quantitative golgi study of the rat cerebellar molecular layer interneurons using principal...

Quantitative Golgi Study of the RatCerebellar Molecular Layer Interneurons

Using Principal Component Analysis

FAHAD SULTAN* AND JAMES M. BOWER

Division of Biology 216-76, California Institute of Technology, Pasadena, California 91125

ABSTRACTIn this study, we applied for the first time a multivariate analysis to describe the anatomy

of cerebellar molecular layer interneurons. Forty variables extending over a variety ofmorphological features (geometrical, topological, and metrical) were obtained from a three-dimensional reconstruction of 26 rat rapid Golgi-stained neurons. The subsequent principalcomponent analysis showed that the first principal component was strongly correlated withvariables related to the depth of each cell’s soma in the molecular layer. The second principalcomponent was strongly correlated with parameters describing axonal morphology. Finally,an analysis of the distribution of these anatomical features suggested that these cells cannotbe classified into distinct groups but, instead, represent one continuously varying population.Thus, the classical division of molecular layer neurons into deep basket cells and superficialstellate cells is not supported by our analysis. These results have important implicationsfor the development of the cerebellar cortex as well as for the expected patterns of Purkinjecell activity following activation of the granule cell layer. J. Comp. Neurol. 393:353–373,1998. r 1998 Wiley-Liss, Inc.

Indexing terms: neuron; inhibition; development; morphology; taxonomy; basket

The cerebellar cortex may be the best anatomicallycharacterized region of the mammalian brain. The basicorganization of its circuitry was first described almost 100years ago (Ramon y Cajal, 1911), and numerous subse-quent investigators have added substantially to that de-scription (for reviews, see Ito, 1984; Braitenberg et al.,1997). In fact, arguably, the anatomical description of thecerebellum has been quantified to a level not seen in anyother vertebrate brain structure. This is especially true forthe organization of excitatory parallel fiber inputs onPurkinje cells (Braitenberg and Atwood, 1958; Palkovits etal., 1971b; Braendgrad and Gundersen, 1986; Harvey andNapper, 1988; Napper and Harvey, 1988a,b). In this case,several authors have even gone so far as to determinewhether the anatomical relationships described wouldactually fit within the space available in the cerebellarcortex (Palkovits et al., 1971a,c; Harvey and Napper,1991). To our knowledge, this is the only example in whichthis has been attempted in mammalian neuroanatomy.

Although a great deal of information is available concern-ing the anatomy of the excitatory cerebellar cortical cir-cuits, far less information is available concerning thecortical inhibitory molecular interneurons. Nevertheless,recent cell counting indicate that there are 6.9 3 106

inhibitory molecular interneurons in the rat cerebellum(Korbo et al., 1993) and up to 1.5 3 109 in the human

cerebellum (Andersen et al., 1992). In the latter case, thismeans that there may be 50 times more inhibitory interneu-rons than cerebellar Purkinje cells. Furthermore, ourrecent detailed realistic models of Purkinje cells havesuggested that molecular layer inhibitory neurons mayplay a much larger role than was suspected previously indetermining Purkinje cell output (De Schutter and Bower,1994a,b; Jaeger et al., 1997). The necessary next step ofincluding these neurons in our network cortical models(Santamaria and Bower, 1997), however, will require farmore detailed information on their structure than iscurrently available.

For each of these reasons, we have recently undertakenseveral anatomical studies to quantify the morphology ofthe cerebellar inhibitory molecular interneurons and theirconnections (Sultan and Bower, 1996; Sultan et al., 1995).In this paper, we report the results of a quantitative Golgistudy of the morphology of these cells. We have used

Grant sponsor: Human Frontiers Science Program.*Correspondence to: Dr. Fahad Sultan, Sektion Visuelle Sensomotorik,

Neurolog. Universitatsklinik, Auf der Morgenstelle 15, 72076 Tubingen,Germany. E-mail: [email protected]

Received 13 June 1997; Revised 20 November 1997; Accepted 25 Novem-ber 1997

THE JOURNAL OF COMPARATIVE NEUROLOGY 393:353–373 (1998)

r 1998 WILEY-LISS, INC.

light-level reconstruction techniques to obtain 40 differentdescriptors of cellular morphology, looking for relation-ships in these data with principal component analysis(PCA). The results not only provide essential informationfor our modeling investigations but also suggest thatmolecular interneurons represent a single population ofcells with smoothly varying anatomical features, depend-ing on the depth of their somata. This description iscounter to the prevalent idea that these cells are groupedinto two distinctive cells types (cf. Palkovits et al., 1971c;Palay and Chan-Palay, 1974), but it is consistent with theoriginal interpretation of Ramon y Cajal (1911) and themore recent suggestion of Rakic (1972) that these neuronsrepresent one cell class. This interpretation has importantimplications for theories of cerebellar development as wellas for the expected spatial distribution of inhibitory activ-ity following activation of the granule cell layer. Ourresults have been reported previously in abstract form(Sultan and Bower, 1996).

MATERIALS AND METHODS

Histological procedures

These experiments are based on standard rapid-Golgiimpregnation procedures already applied to the cerebel-lum (Palay and Chan-Palay, 1974). Twelve 3-month-oldfemale Sprague-Dawley rats were anaesthetized with 0.7cc Pentobarbital (50 mg/ml) and perfused intracardiallywith 0.1 M phosphate buffer (PB) solution, pH 7.4, followedby a fixative solution of 1% paraformaldehyde and 1.5%glutaraldehyde. The cerebellum was then removed andput in a solution of 2.4% potassium dichromate and 0.2%osmium for 3 days in order to stain individual cells. After 2days in 0.75% silver nitrate, the cerebella were cut to100-µm frozen sections with a microtome. Sections weresubsequently dehydrated and embedded in standard histo-logical mounting media (Permount, Fisher Scientific, NH).

Data acquisition

All of the sections obtained were screened for fullyimpregnated, well-isolated neurons with cell bodies in themolecular layer. The sample of analyzed cells includedneurons with somata at all molecular layer depths sampledfrom the entire cerebellar vermis (Fig. 1).

The complete stained processes of 26 neurons weretraced with a Zeiss axiophot microscope (Thornwood, NY;1003 oil-immersion objective), a camera lucida apparatus,and the semiautomatic Eutectic Neuron Tracing System(ENTS; version 4.1. Raleigh, NC). In addition to digitizing

Fig. 1. Drawing of the rat cerebellar vermis with the molecularlayer outlined as seen in a midsagittal section. The location of all 26neurons analyzed in this study are indicated in Arabic numbers. Alsoshown are Larsell’s folia I–X (Larsell, 1952).

