Apparent Amitosis in the Binucleate Dinoflagellate Peridinium Balticum

J. Cell Set. 31, 273-289 (1976) 273 Printed in Great Britain

APPARENT AMITOSIS IN THE BINUCLEATE DINOFLAGELLATE PERIDINIUM BALTICUM

D. H. TIPPIT AND J. D. PICKETT-HEAPS Department of Molecular Cellular and Developmental Biology, University of Colorado, Boulder, Colorado 80302, U.S.A.

SUMMARY Mitosis and cytokinesis in the free-living binucleate dinoflagellate Peridiniuvi balticum are described. P. balticum contains 2 nuclei; one is a typical dinoflagellate nucleus and the other resembles the interphase nuclei of some eucaryotic cells and is here named the supernumerary nucleus (formerly called the eucaryotic nucleus). The dinoflagellate nucleus divides in the characteristic manner already described for certain other dinofiagellates. The supernumerary nucleus does not undergo normal mitosis; its chromatin does not condense, a spindle is not differentiated for its division, nor are any microtubules present inside the nucleus during any stage of its division. Instead the supernumerary nucleus divides by simple cleavage, which is concurrent with cytoplasmic cleavage. The nucleus cleaves first on its side facing the wall, but later it cleaves circumferentially as the cytoplasmic cleavage furrow draws closer. Invariably at late cytokinesis, a portion of the dividing nucleus passes through the only remaining uncleaved area of the cell. The final separation of the supernumerary nucleus is probably accomplished by the ingrowing furrow pinching the nucleus in two. There is no apparent precise segregation of genetic material during division, nor are there any structural changes inside the dividing nucleus which distinguish it from the interphase nucleus. Certain aspects of amitosis, and previously postulated theories concerning the endosymbiont origin of the second nucleus, are discussed.

INTRODUCTION Many dinofiagellates (Dinophyceae) possess unusual nuclei which display what appear to be primitive features, including the attachment of permanently condensed chromosomes to the nuclear envelope during mitosis (Kubai & Ris, 1969), and very low levels of acid-soluble protein associated with the chromosomes; this protein is different from the histones of more typical eucaryotic cells (Rizzo & Nooden, 1974). Recently, dinofiagellates have been discovered which contain two nuclei; one is the normal dinoflagellate nucleus, and the other has been called a 'eucaryotic' nucleus (Dodge, 1971) because it resembles the interphase nucleus of other eucaryotic cells. This 'eucaryotic' nucleus is bounded by the usual nuclear envelope with pores, it stains positively with the Feulgen, azure B and acetocarmine reagents, and it contains at least one nucleolus-like structure. Thus far, 2 species of such binucleate dinofiagellates have been reported: Glenodinium foliaceum (Dodge, 1971; S. W. Jeffery & M. Vesk, in preparation) and Peridinium balticum (Tomas, Cox & Steidinger, 1973). G. foliaceum has a varied taxonomic history; most recently placed in the genus Glenodinium, it had previously been included in other genera, including Peridinium. Every cell of P. balticum and G. foliaceum so far examined, contains two nuclei, and the 'eucaryotic' nucleus is structurally similar in both species. 274 D. H. Tippit andj. D. Pickett-Heaps The cells of P. balticum and G. foliaceum examined by these workers appear to have been vegetative, and not in any stage of sexual reproduction. This is significant since certain heterotrophic dinoflagellates produce gametes which contain the typical dinoflagellate nucleus, while the vegetative cells of these same organisms have a nucleus like that of other eucaryotic cells (Zingmark, 1970; Soyer, 1971). One might conclude that the cells of P. balticum and G.foliaceum examined were at some stage in gametogenesis with the dinoflagellate nucleus being related to, or created for sexual reproduction. This possibility is refuted by Tomas & Cox (1973) who concluded that both nuclei are present during the vegetative life cycle. Tomas & Cox (1973) also postulate that the eucaryotic nucleus, along with numerous organelles, are derived from an endosymbiont of chrysophyte origin living within the dinoflagellate. Nuclear division has been examined in G. foliaceum using the light microscope (Blanchard-Babillot, 1972); the eucaryotic nucleus is characterized by unusual division since there is not precise staining of individual chromosomes and the nucleus simply constricts or pinches in two during division. The status and function of the 'eucaryotic' nucleus within these dinoflagellates is not clear. Several possibilities may be proposed, for example: (i) it may belong to an endosymbiont as proposed by Tomas & Cox; (ii) it may be related to some aspect of sexual reproduction; (iii) it may be analogous to or have features in common with the macronucleus of ciliated protozoa; or (iv) it could be a structure unique to these particular dinoflagellates. We have examined the division of the 'eucaryotic' nucleus to clarify these possibilities; the formation of a mitotic apparatus for its division would indicate whether it is truly a eucaryotic nucleus, and the type of spindle might then suggest the origin of the postulated endosymbiont, i.e. if it is of chrysophyte origin, then we might expect it to have a mitotic apparatus similar to that of other chrysophytes.

