Postnatal Development of the Cerebellar Cortex in the Rat V. SPATIAL ORGANIZATION OF PURKINJE CELL PERIKARYA JOSEPH ALTMAN AND ARTHUR T. WINFREE Department of Biological Sciences, Purdue University, West Lafayette, Indiana 47907
ABSTRACT The developrnent of the spatial organization of Purkinje cell perikarya was examined in the rat cerebellum from birth to adulthood. Dispersion of the perikarya followingbirth is made possible by the rapid expansion of the cortical surface. Their subsequent regular monocellular alignment is ensured by mechanical factors, the pressure exerted from below by the expanding granular layer and the barrier formed above by the pile of parallel fibers which prevent the penetration of the bulky perikarya into the molecular layer. The perikarya remain in this position even after the slender stem dendrite pierces the molecular layer along the descending axons of basket cells. The increase in interperikaryal distance between Purkinje cells is rapid up to day 12, then declines. This is temporally associated with the growth of the basket cell plexus and glial envelope around the perikaryon. The increase in perikaryal size continues up to day 30. This may be temporally associated with the growth of the Purkinje cell dendritic arbor a s reflected by the expansion of the molecular layer up to day 30. The spatial arrangement OF Purkinje cells within the monocellular sheet was graphically displayed with computer aid. In the adult cerebellum a hexagonal arrangement could be recognized in a proportion of “near-neighborhoods,” consisting of about six Purkinje cells and their neighbors. When the neighborhoods were extended with fixed orientation with respect to the axis of the folium, the hexagonal arrangement disappeared. When orientation was ignored, the superimposed nearneighborhoods could be rotated to produce a hexagonal pattern. In the infant cerebellum the hexagonal arrangement could not be demonstrated before the alignment of Purkinje cells in a mondayer. Thereafter there appeared to be an increase with age in the proportion of hexagonally arranged near-neighborhoods. It was concluded that in the monocellular ganglionic layer Purkinje cells are not aligned in regular rows with respect to the geometrically arranged elements of the supraganglionic layer. The formation of an imprecise hexagonal pattern, like the alignment of Purkinje cells in a monolayer, was attributed to mechanical factors.
The previous paper of this series (Atman, ’75) dealt with the spatial organization of bipolar cells, parallel fibers and glial palisades in the developing suipraganglionic portion of the cerebellar cortex. This paper is concerned with some aspects of the ontogeny of the spatial organization of Purkinje cell perikarya in the ganglionic layer. These include: (a1 the mechanisms underlying the monocellular dispersion of Purkinje cells parallel to the cortical surJ.
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face; (b) changes in the size and intercellular spacing of Purkinje cells; and (c) the origins of the spatial distribution of Purkinje cells within the monocellular sheet. For the latter purpose we employed a computer-aided graphic display technique. We attempted to determine whether or not Purkinje cells in the rat cerebellum become arranged in a regular geometric pattern similar to that reported for adult cats (Palkovits et al., ’71).
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MATERIALS AND METHODS
Tissue used In addition to the extensive collection of developmental material described in detail earlier (Altman, ’72al we made use here of some additional material. The brains of male Purdue-Wistar rats aged 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 60 and 90 days were embedded in paraffin and cut serially at 10p in the coronal, sagittal and horizontal planes. The sections were stained in a systematic sequence with hematoxylin-eosin, cresyl violet, the Weigert-Loyez and Bodian’s protargol-S methods. The cerebella of three 1-year-old rats were cut similarly in the three planes and every section was saved to allow serial reconstructions. Selection of material For the purpose of studying developmental changes in the size, intercellular spacing, and location of Purkinje cell perikarya, the cerebella were scanned for regions sectioned parallel to the monocellular layer of Purkinje cells. Sufficiently extended sheets of Purkinje cells were obtained in one or more cerebella of the following ages: 2, 3, 4, 5, 8, 10, 12, 16, 20, 25, 30, 90 and 365 days. These were photographed and printed at a constant magnification of x 576. The Purkinje cells were traced and the tracings were used for the various quantitative measurements described below. Quuntitative methods Purkinje cell perikaryal area was determined by measuring cells with nucleoli with a Keuffel and Esser compensating planimeter. “Nearest neighbor” separation was established b y measuring with a caliper the edge-to-edge distance between the closest pairs of Purkinje cells. Cells without a nucleolus (that is, those cut peripherally) and Purkinje cells outside or near the periphery of a homogeneous monocellular sheet (whose nearest neighbor may have been outside the plane of sectioning) were not included. The spatial distribution of Purkinje cell perikarya was
determined with a Hewlett-Packard digitizer in the following manner. The tracings of Purkinje cells were fixed to the digitizer surface. The orientation of the bipolar cells of the external germinal layer (the longitudinal axis of the folium) and magnification were fed into the computer. The Purkinje cells within a homogeneous sheet were subdivided into overlapping circular areas containing about 15 to 21 cells. The coordinates of each cell within the area were established by positioning the digitizer cross-hairs over the nominal center of the cell and the information was fed into the computer by pressing a button. With 15 to 21 cells entered, the “center of gravity” of the area was calculated and the distance R found from that center to the outermost cell. So all cells were within a circle of radius R with a mean separation of M = 2 R / m C e l l s closer to the boundary than M micra had incomplete neighborhoods, that is, some of the nearest neighbors might have been beyond the circle; these were rejected. The cells inside a circle of radius R had complete neighborhoods and were accepted. Each of these “inner circle” cells (ranging from 3-91 was taken in succession as the center of the display and its neighbors were plotted (figs. lA,B). Each cell typically had five to six neighbors and this “near neighbor” composite was displayed as a ring of points each at least 1-cell diameter from the center. The points within the annulus should be azimuthally uniform, or form a “cloud,” unless the frequency of neighbors is dependent on direction (as in a crystal lattice). Where directionality is present the structure of the average neighborhood emerges within the annulus as a clustering of cells into some number of discrete clumps. Finally, the near-neighborhood composites of the entire sheet of Purkinje cells could be superimposed, all identically scaled and oriented, to provide an “extended neighborhood” printout (fig.1C). RESULTS
1. Monocellular dispersion of Purkinje cells In the cerebellar cortex of the rat, the
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Fig. 1 Computer display of the spatial arrangement of Purkinje cell perikarya. In the upper portions of A and B the hexagons represent the cell bodies that were located in chosen circular areas. The Purkinje cells within the inner circle were determined to have complete neighborhoods. The spatial arrangement of all cell-pairs within the inner circle are displayed in the lower portions of A and B as dots. Their alignment is with respect to the nominal long axis of the folium, shown as a line below the displays: scale 100 mp. C. The arrangement of superimposed neighborhoods of an entire monocellular Purkinje cell sheet. Distances between Purkinje cells are from center-to-center of perikarya.
