J. exp. Biol. (1980), 87, 149-161 j ,QWith 7 figures

Printed in Great Britain

MICROTUBULES AND THE PROPAGATION OF BENDINGWAVES BY THE ARCHIGREGARINE, SELENIDIUM FALLAX

BY J. S. MELLOR AND H. STEBBINGS

University of Exeter, Department of Biological Sciences, Washington Singer Laboratories,Exeter EX4 A<QG, U.K.

{Received 26 October 1979)

SUMMARY

1. The trophozoites of Selenidium fallax propagate bending waves at ratesof up to 35 ftm s"1, of a similar character to those manifested by eukaryoticcilia and flagella. A beat frequency of 0-12-0-15 Hz appears average, thoughrates outside this range have been recorded. Translatory locomotion at up to6 /im s"1 has been observed. The protozoan demonstrates the presence of anactive bending mechanism, probably along its entire length, and a means ofcoordinating adjacent bends.

2. The Reynolds number for the motion is IO^- IO" 4 , suggesting that thehydrodynamic aspects of the trophozoite movement are amenable to analysisby similar means to those already employed for cilia and flagella.

3. It is possible that the protozoans exhibit a sliding microtubule mech-anism, which could be very usefully compared with that occurring in theciliary axoneme.

INTRODUCTION

Archigregarines of the genus Selenidium are found in the digestive tracts of manyspecies of polychaete worms. The vegetative stage or trophozoite is itself vermiformand normally anchored by its anterior end to the intestinal epithelium of the host. Theremainder of the trophozoite is thus free to move within the gut cavity.

When Giard (1884) named the archigregarine in Nerine cirratulus as Selenidiumpendula he not only founded the genus but also set the trend for describing the move-ments characteristic of archigregarine trophozoites; 'le nom rapelle les mouvementspendulaires caracte'ristiques de tout le group'. For nearly a century there has beenlittle progress in furthering this essentially correct but oversimplified view of tro-phozoite motility, except perhaps in recognizing the organism's ability to coil anduncoil like a watchspring (Ray, 1930; Vivier & Schrevel, 1964; Macgregor & Thomas-son, 1965). Possibly Stebbings, Boe & Garlick (1974) came closest to recognizing thetrue potential of trophozoite movement by describing it as 'whip-like', and by notingthe great degree of variation in amplitude of the beat form from one trophozoiteto another.

Several authors have carried out ultrastructural studies describing a system oflongitudinally aligned microtubules beneath the pellicle of the trophozoites (Vivier &Schrevel, 1964; Macgregor & Thomasson, 1965; Schrevel, 1971; Stebbings et al. 1974)

J. S. MELLOR AND H. STEBBINGS

Fig. i. Diagram to explain the principle of analysis using the arc-line model. First a set ofcircles of known radius inscribed on sheets of tracing paper were used to locate the centre ofeach bent region of the photographic images of the trophozoites. This was done by simplyoverlaying the circles until a suitable fit with the outer curvature of the bend was obtained.Using these centres, circles were drawn passing along the midline of the trophozoite in the bentregion. This gives A, the radius of curvature of the bends. Secondly, lines were drawn tangen-tially to adjacent circles, to locate the straight regions between the bends (2C). The angle be-tween the lines forming the straight regions was measured in order to determine the anglesubtended by the bends (a). The centre of a bend (E) was taken to be the point of intersectionof that bend with a line bisecting the tangents of the straight regions bordering it. The lengthof the bends (B) was calculated as the product of the bend angle (a) and the radius of curvature{A). The positions of the centres of bends (£) and straight regions (D) were found by placingcotton along the length of the image midline between the anterior end and the centre to belocated. The half wavelength was taken to be the chord length (G) between the midpoints ofthe straight regions either side of the bend, and perpendicular to the line joining the centre ofcurvature to the centre of the bend. The amplitude (F) of the bend was taken to be the per-pendicular distance from the centre of the bend to the half wavelength (G). (From Brokaw,1970.)

and these constitute the only structures identified which could play a mechanisticrole in the motility of the organism. So far, however, there has been no detailedanalysis of the movement itself - a fundamental requirement if the function of themicrotubules is to be accurately assessed - and this we present here.

