/ . Embryol. exp. Morph. Vol. 19, 2, pp. 109-19, April 1968 109With 2 plates

Printed in Great Britain

Analysis of the development of the nervous systemof the zebrafish, Brachydanio rerio

I. The normal morphology and development of thespinal cord and ganglia of the zebrafish

By JUDITH SHULMAN WEIS1

From the Department of Biology, New York University

INTRODUCTION

In teleost fishes, unlike many other vertebrates, the spinal cord originates as asolid structure, the neural keel, which subsequently hollows out. Unlike verte-brates in which the neural tube is formed from neural folds, and where theneural crest arises from wedge-shaped masses of tissue connecting the neuraltube to the general ectoderm, teleosts do not possess a clear morphologicalneural crest. Initially, the dorsal surface of the keel is broadly attached to theectoderm as described by Shepard (1961). As the neural primordia become largerand more discrete, the region of attachment narrows, and cells become loose(the 'loose crest stage'). These cells represent the neural crest. Subsequently theybegin to migrate and to differentiate into the various derivatives of neural crest.

Both sensory and sympathetic neurons arise from neural crest. At the time oftheir migration the cells are not morphologically distinguishable. Only afterthe sensory cells have aggregated into the primordia of the dorsal root gangliado they become morphologically identifiable as nerve cells, by the oval shapeof the cell body, appearance of neurofibrils, and outgrowth of axon fibers(Levi-Montalcini, 1964). The subsequent growth of the ganglia is due to additionof more migrating cells, mitotic activity of cells within the ganglia, and sizeincrease of individual cells as they mature. Balfour (1877) described the cephalo-caudal development of spinal ganglia in Elasmobranchs from two club-shapedmasses of cells at the summit of the spinal cord or crest, which migrated ventrallymaintaining contact with the cord. Harrison (1901) observed a similar develop-ment of spinal ganglia in Salmo salar, although he believed that the cells migratedout from the spinal cord.

Detweiler (1937) vitally stained the neural crest of Amblystoma with Nile bluesulfate, and observed the migration of cells and condensation to form ganglia.Weston (1963) observed this migration in the chick by radioactively labelled

1 Author's address: Department of Zoology and Physiology, Rutgers University, Newark,New Jersey, U.S.A.

8 JEEM 19

110 J. S. WEIS

grafts of neural crest which developed into spinal ganglia, sympathetic ganglia,melanoblasts, and Schwann sheath cells.

The precursors of the sympathetic nerve cells migrate from the crest somewhatearlier than the sensory cells (Yntema & Hammond, 1947). At the time of theirmigration they do not differ from other neural crest derivatives. When they haveaggregated in two columns dorsolateral to the aorta, they begin to resemblenerve cells with elongated cell bodies and axons which show an affinity forsilver. Some cells move anteriorly and assemble in the head as the cervicalsympathetic ganglia. The sympathetic cells then undergo an increase in numberand size by mitotic activity and growth of individual nerve cells.

There has been considerable controversy in the past over the origin of thesympathetic nervous system, with various investigators advocating spinal nerves,spinal ganglia, neural tube, mesenchyme, and neural crest as possible sources.The review by van Campenhout (1930 a) considers the various theories whichhave been put forth. Conclusive evidence was obtained by van Campenhout(19306), who experimentally investigated the development of the sympatheticsystem in Rana. His results indicated that the sympathetic chain was derivedfrom the neural crest and had no contribution from the spinal cord. He foundthat sympathetic elements could migrate longitudinally beyond the limits of thesegments from which their primary migration took place. Therefore, if a shortlength of neural crest was removed, cells from adjacent normal levels movedinto the depleted area and grouped into ganglia. The animal therefore had nospinal ganglia in the operated region but did have sympathetics. This is one ofthe reasons for the confusion in the literature.

In teleosts the chain extends as far forward as the trigeminal nerve. Thepreganglionic fibers for the head region arise from the spinal cord in the trunkregion and pass forward to the cranial sympathetic ganglia (Young, 1950).

