pellionisz a, szentàgothai j. brain res. 1974 mar 15;68(1 ......dynamic single unit simulation of a...

Dynamic single unit simulation of a realistic cerebellar network model. II. Purkinje cell activity within the basic circuit and modified by inhibitory systems. Pellionisz A, Szentàgothai J. Brain Res. 1974 Mar 15;68(1):19-40. PMID: 4470450 See Pubmed Reference at the link http://www.ncbi.nlm.nih.gov/pubmed/4470450 and searchable full .pdf file below

Brain Research, 68 (1974) 19-40 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

19

DYNAMIC SINGLE UNIT SIMULATION OF A REALISTIC CEREBELLAR NETWORK MODEL. II. PURKINJE CELL ACTIVITY WITHIN THE BASIC CIRCUIT AND MODIFIED BY INHIBITORY SYSTEMS

ANDR/~S PELLIONISZ AND J/~NOS SZENT/~GOTHAI

1st Department of Anatomy, Semmelweis University Medical School, Budapest (Hungary)

(Accepted August 31st, 1973)

SUMMARY

In continuation of earlier computer simulation studies 15 of the feedback inhibition exercised by the Golgi cells of the cerebellum, an attempt is made at modeling the behavior of Purkinje and basket cells under somewhat more complex functional circumstances. The simulation study is based on a realistic network model (with respect to numerical and metrical parameters, and consisting of more than 3 × 104 units) of the cat cerebellar cortex, derived from a recent quantitative histological and stereological analysis 9-12. As an input two identical pairs of foci of incoming mossy fiber activity are applied, separated from one another both spatially and temporally. The simulation results showed that the assumption of a rigidly preaddressed wiring in the parallel fiber-Purkinje cell synaptic system (i.e. that parallel fibers would systematically select for contact Purkinje cells standing in register) would hardly be realistic because such a solution would offer no advantage whatever over a randomly connected synaptic system. The results would favor the contention that dendritic geometry of the Purkinje cells has a crucial significance in the sense of the concepts developed by W. Rall. The simulation gives some important hints for the ways in which the specific inhibitory interneuron systems (Golgi and basket cells) add refinement to the operations of the network, particularly in securing integration of the influences of parallel fibers thrown into action by mossy input to spatially and temporally separated foci, especially at the level of Purkinje cells positioned in interfocal areas. Reducing the length of the parallel fibers to one-half of what was suggested by the stereological studies causes a serious breakdown of interfocal neighborhood interactions.

INTRODUCTION

Earlier simulation of the Golgi-inhibition of the mossy fiber-granule cell relay is

20 A. PELLIONISZ AND J. SZENT~.GOTHAI

suggested a leveling effect upon the granule cell field even if the mossy fiber input were well focused. Such an effect, however, could be interpreteJ only with the Pur- kinje cell activity in mind, since these cells are the sole output elements of the cerebellar cortex. This paper, therefore, extends the preceding computer simulation to the investigation of Purkinje cell excitation patterns. This step, although increasing considerably the complexity of the simulation, enables us to gain some insight into a variety of questions raised by recent morphological and physiological findings.

(1) Regular versus random distribution of parallel fiber-PurkhTje cell synapses This problem was raised by quantitative morphological studies 9,11 according

to which synaptic contacts between parallel fibers and Purkinje cells are established only by one-fifth of the parallel fiber population crossing the dendritic arbor. Due to a staggered arrangement of the Purkinje cells it is only every fifth to sixth Purkinje dendritic tree that stands in register. This intriguing coincidence raises the question, whether (a) the synapses of each parallel fiber could be distributed regularly in order to contact systematically all the Purkinje cells standing with their dendritic trees approximately in register; or, conversely, whether (b) the synapses of each parallel fiber are spaced at random, albeit with allover frequency leading to the mentioned statistical result.

The possible functional consequences of these two propositions could be tested by computer simulation.

(2) The significance of parallel fiber length Since the conclusion reached in stereological studies al, that the parallel fibers

of the cat are only 2 mm long, met with some doubts among neurophysiologists, it seems worth-while to have a second look on the significance of parallel fiber length with the aid of the simulation model. Recent preliminary studies have shown that virtual immobilization of the limbs soon after birth 14 causes in the kitten a significant decrease in the length of the parallel fibers (to 50 %, with a corresponding increase in density of the synapses) in the limb projection areas of the cerebellar cortex. This observation would lend itself as a convenient and not unrealistic model for analysing the functional consequences of the reduction of the length of parallel fibers to one- half and to compare the function of such a handicapped network with those of the network deduced from the stereological studies.