perikarya of Purkinje cells disperse to form a monocellular sheet parallel to the cortical surface within a few days after birth (Addison,'11).The dispersion is completed in the early-maturing lobules of tbe vermis by day 4, and in the late-maturing folium and tuber shortly after day 8 [Altman, '76a). This monocellular alignment is made possibZe by the expansion of the surface area of the cerebellar cortex from 'day 4 on (Altman, '691, which is associated with a high rate of cell proliferation in the superficial external germinal layer (Altman, '72a). But what makes this dispersion necessary? What mechanism assures the align-
ment of Purkinje cell perikarya into a regular monocellular sheet? The appearance, in a section stained with Bodian's technique, of a late-maturing (or underdeveloped) lobule of the vermis of an 8-day-old rat is shown in figure 2A, that of an early-maturing lobule in figure 2B. In the underdeveloped lobule the unaligned Purkinje cell perikarya are small and lack apical cones, the granule cells are closely packed in the granular layer, and the parallel fibers are still somewhat diffusely distributed in the molecular layer. In contrast, in the maturing lobule the aligned Purkinje cell perikarya have
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Fig. 2 Cerebellar cortex in an 8-day-old rat. EG, external germinal layer; GR, granular layer; MO, molecular layer; PU, Purkinje cell layer. A. Late-maturing lobule. The primitive Purkinje cells are not yet fully aligned in a monolayer and the parallel fibers are loosely arranged. B. Early-maturing lobule. The Purkinje cells have large apical cones (arrows) abutted against a horizontally aligned pile of parallel fibers. W a n ’ s protargol-S method, x 612.
well-developed apical cones and are abutted against a sharply delineated, apparently taut line of parallel fibers; concurrently the granule cells have become somewhat scattered in the granular layer. On the basis of such observations we
propose that two opposing forces are responsible for the alignment of Purkinje cell perikarya into a monolayer: pressure exerted on the growing Purkinje cell perikarya from below by the expanding granular layer, and the barrier formed above the
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Fig. 3 Parts of the cerebellar cortex in adult rats, Bodian's protargo1-S method. A. Relationship between the monocellular row of Purkinje cells and parallel fibers. Section cut obliquely through the molecular layer. x 325.B. Section cut parallel to the sheet of Purkinje cells at the lower aspect of the perikarya. It shows the zone formed by the relative large perikaryal baskets of the basket axon terminals. x 816.
Purkinje cells by the pile of parallel fibers. chronously arriving mossy fibers (Altman, The expansion of the granular layer is '73a). The restraining force exerted by the caused not only by the progressive ac- parallel fibers may be aided by their cumulation of translocated granule cells becoming anchored to basket cells with but also by their sprouting of dendrites which they start to form synapses during (Altman, '72c) in association with syn- this period (Altman, '72b).
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The pile of parallel fibers progressively expands in the developing molecular layer and forms a permanent upper barrier to the perikarya of Purkinje cells which are apparently never pushed into the molecular layer (fig. 3A). Perhaps their displacement downward into the granular layer is prevented by the rich terminal baskets of basket cells (fig. 3B). Thus in spite of considerable changes in the foliation pattern of the cerebellar cortex during the early postnatal period, the Purkinje cell perikarya remain sandwiched between the molecular and granular layers. When the bulky apical cone of the Purkinje cell becomes transformed into the slender primary dendrite the parallel fibers can no longer bar its penetration into the molecular layer. A previous experimental study with X-irradiated cerebella (Altman, ’76a) suggested that the Purkinje cell primary dendrites pierce the molecular layer along and in interaction with the descending vertical axons of basket cells. The contiguity between Purkinje cell primary dendrites and basket cell axons is also typically seen in normal cerebella (fig. 4).
2. Growth patterns in the size and spacing of Purkinje cell perikay a In extensive monocellular sheets of Purkinje cells, planimetric areal measurements were made of perikarya which contained nucleoli that is, those that were cut transversely close to the middle of the cell body. The results (fig. 5) indicate that areal growth is rapid up to 30 days, then perikaryal growth stops. In an attempt to correlate the growth of Purkinje cell perikarya with the expansion of their dendritic arbors, we measured the width of the molecular layer as a function of age in the dorsal and caudal regions of the pyramis. This was an indirect approach, the rationale being that the width of the molecular layer will reflect the maximal height reached by Purkinje cell dendrites. (In the developing cerebellar cortex there is a formative upper strip of molecular layer which contains densely-packed parallel fibers with few or no dendritic profiles; Altman, ’72b.l The growth curve obtained from day 5 on (fig.
6) when the width of the molecular layer could be reliably measured in this material, did not exactly match the curve for the growth of Purkinje cell perikarya but agreed with it in that an asymptotic level was reached by day 30. In contrast, the increase in “nearest-neighbor” separation of Purkinje cell perikarya followed a different time course. It was rapid up to day 12 and declined or possibly stopped thereafter (fig. 7). Throughout the entire period the variability in spacing was considerable.
3. Spatial arrangement of Purkinje cells in the adult cerebellum According to an idealized model of the adult cat cerebellum (Palkovits et al., ’71) “Purkinje cells are arranged.. . in rows deviating by 11”from the transverse axis of the folium. Neighboring Purkinje cell bodies are arranged in rhomboids, the acute angles between the sides of the rhomboids being 64.5”.. . (p. 101.’’ In the present study the orientation of Purkinje cells in the adult rat cerebellum was examined in extensive monocellular sheets in two 365-day-old animals. Such a sheet is shown in figure 8 with circles indicating the areas in which the Purkinje cell nearneighborhoods were digitized. The distribution of cells within three of these circles is shown in figure 9. The distances from the center point are between the nominal centers of cell perikarya (those plotted in fig. 7 were from edge to edge); the location of neighboring cells are with respect to the nominal long axis of the folium. In some of the “inner circles” the Purkinje cells are clumped in a more (fig. 9C) or less pronounced (fig. 9B1 hexagonal pattern but without a fixed relation to the long axis of the folium. In other circles (fig. 9A) no regular pattern can be discerned. When all the identically oriented nearneighborhoods are superimposed (fig.1OA) the hexagonal arrangement disappears. Similar results were obtained in a more extensive monocellular sheet in the second 1year-old rat (fig. 1OB). In another approach, the number of neighborhoods was progressively extended from a hexagonally arranged neighborhood of six cells to 36
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Fig. 4 Purkinje cells with long stem dendrites to which are apposed the descending axons of basket cells. Bodian’s protargol-S method; oil immersion. x 2,040.
cells. As the size of neighborhood increased the regularity of cell distribution disappeared. In order to test the idea of the existence of a limited, near-neighbor hexag;onal distribution of Purkinje cell perikarya, the superimposed 42 near -neighborhoodsmaking up the composite display in figure 10B were rearranged visually. The aim was to rotate all the near-neighborhoods, ignoring the orientation of the axis of the folium, in such a way as to maximize the
overlap of hexagonal configurations where those were discernible. As shown in figure 11, the emergence of a composite hexagonal pattern was dependent on “randomization”with respect to the orientation of the long axis of the folium. Apparently in the adult rat cerebellar cortex near-neighbor Purkinje cell perikarya may or may not be arranged hexagonally. But this geometric pattern is not fixed with respect to the long axis of the folium and seldom extends beyond the
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AGE IN DAYS Fig. 5 Growth of Purkinje cell perikarya with age. Size was determined by planimetry. Vertical lines, 1 SD; numbers refer to the sample size. The dip in the curve between 10 and 12 days reflects the transformation of the apical cone, which was included in the perikaryal size, into the stem dendrite.
