solution with about 50 specimens was surrounded with petroleum jelly and flattened between slide and cover glass to 150–200 µm. Microscopical observation and photographical recording were made by interferencecontrast optics with external illumination and 2 intervening heat-absorbing filters. The direction of the swimming helix of Paramecium, left-handed or right-handed, was determined from specimens in deep-depression slides through a stereomicroscope.

The method of stroboscopic determination of ciliary frequency is as follows: high flash rates > 50 Hz are continuously slowed down up to the first stopping of cilia, which indicates the true frequency. Stoppage of ciliary beat is also seen at I, etc. of the first stopping flash rate and may give rise to misinterpretations. Flash rates 2 or 3 times higher than the true frequency produce double or triple pictures of each cilium in 2 or 3 positions and therefore can be distinguished from the critical first-stopping flash rate. All experiments were carried out in a temperature-regulated room at about 18 °C. The temperature of the drop was controlled at 20 °C by an electronic thermometer, in situ and during illumination.

Photomicrographs were taken on high-resolution 35 mm Ortho film by an electronic flash. The actual state of movement and the observed region of specimens during exposure were noted. Wavelengths were measured on photographic negatives by means of an object micrometer.

In this paper metachronism is understood as a 2-dimensional system in which maximal interciliary phase-shift (metachrony) occurs at right angles to the axis of minimal phase-shift (synchrony). Problems of interpretation may arise when metachronism in active cilia is observed in profile view in certain planes perpendicular to the cell surface. For example, angular deviations of the plane of observation from the axis of metachrony will produce views of wavelength and wave direction which differ from the true values of these parameters (Text-fig. 1). Thus, various meta-chronal types (Knight-Jones, 1954) appear in profile view as apparently antiplectic (‘antiplectoid’) or as apparently symplectic (‘symplectoid’). A special case of these relations is illustrated in Text-fig. 2.

Models of ciliary metachronism were made from a plastic plate, perforated with 0·2 cm holes, into which bent pieces of steel wire 11 cm long could be fitted. All length proportions of the 10⁴× magnified model were related to photographic views of the ciliated cell surface of Paramecium. A metachronal wave type was constructed by a process of repeated comparison of the wire model with various photographic aspects of the living animal. A model represents schematic approximations of ciliary metachrony at a given temperature and viscosity and at one moment. If the model is viewed at defined angles to the wave fronts, then typical shapes of wave profiles are obtained for each angle, which helps to identify wave angles of corresponding observed wave profiles. According to λ = λ′ · sin α, the true wavelength (λ) is calculated from the apparent wavelength (λ′) seen in the profile and the sine of the wave angle (α).^*

Ciliary activity and metachronism in Paramecium swimming under normal conditions (20°C, 1 cP) have been described elsewhere (Machemer, 1972a). In summary, the power stroke of the majority of the body cilia is directed backwards and toward the right. Metachronal waves are travelling from back left to front right. The metachronal type is dexioplectic, as the power stroke forms an angle of about 90° to the right of the wave direction. In profile views of forward-swimming animals, waves seem to travel forward; the power stroke is directed backward (Plate 1a, arrowheads). This apparent antiplectic (or ‘antiplectoid’) configuration arises from the side projection of the dexioplectic pattern. The swimming helix of the aurelia-type Paramecium is left-handed. Text-fig. 4a gives a graphical representation of these normal conditions.

The properties of ciliary activity change systematically, if the viscosity of the medium is increased at a constant temperature of 20°C. At 2·6 cP metachronal waves are rarely seen in profile views; instead, nearly all cilia in the antero-posterior focal plane are caught at the same stage of their cyclic movement which means that waves are travelling parallel to the longitudinal body axis. Surface views of swimming specimens confirm this assumption (Plate 2a). If viscosity is increased to 5·6 cP, metachrony reappears in profile views. Waves now show apparent symplectic (or ‘symplectoid’) patterns, which are most clearly indicated by groups of power-stroke cilia converging upon one another (see arrowheads in Plates 1b and 2c). In these symplectoid configurations waves and power stroke are directed toward the animal’s posterior end. This is understood from surface views of metachronism at 5·6 cP. By turning clockwise the wave fronts have passed the longitudinal orientation, now travelling from front left to back right (Plate 2b). The properties of the ciliary beat have not dramatically changed if compared with normal conditions. The cycle is still polarized in time; small groups of power-stroke cilia alternate with large groups of recovery-stroke cilia, which represents the time relation between power stroke and recovery stroke (Plate 2c). Spatial polarization was not suppressed by viscosities up to 5· 6 cP. During the recovery stroke sickle-shaped cilia move close to the cell surface. After progressive stiffening from base to tip, and adoption of a reclined position, they perform the power stroke in an approximately straight configuration; their backward bending is due to viscous counterforces of the medium. The exact orientation of the power stroke could not be recognized in the photomicrographs.