Abbreviations

al axonal lengthaxbp number of axonal branch pointbc number basket collateralsdl dendritic lengthdth dendritic thicknessENTS eutectic neuron tracing systemfloc folial locationhco orientation of cell in respect to cerebellar rostral or caudal

endhfo orientation of cell in respect to folium part, i.e., sulcus or

crownHj horizontal curves ‘‘parallel’’ to pia or Purkinje cell layermaxHaxd maximal horizontal axonal-dendritic extensionmaxHax maximal horizontal axonal extensionmaxHd maximal horizontal dendritic extensionmaxrad maximal radial distance of dendritic tips to somamaxVax maximal vertical axonal bouton extensionmaxVd maximal vertical dendritic extensionmHax average horizontal distance of axonal boutons from somamHax1,

mHax2 mean of axonal bouton distribution in horizontal axis of thefirst and second Gaussian

mHd average horizontal distance of dendritic points from somamlh molecular layer heightmVax mean location of axonal boutons in the vertical axismVd average vertical distance of dendritic points from somamxsh distance of maximum of the sholl distribution from soma

mZax mean location of axonal boutons in z-axismZd mean location of dendrite in z-axisndst number of dendritic stemsndbp number of dendritic branch pointsNi normals to either pia or Purkinje cell layernv number of varicosities, i.e., axonal boutonsP nth order polynomial fitted to piaPC principal componentPCA principal component analysisPCL nth order polynomial fitted to Purkinje cell layerrat ratio of first to second Gaussian of axonal boutons distribu-

tionsdHax1,

sdHax2 standard deviation of axonal boutons distribution in hori-zontal axis of the first and second Gaussian

sdHd standard deviation of dendritic distribution in horizontalaxis

sdVax standard deviation of axonal bouton distribution in verticalaxis

sdVd standard deviation of dendritic distribution in vertical axissdZax standard deviation of axonal boutons distribution in z-axissdZd standard deviation of dendritic distribution in z-axissa soma areashi soma location in vertical axissksh skewness of sholl distributionss soma shapez-axis long folial axis

354 F. SULTAN AND J.M. BOWER

the morphology of the dendrite, soma (outline), and axon,we also marked the location of the axonal fiber swellingsand measured dendritic branch thickness. The dendriticthickness was obtained by comparing the dendrite with anoptically controlled circle of adjustable size.

To determine accurately the location of each cell’s somain the molecular layer, we marked the adjacent pialsurface (P) and lower Purkinje cell layer (PCL). This alsoallowed us to reconstruct accurately the curvature of thecerebellar cortex in the region of each stained cell. We alsonoted the location of the cell with respect to the vermallobes I–X (after Larsell, 1952); the folium’s sulcus, crown,or intermediate region (floc); and orientation of its axonwith respect to the adjacent sulcus or crown (hfo) and withrespect to the rostral or caudal end (hco) of the cerebellum.Finally, the number of axonal collaterals (bc) makingpinceau formations (baskets) on Purkinje cell somata wascarefully quantified for each reconstructed neuron. Onebasket collateral was denoted for every collateral thatoriginated from the main axon and participated in thepinceau.

Spatial reconstruction and normalization

Neuron reconstruction. The reconstruction proce-dure used here involved digitizing the location of thedendrite with the ENTS at irregular intervals (bifurcationpoints or points where the dendrite tapers or changes itscourse) and then reconstructing the full extent of thedendrite by extrapolation from these digitized locations.This is a standard procedure that speeds up the digitiza-tion process considerably, because it is not necessary to traceeach segment (Capowski, 1989). However, this means thatonly some points along the dendrite are used for thereconstruction, requiring that the points lying in betweenmust be inserted artificially in order to ensure a uniformrepresentation of the dendrite (Hellwig, 1995). To do this, aprogram was written in Mathematica (version 2.2.3 run ona Sun Sparc Station 2) to interpolate between neighboringand topologically connected points with equal spacing andat an average interval of 1 µm (see Fig. 2A). Theserelationships are described by the following expressions:

Di 5 Î(xi 2 xi11)2 1 (yi 2 yi11)2 1 (zi 2 zi11)2,

tij 5 10,1

Di,

2

Di, . . . ,

Di

Di2 Di [ N,

ddij 5 ENTSi 1 tij(ENTSi11 2 ENTSi),

where Di is the distance (rounded to an integer in µm)between the two adjacent and topologically connectedENTS points, i and i11, and ddij are the newly obtainedpoints.

Reconstruction rotation. To compare the morpholo-gies of different reconstructed cells, it was necessary torotate their representations into a common coordinatesystem. It is well known that the dendrites of the molecu-lar layer interneurons are near planar, similar to thePurkinje cell dendrites, and that the dendritic plane isperpendicular to the parallel fibers (Ramon y Cajal, 1911;Braitenberg and Atwood, 1958; Rakic, 1972; Bishop, 1993).This feature was utilized to rotate these neurons into acoordinate system that conformed with the axes of thecerebellar cortex and in which the xy-plane would corre-

spond to the plane transverse to the folial long axis, andthe z-axis would correspond to the folial long axis. Practi-cally the whole neuron was rotated, such that a randomlychosen subset of dendritic points had minimal variance intheir z-axis coordinates.

Unfolding the cerebellar cortex. The well-known,convoluted, folding morphology of the cerebellar cortexmeans that distances between the axon and the dendrite ofthe same molecular layer interneuron cannot be obtainedby calculating the Euclidean distances. This problem isfamiliar from cartography, in which surfaces of sphereshave to be projected onto a plane for comparison (Fahleand Palm, 1983). However, unlike the general carto-graphic situation, in the cerebellum, the folding does notoccur in a uniform and rigid way. For example, whereascerebellar folding occurs strictly in a direction perpendicu-lar to the parallel fibers (Braitenberg and Atwood, 1958;Braitenberg, 1991; Sultan and Braitenberg, 1993), thespecific folding at the crowns of the folia differ from foliumto folium, inasmuch as they can fold anywhere between45° and 180 degrees (Fig. 1), whereas the cerebellar cortexgenerally folds at 180° in the deep sulci.

To unfold the cerebellar cortex, two second-order polyn-oms were fitted to the previously digitized points delineat-ing the P and the PCL. Care was taken to confirm that thefitting functions followed the original P and PCL course.Then, normals (N) were calculated with respect to theconcave of the two curves at the points Pi(xi, yi), such thatthe area Ai enclosed by Ni, Ni11, the P- and PCL-fittingcurves, equaled 6,000 µm2. The set of Ni was obtained asfollows:

Ni 521

df(xi)/dxx 1 (df(xi)/dx)xi 1 yi,

where f is either P or PCL, depending on which was convexwith respect to the molecular layer.

After obtaining a starting point P1 for N1, the subse-quent Ni were derived by solving

with Ai equaling an integer multiple of 6,000 (Fig. 2B).In a second step, the part of each Ni delineated by the

intersection with P and the PCL was divided into six equalparts, and a second-order polynom (Hj) was fitted (least-squares fit) through the points that demarcated correspond-ing parts on the different Ni (Fig. 2C). In this new

Ai 5

ea

bfP dx 2 e

a

bNidx 1 e

b

cN1dx 2 e

b

cNidx

1 ec

dN1dxe

c

dfPC dx for b , c

ea

cfP dx 2 e

a

cNidx 1 e

c

bfP dx 2 e

c

bfPC dx

1 eb

dN1dx 2 e

b

dPC dx for a , c # b

ec

aNidx 2 e

c

afPC dx 1 e

a

bfP dx 2 e

a

bfPC dx

1 eb

dN1dx 2 e

b

dPC dx for c # a,

5

TAXONOMY OF MOLECULAR INTERNEURONS 355

coordinate system, the Hj lines stand for locations at asimilar relative molecular layer height, and the Ni linesdepict locations that are in a similar vertical position of themolecular layer. Distances across the Hj lines will bedenoted as vertical distances, distances along the Hj lines,i.e., across the Ni lines, will be denoted as horizontaldistances (again, all calculations were performed by usingMathematica on a Sun workstation).

Data extraction

Metric parameters. The following parameters wereobtained with the software provided by the ENTS: Den-dritic length (dl), axonal length (al), and number of varicosi-ties per axon (nv). The largest boundary of the soma (sa)was brought into focus and digitized. The area enclosedwas calculated by the ENTS (Capowski, 1983, 1989). Ameasure of the shape of the soma (ss) was obtained bydividing the largest diameter through the average diam-

eter (2 [area/Pi]1/2). The average dendritic thickness (dth)was obtained by averaging the thickness of the points thatwere added according to the interpolation procedure (Fig.2A, points ddij), assuming that the dendritic thickness atthe interpolated point’s position equaled the measureddendritic thickness at the more proximal point (Fig. 2A,point ENTSi).

