MICROTUBULES AND THE PROPAGATION OF BENDING WAVES BY THE ARCHIGREGARINE, SELENIDIUM FALLAX

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1 J. exp. Biol. (1980), 87, j,q With 7 figures Printed in Great Britain MICROTUBULES AND THE PROPAGATION OF BENDING WAVES 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 rates of up to 35 ftm s" 1, of a similar character to those manifested by eukaryotic cilia and flagella. A beat frequency of Hz appears average, though rates outside this range have been recorded. Translatory locomotion at up to 6 /im s" 1 has been observed. The protozoan demonstrates the presence of an active bending mechanism, probably along its entire length, and a means of coordinating adjacent bends. 2. The Reynolds number for the motion is IO^-IO" 4, suggesting that the hydrodynamic aspects of the trophozoite movement are amenable to analysis by similar means to those already employed for cilia and flagella. 3. It is possible that the protozoans exhibit a sliding microtubule mechanism, which could be very usefully compared with that occurring in the ciliary axoneme. INTRODUCTION Archigregarines of the genus Selenidium are found in the digestive tracts of many species of polychaete worms. The vegetative stage or trophozoite is itself vermiform and normally anchored by its anterior end to the intestinal epithelium of the host. The remainder of the trophozoite is thus free to move within the gut cavity. When Giard (1884) named the archigregarine in Nerine cirratulus as Selenidium pendula he not only founded the genus but also set the trend for describing the movements characteristic of archigregarine trophozoites; 'le nom rapelle les mouvements pendulaires caracte'ristiques de tout le group'. For nearly a century there has been little progress in furthering this essentially correct but oversimplified view of trophozoite motility, except perhaps in recognizing the organism's ability to coil and uncoil like a watchspring (Ray, 1930; Vivier & Schrevel, 1964; Macgregor & Thomasson, 1965). Possibly Stebbings, Boe & Garlick (1974) came closest to recognizing the true potential of trophozoite movement by describing it as 'whip-like', and by noting the great degree of variation in amplitude of the beat form from one trophozoite to another. Several authors have carried out ultrastructural studies describing a system of longitudinally aligned microtubules beneath the pellicle of the trophozoites (Vivier & Schrevel, 1964; Macgregor & Thomasson, 1965; Schrevel, 1971; Stebbings et al. 1974)

2 J. S. MELLOR AND H. STEBBINGS Fig. i. Diagram to explain the principle of analysis using the arc-line model. First a set of circles of known radius inscribed on sheets of tracing paper were used to locate the centre of each bent region of the photographic images of the trophozoites. This was done by simply overlaying 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 bent region. This gives A, the radius of curvature of the bends. Secondly, lines were drawn tangentially to adjacent circles, to locate the straight regions between the bends (2C). The angle between the lines forming the straight regions was measured in order to determine the angle subtended by the bends (a). The centre of a bend (E) was taken to be the point of intersection of that bend with a line bisecting the tangents of the straight regions bordering it. The length of 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 placing cotton along the length of the image midline between the anterior end and the centre to be located. The half wavelength was taken to be the chord length (G) between the midpoints of the straight regions either side of the bend, and perpendicular to the line joining the centre of curvature to the centre of the bend. The amplitude (F) of the bend was taken to be the perpendicular 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 mechanistic role in the motility of the organism. So far, however, there has been no detailed analysis of the movement itself - a fundamental requirement if the function of the microtubules is to be accurately assessed - and this we present here. It has become obvious from our cinematographic studies that in the trophozoites of the Selenidium sp. native to the intestine of Cirriformia tentaculata, the pendular movement is achieved by the anterior formation of bends and their propagation along the length of the trophozoite in a manner similar to that shown by beating cilia and sperm flagella. Waveforms of the latter have proved to be highly amenable to analysis by analogy with either travelling sine waves (Gray, 1955), travelling circular arcs and

3 Bend propagation by Selenidium (a) (b) Fig. 2. Two photographic sequences demonstrating the ability of trophozoites to propagate bending waves. The arrows indicate propagating bends and the numbers, the time sequence in seconds. 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 recovery stroke, being executed in both directions. Propagation ceases, unusually, for some 6 s during 'unbending'. Upon resumption of propagation the bend is practically indiscernible.