The sympathetic systems of the teleosts Ambloplites rupestris, Micropterusdolomieu and Perca flavescens were described by Huber (1900). In the trunkportion, the chains are above the kidney and may be embedded within it. Thecaudal portion is located within the hemal arch. Young (1930) described thesympathetic system of Uranoscopus scaber, a teleost which is unusual in that nopigment is associated with the sympathetic chains. In the anterior trunk regionthe sympathetic ganglia lie close to the spinal ganglia with short rami communi-cantes. In the posterior trunk region the chains approach the midline, becomeflattened between the dorsal aorta and cardinal vein, and become diffuse. Passingbackward between the kidneys, the two chains fuse and pass as a single cordto the end of the abdomen. However, when they enter the hemal canal in thecaudal region they become paired again. In the caudal region the small gangliain each segment are connected to the spinal nerve, and across the midline bytransverse commissures.

In developing amphibia and fish there exists a primary sensory system ofRohon-Beard cells which functions prior to the development of the spinal

Zebrqfish nervous system. I 111ganglia. Beard (1889, 1892) initially described transient dorsal cells within thespinal cords of Lepidosteus, Raja, and other species. These cells also are foundjust outside the spinal cord under the meningeal covering, as a result of migration,and send processes to the skin. They are later cut off from the central nervoussystem, but persist for some time lying outside the cord. Similar cells weredescribed by Fritsch (1886) in Lophius, and by Harrison (1901) in Salmo, whodescribed the cells as arising from the dorsolateral surface of the cord near thelimiting membrane.

Giant supramedullary neurons lying directly dorsal to the cord or in its mediandorsal fissure have been described by Dahlgren (1897), Sargent (1899) and Burr(1928) in a wide variety of fishes, sometimes only in larval stages, and sometimesin mature animals as well.

Tracy (1961) found that the Rohon-Beard cells degenerated early in thetoadfish, Opsanus tau, the spinal ganglia developing at the time of hatching.In the early swimming stages of the amphibian Amblystoma these cells are theonly sensory system (Coghill, 1914). Hughes (1957) described migration ofRohon-Beard cells in Xenopus from within the cord to an extramedulary posi-tion. These cells serve as the afferent trunk system for 200 h of free swimminglife, after which time they are replaced by the dorsal root ganglia.

This paper describes the normal morphology and development of the spinalcord and ganglia of the zebrafish, Brachydanio rerio (Hamilton-Buchanan), as astudy preliminary to experimental modification of their development. The zebra-fish, also known as the zebra danio, is a member of the family Cyprinidae and isnative to India. This species is oviparous and can be bred easily, but capriciously,in captivity. The egg is transparent and about 0-6 mm in diameter. Develop-ment is rapid—only 96 h from fertilization to hatching—at 26 °C. The normaldevelopment of B. rerio has been described by Hisaoka & Battle (1958) andHisaoka & Firlit (1960), who divided the embryological period into a series ofstages. This species has been used extensively in experimental embryology.

MATERIALS AND METHODS

Stocks of mature zebrafish are easily maintained in the laboratory in springwater, and eggs can be obtained throughout the year. Fish are spawned in tankswith a net of plastic screening near the bottom. The eggs, which are demersal,drop through the holes in the screening and thus cannot be eaten by the canni-balistic parents. The eggs are subsequently removed from the tank with a syringe.In nature, the normal time of spawning is conditioned by light and occursnormally at dawn. Using the method of Legault (1958), spawning tanks werecovered at night and uncovered in the morning. Spawning generally occurredshortly after the tanks were uncovered. Eggs can be obtained from an individualfemale once every 5 or 6 days (Hisaoka & Firlit, 1962). One mature female canlay a few hundred eggs at a time. There is, however, a significant mortalityduring development, the most critical period being that of gastrulation.

8-2

112 J. S. WEIS

To see the normal development of the nervous system in this species, eggs atvarious stages of development were fixed in Bouin's fluid. The outer chorionwas removed with fine forceps before dehydration in a graded series of alcoholsto xylene. They were then embedded in paraffin, serially sectioned at 10/* andstained with Delafield's hematoxylin and lightly counterstained with eosin.Young fry were treated likewise. Some fish were raised for 6 weeks, by whichtime they had reached different lengths. They were then fixed, sectioned andstained as above. From each fish, four spinal ganglia were measured: three fromthe anterior end of the spinal cord and one from the posterior end of the coelo-mic cavity. To determine the volume of a three-dimensional structure, uneven inshape, reconstructions were made. The sections were projected to give a mag-nification of x 460, and the outline of the ganglion traced on paper for eachsection in which the ganglion appeared. The outlines of all sections of theganglion were cut out of the paper and weighed on a balance. Weights of leftand right ganglia were pooled for each ganghon weight. This weight of the paperis, or course, relative, but it reflects the mass of the ganglia. This method issubject to a certain amount of error—variation in thickness of the paper, varia-tion in weight of paper of the same area due to different humidity, inaccuracyin cutting, etc. To investigate the extent of these sources of error, sixteen piecesof paper of the same size were weighed and compared with each other. Theirweights on a very humid day were compared with those after being placed in adrying oven for 45 min. The original variation in weight was 0-01 g in 0-60 g,or about 1-5 %. After drying the greatest change was 0-2 g, or about 3 %. Toestimate my errors in tracing and cutting, eighteen ganglia were retraced, recutand reweighed, and the average error was 4 %.