The distance between the radial farthest dendritic tipsand the axon initial segment was calculated for all cells(maxrad). In addition, the distance from the soma of themaximum (mxsh) of the Sholl-sphere distribution of thedendrite (Sholl, 1948) was also computed.

Spatial extent of dendrites and axons in z-axis.

After rotation, the z-axis values of the soma, dendrite, andaxonal fiber swellings were obtained, the values of the den-dritic points and the axonal fiber swellings were subtractedfrom those of the soma, and the mean and standard deviation(sd) were calculated. The values obtained were abbrevi-

Fig. 2. Diagrams illustrating some of the reconstruction andquantification methods used in this study. A: Illustration of themethod that was applied to ensure a homogenous representation ofdendritic points. Here, we interspersed dendritic points (ddij) thatwere not digitized with the Eutectic Neuron Tracing System (ENTS)by interpolating from the points (ENTSi) that were digitized with theENTS (bifurcation points, points where the dendrites tapered orchanged their course). Basically, the distance between two adjacentENTSi points was calculated, and new points (ddij) were interspersedwith 1 µm distance (dij). B,C: Illustrations of methods used to calculatethe spatial distribution of the dendrites and axons in the vertical aswell as the horizontal cerebellar axis. In B, normals were calculated(starting with an arbitrary chosen normal N1) such that the areaenclosed by the two normals (N1 and Ni) and the curves fitted to the pia(P), and Purkinje cell layer (PCL) equaled the i-1 multiple of 6,000µm2. This yielded spatially equivalent horizontal intervals. Subse-quently, the part of the normals Ni delineated by the P and PCL weredivided further into six intervals (C), and curves Hj were fitted to thecorresponding points on the different normals yielding equally spacedvertical intervals. For other abbreviations, see list.


ated as follows: The mean dendritic z-axis values (mZd),the standard deviation of the dendritic z-axis value (sdZd),the mean axonal z-axis values (mZax), and the standarddeviation of the axonal z-axis values (sdZax).

Spatial extent of dendrites and axons in the horizon-

tal and vertical axes. To obtain the probability densityfunction (PDF) for the spatial extent of the dendrites andaxons in the vertical and horizontal axes, the followingprocedure was followed: For every cell, a set of Ni and Hjwas calculated, and the number of digitized dendriticpoints and axonal fiber swellings was computed for eachinterval (Ni, Ni11) and (Hj, Hj11). The interval in which theaxonal initial segment was located was also computed andwas taken as soma location in the vertical (shi) andhorizontal axes. The widths of the Ni intervals was ob-tained by dividing the area Ai through the midintervalheight. The widths of the Hi intervals were calculated bydividing the Ni part delineated through the intersectionwith the P and PCL, i.e., corresponding to the molecularvertical height (mlh), through six (Fig. 2C) and taking theaverage for all Ni.

The average horizontal distance from the soma/axoninitial segment was calculated as:

mH 5 oi

xiPDF[xi],

with PDF denoting the PDF for either the dendritic or theaxonal structure, as described above. This was done forseveral of the parameters studied here: mVd, mHd, mVax,mHax, [mean (m), vertical (V), horizontal (H), dendritic(d), and vertical axonal (ax) distances). The standarddeviation was obtained from a Gaussian function fitted tothe respective cumulative density function: sdVd, sdHdand sdVax. In addition, we also calculated the maximalextent for the dendrites (maxHd, maxVd) and axons(maxHax, maxVax) in the vertical and horizontal axesseparately and for the dendrite and axon combined for thehorizontal axis (maxHaxd).

Gauss curve fitting for the axonal horizontal distri-

bution. To compare the axonal horizontal distributionfunctions of the cells, we parameterized the distributionsby fitting them with a double Gaussian of the form

CDF 51

2a(1 1 exp(x2mHax1/sdHaxiÎ2))

1(a 2 1)

2a(1 1 exp(x2mHax2/sdHax2Î2)),

and obtained the parameters mHax1, sdHax1, mHax2,sdHax2, and 1/(a-1), which denote the mean and standarddeviation of the first Gaussian, the mean and standarddeviation of the second Gaussian, and the ratio of the twoGaussian (rat), respectively. The parameters were ob-tained by using the iterative Levenberg-Marquardt method(Press et al., 1992), which continuously shifts searchbetween a steepest descent and a quadratic minimization.Care was taken to chose iterative starting points thatyielded good fits, and the search outcome was alwaysvisualized and checked. To facilitate comparison betweencells, the iteration starting points for mHax1 and mHax2were chosen, such that the result would yield mHax1smaller than mHax2. The x2 value for every fit wasdenoted, and statistical significance was tested.

Topological parameters. Several topological param-eters describing the dendritic and axonal tree were alsoobtained: the number of dendritic stems (ndst) and thetotal number of dendritic (ndbp) and axonal (axbp) branchpoints. Axonal branching points that occurred in thebasket formation were not included. In addition, theskewness (sksh) of the Sholl-sphere distribution of thedendrite (Sholl, 1948) was also computed.

Data analysis

Unidimensional and bidimensional analysis. Mostof the variables and their distributions were characterizedby their mean and their standard deviation by usingMathematica. x2 Tests were applied for fitting and testingthe cumulative distribution functions. In addition, correla-tion coefficients were calculated and displayed for thoseparameters that showed high loadings with the primaryprincipal components.

Multidimensional analysis. To look for associationsin the data, we applied PCA to the 40 parameters. PCA is amultivariate descriptive method that has the aim of reduc-ing the high dimensionality of an observed set of param-eters to a smaller number of ‘‘unobserved’’ factors, orcomponents, thus, making the original set of data moreinterpretable. In addition, the loadings of the parameterswith the factors are also obtained, and this often allows theinterpretation of the factors in relation to the variables aswell as grouping of individuals in the data set. PCA hasbeen applied previously in several other neuroanatomicalstudies (Harpering et al., 1985; Pearson et al., 1985; Yelniket al., 1987, 1991; Fenelon et al., 1994; see Discussion).

Space does not allow a complete description of PCAtechniques. The unfamiliar reader is referred to Yelnik etal. (1991) and Johnson and Wichern (1992) for backgroundinformation. However, in general, PCA is performed bytransforming the parameters into an orthogonal set byobtaining the eigenvectors and eigenvalues of the param-eters’ correlation or, preferably, the covariance matrix.Because the parameter values differed largely in thecurrent data set (e.g., soma shape varied in a tenthfraction, whereas dendritic length differed in hundreds ofµm), it was necessary to refer to the correlation-matrixapproach (Basilevsky, 1994; Johnson and Wichern, 1992).In addition, we performed a varimax rotation of theprincipal plane both to maximize the high loadings of bothcomponents and to minimize their low loadings (Johnsonand Wichern, 1992). We also tested the matrix for equalcorrelation and found that the correlations observed dif-fered significantly from random. Again, all calculationswere performed in Mathematica.

RESULTS

Reconstructed neurons

Reconstructions of a total of 26 molecular layer neuronsare analyzed in this report. Figure 1 shows the location ofeach of the reconstructed cells with respect to lobules I–X(taken from Larsell, 1952). Nine cells were located in thelobus anterior, with the remaining cells in the lobusposterior. Lobules V and VIII had a maximum of fiveneurons each. With respect to the different subregions ofindividual folia, 20 neurons were located intermediately,and the remaining cells were divided equally between thecrown and the sulcus of the folia. Our analysis showed noconsistent differences between cells found in different foliaor in different parts of the folia. With respect to the vertical


position in the molecular layer itself, the majority of thecells analyzed (n 5 14) were located in the middle molecu-lar layer, ten cells were digitized from the lower molecularlayer, and two cells were from the upper molecular layer.The position of the neuron within the molecular layer, asdescribed below, had a substantial effect on cellular mor-phology.