ABBREVIATIONS ON PLATES c chromosomes no nucleolus cf cleavage furrow P pores d dinoflagellate nucleus t microtubules 8 girdle tr trichocy8ts n supernumerary nucleus V vacuole

Fig. 1. Scanning micrograph of P. balticum with the characteristic girdle (g) encircling the cell, x 2800. Fig. 2. Cell surface, containing numerous pores (p); small vesicle-like structures (v) sometimes surmount the pores, but more frequently line the sutures, x 7100. Figs. 3, 4. Interphase vegetative cells stained with acetocarmine. Each contained 2 strongly staining bodies, the supernumerary nucleus (n) and the dinoflagellate nucleus (d). The permanently condensed chromosomes of the dinoflagellate nucleus give it a striated appearance. The interphase supernumerary nucleus is highly irregular in shape; sometimes it is composed of interconnecting lobes (Fig. 3), or it may be ovoid as in Fig. 4. x 2000. Division in Peridinium 276 D. H. Tippit andj. D. Pickett-Heaps Division in Peridinium 277

MATERIALS AND METHODS Peridinium balticum from the Culture Collection of Algae at Indiana University (Cat. no. LB1563), was grown in Erdschreiber medium (James, 1969) at 18 °C on a 15/9 h light/dark cycle. The cells were illuminated at a range of 30-1 era (12 in.) with General Electric Fluores- cent plant lights (13 W). For transmission microscopy, cells were fixed in 1 % glutaraldehyde for 30 min in culture medium, washed in culture medium and then fixed in 1 % osmium tetroxide, also in culture medium for 1 h, and finally washed in distilled water. The cells were dehydrated in acetone and then embedded in Spurr's (1969) resin. Preselected cells were remounted and sectioned; the sections were collected on Formvar-coated grids and stained with lead and uranium, then viewed in a Philips EM 200 electron microscope. For scanning microscopy, the cells were collected on a Solvinert Millipore filter, treated with 1 % Glusulase (Endo Labs., Garden City,. New York) for 30 min and then fixed in 1 % osmium tetroxide for 30 min. The cells were dehydrated in acetone, passed through the critical point drying procedure (as in Marchant, 1973), coated with carbon and gold and examined at 20 kV in a Cambridge Stereoscan S4 scanning electron microscope. For light microscopy, cells were fixed in 3 :1 absolute ethanol: acetic acid for 1 h, stained with acetocarmine (Jensen, 1962) and photographed with Zeiss-Nomarski differential interference contrast optics.

RESULTS Dodge (1971) tentatively named the second nucleus of the binucleate dinoflagellates^ the 'eucaryotic' nucleus based upon upon its interphase structure. We will show that this 'eucaryotic' nucleus does not divide like typical eucaryotic nuclei, nor does it differentiate condensed chromosomes during its division. Hence we now feel that the term 'eucaryotic' is misleading and until more is known about the function of this nucleus, we prefer the neutral term 'supernumerary nucleus' to describe it. We continue to call this structure a nucleus as did Dodge (1971) and Tomas et al. (1973), based upon its morphological appearance and the presence of DNA within it demon- strable by histochemical techniques.