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AGE IN DAYS Fig. 7 Changes in edge-to-edge separation between closest pairs of Purkinje cell perikarya as a function of age. Vertical lines, 1 SD; numbers refer to the sample size.
near-neighbor boundaries of a family of about six cells (15-30cell pairs). From this it follows that Purkinje cell perikarya in the adult rat cerebellum are not wranged in rows aligned in a fixed manner with respect to the long axis of the folium. 4. Ontogeny of the spatial arrangement of Purkinje cells The cerebellar cortex of the inKant rat is ideally suited for the examination of the spatial distribution of Purkinje cells because the orientation of bipolar cells of the external germinal layer provides a clear marker of the direction of the parallel fibers and the long axis of the folium (fig. 12). During the first few days after birth, before the Purkinje cells have fully dispersed to form a monolayer, little orderliness can be discerned in their spatial relations. Clumps of contiguous cells irregularly alternate with spaces unoccupied by perikarya (figs. 12A,B).It is not known if the contiguous cells are structurally linked to each other but desmosome-like attachment placques between Purkinje cell peri-
karya were noted during this early phase of development (Altman, '72b: p. 4021. Beginning on day 4 in some regions, and a few days thereafter in others, the irregular clumps and rows disappear and by day 8 (fig. 12C) the dispersion of Purkinje cells resembles that seen in the adult. Examples of superimposed printouts of the distribution of Purkinje cells with respect to the orientation of bipolar cells are shown in figure 13. As in the adult rat cerebellum, no regularity is discernible in the spatial arrangement of cells in extended neighborhoods. The progressive increases in cell separation (distances from center point in the graphs) reflect both a growth in perikaryal size (fig. 5 ) and an increasing edge-to-edge separation (fig. 7). With respect to the near-neighbor arrangement of Purkinje cells, the following observations were made. Not a single regularly arranged neighborhood could be found in the 2- and 3-day-old cerebella. A few instances of hexagonally arranged neighborhoods were seen in the 4- and 5-day-old cerebella; and instances of these increased from day 8 on-
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
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Fig. 9 Computer display of the spatial arrangement of Purkinje cells in three near-neighborhoods (theneighbors of 5-6 cells) in a 1-year-old rat cerebellum. A regular arrangement is not evident in A; a hexagonal pattern is suggested for 15, and is evident in C. The line shows the nominal orientation of the folium. The distances from the center point are between nominal perikaryal centers. Scale 100
m.
ward. In line with these observations, in the 2- and 3-day-old cerebella a regular pattern in the arrangement of Purkinje cells could not be obtained by rotating the near-neighbor printouts (fig. 14).A hexagonal pattern was detectable in some, though not all, of the 4- and 5-day-old cerebellar examples. From day 8 olnward a hexagonal pattern began to emerge even in instances where the sample size of neighborhoods was not large. DISCUSSION
The monocellular alignment of Purkinje cell perikarya is a widespread and stable Fig. 8 Photomicrograph of an extensive monocellular sheet of F’urkinje cells in a 1-year-old rat. The circles indicate the areas that were separately fed into the computer. These were overlapped so tlhat the “inner circles” (&. 1)used for the displays Formed approximately a nonoverlapping full sampling of all cells with complete neighborhoods. Hematoxylin-eosin. x 240.
feature of the cerebellar cortex of higher vertebrates. Our observations with the Bodian technique suggested that the arrangement may be a result of several mechanical events. Dispersion of Purkinje cells is made possible by the adequate expansion of the surface of the cerebellar cortex during early development due to the rapid proliferation of the cells of the external germinal layer and the onset of parallel fiber formation. Indeed, if the expansion of the cortical surface is prevented by low-level X-irradiation started at birth, which destroys the cells of the external germinal layer, the Purkinje cell perikarya, which grown normally in size, do not disperse (Altman and Anderson, ’72). Three observations support the idea that mechanical forces assure the alignment of Purkinje cell perikarya into a monolayer. First, this alignment is chronologically associated with the formation of a taut pile
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
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Fig. 10 Spatial distribution of Purkinje cell in extended neighborhoods in two 1-year-old rat cerebella. Superimposition of all the near-neighborhoods with the orientation of the axis of the folium held constant masks the hexagonal arrangement of some of them. Line shows nominal orientation of the folia. Scale 100 mp.
Fig. 11 The 42 near-neighborhoods shown in figure 10B were rotated visually to maximize the overlap of hexagonally arranged Purkinje cells. Reemergence of the hexagonal arrangement was coupled with randomization of lines (periphery) marking the orientation of the long axis of the folium. (Some of the orientation lines represent more than one near-neighborhood.)
of parallel fibers over the Purkinje cells and the emergence of a granular layer beneath them. Under normal conditions the pile becomes progressively thicker while the cerebellar cortex is developing. Corroborating this relationship, our obser-
vations in adult cerebella showed that the sheet of Purkinje cell somata tends to follow the contour of the pile of parallel fibers (fig. 3A). Finally, if the cerebellum is X-irradiated after the monocellular alignment of Purkinje cell bodies, such that fur-
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Fig. 12 Photomicrographs of sheets of Purkinje cells from rats aged 3 days (A), 4 days (B) and 8 days (C).The orientationof the bipolar cells of the external germinal layer (upperpart of each figure) provides a marker for the long axis of the folium. Hematoxylin-eosin. x 274.
ther acquisition of parallel fibers is prevented, the Purkinje cells become scattered again (Altman and Anderson, '73). This secondary disarrangement of Purkinje cells may be partly due to the misdirected growth of Purkinje cell stem dendrites in the absence of basket cells (Altrrian, '76a) but perhaps as important a factor is the in-
terference with the incremental growth of parallel fibers. There is a temporal correlation between the growth of Purkinje cell perikarya and the increase in the height of the molecular layer. Presumably the latter provides the opportunity for the upward growth of the Purkinje cell dendritic system, and its ex-
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Fig. 13 Spatial distribution of Purkinje cells in extended neighborhoods in cerebella of rats of the following ages: 3 days (A); 4 days (B); 5 days (C);10 days (D); 12 days (El.Superimposition was done by the computer with orientation lines held constant. The pattern for 16 days is shown in figure 1C.