General cell morphology

Figure 3 shows the complete morphology of all of the 26neurons reconstructed in this study. Figure 3 also showsthe curves that were fitted to the P and the PCL and thenormalization lines demarcating the horizontal and verti-cal intervals within the molecular layer. These chartsindicate that the cells were located in folia with varyingcurvatures and that their somata were located at variousdepths in the molecular layer. It can also be seen that themorphology and the extent of axonal and dendritic branch-ing varied considerably.

The overall morphology of the cells found here is similarto previous descriptions (Ramon y Cajal, 1911; Rakic,1972; Palay and Chan-Palay, 1974; Braitenberg, 1991).The somata had round-to-ovoid shapes, and, in the currentdata, these cells had soma profile areas ranging from 50µm2 to 110 µm2, with an overall average of 69 µm2

(sd 5 15). The shape of the soma profile, computed as theratio of the maximal soma diameter to the average somaratio, ranged between a near spherical 1.1 and an elliptical1.9, with an average of 1.35 (sd 5 0.18).

Each of these neurons, as in previous descriptions, hadbetween two and four main dendrites emerging from thesoma. The dendrites generally had a stellar shape, oftenradiating toward the pia and, less frequently, descendingtoward the Purkinje cell layer, leading to an asymmetricform. The dendrites were generally slender, with fewvaricosities and a moderate number of bifurcations, gener-ally tapering into very thin final processes. Quantitatively,in our data, the average tree consisted of 3.1 dendriticstems (sd 5 1.1) and included 79 branching points (sd 5 40).The average length of the dendrites was 1,189 µm(sd 5 366), with an average thickness of 0.55 µm (sd 50.15). Because the proximal point’s thickness was used asthe interpolated point’s thickness (see Materials and Meth-ods), the average dendritic thickness is generally overesti-mated by 5%.

At the terminal end of the dendritic branches, some ofthe fine processes could resemble spines (Fig. 4F), but,generally, they showed a large variety in their length(ranging anywhere between 0.5 µm and several µm; seeFigs. 4F, 5A). In addition, only a few had the typicalspine-head enlargement. Because of this ambiguity, nofurther attempt was made to distinguish these processesinto spines. The probability distribution function of thedendritic intersections with circles at radians of different

A

Fig. 3. A–E: Traces representing all 26 reconstructed and rotatedneurons are displayed. The largest singular dot depicts soma location,and the smaller dots show axonal swelling locations. The dendrite canbe seen as a fine, continuous line with multiple bifurcations. Thenormalization lines (see Fig. 2B and C) obtained for each neuron arealso shown. The normals were calculated to the top ‘‘horizontal’’ curve.In the group of horizontal curves, the outer curve that is drawn with aheavier line indicates the Purkinje cell layer; the other line indicatesthe pia. Distances are in µm.


distances from the soma (Sholl-sphere diagram) had anaverage skewness of 0.47 (sd 5 0.4), and the location of themaximum, on average, was at 33 µm from the soma (sd 5 28).

Each cell had one main axon with an average recon-structed length of 1,393 µm (sd 5 451) and with, onaverage, 2.6 axonal basket collaterals (sd 5 2.6). Of the 26interneurons, nine did not participate in the pinceau at all,and the others showed a large range (one to seven collater-als). The main axon, as described previously (Palay andChan-Palay, 1974), could either maintain a distinct horizon-tal course (i.e., parallel to the Purkinje cell layer andperpendicular to the parallel fibers; see Fig. 6) or bifurcaterepeatedly in a more haphazard fashion (Fig. 4c). Themain axon generally gave off branches shortly after emerg-

ing from the soma and often continued for a distancethereafter. Emitted collaterals either coursed transversely,ascending or descending to possibly participate in theformation of the basket and the pinceau. These axons, onaverage, had 149 boutons (sd 5 61), yielding an axonalbouton density of 0.11 bouton per µm (sd 5 0.045).

Spatial orientation of dendrites and axons

The spatial organization of the dendrites and axons withrespect to the geometry of cerebellar cortex, in general, isalso similar to previous descriptions (Palay and Chan-Palay, 1974), with the long axis of both the dendrites andthe axon extended perpendicular to the orientation of the

Figure 3 (Continued)

BTAXONOMY OF MOLECULAR INTERNEURONS 359


C


DTAXONOMY OF MOLECULAR INTERNEURONS 361

parallel fiber system. In the current study, this wasquantified by dividing the molecular layer horizontallythrough the Ni lines (Fig. 2B) into 7–67 intervals(mean 5 23; sd 5 11) at an average distance of 29 µm per

interval. The vertical level of the molecular layer wassegmented by using the Hj curves (see Fig. 2C) into sixequal parts, with the P as the upper border and the PCL asthe lower border. The intervals were valued 1 through 6,


E362 F. SULTAN AND J.M. BOWER

Fig. 4. Displayed here and in Figures 5 and 6 are photomicro-graphs of several of the neurons that were reconstructed in this study.A: A typical basket cell. The reconstruction of this cell can be seen inFigure 3A (second trace from the top). The axon of the cell is delineatedwith black arrowheads, the arrow indicates the axon initial segment,and the white arrowheads indicate the dendrite of the cell. B: Thedistal part of an axon with several basket collaterals (asterisks)emerging to participate in basket formations (arrows). C: A neuronlocated in the middle part of the molecular layer (its reconstruction is

displayed in the left middle row in Fig. 3E). White and blackarrowheads depict the dendrites and the axon of the cell, respectively.D: The axon of the neuron that is reconstructed in Figure 3A (bottom).Arrowheads point indicate axonal boutons. E,F: The same neuron atdifferent enlargements. The white and black arrowheads in E depictdendrites and the axon, and the arrowheads in F indicate differentdendritic appendages. Pcl, Purkinje cell layer; GR, granular cell layer.Scale bars 5 50 µm in A,B,E, 20 µm in C, 5 µm in D, 10 µm in F.

with 1 nearest to the P and 6 nearest to the PCL. Theaverage interval height was 34 µm.

The distribution of the digitized dendritic points and ofthe axonal boutons along the z-axis, i.e., the long axis ofthe folium, was characterized by the standard deviation ofeach cell. On average, the cells had an sdZd of 4 µm(sd 5 0.9) for the dendrite and 12.4 µm (sd 5 3.6) for theaxonal boutons of all cells.

The distribution of the neuronal process along thevertical axis (orthogonal to the parallel fibers and normalto the P) was also described through their standarddeviation and, on average, was one molecular layer inter-val (sd 5 0.29) for the dendrites and 0.76 (sd 5 0.23) for theaxonal boutons, with average molecular layer height inter-vals of 34 µm. The axonal boutons were located on average0.04 molecular layer interval (sd 5 0.61) below the cell

Fig. 5. A,B: Two neurons that were found in the deeper parts of themolecular layer are shown that correspond to the reconstructions seenin Figure 3C (bottom left) and Figure 3E (top left), respectively. Theblack arrowheads indicate the dendrite in A the axon in B. The arrowin A indicates the axon initial segment, and the asterisks correspond tothe cell soma in A and to the basket collaterals in B. White arrowheads

in A correspond to the ascending part of a granule cell axon, and it canbe seen that there is very good alignment between this indicator of thevertical axis and the normals seen at the corresponding position in thereconstruction. Gr, granular cell layer; Ml, molecular layer; Pcl,Purkinje cell layer. Scale bars 5 50 µm.