The interphase cell A scanning micrograph of an interphase cell is shown in Fig. 1. Details of the theca (Fig. 2) show the pores and blisters already described in Peridinium trochoideum (Kalley &Bisalputra, 1970). There is an additional feature on the surface of P. balticumy

Fig. 5. Interphase cell, similar to that in Fig. 3. The supernumerary nucleus (fi) is lobed. Within the dinoflagellate nucleus are characteristic, permanently condensed chromosomes (c) and a prominent nucleolus (no). Numerous vacuoles (v) line the cell periphery, and trichocysts (tr) are common near the vacuoles. The girdle (jg) shown in Figs. 1 and 4, is clearly seen in longitudinal section, x 6500. Fig. 6. Mid-division of the dinoflagellate nucleus. Channels (small arrows) containing microtubules extend through the nucleus, perpendicular to the cleavage furrow. The supernumerary nucleus (n) is always ovoid and elongated prior to division, and undergoes no structural changes during division of the dinoflagellate nucleus. Nucleolar material (large arrow heads) is scattered through the supernumerary nucleus, x 3900. 278 D. H. Titbit and 7. D. Pickett-Heaps Division in Peridinium 279 namely small vesicles which sometimes appear on top of the pores but more frequently along the sutures (Fig. 2). An accurate description of the internal organization of interphase Peridinium balticum is given by Tomas et al. (1973); their micrographs show interphase cells (Tomas et al. 1973: fig. 5; Tomas & Cox, 1973: fig. 1) containing supernumerary (eucaryotic) nuclei which are ovoid as in Fig. 4. However, the interphase supernumerary nucleus is highly irregular in shape, sometimes being composed of interconnected lobes (Figs. 3, 5). It is not known if the nuclear shape relates to stages in the cell shape.

Division Prior to division, the nuclei lie side by side, approximately bisected by the plane of the girdle (Fig. 7). The predivision supernumerary nucleus is always ovoid, larger and more elongated than during interphase (compare Fig. 7 with Fig. 4). Its nucleolus fragments (Fig. 6), although this may also occur during interphase. The supernumerary nucleus remains perpendicular to the future cleavage furrow while the dinoflagellate nucleus divides (Figs. 6, 8). As in Crypthecodinium (Kubai & Ris, 1969), bundles of extranuclear microtubules invaginate the nuclear envelope of the dinoflagellate nucleus from the side facing the wall, forming channels through the nucleus, although the nuclear envelope does not break down. Microtubules never enter the dinoflagellate nucleus and the chromosomes attach to the nuclear envelope. Mitosis in the dinoflagellate nucleus of P. balticum appears to resemble that already described for Cryptlteco- dinium, and so we have not investigated it in detail. Cytoplasmic cleavage is initiated circumferentially around the cell by the time of late division of the dinoflagellate nucleus (Figs. 15,16). During earlier stages of division in the dinoflagellate nucleus, the supernumerary nucleus remains structurally unchanged (Figs. 6, 8); the first sign of its impending division is the appearance of an invagination on its side near the wall, adjacent to the newly appearing cleavage furrow

Figs. 7-14. A sequence of light micrographs showing nuclear division; the cells are stained with acetocarmine. Figs. 7-11, 13, 14, x 1500; Fig. 12, x 1800. Fig. 7. The dinoflagellate nucleus (d) and the supernumerary nucleus (n) lie side by side and are bisected by the plane of the girdle. The supernumerary nucleus is larger and more elongated than during interphase (see Fig. 4). Fig. 8. The dinoflagellate nucleus (d) divides while the supernumerary nucleus remains unchanged. Fig. 9. After division of the dinoflagellate nucleus, the supernumerary nucleus begins cleaving on its side facing the wall (arrow). Fig. 10. The dinoflagellate daughter nuclei (d) round out somewhat, and then the supernumerary nucleus cleaves from both sides (arrows). Fig. 11. Late division of the supernumerary nucleus; the 2 halves are connected by a narrow neck of nucleoplasm. Fig. 12. Final stages of division of the supernumerary nucleus; small strands of nucleoplasm (arrow heads) extend toward the opposite daughter nuclei. Fig. 13. Four nuclei immediately after cytokinesis. Fig. 14. Two recently formed daughter cells, each containing 2 nuclei. 280 D. H. Tippit andj. D. Pickett-Heaps 15