Cells were counted in one ganghon per fish (ganglion 2). The counts weregenerally done under x 750 magnification, and each nerve cell whose nucleuswas present was counted on each section. Left and right counts were pooled.At a different date, the cells were recounted without reference to the earliernumber. The largest discrepancies were about 10 %, and the average error wasconsiderably smaller. To correct for the spread of nuclei between sections, theFloderus correction formula as described in Ebbeson & Tang (1965) was applied.

In this same ganglion the nuclear size was measured with a calibrated ocularmicrometer. In sections through the middle of the ganglion, the greatest diameterof the nuclei of the majority of the larger neurons was measured.

RESULTS

In this study of the development of certain parts of the nervous system,samples were chosen to correspond to the stages of Hisaoka & Battle (1958).At stage 18 (14 h at 26 °C.) the solid neural keel is forming above the notochord,which is flanked by a mesodermal sheet on either side (Plate 1, fig. A). Thecavity first appears in the brain at stage 20 (24 h), when the optic vesicles are

/. Embryol. exp. Morph., Vol. 19, Part 2 PLATE 1

All sections cut at 10/t, stained with hematoxylin and eosin.Fig. A. Stage 18 (14 h). Axis formation; the neural keel is forming dorsal to the notochord.K, Neural keel; N, notochord; Y, yolk.Fig. B. Stage 21 (27 h). The neural tube is well-defined and hollow, with broad attachmentto the dorsal ectoderm. C, Neural crest; N, notocord.Fig. C. Stage 24 (72 h). White matter is free of cells, migration of neural crest has occurred;melanin pigment visible. P, Melanin pigment.Fig. D. One week after hatching; Rohon-Beard cells are seen lateral to the spinal cord. RB,Rohon-Beard cells.

j . s. WEIS facing p. 112

J. Embryol. exp. Morph., Vol. 19, Part 2

Fig. E. Two and a half weeks after hatching. Rohon-Beard cells still visible laterally, butspinal ganglia forming dorsally. G, Spinal ganglia; RB, Rohon-Beard cells; M, Mauthner'sfibers.Fig. F. Mature animal. Section through trunk region showing typical position of spinalganglia. G, Spinal ganglia.Fig. G. Mature animal. Section through cervical region showing the ventral position of theganglia in this portion of the body, and the thick neural arch cartilage dorsal and lateral tothe spinal cord. A, Neural arch; G, spinal ganglia; R, roots of spinal nerve.Fig. H. Mature animal. Section through caudal region showing sympathetic ganglia ventralto the aorta; commissure connecting ganglia is visible. S, Sympathetic ganglia.

j . s. WEIS

Zebrafish nervous system. I 113

forming. At stage 21 (27 h) the cord itself has become hollow, and the notochordis becoming vacuolated (Plate 1, fig. B). The cells concentrated around the smallneural canal are the forerunners of the ependymal layer. At this stage the opticcup has formed and lens induction has taken place. At stage 22 (37 h) a distinc-tion can be seen between the white and gray matter, the cells becoming con-centrated in the interior of the cord. The neural canal is quite ventral in position.By this time otic vesicles have formed. At stage 23 (50 h) some neural crest cellshave migrated out, and melanin pigment is seen around the spinal cord. Initiallythe melanin is densest immediately dorsal to the spinal cord at the original siteof the crest cells. The cells then migrate laterally and ventrally. At stage 24(72 h) the gray matter of the cord is filled with large undifferentiated cells(Plate 1, fig. C). This appearance is retained through the time of hatching.The Rohon-Beard cells are first distinguishable at stage 22-23. They are initiallyin lateral positions within the cord, but are subsequently found just outside thecord under the meningeal covering as a result of migration. By stage 24 cellswere seen chiefly in this extramedullary position. They persist for 3-5 weeks assmall groups of cells lateral to the cord, between the two meningeal coverings(Plate 1, fig. D). No supramedullary cells, as described by Sargent (1899), wereever seen in this species. The cells are subsequently obscured by the connectivetissue cells which surround the cord to form the neural arches.