4 152 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 Hiramoto & Baba (1978) have demonstrated that the changes in angular direction of beating sperm flagella can be accurately expressed as a sine function of time plus a constant, i.e. theflagellawaveforms are ' sine-generated'. This type of wave gives good approximations to both meander curves (Langbein & Leopold, 1966; Leopold & Langbein, 1966) and arc-line curves (Sarashina, 1974). Although we have made use of the latter as an initial means of analysing the movement of trophozoites, we discuss the propriety of other wave analogues. MATERIALS AND METHODS Cirriformia tentaculata, the polychaete host, was collected from the shore at Ladram Bay, Devon, cleaned, and maintained in aerated seawater at 10 C. Providing injured worms were discarded, both the host and its archigregarine population could be kept for days without any visible deterioration in their condition. Small pieces of heavily infected intestine were excised by a longitudinal incision under seawater. Opening the gut often caused the release of unattached trophozoites and these were also collected, for observation, using Pasteur pipettes. Free trophozoites, or pieces of intestine with trophozoites attached, were mounted in seawater on 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 and magazine mounted on the microscope. Ilford 16 mm Pan F was used and a Xenon arc lamp provided the illumination. Ultra-violet and infra-red filters were used in conjunction with the Xenon arc lamp at all times. Other pieces of intestine were placed in small glass embryo cups with a plentiful covering of seawater and the trophozoites observed using a Vickers stereo binocular microscope. Approximately trophozoites attached to a single piece of intestine could be examined by this method. The activity of the trophozoites was monitored at 30-min intervals by taking a sample of any six organisms and noting their beat frequency. The number of beats performed over a 30 s period was counted to the nearest quarter beat for each individual. All experiments were conducted at room temperature. Fig. 3. (a) A photographic sequence demonstrating the ability of trophozoites to coil and uncoil. Coiling has a propagative basis but is always asymmetric, (b) 35 mm still photograph taken on Ilford HP5. Occasionally trophozoites may maintain one or more complete waves on the midzone, depending upon the wavelength measured along the trophozoite. Note that bends in the region of the nucleus (AT) are unaffected by its presence, (c) Three enlargements of a free trophozoite 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 right hand bend (i) is decaying while the following left hand bend (ii) is still forming. At 5 8, the right hand bend is no longer discernible, and the left hand has almost entirely decayed in coordination with it. At 9 s, (ii) is now reformed and propagates normally as both bends did during the decay. It is interesting that the lone bends appear to give the best fit to arc-line curves. 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.

5 Bend propagation by Selenidium 153 J9-0

6 J. S. MELLOR AND H. STEBBINGS Location of bends (Mm) Fig. 4. A test for the suitability of fit of the arc-line model is given by the ratio between the chord length at half-amplitude (H) to that at the half-wavelength (G). This ratio has been plotted against the distance of two adjacent bends, of opposite sign, (#, O) from the anterior end of the trophozoite in Fig. 26. The solid horizontal line represents the value for sinusoidal bends (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 of approximately 500 times, from individual frames selected at 0-5 or 1 s intervals. This was carried out over a s period so that at least one full beat-cycle was obtained for analysis. A modification (Goldstein, 1976) of the arc-line method of analysis pioneered by Brokaw and co-workers (1963, 1965) was used to follow the development and propagation of bends (see Fig. 1). RESULTS Trophozoites attached to the gut and placed in embryo cups containing seawater could continue beating for up to 12 h, although 95% of any sample population had normally ceased to do so approximately 6 h after removal from the host. An initial beat frequency of beats min" 1 (o-23-o-3 Hz) was occasionally recorded, but a rate half this was typically attained within the first hour. Thereafter, both the rate of movement and percentage motility declined. Many trophozoites beat in approximately one plane (Figs. 2, 3) but deviations from planarity can occur as a result of rotation and twisting at the anterior attachment end. The apparent suitability of the arc-line model as a method of analysis for the planar waveforms is demonstrated by Fig. 4. Experimental values of (+ 0-05) were commonly obtained for the ratio of the chord length at half amplitude to that at half wavelength for fully formed bends of different organisms. Since sinusoidal waves must, by definition, give a value of f r tne same ratio (Brokaw & Wright, 1963), the waves of the trophozoites would not appear to be of this nature. Close inspection of the waveforms with the unaided eye, however, suggests a degree of continuity between the bent regions and, as will be discussed later, a meander or sine-generated wave may well be a more appropriate analogue than arc-line curves. In spite of this, developing bends 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 extremity. If the total lengths of the analysed trophozoites were calculated from the model for comparison with their actual lengths, errors of no more than 6% arose.