Paramecia in a medium of 40 cP alternate between slow forward and backward swimming movement. Clear symplectoid waves appear in profile views (arrowheads in Plate 3a, b). The apparent wavelength varies, but is strongly decreased if compared to metachrony at lower viscosity. This is consistent with surface views, which show an increased angle between the longitudinal body axis and the wave fronts (Plate 4b, c). Waves move from front to back or, in the case of backward swimming, from back to front. Cilia in a medium of 40 cP have assumed a more helicoid shape, but the polarized nature of the beat is still well discernible (Plate 4a).

Locomotion of Paramecium in both directions is also observed at a viscosity of 35 cP, but metachronism is no longer a permanent phenomenon over the entire cell surface. In forward-moving animals metachronal waves usually occupy the most anterior portion of the cell, but get increasingly disorganized toward the posterior end. Wave profiles are symplectoid (arrowhead in Plate 4d). The waves move in the backward left direction, which is also the main orientation of the helicoidally winding cilia (Plate 4e).

Residual metachronism of small surface areas was also observed at viscosities of 440 cP and 930 cP in moving animals. Wave properties are not different from those at 135 cP, except for a more pronounced helicoid shape of the cilium, smaller amplitudes, and near-absence of polarization of the ciliary cycle.

A survey of viscosity-dependent changes in ciliary metachrony reveals four general features. (1) The direction of wave transmission in forward-swimming animals gradually turns clockwise from front right to back left, when viscosity is increased. This is accompanied by (2) the transition of profile wave patterns from antiplectoid to symplectoid. (3) The polarization of the ciliary beat is increasingly replaced by helicoid undulations, and (4) metachronal coordination gradually breaks down at viscosities of more than about too cP.

A more detailed study of viscosity-modified ciliary activity would require reconstruction of complex spatial patterns of ciliary bending from their 2-dimensional aspects. In the following section the method of mutual comparison of observed and modelled metachrony (Machemer, 1972 a) is applied to metachronal patterns at a viscosity of 40 cP.

The wire model of ciliary metachrony (Plate 5) contains 7 distinct stages of the ciliary cycle, which were related to a great number of different photographic representations of cilia beating at 40 cP. The number of bending stages per wave results from the average wavelength of 12–14µm, covering usually 7 ciliary units. In the model the waves move from front left to back right as a common direction of wave propagation at this viscosity. The power stroke toward the back left and the counterclockwise recovery stroke are seen as distortions of the helicoid bending of the cilium rather than separate phases (compare with stages 1–7 in Plate 6f). More information comes from vertical sections of the model. The ends of recovering cilia form the walls of deep troughs between the wave crests. The crests are represented by the ends of cilia at the start of and during the course of the power stroke. The true wavelength appears in profile views perpendicular to the wave fronts (wave angle 90°). Long waves result from views at wave angles near 0° and 180°. In a very broad range of angles, from about 70° to 180°, the profiles of the waves show a symplectoid pattern with converging groups of power-stroke cilia. At angles between o° and 40°, on the other hand, diverging power-stroke cilia indicate an antiplectoid metachrony. The generalized properties of metachrony at this viscosity are represented in Text-fig. 2. With an angle of about 55° between the directions of the beat and the wave, the metachronal type is dexiosymplectic. As the directions of the wave and of the power stroke do not deviate much from the longitudinal body axis, nearly all observable profiles of the waves are symplectoid. Antiplectoid patterns would be expected in the rare case of viewing approximately parallel to the animal’s longitudinal axis.

Examples of wave-angle determination in profile views of metachronal waves are demonstrated in Plate 6a–d. Though model profiles cannot reproduce all individual variations of the ciliary beat, such as amplitude and timing between power stroke and recovery stroke, and can hardly imitate the shallow plane of focus of interferencecontrast optics, the similarities between corresponding observed and model waves are sufficient for clear identification of the wave angle.^* Wave angles between 110° and 140° are very frequent in forward-swimming and backward-swimming animals. Different angles near the anterior and posterior ends of the animal may result from waves joining together and from the more spherical contour of the surface. A quantitative approach in the determination of metachronism at 40 cP is given in Tables 1 and 2. Readings of wave angles at 5 sections of the cell profile in different forwardswimming individuals show that the waves are somewhat steeper at the anterior and posterior ends, if compared to the mid-sections (Table 1). The true wavelength, calculated from the apparent wavelength, is rather constant. Direct measurement of wavelength from surface views confirms the calculated values.