Fig. 6. Montage of an interneuron found in the middle molecular layer with the correspondingreconstruction seen in Figure 3D (middle left). The asterisk indicates a basket collateral, the arrowindicates the soma, and the arrowheads indicate the axon. Ml, molecular layer; Pcl, Purkinje cell layer.Scale bar 5 50 µm.


Fig. 7. In A–C, different steps are illustrated to show how D wasobtained. A: One of the cells shown in a fashion similar to that inFigure 3, with the dendritic and axonal fields outlined. B: Display ofthe two cumulative density functions (CDFs) that were obtained forthe same cell (dendrite in black and axon in gray). The abscissa showsthe distances between the intervals along the horizontal axis in µm(coinciding with the abscissa in A). The ordinate corresponds to thevalues of the cumulative distribution functions. In addition, theinterval of soma location is marked by an arrow. C: Two transforma-tions have been applied to the CDF for didactic purposes: First, thetwo CDFs have been shifted to the left, so that the location of the soma

interval now coincides with 0, and, second, the dendritic CDF curvehas been subtracted from 1. D: The three-dimensional graph showingthe results obtained for all 26 cells. The single neurons are stacked inthe z-axis depending on the horizontal extent of their axons: Cells witha larger horizontal axonal spread are displayed toward the foregroundof the graph. The graph shows a continuous transition of axonaldistribution functions from those with more local (close to the den-drites) to more nonlocal distributions. In contrast, the dendriticdistribution functions show a more uniform range. The even spread ofaxonal cumulative distribution functions in our sample indicates nogrouping with respect to the horizontal axonal extent.

soma, whereas the dendritic points were located on aver-age 0.76 (sd 5 1) above the cell soma.

With regard to the horizontal axis (orthogonal to parallelfibers and orthogonal to the vertical axis), the averagelocation of the mean dendritic points was at a distance of213 µm (sd of the means 5 24) from the soma, whereasaxonal boutons were at 91 µm (sd of the means 5 67). Thecells were orientated such that the mean dendritic valuewas smaller than that of the axonal bouton’s value. Themaximal dendroaxoboutonic reach of the neurons, onaverage, was 345 µm (sd 5 149). The maximal dendriticspread was 174 µm (sd 5 66), and the axonal spread was266 µm (sd 5 123).

The cumulative distribution function of the axonal bou-tons with regard to their horizontal distance from thesoma is shown in gray in Figure 7D for all cells. Thedistribution functions were fitted with a double Gaussian,with the x2 values #0.02. The ratio between the twoGaussians and the mean and standard deviation of the twoGaussians were obtained to characterize the cumulativedistribution function. These parameters are shown inTable 1.

Quantitative multivariate morphology

After describing the average morphological characteris-tics of these neurons, next, we were interested in determin-ing whether there was any clustering of morphologicalfeatures in the data set. In other words, we wanted todetermine whether any of the 40 quantified variables werecorrelated. To quantify this comparison. we have usedPCA. The results are shown in Figures 8 and 9. Figure 8shows how the different parameters cluster in the princi-pal plane, i.e., with respect to the first and second principalcomponents. This graph indicates that the strongest vari-ables along the first principal component are the meanvertical location of axonal boutons (mVax), the number ofbasket collaterals (bc), the soma location (shi), and themaximal dendritic tip distance from soma (maxrad). Bytaking 0.5 as a threshold value, two groups of variables canbe isolated. Further inspection has shown that one isassociated with the depth of cells in the molecular layer,and the other is associated with the extent of the axonalconnections.

Horizontal extent of the axon. Considering the group-ing associated with the second principal component first,Table 2 shows that the grouped parameters are relatedmainly to the horizontal extent of the axons. These param-eters include the maximal horizontal span of the axonalboutons distribution (maxHax), the mean horizontal loca-tion of the axonal boutons (mHax), the mean horizontallocation of the second (distal) component of the axonalbouton distribution (mHax2), the total horizontal dendroax-onic span of the neuron (maxHaxd), the standard deviationof the horizontal second axonal component (sdhax2), andthe axonal length (al). In this group, the largest correla-tions were observed between maxHax, mHax, and mHax2,

simply showing that the horizontal axonal bouton distribu-tion is distinguished largely by its distal extent. However,the data also suggest that there is a relationship betweenthe spatial extent of the axon and the dendrite, implyingthat the extent of influence of these neurons is related tothe area over which they collect synaptic input.

Variation of cell properties with somatic depth. Fig-ure 8 shows that the strongest correlation in the data isassociated with parameters reflecting the depth of thesoma in the molecular layer. Table 3 shows the specificcorrelations, several of which were completely expected(see Discussion). For example, the mean vertical locationof axonal boutons (mVax), the mean vertical location of thedendrite (mVd), the vertical standard deviation of thedendritic distribution (sdVd), and the maximal spread ofthe dendrite in the vertical axis (maxVd) are all highlycorrelated. Several other parameters are somewhat lessobvious, however. For example, the analysis reveals arelationship between depth in the molecular layer and thesomatic profile area (sa), the maximal dendritic distancefrom soma to tip (maxrad), the radial location of themaximum in the sholl distribution (mxsh), overall den-dritic thickness (dth), the maximal horizontal spread ofdendrite (maxHd), and the number of basket collaterals(bc).

Taxonomy of molecular interneurons

Taken together, this analysis shows that, in general,cells deeper in the molecular layer tend to be larger in sizethan superficial cells. In addition, deeper cells provideaxon collaterals that make ‘‘basket’’ endings on Purkinjecell somata, whereas the most superficial cells tend not todo so. In this sense, our data would appear to support thelargely accepted division of molecular layer interneuronsinto superficially positioned stellate cells and more deeplypositioned basket cells (Palkovits et al., 1971c; Ito, 1984).However, since the time of Ramon y Cajal (1911), someauthors (including Ramon y Cajal himself) have arguedthat these are not two separate cell types at all but,instead, one cell class with continuously varying morpho-logical features (Scheibel and Scheibel, 1954; Fox et al.,1967; Rakic, 1972). Others have differentiated this type ofneuron into as many as five different cell classes (Eccles etal., 1967; Palay and Chan-Palay, 1974).

Although each of the studies referenced above used adifferent set of criteria for cell classification (see Table 4),the quantitative data collected in this study provide uswith the opportunity to consider cell type classificationfrom the point of view of a much wider range of morphologi-cal features. Figure 9 shows the results of a multivariateanalysis applied to these data. In this diagram, theparameters associated with individual neurons are plottedin relation to the first two principal components. Inaddition, the figure highlights the two parameters that arethe most associated with the basket cell/stellate cell distinc-tion; the number of basket cell collaterals (Fig. 9, Arabicnumbers) and depth of the cell in the molecular layer (Fig.9, shown by the size of the number). Examination of thisfigure shows that, in fact, these features are representedcontinuously. In other words, the data support the viewthat the molecular layer interneurons represent one popu-lation of cells, which vary continuously in their morphol-ogy depending on the depth of the soma in the molecularlayer. This has important implications for both the develop-ment and the function of cerebellar cortex (see Discussion).

TABLE 1. Parameters of the Double-Gaussian Fits to the HorizontalAxonal Distributions

Ratio Gauss 1to Gauss 2

Mean ofGauss 1

(µm)

Mean ofGauss 2

(µm)

Standarddeviationof Gauss 1

(µm)

Standarddeviationof Gauss 2

(µm)

2.4 (S.D. 5 1.3) 29 (S.D. 5 35) 153 (S.D. 5 86) 22 (S.D. 5 14) 59 (S.D. 5 34)


Estimating the probability of interneuronto Purkinje cell contacts

As with any neuron, the spatial relationship betweenthe inputs and outputs of the molecular layer interneuronsis likely to be very important for their contribution tocerebellar function. In the particular case of the cerebel-lum, the highly regular path of the parallel fibers meansthat anatomical data can be used to quantify these relation-ships to an unusual extent (Braitenberg and Atwood,1958). For example, in principle, given the known course ofthe parallel fibers, a comparison between the spread of thePurkinje cell dendrite and the dendritic and axonal spreadof the inhibitory interneurons should make it possible toinfer how many Purkinje cells will be excited and inhibitedby a particular parallel fiber input.