By the time of hatching, Mauthner's fibers are seen ventrolateral to the centralcanal of the spinal cord. These large axons run posteriorly in the spinal cord andare traceable to the caudal end of the spinal cord.

By 2 weeks after hatching, the spinal cord is approaching the mature condition.The gray matter becomes organized in the shape of an inverted Y, the two dorsalhorns lying so close together that there is hardly any white matter between them(Plate 2, fig. E). The small, oval-shaped neural canal is ventral in position andsurrounded by an ependymal layer. The large Mauthner's fibers lie ventrolateralto it. The large ventral horn cells with large granular nuclei and conspicuousnucleoli have a net of processes extending outward. The largest cells are mostfrequently found medially, near the neural canal. They have a large amount ofcytoplasm, and nuclei about twice the size of those of neighboring cells. Ventro-lateral motor neurons were generally somewhat smaller than mediodorsal ones.

At 2-4 weeks after hatching the spinal ganglia first appear as localizedcondensations of neural crest material dorsolateral to the cord. The cells are atfirst undifferentiated, appear mesenchymal, and are not clearly separable fromconnective tissue. Subsequently, the cells take on a bipolar appearance, and theganglia become well-defined and clearly separated from surrounding tissue. Itis not possible to give an exact timetable for the development of spinal ganglia,since their rate of development is determined by the growth rate of the individualanimal, which can vary extensively among animals of the same brood. There-fore, the state of development of the nervous systems of two animals of the samebrood which have reached different sizes will be correspondingly different. If an

114 J. S. WEIS

animal is stunted, not only is the rate of body growth slowed down, but also therate of development and differentiation of organ systems. In litter-mates allsacrificed at the same date, it may be possible to see a wide spectrum of develop-mental stages, from those with remaining Rohon-Beard cells to those withwell-differentiated ganglia.

When first forming, the ganglia often appear as thin rows of cells along thelateral and dorsolateral surfaces of the cord. They are sometimes thicker attheir ventral ends, at the site of the Rohon-Beard cells, indicating that perhapsthe Rohon-Beard cells may be incorporated into the spinal ganglia. It wouldappear as if the neural crest cells migrate ventrally until they reach the Rohon-Beard cells, and then add on to them dorsally so that there is temporarily a singlecomposite structure. In other cases, however, there is a clear separation betweenthe Rohon-Beard cells laterally and the developing spinal ganglion dorsally;occasionally there is a thin connexion between them (Plate 2, E). In olderspecimens, however, the 'bulge' at the ventral end of the ganglion is neverpresent, all ganglia tapering sharply at their ventral ends. This would seem toindicate that the original Rohon-Beard cells have disappeared, and that the cellsin the mature ganglion are only those derived from the neural crest severalweeks after hatching.

The ganglion cells themselves are large and elongate, with large nuclei,distinct basophilic nucleoli (usually one, but sometimes two) and tapering cyto-plasm with basophilic Nissl substance typical of nerve cells. Many cells retain abipolar appearance when mature. This has been previously noted in fishes byvon Lenhossek (1892) and Martin (1895), and is in contrast to other vertebratesin which all spinal ganglion cells become unipolar when they mature. Thenuclei are spherical or oval in shape, and elongated along the plane of elongationof the entire ganglion (roughly dorsoventral). The ganglia themselves areelongate, roughly tear-drop-shaped, and are typically found dorsolateral to thecord, wedged in between it and the muscle mass (Plate 2, fig. F). The gangliaoften extend upward, far beyond the dorsal end of the spinal cord. However,the first three spinal ganglia are large, round, and lie ventrolateral to the spinalcord, like more typical vertebrate spinal ganglia. These three ganglia are foundin the cervical region, where the vertebrae are provided with unusually thickneural arches (Plate 2, fig. G). The ganglia are located below the ventral ends ofthe neural arches. The ganglia chosen for examination were the first three pairsposterior to these ventrally located ones; that is, the first three pairs of 'typical'spinal ganglia. The first of these, which is designated as 'ganglion number 1',appears just posterior to the termination of the thick neural-arch cartilage whichhad been occupying the space dorsal and lateral to the spinal cord. This firstganglion is frequently somewhat intermediate in position, usually long and thin,and not extending as far dorsally as the succeeding ganglia, which were moretear-drop-shaped. The other ganglia chosen for examination were located at thelevel of the cloaca. In an occasional fish the ganglia at the level of the cloaca and