Wave angles of backward-swimming animals exceeded slightly those of forwardswimming animals on the average; the wavelength seems to be somewhat reduced, though over the midsections it equals that observed during forward swimming. The striking similarity of the metachronal patterns in forward-swimming and backward-swimming animals is demonstrated in the generalized reconstructions of the wave systems in Text-fig. 4 d, e.

The stroboscopical determination of frequency depends on rather uniform and permanent activity in ciliary populations. These conditions are found in the oral groove of Paramecium, where, in addition, a reduced amplitude of beat and modified bending sequences of the paired cilia makes metachronal waves more conspicuous (Plate 1a). Frequency data for the peristomal cilia, plotted against viscosities between i and 49 cP, show that the frequency falls linearly with exponentially rising viscosity (Text-fig. 3).

In strobe illumination metachronal waves on the body surface cannot be identified as easily as in the peristomal groove. They appear as periodic elevations on the surface representing cilia during the recovery stroke. A preliminary comparison between frequencies of cilia on the body and in the groove did not lead to clear results. Body cilia more often change their frequency; they may beat slower or faster than cilia in the peristome. Anterior and posterior body cilia do not beat with strictly identical frequencies. If cilia in the anterior mid-region were brought to a stroboscopic standstill, an apparent centripetal movement of anterior and posterior waves was often observed. This indicates a gradient of decreasing frequency toward the posterior.

Analysis with the modelling technique shows that the power stroke, which is directed backwards and to the right at normal viscosity (Machemer, 1972a), shifts clockwise when the viscosity is raised to 40 cP so that its new direction is backwards and to the left (Plate 6e, f).

The term of ‘beat direction’ does not adequately describe the spatial properties of the power stroke of the ciliary cycle in protozoa. As this cycle has a spherical envelope, different vectors are adding up in the course of the power stroke. Increased viscosity enhances the spherical deformation of the power stroke and reduces its transverse amplitude. On the other hand, the helicoid component of the cycle increasingly contributes to the creation of translational water currents. The term ‘resulting force of ciliary beat’ would therefore better describe the net interaction of cilium and medium. For practical reasons I continue to use ‘power stroke’ or ‘beat direction’ under conditions of high viscosity, even if ‘resulting force of ciliary beat’ is meant.

As it is difficult to determine ciliary beat direction from photographs, indirect evidence was sought by observing the sense of swimming helices at different viscosities. Table 3 shows that up to 5-6 cP all observed animals swam in a left-hand helix (as seen in the direction of locomotion). At 12 cP 22% swam left-handed, 57% right-handed, and 21% showed no rotation at all. Beyond 12 cP viscosity only right-hand helices were found. Spontaneous backward swimming occurred only in media of 12 cP and higher. In all these cases the helix was right-handed. These results are interpreted by assuming that the swimming helix is, in the first line, produced by an oblique orientation of the power stroke (Bullington, 1930): left-hand helices of forward-swimming animals would result from cilia beating backwards and to the right, right-hand helices would result from cilia beating backwards and to the left. Observations at viscosities of 1 cP and 40 cP, combined with model reconstructions of ciliary metachrony, support this interpretation. Additional evidence comes from the fact that with increasing viscosity the power stroke turns clockwise to a lesser extent than does the direction of metachrony. So the longitudinal orientation of waves fronts at 2-6 cP should not be associated with a straight backwards beating, and in fact a left-hand helix is observed. Judged from the wave orientation, the transition from left-handed to right-handed helices should occur above 2-6 cP and below 40 cP, which is in harmony with the data in Table 3. Direct and indirect results relating to the orientation of the power stroke at different viscosities are summarized in Fig. 4.

The rate of metachronal wave propagation or wave velocity (𝓋) is determined by the wavelength (λ) and the time of one ciliary cycle or the reciprocal of the frequency (f) of the beat: 𝓋 = λf. The frequency is strongly reduced by increased viscosity, and the wavelength does not show a remarkable increase between 1 cP and 40 cP; the wave velocity therefore falls with increasing viscosity (Text-fig. 5). The diagram in Fig. 5 combines frequency readings of peristomal cilia with averaged data^* on wavelength of body cilia. Thus the values of wave velocity are approximations. Wave velocities in the peristome might be a bit smaller than plotted in Fig. 4, since the wavelength is shorter in the oral groove as compared to that on the body surface (Machemer, 1972 a).