To estimate this spatial property, we used our interneu-ron reconstruction data to determine the extent to whichinhibitory neurons could make synaptic contacts withPurkinje cells, assuming that the two cells could share theinput from a single parallel fiber. Furthermore, we as-sumed a 250 µm width in the Purkinje cell dendrite

(Harvey and Napper, 1988) and, for each reconstructedcell, then calculated the degree of dendritic (Purkinje cell)and axonal (interneuron) overlap (Fig. 10A). The numbersof axonal boutons were normalized by dividing the numberof measured boutons by the number of Purkinje cells foundin the area spanned by the axon of each interneuron(Purkinje cell density 5 1,000/mm2; Harvey and Napper,1988). The average number of contacts was 8.7.

The results are shown in Figure 10B. Given the morphol-ogy of the interneurons, we would expect that the majority(75%) of parallel fiber inputs are capable of evoking acombined excitation and inhibition in a given Purkinjecell; nevertheless, a large proportion (25%) is seen forinputs that evoke only inhibition. This calculation alsoshows that half of the excitatory inputs could evoke zero tofive inhibitory synapses, whereas the other half couldevoke five to 25 inhibitory synapses.

DISCUSSION

The main objective of this study was to acquire thedetailed quantitative anatomy necessary to construct net-

Fig. 8. The principal plane displayed with all 40 parameters. It canbe seen that the parameters that correlate highly with the firstprincipal component (PC) are the vertical location of the axonalboutons (mVax), the number of basket collaterals (bc), the location ofthe soma (shi), and the maximal dendritic tip distance from soma(maxrad). By taking 0.5 as a threshold value, two groups of param-

eters can be isolated: One correlates highly with the first principalcomponent, i.e., the vertical component, and the other correlateshighly with the second principal component, i.e., the horizontalcomponent. For further details, see Results and Discussion. For otherabbreviations, see list.


work models of the cerebellar microcircuit (cf. Santamariaand Bower, 1997). The data we have acquired, however,also suggest that several revisions are necessary in thebasic description and classification of the inhibitory inter-neurons of the cerebellar molecular layer. These changes,in turn, have relevance to both the development of thecerebellum and its functional organization.

Comparison with othermorphometric studies

Our basic morphological description of the molecularlayer interneurons (see Results) is similar to numerousprevious reports (for review, see Mugnaini, 1972). How-ever, our specific objective was to provide a more quantita-tive morphometric description of the sort necessary toconstruct realistic network models (Bower and Koch,1992). Although most previous descriptions of these neu-rons in the literature have been qualitative, there areseveral recent studies that obtained data similar to ourown. For example, Leranth and Hamori (1981) measuredthe length of one basket cells dendrite in a rat andobtained a value of 1,580 µm, which is 33% higher andslightly more than one standard deviation above theaverage value obtained here (1,189 µm). The averagethickness of the dendrite obtained in that study (0.75 µm)was also somewhat higher than our average (0.55 µm).Cells located more deeply in the molecular layer, as we

have demonstrated in this study, have larger and thickerdendrites. Unfortunately, Leranth and Hamori did notindicate the depths at which their samples were taken.

In a more recent study, Pouzat and Kondo (1996) stainedstellate cells (cells located in the upper molecular layer)intracellularly with neurobiotin in rat cerebellar slices andmeasured an average axonal length of 970 µm for theirlong-range stellate cells (i.e., cells with horizontally fur-ther reaching axons) and 520 µm and 930 µm for twoshort-range stellate cells. These values are lower than theaverage lengths we obtained (1,393 µm) possibly due to theyounger animals used in their study. The same study alsomeasured the average axonal bouton density and obtainedessentially the same value of synapse per µm for cellssuperficial in the molecular layer (0.15 synapses per µm).Cells lower in the molecular layer, as pointed out inResults, also have a lower density of synaptic boutons(0.08 synapses per µm vs. 0.14 for the more superficialcells). Finally, Bishop (1993) and King et al. (1993) stainedbasket cells in the cat intracellularly with horseradishperoxidase and found a number of descending basketcollaterals (5.9) in their sample comparable to what wefound for cells in the lower one-third of the molecular layerin rats (5.5).

Taxonomy of the molecular interneurons

Perhaps one of the more important consequences of ourquantification of cellular morphology concerns the classifi-cation of the molecular layer interneurons. Previous au-thors, as mentioned above, have varied considerably inhow they classified these cells. In the first, careful descrip-tion of these cells, Ramon y Cajal (1911) proposed that theyactually constituted one cell type with features that variedsystematically with depth. A similar conclusion has beendrawn by several authors since then (Scheibel and Schei-bel, 1954; Fox et al., 1967; Rakic, 1972). Others, however,have suggested that these cells should be grouped into asmany as five distinct cell classes (Eccles et al., 1967; Palayand Chan-Palay, 1974). Nevertheless, the standard text-book description still divides molecular layer interneuronsinto only two types, the deep basket cells and the superfi-cial stellate cells (Ito, 1984). One important point concernsthe representative validity of our sample, because we hadonly a few cells from the upper one-third of the molecularlayer. But, because most studies conducted so far have notreported any systematic differences between cells fromdifferent layers of the upper half of the molecular layer(Ramon y Cajal, 1911; Scheibel and Scheibel, 1954; Rakic,1972; Palay and Chan-Palay, 1974; Pouzat and Kondo1996), we are encouraged to regard our sample as beingrepresentative of the whole molecular layer.

It has been clear for some time that cell classificationschemes should be based on a ‘‘polythetic’’ approach rely-

TABLE 2. Parameters With High Correlation With the SecondPrincipal Component

Measure1 al mHax2 sdHax2 mHax maxHax maxHad

al 1.mHax2 0.44 1.sdHax2 0.18 0.61 1.mHax 0.34 0.9 0.6 1.maxHax 0.46 0.86 0.74 0.81 1.maxHad 0.57 0.83 0.59 0.84 0.83 1.Second PC loading 0.63 0.85 0.71 0.82 0.9 0.8

1For abbreviations, see list.

Fig. 9. The principal plane, i.e., the plane spanned by the first andsecond principal components, is plotted in this figure. The twocomponents accounted for 34% of the total variance of our 40 param-eters. The data points seen here are the 26 individual neurons plottedwith respect to their scores with the two components. In addition, twoparameters that had strong correlations with the first principalcomponent are displayed. The first variable is shown by the values ofthe numerals and corresponds to the number of basket collaterals inthe individual cell. The second variable corresponds to the heightlocation of the cell body in the molecular layer, with large numeralsindicating a location nearer to the Purkinje cell layer. Conversely, thecorrelation between the depth position of the neuron and the numberof basket collaterals is evident. In addition, the data do not show anyobvious grouping with respect to the number of basket collaterals,indicating that basket cells do not form a distinct group.


ing on the evaluation of many different parameters (Tyner,1975; Rowe and Stone, 1977). Although there are someexamples of neurons that distinguish themselves fromothers due to one single feature, e.g., cerebellar granulecells with their parallel fibers, more often, additional

features must be evaluated to form a classification scheme(Harpering et al., 1985; Yelnik et al., 1987, 1991; Fenelonet al., 1994). So far, all of the classification schemes for theneurons considered in this study have used a single or onlya few morphological criteria for classification. The stan-

TABLE 3. Parameters with High Correlation to the First Principal Component

Measure1 sa bc shi sdVd mVd mVax dth mxsh maxHd maxVd maxrad

sa 1bc 0.5 1.shi 0.45 0.7 1.sdVd 0.25 0.45 0.63 1.mVd 0.3 0.42 0.82 0.37 1.mVax 0.51 0.67 0.85 0.67 0.71 1.dth 0.53 0.6 0.58 0.21 0.47 0.45 1.mxsh 0.56 0.63 0.43 0.20 0.08 0.47 0.49 1.maxHd 0.3 0.53 0.53 0.52 0.39 0.48 0.5 0.4 1.maxVd 0.4 0.23 0.51 0.74 0.45 0.68 0.17 0.22 0.26 1.maxrad 0.53 0.54 0.54 0.71 0.23 0.63 0.35 0.47 0.63 0.51 1.First PC loading 0.72 0.8 0.79 0.62 0.53 0.82 0.68 0.67 0.59 0.55 0.74

1For abbreviations, see list.