It has become obvious from our cinematographic studies that in the trophozoitesof the Selenidium sp. native to the intestine of Cirriformia tentaculata, the pendularmovement is achieved by the anterior formation of bends and their propagation alongthe length of the trophozoite in a manner similar to that shown by beating cilia andsperm flagella. Waveforms of the latter have proved to be highly amenable to analysisby analogy with either travelling sine waves (Gray, 1955), travelling circular arcs and

Bend propagation by Selenidium

(a)

(b)

Fig. 2. Two photographic sequences demonstrating the ability of trophozoites to propagatebending waves. The arrows indicate propagating bends and the numbers, the time sequence inseconds. AT m nucleus. One full beat cycle is represented, (a) Total length of trophozoite, 223/tm; average beat frequency, 98 beats min"1 (016 Hz). (6) Total length of trophozoite, 156 /tm;average beat frequency, 24 beats min"1 (004 Hz). Note the similarity to a planar ciliary re-covery stroke, being executed in both directions. Propagation ceases, unusually, for some 6 sduring 'unbending'. Upon resumption of propagation the bend is practically indiscernible.

152 J. S. MELLOR AND H. STEBBINGS

interconnecting straight lines with abrupt transitions between them (Brokaw &Wright, 1963; Brokaw, 1965; Goldstein, 1976) or meander-like waves (Rikmenspoel,1971; Silvester & Holwill, 1972). More recently too, Rikmenspoel (1978) and Hira-moto & Baba (1978) have demonstrated that the changes in angular direction ofbeating sperm flagella can be accurately expressed as a sine function of time plus aconstant, i.e. the flagella waveforms are ' sine-generated'. This type of wave gives goodapproximations to both meander curves (Langbein & Leopold, 1966; Leopold &Langbein, 1966) and arc-line curves (Sarashina, 1974). Although we have made useof the latter as an initial means of analysing the movement of trophozoites, we discussthe propriety of other wave analogues.

MATERIALS AND METHODS

Cirriformia tentaculata, the polychaete host, was collected from the shore atLadram Bay, Devon, cleaned, and maintained in aerated seawater at 10 °C. Providinginjured worms were discarded, both the host and its archigregarine population couldbe kept for 10-14 days without any visible deterioration in their condition.

Small pieces of heavily infected intestine were excised by a longitudinal incisionunder seawater. Opening the gut often caused the release of unattached trophozoitesand these were also collected, for observation, using Pasteur pipettes. Free tropho-zoites, or pieces of intestine with trophozoites attached, were mounted in seawateron a slide and examined using a Wild M20 microscope and bright field illumination.Cine film of six beating trophozoites was taken at 10 f.p.s. using a Vinten body andmagazine mounted on the microscope. Ilford 16 mm Pan F was used and a Xenonarc lamp provided the illumination. Ultra-violet and infra-red filters were used inconjunction with the Xenon arc lamp at all times.

Other pieces of intestine were placed in small glass embryo cups with a plentifulcovering of seawater and the trophozoites observed using a Vickers stereo binocularmicroscope. Approximately 100-300 trophozoites attached to a single piece of intestinecould be examined by this method. The activity of the trophozoites was monitoredat 30-min intervals by taking a sample of any six organisms and noting their beatfrequency. The number of beats performed over a 30 s period was counted to thenearest quarter beat for each individual. All experiments were conducted at roomtemperature.

Fig. 3. (a) A photographic sequence demonstrating the ability of trophozoites to coil anduncoil. Coiling has a propagative basis but is always asymmetric, (b) 35 mm still photographtaken on Ilford HP5. Occasionally trophozoites may maintain one or more complete waves onthe midzone, depending upon the wavelength measured along the trophozoite. Note that bendsin the region of the nucleus (AT) are unaffected by its presence, (c) Three enlargements of a freetrophozoite in which right hand bends decay totally at about 100/mn from the anterior end.This is not an uncommon phenomenon in attached or free trophozoites. At time O 8, the righthand bend (i) is decaying while the following left hand bend (ii) is still forming. At 5 8, theright hand bend is no longer discernible, and the left hand has almost entirely decayed incoordination with it. At 9 s, (ii) is now reformed and propagates normally as both bends didduring the decay. It is interesting that the lone bends appear to give the best fit to arc-linecurves. Total length of trophozoite, 350 fan; propagation rate, 15 fim s"1; swimming speed,32 fim 8~'; swimming always occurs with the anterior, attachment end leading.