(3) The significance of dendritic geometry The role of dendritic geometry in the summation process on single cells was

pointed out first theoreticallyl6,17. Now, physiological observations 7 of dendritic spikes also suggest quite strongly a kind of separated integration in the main dendritic branches, that seems to be far from a simple algebraic summation over the whole dendritic tree. Llinfis ~, while emphasizing the significance of the temporospatial parallel fiber input to one single Purkinje cell, distinguished two theoretical integration mechanisms: (i) a vertical i.e. algebraic summation in one of the principal den-

SIMULATION OF A CEREBELLAR NETWORK MODEL, II 21

drites, generating a dendritic spike, and (ii) a transverse integration in which summation would occur between the several principal dendrites of the same cell.

With regard to these considerations it was challenging to study in this computer simulation the possible differences between two alternative concepts of the Purkinje cell: (a) as a simple device for algebraic summation of all parallel fiber activities, without considering dendritic geometry, and (b) as a dendritic model compartmental- ized into 4 principal dendrites upon which the parallel fibers act.

(4) The individual character of Purkinje cell activity The earlier hypotheses on the operational features of the cerebellar neuron

network18,19 envisaged collective activities of larger assemblies of Purkinje cells, arranged in longitudinal rows, rather than individual funtions. Subsequent physiological studies 4 appeared to support this view, however, as is now quite obvious, largely in consequence of the local stimulation of larger populations of parallel fibers. A very preliminary and rather static computer simulation lz revealed that in the case of a random mossy input the network model of Szenthgothai would yield individual Purkinje cell activities in addition to the assumed longitudinal rows. However, already at this very early stage an attempt was made to visualize by paper and pencil extrapolation the possible interactions between partially overlapping foci of activity (Eccles et al. 4, Fig. 123B; Eccles z, Fig. 4-13). Direct electrophysiological evidence for highly individual behavior of closely neighboring Purkinje cells was observed independently by Eccles et al. 3 and Llinhs et al. 8. This individuality of the Purkinje cells might be due either to a priori differences in Purkinje cells, or alterna- tively - - as a much more parsimonious explanation - - to differences in the positions of the several Purkinje cells in the actual field of stimulation. Computer simulation might be a suitable method for making a preliminary choice between these two alternatives.

(5) Differences in operations of Purkinje cells in the basic circuit and when modified by inhibitorv neuron systems

Since the delayed appearance of highly specialized inhibitory interneuron systems (Golgi and basket cells) is one of the prominent features in vertebrate cerebellar phylogenesis 6, it might be a good strategy to limit the simulation study of the Purkinje cells in the first approach to the basic circuit. Subsequently one might look for the improvements after introduction into the network of Golgi and basket inhibition.

THE MODEL

The simulation follows both with respect to structural and functional assumptions and as regards simulation techniques very closely along the lines presented earlier 1~. The excitation patterns in fields of different kinds of cells (granule, Golgi, Purkinje and basket cells) are computed at successive (2 msec) points of time during an arbitrarily chosen spatiotemporal excitation pattern in the field of mossy terminals.

Apart from the extension of the model to Purkinje and basket cells, this simula-

22 a . PELLIONISZ AND J. SZENT,~GOTHAI

tion differs significantly f rom the earlier study 15 by a spatially and temporally more

complex and dynamic pattern of the mossy input that is being applied.

Structural features of the network model The spatial arrangement of neuronal elements of the simulated network re-

mained virtually the same as illustrated in Fig. 1 of the earlier study 15, with the cha-

racteristic staggered position of the Purkinje cells 9. The parallel fibers were not illustrated in that study; however, it was assumed that they started from the position of their respective granule cells and ran for about 1.1 mm in both directions in the

longitudinal axis of the folium (vertically in Fig. 1 of ref. l 5). They are assumed to cross the dendritic trees of 216 Purkinje cells in the normal adults (108 in the immobilized kittens, see paragraph 2 of the Introduction). Hence, each Purkinje cell could contact theoretically 75 × 216 = 16,200 parallel fibers in this simplified (numerically