TABLE 4. Different Previous Classification Schemes

Ramon yCajal (1911)

Scheibel andScheibel (1954)

Fox et al.(1967)

Eccles et al.(1967)*

Palkovits et al.(1971) *

Rakic(1972)

Palay andChan-Palay

(1974)*

Deep stellate cells orbasket cells

Long axon stellate cells Basket cells Basket cells a Basket cells Deep stellate cells Basket cells

Basket cells bSuperficial stellate cells

with varitiesShort axon stellate cells Short axon stellate cells Stellate cells a1 Stellate cells Superficial stellate cells Superficial short axon

stellate cellsLong axon stellate cells Stellate cells a2 Deep long axon stellate

cellsStellate cells b Deep stellate cells

Vertical cell location1

Axonal range andmorphology1

Axonal range1 Baskets1

Axonal range1Baskets1


Axonal morphology andrange1

Soma shape1 Vertical cell location1 Baskets1


Axonal morphology andrange1

*Schemes with several classes of interneurons.1Parameters used for classification.

Fig. 10. Illustration of the method used to estimate the expectedamount of overlap between excitation and inhibition reaching aneighboring Purkinje cell and a molecular Interneuron. The twocurves in A correspond to the dendritic (dashed) and axonal cumula-tive distribution functions (the same as in Fig. 7B). Basically, for everydendritic interval di Purkinje cell soma locations were calculated, such

that the Purkinje cell dendrite, Dij, still overlapped with the interval,di. In a second step, the amount of interneuron axonal overlap with Pijwas determined. The results are displayed in B, with the x-axisshowing the number of axonal interneuron boutons that we wouldexpect on a single Purkinje cell.


dard division of these cells into basket and stellate cells,for example, depends principally on two features, theirdifferent depths (basket cells are deeper than stellate cells)and, importantly, whether their axons contribute basketendings onto the somata of nearby Purkinje cells (Eccles etal., 1967; Palay and Chan-Palay, 1974).

In the current case, our multivariate analysis of cellularmorphology suggests that there is a significant overlap inthe anatomical features of these 26 reconstructed cells. Inparticular, we have found that the location of a cell’s somain the molecular layer appears to be a significant determi-nate of morphological properties, as suggested by Ramon yCajal (1911). Consistent with previous classificationschemes (Eccles et al., 1967; Palay and Chan-Palay, 1974),the particular feature that is most striking is the depen-dence on depth for the generation of the basket-typeending (Fig. 8). However, our analysis shows that thisproperty actually varies smoothly with depth (Fig. 9). Ourdata, therefore, support Ramon y Cajal’s original specula-tion that these neurons represent one cell type. Accord-ingly, we support the proposal by Rakic (1972) that they bereferred to as molecular layer interneurons rather thanbasket and stellate cells.

Phylogenetic considerations

Although taxonomists are well known for somewhatarduous arguments over classification schemes, it is clearthat correct classification can reveal important biologicalinformation for our understanding of cerebellar corticalevolution. For example, it has been suggested that onlystellate cells exist in lower vertebrates and that typicalbasket (pinceau)-type contacts exist only in birds andmammals (Ariens Kappers et al., 1936; Llinas and Hill-man, 1969). If we are correct that stellate and basket cellsdo form a single cell class, then the development of basketcontacts could have emerged from prebasket-like stellatecells. Interestingly, such cells have been described previ-ously in the chameleon (Ramon y Cajal, 1911). Becausethese reptiles also have large cerebella (Altman and Bayer,1996), the gradual emergence of basket cells could berelated to the overall increase in neuron number.

Developmental implications:Vertical organization

Correct classification can also have important implica-tions for theories of neuronal development. In the particu-lar case of these interneurons, Rakic (1972) linked ahypothesis for the development of the molecular layer tothe idea that these cells represent one cell type withdepth-dependent differences in cellular morphology. It hasbeen shown that the vertical location of the cell within themolecular layer corresponds to the time the neuron wasgenerated, with older cells located in deeper parts of themolecular layer (Altman, 1969). Rakic proposed that differ-ences in the level of maturity at different depths lead tosubstantially different developmental environments forthese neurons that are reflected directly in their morphol-ogy.

Several aspects of the data obtained in this study agreewell with the developmental model proposed by Rakic(1972). In particular, the dendritic parameters correlatedwith the first principal component all appear to reflect thepredicted behavior. Rakic proposed that neuronal growthin the molecular layer interneurons should differentiallyoccur toward the least developed regions of the molecular

layer. Given the inward to outward developmental patternof this layer (Ramon y Cajal, 1911), this means thatdendritic processes should be oriented toward the outsideof the layer. Thus, for example, Rakic proposed that thedendritic span of the cell in the vertical direction should becorrelated with the vertical location of the cell, with cellsdeeper in the molecular layer having dendrites that spanlarger parts of the molecular depth (see Fig. 3 in Rakic,1972). We have found that the standard deviation of thedendritic point distribution in the vertical direction (sdVd)and the maximal vertical dendritic span (maxVd) arecorrelated to the cell’s location in the molecular depth. Thesame point can be made for the maximal radial distancefrom the soma to the dendritic endings (maxrad). At thesame time, several other positive correlations we foundwith the first principal component would also appear to beconsistent with the Rakic model, although no explicitpredictions were made previously. These include the aver-age neuron’s dendritic points location in the verticaldirection (mVd), the distance from the soma of the maxi-mum of the dendritic sholl distribution (mxsh), and themaximal horizontal spread of the dendrite (maxHd).

The model proposed by Rakic (1972) also does not makeany explicit predictions concerning the growth pattern ofthe axons. Nevertheless, some of the axonal parametersobtained in this study, number of basket collaterals (bc)and mean vertical location of the axonal boutons (mVax)correlate strongly with the first principal component.Interestingly, our results further indicate that, althoughthey show a vertical organization, in fact, these axons donot grow preferentially into the upper regions of thecortex. Instead, they show a slight tendency to be directedtoward the deeper regions. This could simply reflect thefact that the interneuron’s axonal targets, the Purkinje celldendrites, would still be located in deeper parts of themolecular layer at the time the interneuron axons begin toemerge. If this is the case, then we should also expect theinterneuron synapse to be located on the more proximalpart of the Purkinje cell dendrites (Bower, 1997), which isthe region of the dendrite that develops first (Altman,1972).

Developmental implications:Horizontal organization

The principle feature identified by the second principalcomponent is the horizontal spread of the axon. Interest-ingly, some of these features have been used previously tosupport a division of stellate cells into two classes, longand short range (Scheibel and Scheibel, 1954; Fox et al.,1967; Eccles et al., 1967; Palay and Clan-Palay, 1974).Based on our morphometric analysis, we do not believethat this division is appropriate either. Instead, the recon-structed cells seem to vary smoothly with respect to thehorizontal length of their axons.