7 Bend propagation by Selenidium 180 i- Fig. s. A graph showing the locations of the centres of the bends (solid lines) and the straight regions (broken lines) relative to the anterior end of the trophozoite of Fig. za. Both bends and straight regions are propagated at a rate of 25 /im s" 1. The horizontal line represents the level of the nucleus, through which bends propagated unhindered. For convenience, bends and straight regions of opposite sign, ( + ) or ( ), have been plotted as if of the same sign. The length of fully formed bends ranged between /im in different trophozoites. A similar length 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 to 400 fim long, with a maximum diameter of about 20 /im. The proportion of the total length made up by the mid-zone (40-55%) and its precise location along the length of the trophozoites varies between organisms (compare Figs. %b and 3c). This midzone seems particularly important with regard to bend formation and propagation. Developing bends propagate slowly during formation and are two-thirds or fully formed on arrival at the beginning of the mid-zone, whereupon rapid propagation commences (Figs. 2 a and 5). Similar two-stage propagation rates have also been reported 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 the way 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 the diameter of the cell. When the posterior taper is reached, 'unbending' commences as shown by Figs. 26 and 6a. The propagation rate remains constant, as a rule, but the bends usually become indiscernible before they reach the posterior tip. Rapid propagation is times faster than that during bend formation, and rates of Z" 71 s -1 have been recorded for beat frequencies ranging from beats min" 1 (0-04- ^17 Hz). The correlation between the beginning and end of the mid-zone, and the

8 156 J. S. MELLOR AND H. STEBBINGS Location of bends (jim) r 30 (b) = Location of bends (/im) Fig. 6. Graphs showing the variation in angle and amplitude of bends as they are propagated from the anterior end of the trophozoite of Fig. zb. The same bends as those in Fig. 4 are represented, (a) Consecutive bends of opposite sign are symmetrical. In different organisms the angle of fully formed bends varied between radians; the radius of curvature, /im. (6) Measured amplitudes ranged between 11-35/tm for different organisms. All the characteristics of the wave are relatively constant along the mid-rone of constant diameter of the trophozoite. onset of rapid propagation and unbending respectively could be pinpointed to within In healthy organisms, consecutive bends of opposite sign are symmetrical, increasing to similar final angles at similar rates (Fig. 6a). As a result, a developing bend appears to be coordinated with the preceding bend and, later in the cycle, with the following bend. Instantaneous symmetry, however, may only be visible during parts of the cycle, an aspect which will ultimately depend upon the ratio of the mid-zone length to the wavelength measured along the trophozoite. Since the latter varies for different organisms between 160 and 300 /tm ( fim along the jc-axis) the mid-zone: wavelength ratio is typically < 1, though exceptions do occur (Fig. 3 A). Depending upon the rate of bend formation and the final angle subtended by developing bends, the entire 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 trophozoites, about 40 fim in length. These organisms are composed of an anterior and posterior taper only, their maximum diameter being at the junction of the two. Motility does, in this case, involve very simple pendular movements - bends of opposite sign are developed consecutively at the anterior end but propagation is very limited.

9 Bend propagation by Selenidium Fig. 7. Radius of curvature of bend pairs (CO. A A) plotted chronologically for the trophozoite of Fig. 3 c. Benda of one sign can propagate in the absence of those of opposite sign. Broken lines represent the decaying bend*. Coiling and uncoiling movements are sometimes exhibited by attached trophozoites but are more typical of free organisms (Fig. 3 a). The coiling motion is often accompanied by a helical twisting, larger trophozoites being capable of producing two to three full turns. Although coiling undoubtedly has a propagative basis it differs from the wave motion in that it is highly asymmetric, unless, as occasionally occurs, the entire protozoan rolls through 180 during uncoiling to give the appearance of symmetry. Careful measurement has shown that a length difference between the inner and outer curvature of over 100 fim may be generated during coiling. In trophozoites propagating waves, lesser differences in the region of 20 /tm may occur, as in Fig. zb where the organism maintained one bend only at times o, 12-0 and 24-0 s. Overall length changes of the trophozoites, however, were not observed. Stationary coils or bends may be held in position distally, while other bends continue to propagate normally from the anterior end. On approaching the non-propagating region, the travelling bends gradually increase in radius of curvature and decline in amplitude until they disappear completely. The slow decline in beat frequency apparent under the experimental conditions used was accompanied by a gradual decrease in the extent to which bends were propagated along the trophozoites. This was as a result of fully formed bends no longer maintaining a constant amplitude along the length of the trophozoite from the onset of rapid propagation. The point at which the bends had completely decayed shifted slowly with time towards the attachment end, until the organisms were beating purely by the 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 the protozoans also tended to change during this process, with the trophozoites becoming markedly shorter and broader as the decay continued. When attached to the gut and mounted on slides, trophozoites were observed beating 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