The wave velocity tends to become stabilized under constant environmental conditions, even if the frequency changes. So the posteriorly directed decrease in frequency, observed by stroboscope in the anterior part of the cell, is accompanied by a small increase of the average wavelength in the same direction at increased viscosity (Tables 1, 2) as well as under normal conditions (Machemer, 1972a). The simplest explanation of the stability of wave velocity would be to see the wavelength as a reciprocal function of frequency. A comparison between data for f and λ in animals swimming at 40 cP shows, however, that the average wavelength in backwardswimming animals is smaller (12·7 µm, Table 2) than in forward-swimming animals (14·3 µm, Table 1), though mean values of frequency are identical (14·1 Hz). This suggests that it is not the frequency itself which alters wavelength, but some other frequency-dependent parameter, such as the time relation between power stroke and recovery stroke.

The timing of the ciliary cycle and the amplitude of the beat were not quantitatively related to the viscosity of the medium. However, from the observation of wave patterns at 1 cP and 40 cP it is safe to conclude that the power stroke, which under formal conditions takes $17$ to $27$ of the period of one cycle, is lengthened in time with increasing viscosity, because of the slower propagation of stiffening in the ciliary axis and decreased velocity of the power stroke. At viscosities above 135 cP power stroke and recovery stroke seem to be transformed into a harmonious helicoidal gyration. The ‘depolarization’ of the cycle is accompanied by a reduction of amplitude. This is clearly demonstrated by the envelopes of model cilia representing activity at 1 cP and 40 cP (Text-fig. 6).

The data presented above show very obvious changes of ciliary activity and metachrony in response to increased viscosity of the medium. It is significant that the transformations of beat and metachronism occur together so as to suggest that they are intimately related to each other. This is consistent with a mechanical hypothesis of ciliary metachronism, namely that the physical properties of the fluid medium determine the origin and form of metachronal coordination in the ciliary population. I will now consider the observations which speak in favour of the mechanical concept.

1. The wavelength, which expresses the amount of phase-shifting between adjacent cilia, increases with rising viscosity. Increased viscosity is known to enhance the coupling of particles in motion.

2. The angle between the direction of the power stroke and of the wave transmission tends to be constant under constant physical conditions. The method of model comparison, which is based on the reproducibility of metachronal types, was used to identify metachronal patterns at different viscosities. During spontaneous reversal of Paramecium at 40 cP the direction of metachronism shifts by an angle similar to the shift in direction of the power stroke. Smaller shifts in wave inclination under constant conditions occur simultaneously with similar shifts in the direction of the power stroke (Plate 4 c).

3. In forward-swimming animals the power stroke and the metachronal waves both shift orientation progressively clockwise with rising viscosity of the medium.

All these observations suggest that the wave direction is determined by the beat direction acting through the hydrodynamic properties of the medium. Three basic relations between ciliary activity and metachronism are proposed in the following working hypothesis.

1. It is postulated that metachronism arises in a ciliated surface if mechanical interaction in one direction across the field exceeds that in any other direction. This may result from the spatial distribution of cilia as well as from spatio-temporal properties of the ciliary cycle.

2. It is further postulated that the orientation of a metachronal pattern is determined by the vectors of force parallel to the cell surface produced during the ciliary cycle. The lines of synchronization (wave fronts) tend to be oriented parallel to the strongest vectors of force. The wave fronts, on the other hand, tend to spread in the direction of least mechanical action of each cilium on its neighbours.

3. Finally, it is postulated that the difference in phase-shift along the axis of metachrony as compared to the axis of synchrony (zero shift), seen as the metachronal wavelength, results from the difference in strength between the vector of greatest force (e.g. produced by power stroke) and the vector normal to that vector. As decreasing polarization of the ciliary beat reduces the differences between these vectors, the metachronal wavelength is expected to increase with decreasing polarization of ciliary beat.

These three elements of a mechanical hypothesis of ciliary metachronism will be briefly considered and illustrated by the envelopes of model cilia at viscosities of 1 cP and 40 cP (Text-fig. 6). A surface view of the ciliary envelope, combined with the coordinates of the accompanying metachronal pattern (Fig. 6a), shows that the beat irection nearly coincides with the orientation of the wave fronts. Even if differences in angular velocity between power stroke and recovery stroke are not taken into consideration, the differences in ciliary movement in the plane of the wave front (Fig. 6b) compared to that in the plane of metachrony (Fig. 6c) are enormous. This supports points 1 and 2 of the hypothesis.