pansion is coupled with the enlargement of the trophic center of the cell. In contrast, the spatial separation between Purkinje cell perikarya must be governed by different mechanisms as the increase in cell-tocell separation slows down or may come to an end by day 12, at a time when the expansion of the Purkinje cell dendritic arbor just begins. We postulate that the initial increment in the separation between Purkinje cell perikarya is due to the progressive acquisition of an envelope consisting of basket cell terminals (fig. 3B) and glial sheaths; this growth process reaches its peak by day 12 (Altman, '72b, fig. 13). Mechanical events can account not only for the alignment of Purkinje cell perikarya into a monocellular sheet but also for the arrangement of Purkinje cells within that sheet. Unlike in the cat (Palkovits et al., '711, the grouping of Purkinje cell perikarya in the adult rat is not fixed with respect to the orientation of the long axis of the folium. A certain proportion of nearneighborhood cells display a hexagonal pattern, as previously described by Smoljaninov (quoted from Palkovits et al., '71). However, if the neighborhoods are extended by the computer technique de-
scribed, the arrangement of the cells becomes random. If the axis of the folium is disregarded the near-neighborhoods can be visually rotated to produce a composite hexagonal pattern. This approach is not a stringent one. The clear hexagonal pattern shown in figure 11 was produced from an aggregate of near-neighborhoods in which only 30% could be visually identified as hexagonal (with an uncertain proportion of incomplete hexagonals present). The fact that the weak grouping of Purkinje cells is random with respect to the axis of the folium suggests that the orientation of parallel fibers, which determines the orientation of the planar arbor of Purkinje cells (Altman, '73b; '76b1, is not a positive contributing factor. Indeed, the hexagonal arrangement emerges before the onset of the dendritic development of Purkinje cells, concurrently with the alignment of Purkinje cell perikarya in a monolayer. Perinatally, when the Purkinje cell bodies are several cells deep, they are not arranged in a hexahedral pattern. When the perikarya become sandwiched between the expanding granular and molecular layers, and are also presumably compressed within the sheet, they tend to
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Fig. 14 Visual superimposition of near-neighbors of Purkinje cells from rats aged 2 days (A), 3 days (B), 4 days (C, D), 5 days (El, 8 days (Fland 16 days (GI. A hexagonal arrangement could not be obtained before day 4 and remained imprecise thereafter. Compare with the pattern obtained in an adult (fig. 11).
assume the most economic packaging pattern, i.e., a hexagonal one. The apparent enhancement of the hexagonal distribution of Purkinje cells with age may be partly accounted for by temporal differences in their growth in volume and intercellular spacing. If the spacing of Purkinje cell perikarya does not increase after day 12 but their volume does, this will lead to an increasingly tighter packing such that more and more of them are pressed into a hexagonal pattern. However, since Purkinje cell perikarya., even in the horizontal plane, are rarely perfectly spherical and they are presumably exposed to various mechanical pressures dixing development, the imperfection of their hexagonal arrangement is not surprising.
In summary, the precise alignment of Purkinje cell perikarya in a monolayer can be accounted for by mechanical forces exerted early during development by the molecular and granular layers between which the growing cell bodies become sandwiched. Presumably such an alignment parallel to the cortical surface is of functional significance as it assures that the dendrites of Purkinje cells are contacted by the horizontally distributed parallel fibers at equivalent heights. However, within this regular monocellular sheet the Purkinje cell perikarya are distributed rather irregularly, with only a proportion of them displaying a limited (near-neighborhood) hexagonal pattern. This is in contrast with the regular alignment not only of
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parallel fibers in the horizontal and longitudinal planes, but also of basket cell axons in the vertical and transverse planes, and with the planar, transverse orientation of Purkinje cell dendrites. Palkovits et al. ('71) suggested that the irregularities seen in the arrangement of Purkinje cell perikarya could be compensated for by the regular arrangement of their dendrites. The latter is developmentally assured by the presence of basket, stellate and granule cells (Altman, '76b). Perhaps the ganglionic layer represents a transitional interface between the molecular layer, all components of which display a fixed geometric organization, and the granular layer, in which a geometric pattern cannot be discerned. ACKNOWLEDGMENT
We wish to thank Sharon Evander for the histology, Janet Rybka for the computer work and Zeynep Kurgun-Chen for the photography. This research is supported by the National Institute of Mental Health and the U.S. Energy Research and Development Administration. LITERATURE CITED Addison, W. H. F. 1911 The development of the Purkinje cells and of the cortical layers in the cerebellum of the albino rat. J. Comp. Neur., 21: 459-487. Altman, J. 1969 Autoradiographic and histological studies of postnatal neurogenesis. 111. Dating the time of production and onset of differentiation of cerebellar microneurons. J. Comp. Neur., 136: 269-294. 1972a Postnatal development of the cere-
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bellar cortex in the rat. I. The external germinal layer and the transitional molecular layer. J. Comp. Neur., 145: 353-398. 1972b Postnatal development of the cerebellar cortex in the rat. 11. Phases in the maturation of Purkinje cells and of the molecular layer. J. Comp. Neur., 145: 399-464. 1972c Postnatal development of the cerebellar cortex in the rat. 111. Maturation of the components of the granular layer. J. Comp. Neur., 145: 465-514. 1973a Experimental reorganization of the cerebellar cortex. 111. Regeneration of the external germinal layer and granule cell ectopia. J. Comp. Neur., 149: 153-180. 1973b Experimental reorganization of the cerebellar cortex. IV. Parallel fiber reorientation following regeneration of the external germinal layer. J. Comp. Neur., 149: 181-192. 1975 Postnatal development of the cerebellar cortex in the rat. IV. Spatial organization of bipolar cells, parallel fibers and glial palisades. J. Comp. Neur., 163: 427-448. 1976a Experimental reorganization of the cerebellar cortex. VI. Effects of X-irradiation schedules that allow or prevent cell acquisition after basket cells are formed. J. Comp. Neur., 165: 49-64. 1976b Experimental reorganization of the cerebellar cortex. VII. Effects of late X-irradiation schedules that interfere with cell acquisition after stellate cells are formed. J. Comp. Neur., 165: 65-76. Altman, I., and W. J. Anderson 1972 Experimental reorganization of the cerebellar cortex. I. Morphological effects of elimination of all microneurons with prolonged X-irradiation started at birth. J. Comp. Neur., 146: 355-406. 1973 Experimental reorganization of the cerebellar cortex. 11. Effects of elimination of most microneurons with prolonged X-irradiation started at four days. J. Comp. Neur., 149: 123-152. Palkovits, M., P. Magyar and J. Szenthgothai 1971 Quantitative histological analysis of the cerebellar cortex in the cat. I. Number and arrangement in space of the Purkinje cells. Brain Res., 32: 1-13.