Fig. 15. Late division of the dinoflagellate nucleus and early cleavage of the supernumerary nucleus. The supernumerary nucleus cleaves on the side facing the wall, concurrent with cytoplasniic cleavage which is initiated circumferentially around the cell. Both nucleus and cell cleave roughly in the same plane (arrowheads), x 4300. Fig. 16. The cleavage in the supernumerary nucleus deepens and widens. The flagella (circle) are on the side of the cell closest to the dinoflagellate nucleus, x 4200. Division in Peridinium 281 in the cytoplasm (Figs. 9, 15). This nuclear invagination is not merely the result of cytoplasmic cleavage forcing the indentation upon the nuclear surface. The invagination having been initiated, now grows wider and deeper (Fig. 16); usually it does not bisect the nucleus equally (Figs. 9-11, 15, 16, 19). When the dividing cell is cut in cross- or tangential-section through the cleaving region (Fig. 17 - this cell is approximately at the same stage of division as the cell in Fig. 16), the dividing supernumerary nucleus has a circular profile. Bundles of parallel microtubules are clearly visible in the cytoplasm near the supernumerary nucleus (Figs. 17, 18); using serial sections, each of the bundles of the microtubules (for example, those seen in Fig. 17) can be traced until they enter the channels which invaginate the dinoflagellate nucleus. These microtubule-containing channels are also clearly visible in longitudinal sections, for example in Figs. 6 (arrows) and 16. Thus, these microtubules constitute part of the mitotic apparatus of the dinoflagellate nucleus; no microtubules are present inside the supernumerary nucleus, nor outside its membrane, except those comprising the dinoflagellate spindle. No chromosomes or condensed chromatin are detectable within the supernumerary nucleus at any stage of its division. At late cytokinesis, the supernumerary nucleus appears to cleave circumferentially, but the indentation on the side which cleaved first is always slightly larger (Figs. 10, 19-compare with Figs. 9, 15). The cleavage furrow now grows fastest from the side of the cell which contains the dinoflagellate nucleus, and, invariably, the narrow neck of the dumb-bell shaped supernumerary nucleus passes through the uncleaved portion of the cell across the path of the ingrowing furrow (Fig. 19). As the furrow draws closer, the neck decreases in diameter and becomes stretched along the longitudinal axis of the cell (Figs. 11, 20; the latter is at a slightly later stage of division than the cell in Fig. 19). In cross-section, the neck of the supernumerary nucleus is circular as before but considerably smaller than at earlier stages of division (Fig. 21; compare with Fig. 17). There are now no bundles of microtubules in the cytoplasm (as in Figs. 17, 18) since mitosis in the dinoflagellate nucleus is complete. The few microtubules which constitute the remnants of the dinoflagellate spindle, lie in the cytoplasm near each dinoflagellate nucleus. Serial sections of the cell shown in Fig. 20 indicate that cleavage is virtually complete; however, the neck of the cleaving supernumerary nucleus is still present in the remaining strand of cytoplasm, almost touched by the ingrowing furrow of the cell, As before, no microtubules could be detected inside the supernumerary nucleus although now other microtubules appear near the cleavage furrow (Fig. 21), as described in Ceratium by Wetherbee (1975). Viewed in cross-section, the growth of the cell's cleavage furrow proceeds like a draw string being tightened; the final separation of the supernumerary nucleus is probably accomplished by the ingrowing furrow pinching the narrow neck of the nucleoplasm in two. After cytokinesis is completed, portions of the supernumerary nucleus still extend towards the furrow (Fig. 12), but later the daughter nuclei may temporarily round off slightly (Figs. 13, 22) before they become somewhat irregular in shape (Fig. 14); the shape changes of the supernumerary nucleus are not followed after cytokinesis. 282 D. H. Tibtit and J. D. Pickett-Heafis Division in Peridinium 283