Bend propagation by Selenidium 153

J9-0

J. S. MELLOR AND H. STEBBINGS

10

0-75

0-5

0-25

|10 20 30 40 50 60Location of bends (Mm)

70 80 90

Fig. 4. A test for the suitability of fit of the arc-line model is given by the ratio between thechord length at half-amplitude (H) to that at the half-wavelength (G). This ratio has beenplotted against the distance of two adjacent bends, of opposite sign, (# , O) from the anteriorend of the trophozoite in Fig. 26. The solid horizontal line represents the value for sinusoidalbends (0667) and the broken line, the level predicted by the model (08).

In order to analyse the film obtained, prints were made, to a final magnification ofapproximately 500 times, from individual frames selected at 0-5 or 1 s intervals. Thiswas carried out over a 15-40 s period so that at least one full beat-cycle was obtainedfor analysis. A modification (Goldstein, 1976) of the arc-line method of analysispioneered by Brokaw and co-workers (1963, 1965) was used to follow the developmentand propagation of bends (see Fig. 1).

RESULTS

Trophozoites attached to the gut and placed in embryo cups containing seawatercould continue beating for up to 12 h, although 95% of any sample population hadnormally ceased to do so approximately 6 h after removal from the host. An initialbeat frequency of 14-18 beats min"1 (o-23-o-3 Hz) was occasionally recorded, but arate half this was typically attained within the first hour. Thereafter, both the rate ofmovement and percentage motility declined. Many trophozoites beat in approximatelyone plane (Figs. 2, 3) but deviations from planarity can occur as a result of rotationand twisting at the anterior attachment end.

The apparent suitability of the arc-line model as a method of analysis for the planarwaveforms is demonstrated by Fig. 4. Experimental values of 0-7-0-9 (+ 0-05) werecommonly obtained for the ratio of the chord length at half amplitude to that at halfwavelength for fully formed bends of different organisms. Since sinusoidal waves must,by definition, give a value of 0-667 f°r t n e same ratio (Brokaw & Wright, 1963), thewaves of the trophozoites would not appear to be of this nature. Close inspection ofthe waveforms with the unaided eye, however, suggests a degree of continuity betweenthe bent regions and, as will be discussed later, a meander or sine-generated wave maywell be a more appropriate analogue than arc-line curves. In spite of this, developingbends could be located to within 5-10/<m of the anterior tip and followed along 70-80% of the trophozoite, the remaining 20-30% being lost mainly at the distal ex-tremity. If the total lengths of the analysed trophozoites were calculated from themodel for comparison with their actual lengths, errors of no more than 6% arose.

Bend propagation by Selenidium

180 i-

Fig. s. A graph showing the locations of the centres of the bends (solid lines) and the straightregions (broken lines) relative to the anterior end of the trophozoite of Fig. za. Both bends andstraight regions are propagated at a rate of 25 /im s"1. The horizontal line represents the levelof the nucleus, through which bends propagated unhindered. For convenience, bends andstraight regions of opposite sign, ( + ) or ( —), have been plotted as if of the same sign. Thelength of fully formed bends ranged between 30-120/im in different trophozoites. A similarlength range was recorded for the straight regions.

Trophozoites are streamlined with two tapers, anterior and posterior, separated,except in very small trophozoites, by a mid-zone of constant diameter. They are up to400 fim long, with a maximum diameter of about 20 /im. The proportion of the totallength made up by the mid-zone (40-55%) and its precise location along the lengthof the trophozoites varies between organisms (compare Figs. %b and 3c). This mid-zone seems particularly important with regard to bend formation and propagation.Developing bends propagate slowly during formation and are two-thirds or fullyformed on arrival at the beginning of the mid-zone, whereupon rapid propagationcommences (Figs. 2 a and 5). Similar two-stage propagation rates have also beenreported for sperm flagella of the sea-urchins Psammechinus vuliaris (Gray, 1955),Lytechinus pictus (Brokaw, 1970) and Stronglyocentrotus purpwatus (Goldstein, 1977).In the trophozoites, the nucleus is normally positioned one-quarter to one-third of theway along the body from the anterior end and, as is illustrated by Figs, 2 a, 36 and 5,does not constitute an obstacle to propagation, even though it occupies most of thediameter of the cell. When the posterior taper is reached, 'unbending' commences asshown by Figs. 26 and 6a. The propagation rate remains constant, as a rule, but thebends usually become indiscernible before they reach the posterior tip. Rapid propag-ation is 2-5-6-7 times faster than that during bend formation, and rates of 8-7-35 Z"71

s - 1 have been recorded for beat frequencies ranging from 2-4-10 beats min"1 (0-04-^17 Hz). The correlation between the beginning and end of the mid-zone, and the