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ABSTRACT The developrnent of the spatial organization of Purkinje cell perikarya was examined in the rat cerebellum from birth to adulthood. Dispersion of the perikarya followingbirth is made possible by the rapid expansion of the cortical surface. Their subsequent regular monocellular alignment is ensured by mechanical factors, the pressure exerted from below by the expanding granular layer and the barrier formed above by the pile of parallel fibers which prevent the penetration of the bulky perikarya into the molecular layer. The perikarya remain in this position even after the slender stem dendrite pierces the molecular layer along the descending axons of basket cells. The increase in interperikaryal distance between Purkinje cells is rapid up to day 12, then declines. This is temporally associated with the growth of the basket cell plexus and glial envelope around the perikaryon. The increase in perikaryal size continues up to day 30. This may be temporally associated with the growth of the Purkinje cell dendritic arbor a s reflected by the expansion of the molecular layer up to day 30. The spatial arrangement OF Purkinje cells within the monocellular sheet was graphically displayed with computer aid. In the adult cerebellum a hexagonal arrangement could be recognized in a proportion of “near-neighborhoods,” consisting of about six Purkinje cells and their neighbors. When the neighborhoods were extended with fixed orientation with respect to the axis of the folium, the hexagonal arrangement disappeared. When orientation was ignored, the superimposed nearneighborhoods could be rotated to produce a hexagonal pattern. In the infant cerebellum the hexagonal arrangement could not be demonstrated before the alignment of Purkinje cells in a mondayer. Thereafter there appeared to be an increase with age in the proportion of hexagonally arranged near-neighborhoods. It was concluded that in the monocellular ganglionic layer Purkinje cells are not aligned in regular rows with respect to the geometrically arranged elements of the supraganglionic layer. The formation of an imprecise hexagonal pattern, like the alignment of Purkinje cells in a monolayer, was attributed to mechanical factors.
The previous paper of this series (Atman, ’75) dealt with the spatial organization of bipolar cells, parallel fibers and glial palisades in the developing suipraganglionic portion of the cerebellar cortex. This paper is concerned with some aspects of the ontogeny of the spatial organization of Purkinje cell perikarya in the ganglionic layer. These include: (a1 the mechanisms underlying the monocellular dispersion of Purkinje cells parallel to the cortical surJ.
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face; (b) changes in the size and intercellular spacing of Purkinje cells; and (c) the origins of the spatial distribution of Purkinje cells within the monocellular sheet. For the latter purpose we employed a computer-aided graphic display technique. We attempted to determine whether or not Purkinje cells in the rat cerebellum become arranged in a regular geometric pattern similar to that reported for adult cats (Palkovits et al., ’71).
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
MATERIALS AND METHODS
Tissue used In addition to the extensive collection of developmental material described in detail earlier (Altman, ’72al we made use here of some additional material. The brains of male Purdue-Wistar rats aged 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 60 and 90 days were embedded in paraffin and cut serially at 10p in the coronal, sagittal and horizontal planes. The sections were stained in a systematic sequence with hematoxylin-eosin, cresyl violet, the Weigert-Loyez and Bodian’s protargol-S methods. The cerebella of three 1-year-old rats were cut similarly in the three planes and every section was saved to allow serial reconstructions. Selection of material For the purpose of studying developmental changes in the size, intercellular spacing, and location of Purkinje cell perikarya, the cerebella were scanned for regions sectioned parallel to the monocellular layer of Purkinje cells. Sufficiently extended sheets of Purkinje cells were obtained in one or more cerebella of the following ages: 2, 3, 4, 5, 8, 10, 12, 16, 20, 25, 30, 90 and 365 days. These were photographed and printed at a constant magnification of x 576. The Purkinje cells were traced and the tracings were used for the various quantitative measurements described below. Quuntitative methods Purkinje cell perikaryal area was determined by measuring cells with nucleoli with a Keuffel and Esser compensating planimeter. “Nearest neighbor” separation was established b y measuring with a caliper the edge-to-edge distance between the closest pairs of Purkinje cells. Cells without a nucleolus (that is, those cut peripherally) and Purkinje cells outside or near the periphery of a homogeneous monocellular sheet (whose nearest neighbor may have been outside the plane of sectioning) were not included. The spatial distribution of Purkinje cell perikarya was
determined with a Hewlett-Packard digitizer in the following manner. The tracings of Purkinje cells were fixed to the digitizer surface. The orientation of the bipolar cells of the external germinal layer (the longitudinal axis of the folium) and magnification were fed into the computer. The Purkinje cells within a homogeneous sheet were subdivided into overlapping circular areas containing about 15 to 21 cells. The coordinates of each cell within the area were established by positioning the digitizer cross-hairs over the nominal center of the cell and the information was fed into the computer by pressing a button. With 15 to 21 cells entered, the “center of gravity” of the area was calculated and the distance R found from that center to the outermost cell. So all cells were within a circle of radius R with a mean separation of M = 2 R / m C e l l s closer to the boundary than M micra had incomplete neighborhoods, that is, some of the nearest neighbors might have been beyond the circle; these were rejected. The cells inside a circle of radius R had complete neighborhoods and were accepted. Each of these “inner circle” cells (ranging from 3-91 was taken in succession as the center of the display and its neighbors were plotted (figs. lA,B). Each cell typically had five to six neighbors and this “near neighbor” composite was displayed as a ring of points each at least 1-cell diameter from the center. The points within the annulus should be azimuthally uniform, or form a “cloud,” unless the frequency of neighbors is dependent on direction (as in a crystal lattice). Where directionality is present the structure of the average neighborhood emerges within the annulus as a clustering of cells into some number of discrete clumps. Finally, the near-neighborhood composites of the entire sheet of Purkinje cells could be superimposed, all identically scaled and oriented, to provide an “extended neighborhood” printout (fig.1C). RESULTS
1. Monocellular dispersion of Purkinje cells In the cerebellar cortex of the rat, the
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Fig. 1 Computer display of the spatial arrangement of Purkinje cell perikarya. In the upper portions of A and B the hexagons represent the cell bodies that were located in chosen circular areas. The Purkinje cells within the inner circle were determined to have complete neighborhoods. The spatial arrangement of all cell-pairs within the inner circle are displayed in the lower portions of A and B as dots. Their alignment is with respect to the nominal long axis of the folium, shown as a line below the displays: scale 100 mp. C. The arrangement of superimposed neighborhoods of an entire monocellular Purkinje cell sheet. Distances between Purkinje cells are from center-to-center of perikarya.