The coincidence of beat direction and wave direction at high viscosity (symplectism) may be understood by considering that the ciliary axis assumes a position closer to the cell surface and the cycle has been transformed toward harmonious helicoid undulations. Under these conditions reference points along the shaft of the cilium perform maximum lateral excursions at right angles to the main axis of the helix and parallel to the observed line of synchronization (point 2 of hypothesis).

Metachrony at 40 cP is obviously the result of combined actions of polarized and helicoidal beating (Fig. 6d–f). Forces of the reduced power stroke (in the direction backwards and to the left) tend to orient synchrony into this direction, but the lateral movements of the inclined cilium (in backwards-left and and forwards-right directions) turn the wave fronts more clockwise by an additional angle (6d). A comparison of the outlines of the cycle in the planes of synchrony (6e) and of metachrony (6f) shows the dominant lateral excursions of 4 ciliary reference points in the plane of synchrony.

The occurrence of dexioplectic - instead of laeoplectic, antiplectic or symplectic - metachronism in Paramecium can be understood by considering the spatial consequences of cilia gyrating counterclockwise^* in a metachronal field. If the ciliary cycle observed in dexioplectic metachronism (Fig. 7a) were forced into 3 other types of metachronism, piles of spatially conflicting cilia would exist during the recovery stroke (laeoplectic metachrony, 7b), the effective stroke (symplectic metachrony, 7c) or both (antiplectic metachrony, 7d). The dexioplectic pattern, on the other hand, appears to provide the wave system with a minimal waste of mechanical energy during the recovery stroke. Point 2 of the hypothesis explains the occurrence of this specific pattern: In Paramecium, in media of normal viscosity, the leading vector of force during the power stroke synchronizes cilia along its axis; thus orthoplectic metachronism (i.e. antiplectism or symplectism) is excluded, as metachronal waves can only travel at right angles to the line of synchronization. Two alternatives remain: dexioplectic or laeoplectic metachrony. However, in a counterclockwise cycle of the cilium, the phase of least mechanical action between adjacent cilia (recovery stroke), occurs to the left hand of an observer facing in the direction of the power stroke (compare surface view of model envelope in Fig. 6a). This leads to a maximum interciliary phase lag toward the left, namely to a dexioplectic metachrony.

Up to a viscosity of 40 cP the ciliary cycle shows an increasing loss of polarization, which may be expressed in terms of a relative increase of lateral forces at right angles to the forces in the power-stroke direction (Fig. 6a, d). At the same time the average wavelength is observed to increase from 10·7 µm to 14·3 µm (point 3 of hypothesis).

An increase in wavelength is also found between the anterior end and the middle of the animal ; it occurs in forward-swimming animals at 40 cP relative to backward-swimming animals; it is seen on the body cortex under normal conditions, if compared to the oral groove (Machemer, 1972 a), and at low temperature in comparison to normal temperature (Machemer, 1972b). In all these cases the increase in wavelength may be explained, as above, by a reduction in polarization of the ciliary cycle and consequent increase of coupling forces in the direction of metachrony relative to forces in the direction of synchrony.

The polarized form of ciliary beat in Paramecium has been known since 1926, when Gelei observed it in instantaneously fixed specimens. Parducz (1954) confirmed Gelei’s observation that the cycle consists basically of a counterclockwise gyration and found the same form of beat in different species of holotrich ciliates (Colpoda, Colpidium, Didinium, Ophryoglena, Tetrahymena, Uronema), of spirotrich ciliates (Balantidium, Nyctotherus) and of opalinids (Opalina, Cepedea, Protoopalina) by an improved instantaneous fixation technique (1967).

In vivo observations indicate that the movements of compound cilia in the hypo-trichous ciliates Euplotes (Gliddon, 1965) and Stylonychia (Machemer, 1965, 1969a) have the same components of activity as cilia in Paramecium. Horridge & Tamm (1969) found, in scanning EM photographs of Opalina, counterclockwise and polarized ciliary gyrations and confirmed these results by in vivo photographs of the wave system (Tamm & Horridge, 1970). In high-speed motion pictures of Paramecium, Kuznicki, Jahn & Fonseca (1970) observed no polarization of ciliary motion in media of high viscosity. The beat is described as counterclockwise helicoid, similar to travelling helices in flagella. My own observations at high viscosity are in agreement with this. On the other hand, the data presented above and elsewhere (Machemer, 1972a) are in conflict with the conclusion of Kuznicki et al. that the unpolarized helicoidal beat is also characteristic of normal conditions of viscosity. Recently, polarized ciliary activity has been recorded in Spirostomum (Boggs, Jahn & Fonseca, 1970) from the analysis of high-speed films.^* There is little doubt that the counterclockwise and polarized ciliary gyration is common in protozoa, although modifications of this form of beat in space and/or time may occur. The transformation of the normal beat into helical undulations at high viscosity, reported in this paper, seems to result basically from an increased retardation of ciliary movement by the medium. Low temperature reduces time differences between power stroke and recovery stroke in Paramecium without severely changing the form of beat and metachrony (Machemer, 1972b). This suggests that temperature-dependent metabolic chains are involved in the temporal aspect of ciliary polarization.