reduced) structural model. However, synaptic connections being established only in a fraction of the actual crossings 11, the model assumes that the average parallel fiber establishes a synaptic contact with one out of 6 crossed Purkinje dendritic trees (one out of 3 in the cerebellar cortex of the chronically immobilized kitten, see paragraph 2 of the Introduction). The spatial distribution of parallel fiber-Purkinje cell synapses is modelled for two extreme alternatives: (a) that every parallel fiber contacts synap- tically exactly every one-sixth of the crossed Purkinje dendritic trees, i.e. with zero standard deviation of this average, and (b) establishing a synapse with equal probability with any one of the Purkinje cells from the first to the eleventh, and so forth.

Basket cells are included into the network model in conformity with the recent quantitative studies 11. For the sake of simplicity, instead of the 6 basket cells per Purkinje cell that jointly control two lateral territories of Purkinje cells, a single representative basket cell is introduced, furnishing with inhibitory contacts 2 × 24 Purkinje cells in two lateral territories as shown in Fig. 1. Therefore, every Purkinje cell, in the complete model matrix, would receive synaptic contacts from 48 different

0 0 0 _ 0 0 0 0 ^

0 0 0 0 0 0 0 0 0 0 0 u

o io ol o 0 ' 0 • .O -o

Fig. 1. Arborization pattern of basket cell axons in the plane view of the cerebellar cortex adapted from ref. II. Purkinje cell bodies appear as rings arranged in the pattern determined previouslyL At far left a single Purkinje cell is shown in full black surrounded by 6 small basket ceils, according to the Purkinje cell:basket cell ratio of 1:6. These 6 cells contribute to the inhibitory baskets of Purkinje cells in two territories on both sides of the vertical passing through the indicated Purkinje cell. One of these territories is indicated by the dash-dot-dash oblong at right. Purkinje cells that would receive inhibitory contacts from one of the 3 of the 6 basket cells are indicated in solid black. Such groups of 6 basket cells (per Purkinje cell) are represented in the simulation by one model basket cell. The transversal span of the basket cell dendritic tree is 75/zm.

SIMULATION OF A CEREBELLAR NETWORK MODEL• I I 23

basket cells, which would correspond well to the estimated 11 real convergence of 50. The dendritic spread of the basket cells is assumed to be 75 # m in the transversal direction of the folium.

To avoid 'edge effects' in the restricted area of simulation the field is connected longitudinally to form a close ring, as has been described in more detail earlier 15.

In the transversal direction the structural matrix is assumed to continue laterally as a mirror image.

Functional assumptions

Input pattern An arbitrary input excitation pattern of mossy terminals was chosen, suited to

test the neighborhood relations of homogenous and heterogenous foci of excitation. Therefore, paired foci (A and B, each spatially identical to that used in ref. 15) are placed with their centers at diagonally opposite corners of the stimulated area. (See a sequence of representative frames of the input time-series in Fig. 3, MF.) Pairs

A and B are separated in time by delaying B for the time d. The time course of each focus was otherwise identical consisting of an exponential rising period, followed by a plateau, and concluded by a period in which the activity of the pair of foci is subsiding to zero (Fig. 3, MF).

Thus the probability (P) that a mossy terminal at a distance from the center o f the focus, r #m, will be excited at time t is:

- - 2 r 2

s 2

P (r, t) = K - e 0

T

1 - - e M =

1 D - - T

T

e

• M where i f T ~< 0

i f 0 < T <~ d i f d < T ~ < D

if T > D

where according to the separation of A and B in the time domain:

T (A) = t T (B) = t - - d

and the parameters are:

100 2 . 100 s = 100 #m; d = msec; D -- - -

3 3 msec; K = 0.75; z = 10 msec.

Single unit activity models of cells in the time domain Golgi and granule cell models are used in this simulation in the same way as

24 A. PELLIONISZ AND J. SZENT/~GOTHAI

in ref. 15. The direct and indirect inputs to Golgi cells were modeled to integrate in

the preferred disjunctive (or) mode; i.e. with the assumption that the Golgi ceils can

be activated either directly by mossy terminals or indirectly over the parallel fibers.

In the simulation o f the basic circuit, lacking inhibitory interneurons, the granule cell

threshold is considered fixed at the value o f 2, i.e. simultaneous mossy input to two

o f the average 4 dendrites is assumed to fire the granule cell.