156 J. S. MELLOR AND H. STEBBINGS

10 20 30 40 50 60

Location of bends (jim)

70 80 •90

(b)

40 r

|30

=3. 20

10

10 20 30 40 50 60 70 80 90Location of bends (/im)

Fig. 6. Graphs showing the variation in angle and amplitude of bends as they are propagatedfrom the anterior end of the trophozoite of Fig. zb. The same bends as those in Fig. 4 arerepresented, (a) Consecutive bends of opposite sign are symmetrical. In different organismsthe angle of fully formed bends varied between 0-8-3-4 radians; the radius of curvature, 22-60/im. (6) Measured amplitudes ranged between 11-35/tm for different organisms. All thecharacteristics of the wave are relatively constant along the mid-rone of constant diameter ofthe trophozoite.

onset of rapid propagation and unbending respectively could be pinpointed to within

In healthy organisms, consecutive bends of opposite sign are symmetrical, in-creasing to similar final angles at similar rates (Fig. 6a). As a result, a developing bendappears to be coordinated with the preceding bend and, later in the cycle, with thefollowing bend. Instantaneous symmetry, however, may only be visible during parts ofthe cycle, an aspect which will ultimately depend upon the ratio of the mid-zone lengthto the wavelength measured along the trophozoite. Since the latter varies for differentorganisms between 160 and 300 /tm (80-160 fim along the jc-axis) the mid-zone: wave-length ratio is typically < 1, though exceptions do occur (Fig. 3 A). Depending uponthe rate of bend formation and the final angle subtended by developing bends, theentire trophozoite oscillates with an angular velocity often approaching 0-25 rad s-1.

The importance of the mid-zone to the constancy of the bend characteristics (Fig.6) is also emphasized by the pattern of beating demonstrated by very small tropho-zoites, about 40 fim in length. These organisms are composed of an anterior and pos-terior taper only, their maximum diameter being at the junction of the two. Motilitydoes, in this case, involve very simple pendular movements - bends of opposite signare developed consecutively at the anterior end but propagation is very limited.

Bend propagation by Selenidium

8 10 12 14 16 18 20 22 24

Fig. 7. Radius of curvature of bend pairs (CO. A A) plotted chronologically for the trophozoiteof Fig. 3 c. Benda of one sign can propagate in the absence of those of opposite sign. Brokenlines represent the decaying bend*.

Coiling and uncoiling movements are sometimes exhibited by attached trophozoitesbut are more typical of free organisms (Fig. 3 a). The coiling motion is often accom-panied by a helical twisting, larger trophozoites being capable of producing two tothree full turns. Although coiling undoubtedly has a propagative basis it differs fromthe wave motion in that it is highly asymmetric, unless, as occasionally occurs, theentire protozoan rolls through 180° during uncoiling to give the appearance of sym-metry. Careful measurement has shown that a length difference between the innerand outer curvature of over 100 fim may be generated during coiling. In trophozoitespropagating waves, lesser differences in the region of 20 /tm may occur, as in Fig. zbwhere the organism maintained one bend only at times o, 12-0 and 24-0 s. Overalllength changes of the trophozoites, however, were not observed. Stationary coils orbends may be held in position distally, while other bends continue to propagatenormally from the anterior end. On approaching the non-propagating region, thetravelling bends gradually increase in radius of curvature and decline in amplitudeuntil they disappear completely.

The slow decline in beat frequency apparent under the experimental conditions usedwas accompanied by a gradual decrease in the extent to which bends were propagatedalong the trophozoites. This was as a result of fully formed bends no longer maintain-ing a constant amplitude along the length of the trophozoite from the onset of rapidpropagation. The point at which the bends had completely decayed shifted slowlywith time towards the attachment end, until the organisms were beating purely bythe formation of non-propagating bends in the same fashion as very small trophozoites.Complete cessation of motility followed shortly after this stage. The shape of theprotozoans also tended to change during this process, with the trophozoites becomingmarkedly shorter and broader as the decay continued.