It is a conclusion of this study that increased viscosity shifts the direction of the power stroke progressively clockwise, and thereby induces the transition from lefthanded into right-handed swimming helices. Grçbecki, Kuznicki & Mikolajczyk (1967) interpreted the viscosity-dependent change to right helices as the result of an increased influence of the asymmetrical body shape of Paramecium, which, they presumed, adds right-pointing vectors to the left-pointing vectors of the ciliary beat. Seravin (1970) rejects this explanation, arguing that the body shape cannot influence the hydrodynamics of moving protozoa, as forces of turbulent drag are much smaller than those of viscosity. In fact, the Reynolds number, expressing the ratio of these forces, is about 10⁻³ for Paramecium, for a single cilium about 10⁻⁴ (Jahn & Bovee, 1968). Seravin tested the swimming behaviour of anterior and posterior halves of Paramecium in 0·5% carboxymethyl cellulose solutions^† and found right-hand swimming helices in anterior as well as in posterior fragments. This elegantly demonstrates that the shape of the oral groove does not play an essential role in the determination of the swimming helix. Seravin’s conclusion, however, that the helix is independent of hydrodynamic factors, seems not yet well established, as at the viscosity used by Seravin any aurelia-type Paramecium will swim in right helices, due to the clockwise turn of the power stroke into a backward-left direction. The nature of this graded reaction of the beating cilium is unknown. Viscosity may be a factor in mechanical triggering, so that, if increased, viscosity may release the power stroke at an ‘earlier’ stage of the ciliary cycle. The methyl cellulose or even increased viscosity itself may also influence membrane properties and thereby change internal concentrations of divalent cations. This question needs experimental investigation.

Current hypotheses on sliding filament mechanisms of ciliary motion (Satir, 1968; Sleigh, 1968) are based on planar ciliary beating, which is found in many metazoan cilia. The structural organization of the cilium seems more suited to the production of gyrational movement than to bending in one plane. The 9 peripheral doublets of fibrils, which are considered to be elements of filament sliding, have a radial, onedirectional arrangement of the dynein-arms on subfibre a. If viewed from tip to base of the cilium, the free ends of the arms point in a counterclockwise direction. This unique symmetry, which excludes any other planes of bilateral or biradial structural organization, has a striking parallel in the basic gyrational performance of protozoan cilia. From a topographical point of view, the ATP-splitting capacity of dynein is found in a most advantageous spatial arrangement to provide energy transfer in a sequential cycle of sliding between adjacent peripheral fibrils.

The relations between the ciliary beat and metachronal wave transmission have always been a point of concern in studies on ciliary metachronism (reviewed by Kinosita & Murakami, 1967). Examples of changing metachronal types of coordination are reported from cilia in mussel gills (Murakami, 1963; Child, 1965), but they seem to be exceptions to a general rule that angles between beat and wave remain constant under constant external physical conditions.

In protozoa, there is no evidence of dramatic changes of metachronal types in ciliated surfaces. Opalina turns the direction of wave propagation simultaneously with turns in beat direction (Okajima, 1953, 1954). Parducz (1956) reports a 90°‘reversal’ of power-stroke direction in Paramecium starting backward swimming; the wave fronts are assumed to turn by a somewhat larger angle. High-frequency films, taken during the ciliary reversal of Paramecium, show that the normal 90°-relation between the power stroke and the direction of wave propagation is maintained (Machemer, unpublished observations). In backward-swimming specimens the wavelength is smaller than in forward-swimming animals (Machemer, 1969b) and pitch and diameter of the swimming helix in both directions differ from each other, which suggests changes in frequency and in the degree of polarization. In a viscosity of 40 cP no obvious difference in the metachronism of forward-swimming and backwardswimming animals was observed, except the differences in wavelength. Sleigh (1966) described in Paramecium a switch from antiplectic to symplectic metachrony, when the viscosity was increased up to 7 cP. The present data indicate that beyond 2·6 cP a change from antiplectoid to symplectoid patterns will be observed in profile views. This results, however, from the slight clockwise turn of beat and wave direction under the influence of increased viscosity (compare a and c in Fig. 4) ; metachrony essentially changes from dexioplectic to ‘dexio dexio-symplectic’, using the compass-rose terminology. There are other examples in which the spatial relationship of beat and metachrony seems to be incompletely described by their relative directions in one plane (Parducz, 1961, ciliary band in Didinium;Murakami, 1963, ciliary pads in Mytilus gill). The range of variation in metachronal types might turn out to be more restricted if more quantitative data are available. In Paramecium this range seems to be limited between the dexio-plectic and symplectic patterns.