10 158 J. S. MELLOR AND H. STEBBINGS only min. During this short period, it was possible to observe trophozoitfs" undergoing progressive movements along the slide surface at measured rates of up t(j 6 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 a substitute (Holwill, 1974) in the case of attached trophozoites, estimates for Re of io" 4 and io" 8 were obtained. This represents the initial information required for a more complex hydrodynamic analysis of the trophozoite motion. DISCUSSION The constancy of the bend amplitude along the mid-zone of the trophozoites suggests that they possess an energy source, and an active mechanism capable of utilizing it, along at least this entire region, since such waveforms cannot be duplicated by a system powered solely at one end (Gray, 1955; Machin, 1958). The fact that bends propagate through the nuclear region of the trophozoite without any loss of amplitude, angle, etc., is indicative of a peripheral location for the machinery of bend formation and propagation. Trophozoites contain up to 4000 peripheral longitudinal microtubules (Mellor & Stebbings, unpublished data) ordered into 2-3 rows parallel to the outer membrane complex of the cell, and the reversible depolymerization of these microtubules using o-6 M urea has been demonstrated by Schrevel, Buissonnet & Metais (1974) with the trophozoites of S. hollandei. Cessation and recovery of motility was closely associated with the loss and repolymerization, respectively, of the microtubule complement, the trophozoites becoming linear in their absence. The sliding microtubule mechanism by which the axoneme produces ciliary motion (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). That microtubule sliding to produce propagated bends is not a unique property of the array has already been clarified by Mclntosh, Ogata & Landis (1973) and Mc- Intosh (1973) with the protozoan Saccinobaculus, an intestinal symbiont of the woodfeeding roach Cryptocercus punctulatus. In Saccinobaculus, the crystal-like lattice of several thousand closely packed microtubules forming the protozoan axostyle has been shown to propagate bends, at rates of up to 100 /tm s" 1, with the aid of many of the same proteins (e.g. dynein, nexin) which have been found to be so important in the ciliary axoneme (Mooseker & Tilney, 1973; Bloodgood, 1975). Consequently, with the implication that microtubules are involved, it seems possible that a comparable sliding mechanism may be responsible for the trophozoite wave motion. In the

11 Bend propagation by Selenidium 159 phozoites of S.fallax, the microtubules are separated by a centre to centre distance approximately 40 nra, within and between the rows (Stebbings et al. 1974), a spacing which is not inconsistent with the proposal that microtubule interactions produce motility in this organism. However, the sites of mechanochemical transduction, the precise lengths of individual microtubules and the rearrangements they undergo with bending have yet to be thoroughly investigated. The propagation of bends of one sign only (Figs. 3 c and 7) suggests the existence of two similar systems responsible for developing and transmitting bends of opposite sign. That consecutive bends in healthy organisms are symmetrical, developing and propagating at similar rates, on the other hand, implies that the two systems are normally highly coordinated. This is indeed reminiscent of the regulated activation of doublet sliding (e.g. Rikmenspoel, 1971) and coordinated production of shear resistance (Warner & Satir, 1974) occurring in the axoneme, since, for instance, extracted reactivated sperm flagella of the sea-urchin L. pictus demonstrate a similar phenomenon (Goldstein, 1976). In our analysis of the movement of trophozoites we have used the arc-line model because it provides a convenient means of demonstrating the propagation of bending waves in a system hitherto unstudied. Since the trophozoite comprises an entire cell and constituents, it seems likely that such a system would conform to the elastic rod envisaged by Silvester & Holwill (1972) in their discussion of the meander waveform. As Macgregor & Thomasson (1965) have indicated - 'Nothing in S. fallax...other than 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" are the fibrils which lie beneath'. A completely objective analysis of the waveforms produced by the trophozoites is, however, beyond the realms of this article, and so sinegenerated 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 the Reynolds number for the motion was obtained. Of the two external forces which could potentially oppose the beating trophozoites, the magnitude of the viscous resistance 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 required in order to elucidate the relative importance of the external viscous resistance, the internal elastic and internal viscous resistance as the major forces opposing the formation and propagation of bends by archigregarines, the protozoan provides a novel opportunity to study the energetics of the movement of an entire cell by similar means to those already employed for cilia and flagella. How do the movements performed by the trophozoites in seawater relate to those occurring in situ} When the host intestine was opened, it contained either a fairly solid matrix of sand, organic detritus and mucus, or a dark brown fluid which appeared to be of a higher viscosity than seawater. Clearly, seawater alone is quite a different environment to that which the trophozoites normally inhabit. The presence of a close packed matrix in the intestine during certain stages of the polychaete's digestion probably does not allow the beating and coiling motions exhibited when trophozoites are placed in seawater. The initial instability of the beat frequency after 6-2