Zebrafish nervous system. I 115some located farther caudally were situated in the ventral position. Theseganglia however, were still elongated and tear-drop-shaped, but their orientationwas 180 ° from that of the typical ganglia. Therefore, they do not resemble themuch larger, round, ventrally located ganglia in the cervical region. In onespecimen, one member of the pair was dorsally located while the other wasventral. In a few specimens, cells were concentrated at both ends of the ganglion,

Table 1. Weights of paper reconstructions, corrected cell counts, andnuclear diameters of ganglia from Brachydanio rerio of different lengths.

Standardlength*(mm)

4

6

8

10

14

16

Ganglion

123

Cloacal

123

Cloacal

123

Cloacal

123

Cloacal

123

Cloacal

123

Cloacal

Weight

7-67-3

9-47-2807-5

15117016-618-4

20-425-327-128-8

59-559-556-5570

85068-5980980

S.E.

1-71-5

110-90-60-9

0-91-51-21-8

1-52-51-92-8

3-54-50-530

508-53090

Cell count f

141

24-9

45-2

61-8

900

90-8

S.E.

0-8

2-8

5-7

2-6

150

110

Nucleardiameter %

2-4-3-6

3-6^-8

4-8-6-0

6-0-7-2

7-2-8-4

7-2-8-4

* Standard length—snout to caudal peduncle.t Based on all neurons whose nuclei were present, counted in all sections in which the

ganglion appeared. Counts for left and right pooled, then corrected.% Based on maximum-sized nuclei contained in sections through the middle of the ganglion,

in all fish.

and were sparse in the middle, indicating great variability of these caudallylocated ganglia. In the vast majority offish examined, however, the cloacal andcaudal ganglia retained the typical dorsal position.

In contrast with the development of the spinal ganglia, the sympatheticsystem makes its appearance somewhat later in development, a month or so

116 J. S. WEIS

after hatching. In the trunk portion of the body, the two sympathetic chainslie lateral to the aorta and are embedded in the kidney, and therefore extremelydifficult to see. In the caudal portion of the body the sympathetic chains liewithin the hemal canal, ventral and lateral to the aorta. The small ganglia oneach side are connected to each other by transverse commissures (Plate 2,Fig. H). The ganglia are quite small, and favorable sections could not be obtainedin many specimens. Frequently melanin obscured the ganglia. Consequently,most attention was devoted to the spinal ganglia.

The data from paper reconstructions of spinal ganglia from fish of differentsizes are presented in Table 1. In 4 mm fish, ganglia averaged 7-5; in 6 mm fishthey averaged 8-0; in 8 mm fish, 16-8; in 10 mm fish, 25-4; in 14 mm fish, 58-1;and in 16 mm fish, 85-1. These data indicate that as the fish grow, the gangliagrow in proportion to the size of the fish. Fish size would therefore appear to bemore important than age in determining ganglion size.

The cell counts and measurements of nuclear diameters of cells in ganglion 2are also presented in Table 1. Ganglia from 4 mm fish averaged 14-1 cells,(corrected value) 6 mm fish averaged 24-9 cells, 8 mm fish averaged 45-2 cells,10 mm fish averaged 61-8 cells, 14 mm fish averaged 90-0 cells, and 16 mm fishaveraged 90-8 cells. Through this size range, nuclear diameters increased from2-4 to 8-4 fi. These data indicate that the number of cells in the ganglia increaseswith the length of the fish, and that the size of the ganglion cells likewiseincreases with fish size.

DISCUSSION

It has been observed that in the developing zebrafish the Rohon-Beard cellspersist for several weeks after hatching, and that the spinal ganglia form rela-tively late. This is probably related to the fact that the fish hatch in only 4 daysand are still in a very immature state at that time. In contrast, Fundulus takesapproximately 2 weeks to develop, and hatches in a much more advanced state,with its spinal ganglia already formed (personal observation). It might beconsidered that many of the same developmental events are taking place inFundulus before hatching as in Brachydanio while already actively swimmingaround.