Fixed angles between power-stroke direction and wave-transmission direction were not always considered to be an essential element of mechanical control of ciliary metachronism. Gray (1930) postulated that cilia beating in a field affect one another in such a way as to produce the least phase difference between neighbours (minimum interference principle) and that the wave direction does not depend on mechanical but on structural conditions of ciliary arrangement. This concept is not fully confirmed by the properties of metachronal transmission in Paramecium and Opalina, where the waves are turned in harmony with the power stroke and regardless of existing surface structures.

From a mathematical treatment of the physical conditions of coupling between flagella or cilia, Machin (1963) concludes that synchronization is the result of suppression of all frequencies differing from the frequency of a ‘master’ organelle with a maximum amplitude. With regard to metachronism Machin shares Gray’s concept by stating that ‘there is no reason to assume that the direction of propagation of the metachronal wave will be in any way related to the direction of the effective stroke of the individual cilia’.

Jahn (1964) and Jahn & Bovee (1964) promoted a hydrodynamic theory concerning the origin of ciliary metachrony from mechanical effects of the power stroke on the medium. Metachrony is postulated to result directly from the power stroke through a transmissionsl delay. Lateral effects of the pressure wave account for synchronization of metachronal rows. This theory has not been worked out in sufficient detail to explain simultaneous occurrence of synchrony and metachrony.

The implications of metachronal coordination of cilia are somewhat simplified in a mechanical hypothesis by Sleigh (1966), who considers the interaction of cilia in one direction. Symplectism is understood to be the result of mechanical coupling of cilia in the direction of the power stroke. Antiplectism is expected to occur in more widely spaced ciliary populations, where sufficient coupling forces are found only during the slow recovery stroke. As returning cilia move against the powerstroke direction, metachrony is also expected to travel this way. Sleigh (1969) postulates synchronization of two neighbouring cilia if the mutually exerted lateral forces of the power stroke are identical. This is assumed to be realized best in planar beating cilia. It is a property of Sleigh’s concept that the transmission of metachrony rather than ciliary synchronization is closely related to the direction of ciliary beat. The present hypothesis differs from this view by coupling synchronization to the power stroke or - in more general terms - to the strongest vector of force produced by the ciliary cycle.

The relations between wave velocity and frequency, expressed by the equation 𝓋 = λf, have been interpreted by Sleigh (1956, 1957) in terms of a neuroid mechanism of ciliary coordination. The peristomal compound cilia of Stentor, the membranelies, showed decreasing frequency but constant wave velocity, if the viscosity of the medium was raised (up to 3-·6 cP). Similar results were observed when MgCl₂ was removed from the medium or a cut was made across the membranellar row proximal to the observed region. Sleigh suggested that in Stentor frequency and wave velocity are independent variables and hence represent two separable processes in the metachronal coordination of cilia: spontaneous ciliary activity and internally conducted interciliary co-ordination. This conclusion may be unjustified for the following reasons. An independent variation of frequency and wave velocity is also found in the lateral cilia of mussel gills; Gray (1930) observed stability of wave velocity by reciprocal relations between frequency and wavelength if the experimental conditions were kept constant; under the influence of increased viscosity (15 cP) the wave velocity increased, while frequency remained constant (Gosselin, 1958). However, metachronism in lateral cilia of Mytilus and Modiolus is believed to be mechanically conducted, for glycerinated models of these cilia retain metachronal coordination (Child, 1965). It therefore seems more reasonable to look for a mechanical explanation of independent variations of frequency and wave velocity in various ciliary systems. The stabilization of wave velocity, for example, found in Mytilus, Stentor and Paramecium, can be explained on mechanical principles if decreased frequency is accompanied by decreased polarization of the beat, which leads, according to point 3 of the present hypothesis, to an increase in wavelength.