DISCUSSION The supernumerary nucleus of P. balticum does not undergo normal mitosis, although the adjacent dinoflagellate nucleus apparently divides in the characteristic manner already described for the dinoflagellate studied by Kubai & Ris (1969). The chromatin of the supernumerary nucleus does not condense, neither is there a spindle apparatus or microtubules present in it during any stage of its division; instead the nucleus cleaves as the cell cleaves, without any apparent precise segregation of genetic material. It is unlikely that membrane growth separates the chromatin in any organized fashion, since the contents of the nucleus remain evenly dispersed throughout the dividing nucleus. Perhaps the most unusual feature of the division in the supernumerary nucleus in P. balticum is that microtubules are not present inside the dividing nucleus, nor do they participate in its division. Microtubules are a common feature of nuclear division in all eukaryotic cells known to us, although the functional role of microtubules during mitosis varies greatly. For example, in the dinoflagellate Crypthe- codinium (Kubai & Ris, 1969), the microtubules are extranuclear during mitosis and the chromosomes have been postulated to separate membrane growth exclusively; in another dinoflagellate, Amphidinium (Oakley & Dodge, 1974), the microtubules are still extranuclear; however the chromosomes attach to specialized kinetochore regions along the nuclear envelope and the daughter chromatids may be separated by chromosomal microtubules. Elsewhere, in the macronucleus of certain ciliated protozoa (Tucker, 1967; Millecchia & Rudzinska, 1971) and in the amoeboflagellate Naegleria (Schuster, 1975), microtubules are present inside the nucleus during division but appear not to participate actively in genome separation. The lack of microtubules during division of the supernumerary nucleus, and the absence of other morphological changes accompanying its division, such as condensation of chromatin, indicate that it divides amitotically (i.e. division in the interphase state, usually accomplished by a simple constriction into two sometimes unequal halves, without any regular segregation of genetic material). We feel that these observations concerning division in the supernumerary nucleus of P. balticum are significant in attempting to ascertain its nature and significance. Most ciliated protozoa contain 2 different types of nuclei: the macronucleus, which divides without apparent segregation of genetic material, and yet supports vegetative growth and reproduction, and the micronucleus, which functions during conjugation. Much is known about the DNA of certain hypotrichious ciliates; this information is useful in understanding their macronuclear division, and so may have relevance to P. balticum and other organisms which also divide without accurate segregation of the

Fig. 17. The cleaving supernumerary nucleus (n) in cross-section; this cell is at approximately the same stage of division as the cell in Fig. 16. The circles enclose bundles of microtubules which are part of the dinoflagellate spindle; portions of the dinoflagellate nucleus (d) are visible, x 17600. Fig. 18. Detail of Fig. 17, showing bundles of microtubules (t) and portions of both the dinoflagellate nucleus (d) and supernumerary nucleus (n). x 45 600. 19 CHL 21 284 D. H. Tippit andj. D. Pickett-Heaps Division in Peridinium 285 cell's genetic complement. The macronucleus of ciliates breaks down during conjugation and later a micronucleus is converted into a new macronucleus. In certain hypotrichs, this conversion is accompanied by profound changes in the DNA of the developing macronucleus (Ammermann, 1965; Prescott, Murti & Bostock, 1973). First, many rounds of DNA synthesis give rise to polytene chromosomes, which are then cut into bands; most of the DNA is then degraded and the remaining DNA (less than 10 %) undergoes many further rounds of replication until the final DNA content of the macronucleus is many times that of the original diploid macronucleus. Throughout development of the macronucleus, most repetitive sequences of micronuclear DNA and some unique micronuclear DNA components are eliminated (Lauth, Heumann, Spear & Prescott, 1975). The high molecular weight DNA of the micronucleus is degraded into small, gene-size segments, 0-2-2-2 /(m long, which later constitute the DNA of the mature macronucleus (Prescott et al. 1971), and appear to be its functional transcriptional units (Murti, Prescott & Pene, 1972). In Oxytricha, the macronucleus contains an estimated 17000 different kinds of DNA pieces or genes and each kind is present about 1000 times per macronucleus, or 2000 times per cell, since each cell contains 2 macronuclei (Lauth et al. 1975). The small DNA pieces aggregate together into dense bodies which apparently do not segregate in any organized fashion during division. However, since there are so many copies of every DNA piece per cell, slightly unequal distribution of the genes will not have immediate serious repercussions, particularly since there is random mixing of all its DNA prior to division (Kimball & Prescott, 1962). Certain hypotrichous ciliates are not viable after more than 400—500 divisions and must be 'revitalized' by conjugation (Ammermann, 1971; Sonneborn & Schneller, 1955); Ammermann has suggested that senescence results in some hypotrichous ciliates when certain DNA pieces (or chromosome bodies) become too unevenly distributed or missing entirely from a cell following cycles of continuous random distribution during division. A stochastic model for this process has been presented by Kimura (1957); his formula allows prediction of the number of times that any cell which segregates its chromosomes or DNA pieces randomly will divide before 99-100 % of the progeny have lost one kind of DNA piece or chromosome due to chance. Generally the making of many copies of each gene seems to be a logical pre- requisite for a viable cell dependent upon an amitotically dividing nucleus. There is one other useful comparison between the supernumerary nucleus of P. balticutn and the macronucleus of ciliates. The macronucleus of some ciliates