When attached to the gut and mounted on slides, trophozoites were observedbeating for a minimum period of 2 h. However, the beating of free trophozoites,examined in the same manner, decayed rapidly (e.g. Fig. 3 c), lasting a maximum of

6 EXB 87

158 J. S. MELLOR AND H. STEBBINGS

only 30-40 min. During this short period, it was possible to observe trophozoitfs"undergoing progressive movements along the slide surface at measured rates of up t(J6 fim s~l. The relative magnitudes of the two external forces (viscous and inertial)resisting such movement of the trophozoites can be determined using equation (i)for the Reynolds no.,

(i) Re = —, where / = diameter of trophozoite

v = swimming speed•n = viscosity) r , ,. ,.

. } or the surrounding medium.p = density J

Inserting either the swimming speed, or the product of frequency and amplitude as asubstitute (Holwill, 1974) in the case of attached trophozoites, estimates for Re ofio"4 and io"8 were obtained. This represents the initial information required for amore complex hydrodynamic analysis of the trophozoite motion.

DISCUSSION

The constancy of the bend amplitude along the mid-zone of the trophozoitessuggests that they possess an energy source, and an active mechanism capable ofutilizing it, along at least this entire region, since such waveforms cannot be duplicatedby a system powered solely at one end (Gray, 1955; Machin, 1958). The fact thatbends propagate through the nuclear region of the trophozoite without any loss ofamplitude, angle, etc., is indicative of a peripheral location for the machinery of bendformation and propagation. Trophozoites contain up to 4000 peripheral longitudinalmicrotubules (Mellor & Stebbings, unpublished data) ordered into 2-3 rows parallelto the outer membrane complex of the cell, and the reversible depolymerization of thesemicrotubules using o-6 M urea has been demonstrated by Schrevel, Buissonnet &Metais (1974) with the trophozoites of S. hollandei. Cessation and recovery of motilitywas closely associated with the loss and repolymerization, respectively, of the micro-tubule complement, the trophozoites becoming linear in their absence.

The sliding microtubule mechanism by which the 9 + 2 axoneme produces ciliarymotion (Satir, 1965, 1967, 1968) has also been adopted for flagella (Brokaw, 1971,1972) and is now well supported both experimentally and theoretically (Summers& Gibbons, 1971, 1973; Gibbons & Gibbons, 1973, 1974; Warner & Satir, 1975;Sale & Satir, 1977; Hiramoto & Baba, 1978; Holwill, Cohen & Satir, 1979). Thatmicrotubule sliding to produce propagated bends is not a unique property of the9 + 2 array has already been clarified by Mclntosh, Ogata & Landis (1973) and Mc-Intosh (1973) with the protozoan Saccinobaculus, an intestinal symbiont of the wood-feeding roach Cryptocercus punctulatus. In Saccinobaculus, the crystal-like lattice ofseveral thousand closely packed microtubules forming the protozoan axostyle has beenshown to propagate bends, at rates of up to 100 /tm s"1, with the aid of many of thesame proteins (e.g. dynein, nexin) which have been found to be so important in theciliary axoneme (Mooseker & Tilney, 1973; Bloodgood, 1975). Consequently, withthe implication that microtubules are involved, it seems possible that a comparablesliding mechanism may be responsible for the trophozoite wave motion. In the

Bend propagation by Selenidium 159

•phozoites of S.fallax, the microtubules are separated by a centre to centre distanceapproximately 40 nra, within and between the rows (Stebbings et al. 1974), a

spacing which is not inconsistent with the proposal that microtubule interactionsproduce motility in this organism. However, the sites of mechanochemical transduc-tion, the precise lengths of individual microtubules and the rearrangements theyundergo with bending have yet to be thoroughly investigated.

The propagation of bends of one sign only (Figs. 3 c and 7) suggests the existenceof two similar systems responsible for developing and transmitting bends of oppositesign. That consecutive bends in healthy organisms are symmetrical, developing andpropagating at similar rates, on the other hand, implies that the two systems arenormally highly coordinated. This is indeed reminiscent of the regulated activationof doublet sliding (e.g. Rikmenspoel, 1971) and coordinated production of shearresistance (Warner & Satir, 1974) occurring in the 9 + 2 axoneme, since, for instance,extracted reactivated sperm flagella of the sea-urchin L. pictus demonstrate a similarphenomenon (Goldstein, 1976).