Recently, hypotheses have been put forward to explain the regulation of ciliary metachronism by physiological gradients in the cell cortex. According to Grçbecki (1965) a stomatocaudal gradient induces metachronal waves in ciliates to travel from the posterior end over the anterior pole to the cytostome during normal forward locomotion. I have proposed that metachronal patterns in ciliates result from the interaction of an antero-posterior body gradient and a cytostomal gradient (Machemer, 1969c). Electrophysiological studies of the membrane properties of Paramecium (Eckert & Naitoh, 1970) showed that the velocity of electric pulses, travelling along the cell membrane, is more than 100 times as fast as that of metachronal waves. This result strongly favours the opinion that metachronal wave propagation cannot be related to physiological gradients apart from ciliary activity. Eckert & Naitoh point out that gradients of ciliary action must result from topographically fixed properties of the cilia themselves or the associated membrane, and propose that the direction of wave propagation is determined by the direction of the power stroke. The present observation of an antero-posterior gradient of frequency and the demonstration of systematic relations between ciliary activity and metachronism in Paramecium confirm this conclusion.

I am grateful to Dr Roger Eckert for a critical reading of the manuscript. This work was supported in part by a grant from the Deutsche Forschungsgemeinschaft. The manuscript was prepared with support of USPHS grant NS 05670.

The present hypothesis on the origin of ciliary metachronism receives further support from recent observations by E. Aiello and M. A. Sleigh (personal communication) that the recovery stroke of the lateral cilia of the Mytilus gill occurs as a clockwise gyration (ss seen from above) rather thsn a planar movement as widely supposed. This finding is consistent with the progression of the metachronal waves 90° to the right of the direction of the power stroke in Mytilus. Thus, as in Paramecium, the waAes propagate in that direction (determined by the recovery stroke) in which the hydrodynamic forces coupling the cilia are assumed to be lowest.

PLATE I

Forward-swimming animals, (a) Normal viscosity (1 cP), ventral view; arrowheads indicate antiplectoid waves, (b) Viscosity of 5·6 cP, ventral view; symplectoid waves shown by arrowheads. Vertical brackets in these and the following prints indicate 10 µm.

PLATE 2

Details of ciliary metachronism at viscosities of 2-·6 cP (a) and 5·6 cP (b, c). (a) Anterior end, surface view of longitudinal wave crests at 2·6 cP. (b) Posterior end, surface view of wave fronts travelling backward-right; arrowheads indicate optical cross-sections of cilia during power stroke (stages 1–2 in Plate 6e). (c) Midpart of the cell, oblique surface view at 5-6 cP; characteristic converging group of cilia during power stroke in a symplectoid wave (arrowhead); note surface-attached sickle-shapes of cilia in the recovery stroke (stages 4–6 in Plate 6e). Anterior ends upwards in all prints.

PLATE 3

Animals at a viscosity of 40 cP. (a) Fortcard-swimming animal, dorsal; wave fronts in the oral groove region parallel to focal plane (left-hand side of body in the print); typical symplectoid waves on the opposite body surface (arrowhead). (6) Backward-swimming animal, dorsal, with symplectoid waves in profile (arrowhead).

PLATE 4

Details of metachrony of forward-swimming animals at viscosities of 40 cP (a–c) and 135 cP (d, e). (a) Posterior midsection; oblique view of a series of waves, travelling in backward-right direction. (b) Anterior end, ventral-left, surface view of wave crest, (c) Posterior midsection, surface view of exceptional case of waves travelling in backward-left direction; note the angular turn of whole pattern in comparison to typical configuration in Plate 5. (d) Posterior end, profile of waves at 135 cP which are symplectoid (arrowhead), (e) Midsection, surface view with wave front (arrowhead); waves travel in backward-left direction.

PLATE 5

Model of ciliary metachrony in a forward-swimming Paramecium at a viscosity of 40 cP and normal temperature (20°C). Planes of optical sections across the model are determined by the angular deviation from the line of ciliary synchronization in the clockwise direction. Surface pattern of model corresponds to ectoplasmic ridges, ant., anterior direction.

PLATE 6

(a–d) Comparison of metachronal wave profiles of Paramecium at a viscosity of 40 cP with corresponding model wave profiles for the purpose of wave-angle determination, (a) Cilia on the dorsal surface (Plate 3 a). (b) Anterior right-hand edge of body, (c) Waves on anterior left-hand end. (d) Profile of left-hand side of body in a iackward-swimming animal ; polarization of ciliary cycle appears to be stronger than during forward swimming, (e,f) Cycles of model cilia in a metachronal system during forward locomotion, (e) Normal conditions (1 cP, 20°C); (f) Increased viscosity (40 cP, 20°C). Small arrows, direction of metachrony; large arrows, direction of power stroke. Numbers 1–3 indicate stages of power stroke, 3–7 stages of recovery stroke. Reference points a-d mark four sections of equal length on the cilium, post., posterior direction.