With respect to developmental models, Rakic (1972) didnot consider axonal organization in his predictions. Ourdata support the contention that the vertical and horizon-tal organization of these cells may be under differentdevelopmental control, in that, by definition, the twoprincipal components in our analysis are orthogonal to oneanother. Based on previous studies in numerous othersystems, it seems quite likely that more complicatedmechanisms than those described by Rakic for the den-drite govern axonal contact and outgrowth (Dalva et al.,1994; O’Leary, 1994). In this regard, previous authors have


considered the possible mechanisms of control of axonaloutgrowth in these neurons. For example, Manova et al.(1992) suggested that the growth pattern of the interneu-rons axon could be influenced by their chemotactile affinityfor Purkinje cells, because a simultaneous expression ofthe c-kit receptor in the interneurons and its ligand, KL, inPurkinje cells was found. One could then further speculatethat the axonal growth pattern is determined by differentcytochemicals expressed by different Purkinje cells; and,although some cytochemical markers do delineate differ-ent Purkinje cells in the anterior-posterior axis of thecerebellum (equivalent to our horizontal axis), neverthe-less all of them seem to delineate parts of the cerebellum(for review, see Herrup and Kuemerle, 1997) that are muchlarger than the axonal extent of the interneurons. Oneother important observation also does not favor the Pur-kinje cells as the organizing element for the interneuronsaxonal outgrowth, because the loss of Purkinje cells inPurkinje cell degeneration mutants does not seem to affectthe survival or integrity of the molecular interneurons(Landis and Mullen, 1978).

Another general axonal guidance mechanism, activity-dependent plasticity (Constantine-Paton and Law, 1978;Shatz, 1996), has not yet been studied or suggested for themolecular interneurons. Possibly, this mechanism couldemerge as a network property (Sanes and Takacs, 1993),i.e., through synaptic inhibitory interneuron-to-interneu-ron interaction or/and through the spatial characteristicsof fractured granular cell excitatory inputs (Shambes etal., 1978).

Functional considerations

Beyond these speculations on the development of cellu-lar morphology, our results are likely to have severalpractical implications for cerebellar physiology and theory.The cerebellum, as we have pointed out previously (Bower,1997), is unusual in the number of functional theories thatderive from the anatomical organization of its circuits (cf.Braitenberg and Atwood, 1958; Marr, 1969; Albus, 1971;Eccles, 1973; Bower, 1997). For this reason, the functionalsignificance of the molecular interneurons has long been ofinterest, particularly because these cells synapse directlyon the Purkinje cells, which, themselves, are the solecerebellar cortex output (Ito, 1984). However, most consid-erations of the functional consequences of the molecularlayer interneurons have previously been discussed in thecontext of the excitatory inputs on Purkinje cells from theparallel fibers and, as we have pointed out, were based onnonquantitative neuroanatomy. In this section, we willconsider several of those speculations in light of ourcurrent data.

Spatial interactions: Beam hypothesis

The unusual geometry and the vast amount of conver-gence between the parallel fibers and the Purkinje cells isat the center of most theoretical models of cerebellarfunction (cf. Braitenberg and Atwood, 1958; Marr, 1969;Albus, 1971; Eccles, 1973; Karachot et al., 1994). For manyyears, it has been assumed by anatomists, physiologists,and theorists that, given this pattern, any activation of thegranule cell layer would set up an excitatory ‘‘beam’’ ofactivated Purkinje cells up and down the folium. Szen-tagothai (1963) was the first to propose that, in addition,the orthogonal spread of the axons of the inhibitory

interneurons should result in two zones of inhibitionflanking the excitatory beam.

The physiological evidence for the beam hypothesisusing natural (not electrical) stimuli, as we have pointedout in several recent publications (Bower, 1997), is ambigu-ous (Bell and Grimm, 1969; Eccles et al., 1972; Bower andWoolston, 1983). Instead of a beam of activated Purkinjecells, tactile peripheral stimuli, for example, only activatesPurkinje cells overlying tactilely activated regions of thegranule cell layer (Bower and Woolston, 1983). We haveproposed that this activation is due to synapses associatedwith the ascending branch synapses (Bower, 1997), al-though it has also been suggested that the presence ofbeams requires the correct sequence of activation of thegranule cell layer (Braitenberg and Atwood, 1958; Heck,1993; Braitenberg et al., 1997).

Regardless of the presence or absence of a beam ofparallel fiber activation, physiological data suggest thatthe pattern of Purkinje cell inhibition following naturalperipheral stimuli is also different from that proposed inthe original beam hypothesis (Bower and Woolston, 1983).In particular, Purkinje cells overlying the activated gran-ule cell layer often respond with both excitation andinhibition (Bower and Woolston, 1983), and the activatedPurkinje cell cluster is surrounded on all sides by inhibitedPurkinje cells. The original beam hypothesis, in contrast,proposed that inhibition should only parasagittally flankactivated cells, producing a broad ‘‘inhibitory beam’’ ofinhibited Purkinje cells.

We believe that the data presented in this paper shedlight on several of these spatial features of the Purkinjecell layer responses to granule cell layer activation. First,in the physiological data, inhibition usually follows excita-tion by a few milliseconds, presumably due to the presenceof an additional synaptic delay in the circuit (the granulecell synapse onto the inhibitory interneuron). Second, wehave shown a substantial spatial overlap between thesecell’s axons and dendrites in half of the cells that werereconstructed (Fig. 10B). This overlap is likely to beresponsible for the ability of granule cell layer inputs toboth activate and inhibit the same Purkinje cells, althoughit should be noted that some recorded cells do show onlyexcitatory responses (see Fig. 2 in Bower and Woolston,1983). This result suggests that there may be additionalcomplexity in the pattern of inhibition set up by granulecell layer activation.

The physiological data also demonstrates a more re-stricted spread of inhibition from activated regions of thegranule cell layer than was previously suggested as part ofthe beam hypothesis (Eccles et al., 1967). Although ourdemonstration that molecular layer interneurons axonsextend farther than their dendrites supports some lateralspread of inhibition, the spread of these axons could notsupport the extensive inhibition originally proposed forthe beam hypothesis, although the scale of the originalbeams was based on data in cats. In rats, the average266-µm spread of the axon is quite consistent with theseveral hundred µm spread of inhibition seen in thephysiological data (Bower and Woolston, 1983).

Finally, the published physiological results also demon-strate that inhibition extends to Purkinje cells medial andlateral from an activated region of the granule cell layer(i.e., along the course of the parallel fibers). This was not afeature of the original beam hypothesis. The physiologicalresults also suggest that this ‘‘along the parallel fibers’’


inhibition can interact with excitatory synaptic inputs,suppressing Purkinje cell responses (Fig. 10 in Bower andWoolston, 1983). The current morphological data do notexplain this result, because we have confirmed previousreports that both the dendrite and the axons of theinhibitory interneurons extend orthogonally from the par-allel fibers. Simulations currently underway are intendedto determine whether low firing thresholds for inhibitoryinterneurons to parallel fibers could account for thismedial-lateral spread (Santamaria and Bower, 1997). Therealism of these simulations will be greatly enhanced bythe data provided in this paper. Others interested inconstructing simulations by using the morphologies cancontact the GENESIS database project.

ACKNOWLEDGMENTS

We thank the Max-Planck Gesellschaft and Dr. AlmutSchuz for allowing us to use the Eutectic Neuron TracingSystem.

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quantitative golgi study of the rat cerebellar molecular layer interneurons using principal...

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