The typical dorsolateral position of the spinal ganglia in the zebrafish isdifferent from that in other classes of vertebrates, and from that in a number ofother teleosts which I have examined, namely Fundulus, Rivulus and Pterophyl-lum, in which the ganglia occupy a more ventral position relative to the cord. InFundulus the ganglia are well formed by the time of hatching. Photographsaccompanying the papers of Ray (1950) and Tracy (1961) indicate that inLampanyctus and Opsanus the ganglia likewise occupy ventral positions. How-ever, Rhinichthys (the dace, also in the family Cyprinidae) has ganglia positionedas the zebrafish does, as do the closely related members of the same family, the

Zebrafish nervous system. I 111pearl danio {Brachydanio albolineatus) and spotted danio (B. nigrofasciatus)(personal observation).

From the data on ganglion size, cell number and nuclear diameters, severalfacts can be discerned. One can observe that as the fish grow the ganglia grow,and there is continual increase in cell number, in addition to size increase ofcells during this growth period. This phenomenon might be considered to berelated to the prolonged immature condition of the nervous system in thisspecies. This continual increase in cell number in the fish ganglia is in contrastto the situation in some other vertebrates such as birds and mammals in whichthe number of spinal ganglion cells reached in embryonic stages remains con-stant through the rest of the animal's life, and growth of spinal ganglia isachieved mainly through hypertrophy of cells already present. Mitoses were notobserved in the zebrafish spinal ganglia, so it would seem likely that there is acontinual addition and differentiation of new cells, rather than multiplication ofalready differentiated nerve cells.

SUMMARY

1. In embryos and young fry of the zebrafish, Brachydanio rerio, the sensoryfunction of the nervous system is fulfilled by a primitive transitory system ofRohon-Beard cells. These are replaced 2 or 3 weeks after hatching by thedeveloping spinal ganglia.

2. The spinal ganglia are typically tear-drop-shaped and occupy a dorso-lateral position relative to the spinal cord, with the exception of the first threepairs of ganglia which are large, round, and lie ventrolateral to the cord.

3. As the fish grow, the spinal ganglia grow in size, due to an increase in cellsize, and an increase in cell number. This is different from the situation inmammals and chicks, for example, in which the number of cells reached inembryonic stages remains constant, and growth of ganglia is achieved only bymeans of cell enlargement.

RESUME

Analyse du developpement du systeme nerveux du Poisson-zebre, Brachydaniorerio. I. La morphologie et le developpement normaux de la moelle epiniereet des ganglions rachidiens

1. Chez les embryons et les jeunes alevins de Brachydanio rerio, les fonctionssensorielles du systeme nerveux sont assurees par un systeme primitif transitoirede cellules de Rohon-Beard. Celles-ci sont remplacees par les ganglions rachi-diens en cours de developpement, deux ou trois semaines apres l'eclosion.

2. Les ganglions rachidiens ont une forme larmee typique et se trouvent enposition dorso-laterale par rapport a la moelle epiniere, a l'exception des troispremieres paires de ganglions, qui sont grands, arrondis et situes ventro-lateralement a la moelle.

3. Au fur et a mesure que le poisson grandit, la taille des ganglions rachidiens

118 J. S. WEIS

s'accroit, en raison d'une augmentation de la taille et du nombre de leurs cellules.C'est la une difference avec la situation realisee par exemple chez les mammifereset les oiseaux, oil le nombre de cellules atteint au cours des stades embryonnairesreste constant, et ou la croissance des ganglions est realisee seulement parl'accroissement de la taille des cellules.

I wish to express my appreciation to Dr Alfred Perlmutter for his interest and helpfulsuggestions throughout the course of this study. I wish to thank Dr Elmer Bueker for hisadvice and use of his equipment. My appreciation is extended to my husband, Dr PeddrickWeis, for the use of laboratory space and for his constant interest and encouragementthroughout the course of this study. This work was supported in part by U.S.P.H.S. GrantsNB-05755 and NB-03979. This paper is part of a dissertation submitted in partial fulfilmentof the requirements for the Ph.D. degree at New York University.

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{Manuscript received 16 June 1967, revised 17 October 1967)