As in the earlier Golgi and granule cell model 1~ a simplified algorithm holds

for the neurons introduced: for Purkinje and basket ceils. The functional state

(whether excited or silent) o f each neuron is determined by the equations below, for successive time steps o f 2 msec. The computa t ion is made on the basis o f actual input

excitation compared with the threshold value depending on preceding activities. For

the Purkinje cells two alternative unit models are considered according to paragraph

3 o f the Introduction. (a) Simple Purkinje cell model. In this algebraic summation model the possibility

o f independent activity in the main dendritic branches (dendritic spikes) and the

consequences o f the geometrical positions o f parallel fiber synapses are ignored, i.e. the synaptic weight o f all active parallel fibers is assumed equal to unit (Fig. 2A, dashed line). Let now I (k) denote the input via excited parallel fibers in the k-th

Fig. 2. Schematic representation of a model Purkinje cell shown from above (C) and from in front (B). The dendritic tree is divided into 4 non-overlapping territories corresponding to the main branches. Parallel fibers (very few of them shown in B by circles) belong to 10 different compartments (small dots in C) according to their transversal position in relation to the main dendrites. The synaptic weights attributed to active parallel fibers in different compartments are shown in A. The dashed horizontal line holds for the Simple (algebraic summation) model. The continuous line in A corre- sponds to the 'synaptic weight' attributed to active parallel fibers in the Dendritic Purkinje cell model. Values for the continuous curve are derived from Rall (ref. 17, Table 3C) and are normalized to the dashed line. Two excited parallel fibers at left (shown in black) belonging to the same compartment, i.e. in the same transversal position carry equal relative synaptic weight in the dendritic model.

SIMULATION OF A CEREBELLAR NETWORK MODEL. II 25

time-sample, E (k) the EPSP evoked by this input, S (k) the state of excitation of Purkinje cells (in binary units), and K (k) the actual threshold value; then

I 0 i f E ( k ) < K(k) ,-kC S ( k ) - - i l i f E ( k ) > K ( k ) ÷ C

i E ( k - - 1) E (k) = a

I I (k)

K (k) = I

+ I (k) if S ( k - - l) = 0

if S ( k - - l) = 1

K(k-- 1)-b K ( k - - 1) -k d

if S ( k - - 1) = 0 if S ( k - - 1) = 1

Where the parameters are set to fire every Purkinje cell in the simulated 0-100 msec at least once, while the maximal frequency should not be more than 250 Hz: C = 760; a = 2; b = 0.9; d ---- 180; Kmax = 850.

(b) Dendritic Purkinje cell model. By introducing this compartmental model, the spatial aspects of the Purkinje cell dendritic tree can be included, considering also the possibility for separate dendritic spikes. The dendritic tree (see Fig. 2B) is represented in this model by non-overlapping 4 territories of the main dendritic branches. The generalized output of the cell is determined jointly by the independent activities in the main dendrites. Synaptic weights of the active parallel fibers (represented by full circles in Fig. 2B) are not considered any longer to be equal but depend on the transversal distance of the parallel fiber from the main dendrite. The weights of synaptic inputs are set according to Rall's values (ref. 17, Table 3C) for a 10 compartment dendrite (Fig. 2A, solid line, corresponding - - when normalized - - to dashed line). Vertical integration in individual dendrites is assumed to occur as simple algebraic summation: i.e. the same synaptic weight is attributed to two active parallel fibers (Fig. 2B at far left) having the same transversal but different vertical positions. Dendritic spikes on these main branches are evoked in the model according to the equation given in (a), but I (k) is a weighed function and C, d, Kmax parameters are divided by 4. A generalized spike of the model Purkinje cell is assumed to emerge at any point of time, when at least two dendritic spikes occur simultaneously.

Basket cell activity model. These cells span 75/zm transversally by their dendritic tree, and are assumed to synapse with 675 randomly selected parallel fibers of the beam corresponding to this span. Since this span is one-quarter of that of the Purkinje cells, the same algorithm is used for the basket cells as for one dendrite of the compartmental Purkinje cell model. The 48 basket cell endings impinging on a Pur- kinje axonal pole will then modify by inhibition its S (k) activity to S' (k) as follows. If in the k-th time sample the number of active inhibitory basket endings is denoted by B (k),

S' (k) = S (k) • N where N = ! 0 i f R ( k ) 1> K

I l i f R ( k ) < K w h e r e

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28 A. PELLIONISZ AND J. SZENT,~GOTHAI

B ( k - - 1) R (k) - - + B (k)

where K was set equal to 36 so that one-half of the basket endings can completely inhibit the Purkinje cell activity in the steady state.