12 160 J. S. MELLOR AND H. STEBBINGS removal from the intestine, the degeneration of the beat cycle, and the shortening the trophozoites all imply that seawater alone is not their optimum environment/ certain amount of difficulty was experienced in obtaining film of any one trophozoite demonstrating all the salient features of the beat cycle in perfect form, and the above factors seem largely responsible for this. The near century-long delay in the true characterization of trophozoite motility is probably attributable to these same factors. The most obvious purpose of movement within the gut cavity must surely be that of maintaining a constant flow of nutrients over the trophozoites. The gut contents are sometimes closely packed and this suggests that the hypothetical nutrient flow is, at best, intermittent. However, the intestinal epithelium is equipped with cilia which are 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 the nutritional needs of the trophozoites. It is conceivable then, that the beating and coiling motions may be induced by placing the trophozoites in seawater. Nevertheless, the ability of the protozoan to propagate bending waves makes it a fascinating organism for further research on a number of counts. As well as providing a firm base from which to promote our knowledge of archigregarine motility, it provides an opportunity to improve the understanding of microtubule function per se, and, of equal importance, of microtubule interactions in systems where elastic forces external to the microtubules may be important. To quote Warner & Satir (1974) in referring to the importance of radial spokes in cilary axonemes: ' Unfortunately the differences in bend form and propagation between other microtubule-based systems and true cilia and flagella, including sperm tails, have not yet been analysed.' Although a direct involvement of the microtubules in bend formation and propagation by the trophozoites still awaits adequate confirmation, they do indeed appear to possess a system which could be very usefully compared with the axoneme. Finally, it would seem probable that a single common mechanism producing both the coiling and wave motions is operative within the trophozoite. Any model which purports to explain this mechanism must also be able to account for the combinations of the two different movements which can occur and also for phenomena such as the coordination of developing bends. Therefore a high degree of versatility must be intrinsic to the model. Careful ultrastructural, manipulative, and waveform studies aimed at clarifying this mechanism are currently in progress. We gratefully acknowledge Dr M. E. J. Holwill for interesting discussion of the biophysical aspects presented here and for his criticisms of an earlier version of this manuscript. J. S. Mellor was supported by an S.R.C. postgraduate grant. REFERENCES BLOODGOOD, R. A. (1975). Biochemical analysis of axostyle motility. Cytobios 14, BROKAW, C. J. (1965). Non-sinusoidal bending waves of sperm flagella. J. exp. Biol. 43, BROKAVV, C. J. (1971). Bend propagation by a sliding filament model forflagella.j. exp. Bio. 55, BROKAW, C. J. & WRIGHT, L. (1963). Bending waves of the posteriorflagellumof Ceratium. Science, N. Y. 142, BROKAW, C. W. (1972). Flagellar movement: a sliding filament model. Science, N.Y. 178, GIARD, A. (1884). Note 8ur un nouveau groups de protozoaire parasites des annelides et sur q ^ points de l'histoire des gregarines (S. pendija). C.r. Assoc.fr. Avnnc. Set., Cotigr. Blois, p. 192