perikarya of Purkinje cells disperse to form a monocellular sheet parallel to the cortical surface within a few days after birth (Addison,'11).The dispersion is completed in the early-maturing lobules of tbe vermis by day 4, and in the late-maturing folium and tuber shortly after day 8 [Altman, '76a). This monocellular alignment is made possibZe by the expansion of the surface area of the cerebellar cortex from 'day 4 on (Altman, '691, which is associated with a high rate of cell proliferation in the superficial external germinal layer (Altman, '72a). But what makes this dispersion necessary? What mechanism assures the align-
ment of Purkinje cell perikarya into a regular monocellular sheet? The appearance, in a section stained with Bodian's technique, of a late-maturing (or underdeveloped) lobule of the vermis of an 8-day-old rat is shown in figure 2A, that of an early-maturing lobule in figure 2B. In the underdeveloped lobule the unaligned Purkinje cell perikarya are small and lack apical cones, the granule cells are closely packed in the granular layer, and the parallel fibers are still somewhat diffusely distributed in the molecular layer. In contrast, in the maturing lobule the aligned Purkinje cell perikarya have
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
Fig. 2 Cerebellar cortex in an 8-day-old rat. EG, external germinal layer; GR, granular layer; MO, molecular layer; PU, Purkinje cell layer. A. Late-maturing lobule. The primitive Purkinje cells are not yet fully aligned in a monolayer and the parallel fibers are loosely arranged. B. Early-maturing lobule. The Purkinje cells have large apical cones (arrows) abutted against a horizontally aligned pile of parallel fibers. W a n ’ s protargol-S method, x 612.
well-developed apical cones and are abutted against a sharply delineated, apparently taut line of parallel fibers; concurrently the granule cells have become somewhat scattered in the granular layer. On the basis of such observations we
propose that two opposing forces are responsible for the alignment of Purkinje cell perikarya into a monolayer: pressure exerted on the growing Purkinje cell perikarya from below by the expanding granular layer, and the barrier formed above the
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Fig. 3 Parts of the cerebellar cortex in adult rats, Bodian's protargo1-S method. A. Relationship between the monocellular row of Purkinje cells and parallel fibers. Section cut obliquely through the molecular layer. x 325.B. Section cut parallel to the sheet of Purkinje cells at the lower aspect of the perikarya. It shows the zone formed by the relative large perikaryal baskets of the basket axon terminals. x 816.
Purkinje cells by the pile of parallel fibers. chronously arriving mossy fibers (Altman, The expansion of the granular layer is '73a). The restraining force exerted by the caused not only by the progressive ac- parallel fibers may be aided by their cumulation of translocated granule cells becoming anchored to basket cells with but also by their sprouting of dendrites which they start to form synapses during (Altman, '72c) in association with syn- this period (Altman, '72b).
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The pile of parallel fibers progressively expands in the developing molecular layer and forms a permanent upper barrier to the perikarya of Purkinje cells which are apparently never pushed into the molecular layer (fig. 3A). Perhaps their displacement downward into the granular layer is prevented by the rich terminal baskets of basket cells (fig. 3B). Thus in spite of considerable changes in the foliation pattern of the cerebellar cortex during the early postnatal period, the Purkinje cell perikarya remain sandwiched between the molecular and granular layers. When the bulky apical cone of the Purkinje cell becomes transformed into the slender primary dendrite the parallel fibers can no longer bar its penetration into the molecular layer. A previous experimental study with X-irradiated cerebella (Altman, ’76a) suggested that the Purkinje cell primary dendrites pierce the molecular layer along and in interaction with the descending vertical axons of basket cells. The contiguity between Purkinje cell primary dendrites and basket cell axons is also typically seen in normal cerebella (fig. 4).
2. Growth patterns in the size and spacing of Purkinje cell perikay a In extensive monocellular sheets of Purkinje cells, planimetric areal measurements were made of perikarya which contained nucleoli that is, those that were cut transversely close to the middle of the cell body. The results (fig. 5) indicate that areal growth is rapid up to 30 days, then perikaryal growth stops. In an attempt to correlate the growth of Purkinje cell perikarya with the expansion of their dendritic arbors, we measured the width of the molecular layer as a function of age in the dorsal and caudal regions of the pyramis. This was an indirect approach, the rationale being that the width of the molecular layer will reflect the maximal height reached by Purkinje cell dendrites. (In the developing cerebellar cortex there is a formative upper strip of molecular layer which contains densely-packed parallel fibers with few or no dendritic profiles; Altman, ’72b.l The growth curve obtained from day 5 on (fig.
6) when the width of the molecular layer could be reliably measured in this material, did not exactly match the curve for the growth of Purkinje cell perikarya but agreed with it in that an asymptotic level was reached by day 30. In contrast, the increase in “nearest-neighbor” separation of Purkinje cell perikarya followed a different time course. It was rapid up to day 12 and declined or possibly stopped thereafter (fig. 7). Throughout the entire period the variability in spacing was considerable.
3. Spatial arrangement of Purkinje cells in the adult cerebellum According to an idealized model of the adult cat cerebellum (Palkovits et al., ’71) “Purkinje cells are arranged.. . in rows deviating by 11”from the transverse axis of the folium. Neighboring Purkinje cell bodies are arranged in rhomboids, the acute angles between the sides of the rhomboids being 64.5”.. . (p. 101.’’ In the present study the orientation of Purkinje cells in the adult rat cerebellum was examined in extensive monocellular sheets in two 365-day-old animals. Such a sheet is shown in figure 8 with circles indicating the areas in which the Purkinje cell nearneighborhoods were digitized. The distribution of cells within three of these circles is shown in figure 9. The distances from the center point are between the nominal centers of cell perikarya (those plotted in fig. 7 were from edge to edge); the location of neighboring cells are with respect to the nominal long axis of the folium. In some of the “inner circles” the Purkinje cells are clumped in a more (fig. 9C) or less pronounced (fig. 9B1 hexagonal pattern but without a fixed relation to the long axis of the folium. In other circles (fig. 9A) no regular pattern can be discerned. When all the identically oriented nearneighborhoods are superimposed (fig.1OA) the hexagonal arrangement disappears. Similar results were obtained in a more extensive monocellular sheet in the second 1year-old rat (fig. 1OB). In another approach, the number of neighborhoods was progressively extended from a hexagonally arranged neighborhood of six cells to 36
DEVELOPING CEREBELLUM, V
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Fig. 4 Purkinje cells with long stem dendrites to which are apposed the descending axons of basket cells. Bodian’s protargol-S method; oil immersion. x 2,040.
cells. As the size of neighborhood increased the regularity of cell distribution disappeared. In order to test the idea of the existence of a limited, near-neighbor hexag;onal distribution of Purkinje cell perikarya, the superimposed 42 near -neighborhoodsmaking up the composite display in figure 10B were rearranged visually. The aim was to rotate all the near-neighborhoods, ignoring the orientation of the axis of the folium, in such a way as to maximize the
overlap of hexagonal configurations where those were discernible. As shown in figure 11, the emergence of a composite hexagonal pattern was dependent on “randomization”with respect to the orientation of the long axis of the folium. Apparently in the adult rat cerebellar cortex near-neighbor Purkinje cell perikarya may or may not be arranged hexagonally. But this geometric pattern is not fixed with respect to the long axis of the folium and seldom extends beyond the
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
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AGE IN DAYS Fig. 5 Growth of Purkinje cell perikarya with age. Size was determined by planimetry. Vertical lines, 1 SD; numbers refer to the sample size. The dip in the curve between 10 and 12 days reflects the transformation of the apical cone, which was included in the perikaryal size, into the stem dendrite.