SIMULATION RESULTS

The simulation program (called Clnematized Cerebellar Activity Model: CICAM-2) has been written in F O R T R A N and was run on a CDC 3300 type computer. The consecutive activity patterns were computed at 2 msec time intervals over a total range from 0 to 100 msec after the onset of excitation. The excitation patterns were printed out by line printer and the data stored for further analysis 1~. The dynamic spatiotemporal activity of the simulated network was visualized by a procedure analogous to the technology of animated pictures. The stacked 2-dimensional matrices of different kinds of cells were marked for identification by a color code. The excitation patterns, unfortunately, can be demonstrated in this paper only by representative samples from the cine film, and lacking a color-code the Golgi and basket cells are not visualized directly in order to keep the patterns from be-

coming too involved.

Simulated activity of the basic circuit The simulation program in the first series was run with the Golgi and basket

inhibitory systems switched off, in order to concentrate on the problems of the synaptic organization of parallel fibers and the dendritic activity of Purkinje cells (see paragraphs 1 and 3 of the Introduction). The two alternatives of parallel fiber synapse distribution (Fixed or Random viz. (a) and (b) in Structural features of the network model) and the two alternative models of the Purkinje cells (Simple and Dendritic, viz. (a) and (b) under the heading Single unit activity models in the time domain) make altogether 4 combinations of these models, labeled SF, SR, DF and DR, the first letter referring to the type of Purkinje cell model, and the second to the kind of synapse distribution in the parallel fibers. Sequences of representative frames of the spatiotemporal mossy fiber input (MF) and of the corresponding granule cell and Purkinje cell responses are given in Fig. 3.

Series M F shows the incoming mossy fiber activity (the dots representing excited mossy fiber terminals). The emerging pair of foci A (see the two consecutive 12

Fig. 3 (on preceding two pages). Representative frames of the series of same samples from the simulation of the Purkinje (and granule) cell activities of the basic circuit in 3 different modes of operation, as a result of mossy fiber input (cf. Fig. 5 of ref. 15). In series MF small dots represent excited mossy terminals, while in the other series the small dots correspond to excited granule cells, and large dots represent excited Purkinje cells. The alternative models are denoted by two capital letters: the first refers to the Purkinje cell model (S for Simple, D, for Dendritic), the second for the distribution of parallel fiber synapses (F for regularly fixed, R for Random).


and 14 msec samples) are followed by their period of coexistence with the delayed B foci (see samples at 36 and 68 msec), then the subsiding pair of A foci (samples at 80 and 90 msec) can be followed.

The other 3 series in Fig. 3 demonstrate the granule cell responses (small dots) to this input (that is identical in each of the series being '-~- transformed from the mossy fiber patterns with the non-controlled granule cell threshold of 2).

Series SF, SR, DR demonstrate additionally the Purkinje cell responses (larger dots). The activities can be generally described as follows. Soon after the onset of mossy excitation (at 12-14 msec) the Purkinje activity starts in the excited foci and spreads, resembling vaguely wave-fronts, towards the central area between the foci (36 msec). During the simultaneous persistence of both pairs of foci the Purkinje pattern exhibits a somewhat more diffuse spatial distribution both in the central (neighborhood) area and a slight activity in the foci. Towards the end of the simulation period, while the foci A are subsiding, the Purkinje cells tend to become active in the central area again (samples 80 and 90 msec).

The differences between the SF, SR and DR alternative models do not appear to be significant in this type of display emphasizing spatial relations and giving few representative samples in time. The difference between the SF and SR models seems to be particularly negligible, while it is somewhat more marked in the SR and DR alternatives, where especially the initial activity resembling a wave-front (samples 12 and 14 msec) is somewhat blurred in the DR model due to gaps occurring in the more solid longitudinal columns of active Purkinje cells of the SR model. During the further course of the simulation period (samples 36 and 68 msec) active Purkinje cells appear to gather in the dendritic (compartmental) DR model on the edges of the central area rather than in the center itself. However, the real consequences of the different models with respect to the spatiotemporal activity of Purkinje cells cannot be analysed satisfactorily with the help of static steps of 2-dimensional patterns, i.e. disregarding the fact that a 3-dimensional system is being considered.