Fig. 19. Late division of the supernumerary nucleus. Furrowing now proceeds faster from the side of the cell containing the dinoflagellate nucleus. The last region to cleave contains the remaining neck of the dividing supernumerary nucleus. The dinoflagellate daughter nuclei (d) have reformed. X4100. Fig. 20. Final stages of division of the supernumerary nucleus. This cell is at a slightly later stage than that in Fig. 19. The neck of nuclear material is still present in the remaining strand of cytoplasm. The ingrowing furrow (cf) nearly touches this nucleus, and later, apparently pinches the cleaving nucleus in two. There are no microtubules inside or near the outer membrane of the supernumerary nucleus, x 15400.

19-2 286 D. H. Tippit andj. D. Pickett-Heaps Division in Peridinium 287 extends throughout the cell, and it condenses into an ovoid body prior to division, but later it again becomes stretched or lobed. The supernumerary nucleus of P. balticum may also be ovoid (Fig. 4) or lobed (Fig. 3). In Spirostomum ambiguum, separate nodes of a moniliform macronucleus fuse into a ribbon, which then condense into a round mass (Raikov, 1969); these nodes are similar to the lobes in the supernumerary nucleus (Figs. 3, 5). Generally, the brief rounding-up of the macronucleus in some ciliates prior to division is similar to the rounding-up of the supernumerary nucleus in P. balticum into an ovoid form prior to and during division. In G. foliaceum, however, the supernumerary nucleus is occasionally ovoid (Dodge, 1971), but it divides in the branched or lobed form (Blanchard-Babillot, 1972). Tomas & Cox (1973) postulate that an endosymbiont of chrysophyte origin is responsible for the presence of the supernumerary nucleus. The interphase cells of the 2 binucleate dinoflagellates thus far described appear to contain a membrane identified as a plasmalemma, which extends throughout the cell, separating a portion of the cytoplasm which contains the supernumerary nucleus, chloroplast and numerous organelles from the dinoflagellate cytoplasm and nucleus (Tomas et al. 1973; S. W. Jeffery & M. Vesk, in preparation). In G. foliaceum (also called Peridinium foliaceum), a clearly discernible membrane encloses a portion of cytoplasm which contains the supernumerary nucleus and numerous organelles; the enclosed area of cytoplasm has a different density than the dinoflagellate cytoplasm (S. W. Jeffery and M. Vesk, in preparation). Some major characteristics of the cytoplasm enclosed by the plasmalemma not normally seen in dinoflagellates include a double membrane around the chloroplast and the ensheathment of the chloroplast within a portion of endoplasmic reticulum which is an out-folding of the nuclear envelope; based upon these observations, Tomas & Cox postulate the endosymbiont is of chrysophyte origin. Analysis of chloroplast pigments lends support to this theory; chrysophycean chlorophylls and carotenoids are present exclusively within G. foliaceum and Peridinium sp. (Withers & Haxo, 1975; Jeffery et al. 1975). If the chrysophycean endosymbiont exists within the dinoflagellate, then we might expect it to possess a mitotic apparatus similar to that of the other chrysophytes (Bouck & Brown, 1973; Slankis & Gibbs, 1972). Since division of the supernumerary nucleus in P. balticum is unlike that of any algae thus far observed, nuclear morphology is of no immediate apparent use in determining the origin of the postulated endosymbiont. If the supernumerary nucleus is truly of endosymbiont origin, it is possible that it has lost its ability to differentiate a spindle for vegetative division; at present there is not enough information available for any understanding of the functional significance of this second nucleus.

Fig. 21. Late division of the supernumerary nucleus (circled) in cross-section. The cleavage furrow (cf), lined with microtubules (t), grows circumferentially inward toward the supernumerary nucleus, x 14900. Fig. 22. Late cytokinesis. One dinoflagellate nucleus (d) and one supernumerary nucleus (n) in each daughter cell; the supernumerary nucleus extends toward the furrow following cytokinesis (Fig. 12), but later each nucleus may round out somewhat, x 4000. 288 D. H. Tippit and J. D. Pickett-Heaps This work was supported by grants from the National Institute of Health, Department of Health, Education and Welfare (Grant no. G.M. 19718), and the National Science Foundation (Grant GB 32034)).

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