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Fig. 6 Width of the molecular layer in the pyramis (combined dorsal and caudal aspects) as a function of age. Vertical lines, 1 SD; sample size indicated by numbers.
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AGE IN DAYS Fig. 7 Changes in edge-to-edge separation between closest pairs of Purkinje cell perikarya as a function of age. Vertical lines, 1 SD; numbers refer to the sample size.
near-neighbor boundaries of a family of about six cells (15-30cell pairs). From this it follows that Purkinje cell perikarya in the adult rat cerebellum are not wranged in rows aligned in a fixed manner with respect to the long axis of the folium. 4. Ontogeny of the spatial arrangement of Purkinje cells The cerebellar cortex of the inKant rat is ideally suited for the examination of the spatial distribution of Purkinje cells because the orientation of bipolar cells of the external germinal layer provides a clear marker of the direction of the parallel fibers and the long axis of the folium (fig. 12). During the first few days after birth, before the Purkinje cells have fully dispersed to form a monolayer, little orderliness can be discerned in their spatial relations. Clumps of contiguous cells irregularly alternate with spaces unoccupied by perikarya (figs. 12A,B).It is not known if the contiguous cells are structurally linked to each other but desmosome-like attachment placques between Purkinje cell peri-
karya were noted during this early phase of development (Altman, '72b: p. 4021. Beginning on day 4 in some regions, and a few days thereafter in others, the irregular clumps and rows disappear and by day 8 (fig. 12C) the dispersion of Purkinje cells resembles that seen in the adult. Examples of superimposed printouts of the distribution of Purkinje cells with respect to the orientation of bipolar cells are shown in figure 13. As in the adult rat cerebellum, no regularity is discernible in the spatial arrangement of cells in extended neighborhoods. The progressive increases in cell separation (distances from center point in the graphs) reflect both a growth in perikaryal size (fig. 5 ) and an increasing edge-to-edge separation (fig. 7). With respect to the near-neighbor arrangement of Purkinje cells, the following observations were made. Not a single regularly arranged neighborhood could be found in the 2- and 3-day-old cerebella. A few instances of hexagonally arranged neighborhoods were seen in the 4- and 5-day-old cerebella; and instances of these increased from day 8 on-
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
Figure 8
DEVELOPING CEREBEUUM, V.
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Fig. 9 Computer display of the spatial arrangement of Purkinje cells in three near-neighborhoods (theneighbors of 5-6 cells) in a 1-year-old rat cerebellum. A regular arrangement is not evident in A; a hexagonal pattern is suggested for 15, and is evident in C. The line shows the nominal orientation of the folium. The distances from the center point are between nominal perikaryal centers. Scale 100
m.
ward. In line with these observations, in the 2- and 3-day-old cerebella a regular pattern in the arrangement of Purkinje cells could not be obtained by rotating the near-neighbor printouts (fig. 14).A hexagonal pattern was detectable in some, though not all, of the 4- and 5-day-old cerebellar examples. From day 8 olnward a hexagonal pattern began to emerge even in instances where the sample size of neighborhoods was not large. DISCUSSION
The monocellular alignment of Purkinje cell perikarya is a widespread and stable Fig. 8 Photomicrograph of an extensive monocellular sheet of F’urkinje cells in a 1-year-old rat. The circles indicate the areas that were separately fed into the computer. These were overlapped so tlhat the “inner circles” (&. 1)used for the displays Formed approximately a nonoverlapping full sampling of all cells with complete neighborhoods. Hematoxylin-eosin. x 240.
feature of the cerebellar cortex of higher vertebrates. Our observations with the Bodian technique suggested that the arrangement may be a result of several mechanical events. Dispersion of Purkinje cells is made possible by the adequate expansion of the surface of the cerebellar cortex during early development due to the rapid proliferation of the cells of the external germinal layer and the onset of parallel fiber formation. Indeed, if the expansion of the cortical surface is prevented by low-level X-irradiation started at birth, which destroys the cells of the external germinal layer, the Purkinje cell perikarya, which grown normally in size, do not disperse (Altman and Anderson, ’72). Three observations support the idea that mechanical forces assure the alignment of Purkinje cell perikarya into a monolayer. First, this alignment is chronologically associated with the formation of a taut pile
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JOSEPH ALTMAN AND ARTHUR T. WINFREE
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Fig. 10 Spatial distribution of Purkinje cell in extended neighborhoods in two 1-year-old rat cerebella. Superimposition of all the near-neighborhoods with the orientation of the axis of the folium held constant masks the hexagonal arrangement of some of them. Line shows nominal orientation of the folia. Scale 100 mp.
Fig. 11 The 42 near-neighborhoods shown in figure 10B were rotated visually to maximize the overlap of hexagonally arranged Purkinje cells. Reemergence of the hexagonal arrangement was coupled with randomization of lines (periphery) marking the orientation of the long axis of the folium. (Some of the orientation lines represent more than one near-neighborhood.)
of parallel fibers over the Purkinje cells and the emergence of a granular layer beneath them. Under normal conditions the pile becomes progressively thicker while the cerebellar cortex is developing. Corroborating this relationship, our obser-
vations in adult cerebella showed that the sheet of Purkinje cell somata tends to follow the contour of the pile of parallel fibers (fig. 3A). Finally, if the cerebellum is X-irradiated after the monocellular alignment of Purkinje cell bodies, such that fur-
DEVELOPING CEREBELLUM, V.
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Fig. 12 Photomicrographs of sheets of Purkinje cells from rats aged 3 days (A), 4 days (B) and 8 days (C).The orientationof the bipolar cells of the external germinal layer (upperpart of each figure) provides a marker for the long axis of the folium. Hematoxylin-eosin. x 274.
ther acquisition of parallel fibers is prevented, the Purkinje cells become scattered again (Altman and Anderson, '73). This secondary disarrangement of Purkinje cells may be partly due to the misdirected growth of Purkinje cell stem dendrites in the absence of basket cells (Altrrian, '76a) but perhaps as important a factor is the in-
terference with the incremental growth of parallel fibers. There is a temporal correlation between the growth of Purkinje cell perikarya and the increase in the height of the molecular layer. Presumably the latter provides the opportunity for the upward growth of the Purkinje cell dendritic system, and its ex-
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JOSEPH AL'I"
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Fig. 13 Spatial distribution of Purkinje cells in extended neighborhoods in cerebella of rats of the following ages: 3 days (A); 4 days (B); 5 days (C);10 days (D); 12 days (El.Superimposition was done by the computer with orientation lines held constant. The pattern for 16 days is shown in figure 1C.