In order to overcome this difficulty one can select and display special segments of the total spatiotemporal pattern on the basis of the stored data and by doing so can reduce the number of dimensions. In plotting the summed activity of Purkinje cells against time in the SF and SR simulation modes (Fig. 4, SF = solid line, SR = broken line) it becomes obvious that the simulated two alternatives in the distribution of parallel fiber synapses do not show significant differences in temporal behavior. The spatial pattern of activity is, of course, completely concealed in this kind of display. Therefore, a temporally continuous representation of the single unit activities of spatially sampled Purkinje cells might seem desirable.

The 4 alternative models are compared in Fig. 5 by selecting a single diagonal column of Purkinje cells, from the total matrix, and by displaying their unit activities over the total range of time. Such a column - - deviating about 16 ° from the course of the parallel fibers - - has been chosen in order to visualize the behaviour of a group of Purkinje cells that are in the closest transversal position to a given population of parallel fibers. In Fig. 5 all the 4 combinations of alternatives (SF, SR, DF, DR) are displayed simultaneously.

30 A. PELLIONISZ AND J. SZENTAGOTHAI

P ~ 6O

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Fig. 4. The overall density of excited Purkinje ceils (P, in per cent o f total population) as a function o f time in the SF mode (continuous line) and SR mode (dashed line). Difference between the two models is negligible.

As seen in Fig. 5 the activity patterns of such spatially sampled Purkinje cells are virtually the same, whether the distribution of parallel fibers is assumed to be strictly regular or at random. A very slight alteration is introduced in the wave-front like spread of activity that appears to be more impressive in the SF model. The 'cracks' in the wave-fronts in the random SR model are due to a somewhat less con- sequent increase in delay towards both ends of the selected column. The differences become more conspicuous when comparing the Dendritic Purkinje cell model with the Simple alternative assuming algebraic summation of parallel fiber excitation. Owing to the staggered arrangement of Purkinje cells in the matrix there is a small (16%) difference of their position relative to the parallel fibers. Hence, when the dendritic tree is considered as being subdivided in correspondence to the 4 main branches, this difference results in a considerable variety of the individual activities

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SIMULATION OF A CEREBELLAR NETWORK MODEL. I [ 31

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Fig. 6. Comparison of the behavior of 4 neighboring cells in the various simulated alternatives of the basic circuit. In the DR mode (lower right) 4 cells fall into different classes according to their firing in the 3 intervals of simulated activity (intervals are separated by dash-dot lines). B-detector type of cell (upper row in DR mode) is symbolized by a circle, A-detector (second row) by a triangle, integrator (I-type, fourth row) by asterisk. The same symbols are used in Fig. 11.

of even closely neighboring Purkinje cells (see DF and especially DR in Fig. 5). This observation brings up the question of the individual behavior of neigh-

boring Purkinje cells (paragraph 4 of Introduction). The simulation results can be best demonstrated from this point of view by 'recording' from 4 directly neighboring cells as shown in Fig. 6: Parallel fiber synaptic organization (F or R) appears again to be irrelevant, while a considerable amount of individual behavior appears when the compartmental dendritic model is tested. Finally it becomes possible to classify the Purkinje cells into different categories. Interestingly this is not possible in this randomly chosen group of cells in the SF, SR and the DF model. However, the behavior of the 4 cells is characteristically different in the DR alternative, according to the classification as follows.

The simulated period can be subdivided with respect to mossy input into 3 different sections (Fig. 6, lower right: DR): in the first, only the paired foci A are on, in the second, both pairs A and B are on, and in the third, A foci are off. One may, therefore, label the Purkinje cells yielding spikes in the first period 'A-detectors', those producing spikes in the third period 'B-detectors', and the units yielding spikes both in the first and the third periods integrative (I) Purkinje cells. The 3 types are represented in Fig. 11 by a triangle for A-detectors, a circle for B-detectors and an asterisk for the integrator. Units responding only in the middle period are left blank because they do not carry any information in this context.