13 Bend propagation by Selenidium 161 BBONS, B. H. & GIBBONS, I. R. (1973). The effect of partial extraction of dynein arms on the movel e t of reactivated sea-urchin sperm. J. Cell Sci. 13, GIBBONS, I. R. & GIBBONS, B. H. (1974). Fine structure of rigor wave axonemes from sea urchin sperm flagella. J. Cell Biol. 63, 110a. GOLDSTEIN, S. F. (1976). Form of developing bends in reactivated sperm flagella. J. exp. Bio. 64, GOLDSTEIN, S. F. (1977). Asymmetric waveforms in echinoderm sperm flagella. J. exp. Biol. 3a, 80a- 8, 4. GRAY, H. (1955)- The movement of sea-urchin spermatozoa. J. exp. Biol. 33, HIRAMOTO, Y. & BABA, S. A. (1978). Quantitative analysis offlagellarmovement in echinoderm spermatozoa. J. exp. Biol. 76, HOLWILL, M. E. J. (1974). Hydrodynamic aspects of ciliary andflagellarmovement. In Cilia and Flagella (ed. M. A. Sleigh), pp London: Academic Press. HOLWILL, M. E. J., COHEN, H. J. & SATIR, P. (1979). A sliding microtubule model incorporating axonemal twist and compatible with three-dimensional ciliary bending. J. exp. Biol. 78, JOHNSTON, D. N., SILVESTER, N. R. & HOLWILL, M. E. J. (1979). An analysis of the shape and propagation of waves on the flagellum of Crithidia oncopelti. J. exp. Biol. 80, LANCBEIN, W. B. & LEOPOLD, L. B. (1966). River meanders - theory of minimum variance. U.S. Geol. Survey Prof. Paper 433-H, LEOPOLD, L. B. & LANCBEIN, W. B. (1966). River meanders. So". Am. 314, MACHIN, K. E. (1958). Wave propagation along flagella. J. exp. Biol. 35, MACCRECOR, H. C. & THOMASSON, P. A. (1965). The fine structure of two Archigregarines, Selenidium fallax and Ditrypanocystis cirratuli. J. Protozool. 13 (3), MCINTOSH, J. R. (1973). The axostyle of Saccinobacului. II. Motion of the microtubule bundle and a structural comparison of straight and bent axostyles. J. Cell Biol. 56, MCFNTOSH, J. R., OCATA, E. S. & LANDIS, S. C. (1973). The axostyle of Saccinobacului. I. Structure of the organism and its microtubule bundle. J. Cell Biol. 56, MELLOR, J. S. & HYAMS, J. S. (1978). Metachronism of cilia of the digestive epithelium of C. tentaculata. Micron. 9, MOOSEKER, M. S. & TILNEY, L. G. (1973). Isolation and reactivation of the axostyle. Evidence for a dynein-like ATPase in the axostyle. J. Cell Biol. 56, RAY, H. N. (1930). Studies on some sporozoa in polychaete worms. I. Gregarines of the genus Selenidium. Paratitology 33, RIKMENSPOEL, R. (1971). Contractile mechanisms inflagella.j. exp. Biol. 35, RIKMENBPOEL, R. (1978). Movement of sea urchin sperm flagella. J. Cell Biol. 76, SALE, W. S. & SATIR, P. (1977). The direction of active sliding of microtubules in Tetrahymena cilia. Proc. natn. Acad. Sci. U.S.A. 74, SARASHINA, T. (1974). Numerical analysis on wavy track of nematodes. Rep. Hokkaido Prefect. Agric. Exp. Stn. 23, SATIR, P. (1965). Studies on cilia. II. Examination of the distal region of the ciliary shaft and the role of the filaments in motility. J. Cell Biol. 36, SATIR, P. (1967). Morphological aspects of ciliary motility. J. gen. Pkytiol. 50, SATIR, P. (1968). Studies on cilia. III. Further studies on the cilium tip and a sliding filament model of ciliary motility. J. Cell Biol. 39, SCHREVEL, J. (1971). Contribution a l'etude des Selenidiidae, parasites d'annelides polychetes. II. Ultra8tructure de quelques trophozoites. Protistologica 7, SCHREVEL, J., BUISSONNET, S. & METAIS, M. (1974). Action de l'uree BUT la motilite et Ie9 microtubules sous-pelliculaires du Protozoaire Selenidium hollandei. C.r. hebd. Sianc. Acad. Sci., Paris 378 Serie D, SILVESTER, N. R. & HOLWILL, M. E. J. (1972). An analysis of hypothetical flagellar waveforms. J. theor. Biol. 35, STEBBINCS, H., BOB, G. S. & GARLICK, P. R. (1974). Microtubules and movement in the Archigregarine, Selenidium fallax. Cell Tiss. Res. 148, SUMMERS, K. E. & GIBBONS, I. R. (1971). Adenosine triphosphate-induced sliding of tubules in trypsintreated flagella of sea-urchin sperm. Proc. natn. Acad. Sci. U.S.A. 68, SUMMERS, K. E. & GIBBONS, I. R. (1973). Effects of trypsin digestion on flagellar structures and their relationship to motility. J. Cell Biol. 58, VIVIER, E. & SCHREVEL, J. (1964). Etude au microscope electronique, d'une gregarine du genre Selenidium, parasite de Sabellaria alveolata L. J. Microscopic 3, WARNER, F. D. & SATIR, P. (1974). The structural basis of ciliary bend formation. Radial spoke positional changes accompanying microtubule sliding. J. Cell Biol. 63,

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