pansion is coupled with the enlargement of the trophic center of the cell. In contrast, the spatial separation between Purkinje cell perikarya must be governed by different mechanisms as the increase in cell-tocell separation slows down or may come to an end by day 12, at a time when the expansion of the Purkinje cell dendritic arbor just begins. We postulate that the initial increment in the separation between Purkinje cell perikarya is due to the progressive acquisition of an envelope consisting of basket cell terminals (fig. 3B) and glial sheaths; this growth process reaches its peak by day 12 (Altman, '72b, fig. 13). Mechanical events can account not only for the alignment of Purkinje cell perikarya into a monocellular sheet but also for the arrangement of Purkinje cells within that sheet. Unlike in the cat (Palkovits et al., '711, the grouping of Purkinje cell perikarya in the adult rat is not fixed with respect to the orientation of the long axis of the folium. A certain proportion of nearneighborhood cells display a hexagonal pattern, as previously described by Smoljaninov (quoted from Palkovits et al., '71). However, if the neighborhoods are extended by the computer technique de-
scribed, the arrangement of the cells becomes random. If the axis of the folium is disregarded the near-neighborhoods can be visually rotated to produce a composite hexagonal pattern. This approach is not a stringent one. The clear hexagonal pattern shown in figure 11 was produced from an aggregate of near-neighborhoods in which only 30% could be visually identified as hexagonal (with an uncertain proportion of incomplete hexagonals present). The fact that the weak grouping of Purkinje cells is random with respect to the axis of the folium suggests that the orientation of parallel fibers, which determines the orientation of the planar arbor of Purkinje cells (Altman, '73b; '76b1, is not a positive contributing factor. Indeed, the hexagonal arrangement emerges before the onset of the dendritic development of Purkinje cells, concurrently with the alignment of Purkinje cell perikarya in a monolayer. Perinatally, when the Purkinje cell bodies are several cells deep, they are not arranged in a hexahedral pattern. When the perikarya become sandwiched between the expanding granular and molecular layers, and are also presumably compressed within the sheet, they tend to
DEVELOPING CEREBELLUM, V.
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Fig. 14 Visual superimposition of near-neighbors of Purkinje cells from rats aged 2 days (A), 3 days (B), 4 days (C, D), 5 days (El, 8 days (Fland 16 days (GI. A hexagonal arrangement could not be obtained before day 4 and remained imprecise thereafter. Compare with the pattern obtained in an adult (fig. 11).
assume the most economic packaging pattern, i.e., a hexagonal one. The apparent enhancement of the hexagonal distribution of Purkinje cells with age may be partly accounted for by temporal differences in their growth in volume and intercellular spacing. If the spacing of Purkinje cell perikarya does not increase after day 12 but their volume does, this will lead to an increasingly tighter packing such that more and more of them are pressed into a hexagonal pattern. However, since Purkinje cell perikarya., even in the horizontal plane, are rarely perfectly spherical and they are presumably exposed to various mechanical pressures dixing development, the imperfection of their hexagonal arrangement is not surprising.
In summary, the precise alignment of Purkinje cell perikarya in a monolayer can be accounted for by mechanical forces exerted early during development by the molecular and granular layers between which the growing cell bodies become sandwiched. Presumably such an alignment parallel to the cortical surface is of functional significance as it assures that the dendrites of Purkinje cells are contacted by the horizontally distributed parallel fibers at equivalent heights. However, within this regular monocellular sheet the Purkinje cell perikarya are distributed rather irregularly, with only a proportion of them displaying a limited (near-neighborhood) hexagonal pattern. This is in contrast with the regular alignment not only of
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JOSEPH ALTMAN AND ARTHUR T. W N F R E E
parallel fibers in the horizontal and longitudinal planes, but also of basket cell axons in the vertical and transverse planes, and with the planar, transverse orientation of Purkinje cell dendrites. Palkovits et al. ('71) suggested that the irregularities seen in the arrangement of Purkinje cell perikarya could be compensated for by the regular arrangement of their dendrites. The latter is developmentally assured by the presence of basket, stellate and granule cells (Altman, '76b). Perhaps the ganglionic layer represents a transitional interface between the molecular layer, all components of which display a fixed geometric organization, and the granular layer, in which a geometric pattern cannot be discerned. ACKNOWLEDGMENT
We wish to thank Sharon Evander for the histology, Janet Rybka for the computer work and Zeynep Kurgun-Chen for the photography. This research is supported by the National Institute of Mental Health and the U.S. Energy Research and Development Administration. LITERATURE CITED Addison, W. H. F. 1911 The development of the Purkinje cells and of the cortical layers in the cerebellum of the albino rat. J. Comp. Neur., 21: 459-487. Altman, J. 1969 Autoradiographic and histological studies of postnatal neurogenesis. 111. Dating the time of production and onset of differentiation of cerebellar microneurons. J. Comp. Neur., 136: 269-294. 1972a Postnatal development of the cere-
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bellar cortex in the rat. I. The external germinal layer and the transitional molecular layer. J. Comp. Neur., 145: 353-398. 1972b Postnatal development of the cerebellar cortex in the rat. 11. Phases in the maturation of Purkinje cells and of the molecular layer. J. Comp. Neur., 145: 399-464. 1972c Postnatal development of the cerebellar cortex in the rat. 111. Maturation of the components of the granular layer. J. Comp. Neur., 145: 465-514. 1973a Experimental reorganization of the cerebellar cortex. 111. Regeneration of the external germinal layer and granule cell ectopia. J. Comp. Neur., 149: 153-180. 1973b Experimental reorganization of the cerebellar cortex. IV. Parallel fiber reorientation following regeneration of the external germinal layer. J. Comp. Neur., 149: 181-192. 1975 Postnatal development of the cerebellar cortex in the rat. IV. Spatial organization of bipolar cells, parallel fibers and glial palisades. J. Comp. Neur., 163: 427-448. 1976a Experimental reorganization of the cerebellar cortex. VI. Effects of X-irradiation schedules that allow or prevent cell acquisition after basket cells are formed. J. Comp. Neur., 165: 49-64. 1976b Experimental reorganization of the cerebellar cortex. VII. Effects of late X-irradiation schedules that interfere with cell acquisition after stellate cells are formed. J. Comp. Neur., 165: 65-76. Altman, I., and W. J. Anderson 1972 Experimental reorganization of the cerebellar cortex. I. Morphological effects of elimination of all microneurons with prolonged X-irradiation started at birth. J. Comp. Neur., 146: 355-406. 1973 Experimental reorganization of the cerebellar cortex. 11. Effects of elimination of most microneurons with prolonged X-irradiation started at four days. J. Comp. Neur., 149: 123-152. Palkovits, M., P. Magyar and J. Szenthgothai 1971 Quantitative histological analysis of the cerebellar cortex in the cat. I. Number and arrangement in space of the Purkinje cells. Brain Res., 32: 1-13.
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