In our analysis of the movement of trophozoites we have used the arc-line modelbecause it provides a convenient means of demonstrating the propagation of bendingwaves in a system hitherto unstudied. Since the trophozoite comprises an entire celland constituents, it seems likely that such a system would conform to the elastic rodenvisaged by Silvester & Holwill (1972) in their discussion of the meander waveform.As Macgregor & Thomasson (1965) have indicated - 'Nothing in S. fallax. . .otherthan the folded multilayered pellicle is capable of acting as a stiff skeletal component,and the only structures to which we can attribute the property of "contractility" arethe fibrils which lie beneath'. A completely objective analysis of the waveforms pro-duced by the trophozoites is, however, beyond the realms of this article, and so sine-generated or indeed imperfect arc-line waves (Johnston, Silvester & Holwill, 1979)cannot yet be dismissed as suitable analogues.

As would be expected of an organism the size of Selenidium, a low value of theReynolds number for the motion was obtained. Of the two external forces whichcould potentially oppose the beating trophozoites, the magnitude of the viscousresistance of the surrounding fluid is much greater than that of its inertial resistance,and so the latter may be neglected in comparison. Although further work is requiredin order to elucidate the relative importance of the external viscous resistance, theinternal elastic and internal viscous resistance as the major forces opposing the for-mation and propagation of bends by archigregarines, the protozoan provides a novelopportunity to study the energetics of the movement of an entire cell by similar meansto those already employed for cilia and flagella.

How do the movements performed by the trophozoites in seawater relate to thoseoccurring in situ} When the host intestine was opened, it contained either a fairlysolid matrix of sand, organic detritus and mucus, or a dark brown fluid which ap-peared to be of a higher viscosity than seawater. Clearly, seawater alone is quite adifferent environment to that which the trophozoites normally inhabit. The presenceof a close packed matrix in the intestine during certain stages of the polychaete'sdigestion probably does not allow the beating and coiling motions exhibited whentrophozoites are placed in seawater. The initial instability of the beat frequency after

6-2

160 J. S. MELLOR AND H. STEBBINGS

removal from the intestine, the degeneration of the beat cycle, and the shorteningthe trophozoites all imply that seawater alone is not their optimum environment/certain amount of difficulty was experienced in obtaining film of any one trophozoitedemonstrating all the salient features of the beat cycle in perfect form, and the abovefactors seem largely responsible for this. The near century-long delay in the truecharacterization of trophozoite motility is probably attributable to these same factors.

The most obvious purpose of movement within the gut cavity must surely be that ofmaintaining a constant flow of nutrients over the trophozoites. The gut contents aresometimes closely packed and this suggests that the hypothetical nutrient flow is,at best, intermittent. However, the intestinal epithelium is equipped with cilia whichare particularly active and well coordinated in the ventral groove of the intestine (Mellor& Hyams, 1978), though the mixing produced may not be sufficient to supply thenutritional needs of the trophozoites. It is conceivable then, that the beating andcoiling motions may be induced by placing the trophozoites in seawater.

Nevertheless, the ability of the protozoan to propagate bending waves makes it afascinating organism for further research on a number of counts. As well as providinga firm base from which to promote our knowledge of archigregarine motility, itprovides an opportunity to improve the understanding of microtubule function per se,and, of equal importance, of microtubule interactions in systems where elastic forcesexternal to the microtubules may be important. To quote Warner & Satir (1974) inreferring to the importance of radial spokes in cilary axonemes: ' Unfortunately thedifferences in bend form and propagation between other microtubule-based systemsand true cilia and flagella, including 9 + 2 sperm tails, have not yet been analysed.'Although a direct involvement of the microtubules in bend formation and propagationby the trophozoites still awaits adequate confirmation, they do indeed appear to possessa system which could be very usefully compared with the 9 + 2 axoneme.

Finally, it would seem probable that a single common mechanism producing boththe coiling and wave motions is operative within the trophozoite. Any model whichpurports to explain this mechanism must also be able to account for the combinationsof the two different movements which can occur and also for phenomena such as thecoordination of developing bends. Therefore a high degree of versatility must beintrinsic to the model. Careful ultrastructural, manipulative, and waveform studiesaimed at clarifying this mechanism are currently in progress.

We gratefully acknowledge Dr M. E. J. Holwill for interesting discussion of thebiophysical aspects presented here and for his criticisms of an earlier version of thismanuscript.

J. S. Mellor was supported by an S.R.C. postgraduate grant.

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