In Fig. 6 (DR) the sampled, closely neighboring 4 cells belong to one of the 4 classes. The spatial distributions of these different classes of cells in the apparently most realistic (DR) alternative were determined and plotted by the computer as shown in Fig. 11A. This picture demonstrates the spatial distribution of A- and B-detectors and integrative Purkinje cells over the total simulated field; however, the central areas between the folia are of particular interest. As would be expected integration between

32 A. PELL1ONISZ AND J. SZENT/{GOTHAI

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the two inputs is most abundant in the direction of the parallel fibers (vertical in the diagram), although there is some transversal integration even in this basic model lacking inhibitory interneurons.

Simulation with inclusion of inhibitory interneurons After having shown some operations of the basic circuit, we may now proceed

by introducing the Golgi and basket cell inhibition into the DR alternative of the basic circuit, found to be most 'realistic'.

The basic circuit simulation (Fig. 7, series F) is from the same run as DR in Fig. 3. A comparison with the model including the inhibitory interneuron systems (series C in Fig. 7) reveals certain characteristic differences both in granule cell (small dots) and in Purkinje cell (large dots) activities. On the top of Fig. 7 (P) the overall Purkinje cell activity is plotted against time. This continuous record demonstrates (C curve) the changes brought about by the action of the two specific inhibitory systems (Golgi and basket cells) contrasted against the Purkinje cell activity of the basic circuit. On the basis of Fig. 7 the effects of the inhibitory interneuron systems can be summarized as follows.

Granule cell activity starts (as has been shown already 15) with large amplitude as a result of the lower resting threshold of granule cells (that has to be introduced in order to simulate the action of the Golgi cells) but soon gets suppressed by the inhibitory feedback mechanism of Golgi cells. The result on Purkinje cell activity is consequently a large 'on' response, which can be seen both on the time-display of P, and spatially in the 8 msec sample of C. Note that at this point of time no Purkinje cell activity would be observed in the basic circuit, i.e. if one had a mossy fiber- granule cell transfer with a fixed threshold. Due to the Golgi inhibition the several foci of excited granule cells are disseminated diffusely over the entire field (leveling effectl~). In the early period of the coexistence of all the 4 inputs, however, Purkinje cell activity becomes strongly suppressed in comparison with the basic circuit. Still, Purkinje cell activity is best preserved in the central zone, where the foci are merging (sample at 40 msec). Further increase of Purkinje cell activation occurs at the later stage (sample at 54 msec). This peak is delayed by about 15 msec as compared to the basic circuit. The complete circuit (C) produces also an 'off' response when type A foci are waning (80 msec).

The effect of basket inhibition can be more thoroughly analysed by another mode of display in Fig. 8. Spatial display (S) in this figure is essentially a particular frame from the sequences shown above. At the time, however, the time course of activity is shown too, for the column of Purkinje cells indicated by the oblique lines (cf. Fig. 5).

In the temporal display on the right of Fig. 8 (T) spikes of single Purkinje cells are shown by vertical dashes, while spikes suppressed by basket inhibition are represented by large dots. The upper diagram of this Fig. (C) demonstrates the effect of basket cell inhibition imposed upon the complete circuit (in which Golgi inhibitory system is on). The diagrams at the bottom (F), provide an intriguing comparison by showing the effect when basket cells are introduced into the basic circuit without

34 A. PELLIONISZ AND J. SZENT/~GOTHAI

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Golgi cells. As can be seen in the temporal displays (Fig. 8, T) the effect of the 'feed-

forward ' basket inhib i t ion accounts for the delay of about 15 msec observed in the

overall Purkinje activity ( c f Fig. 7, P). This time-shift in Purkinje cell responses to

massive input , however, is not the same spatially in the two cases shown in Fig. 8.

In the complete circuit (C) basket inhibi t ion tends to suppress the Purkinje cells

SIMULATION OF A CEREBELLAR N E T W O R K MODEL. II 35

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situated within the input foci while leaving relatively more cells active in the central area (see also Fig. 7, C at 40 msec). It is important to note that without a Golgi inhibitory system (F in Fig. 8) a virtually total blackout of Purkinje activity in a contig- uous central field would be observed.

The significance of the specific inhibitory systems is more impressively shown in the model of a defective cerebellar network, as for example would occur in a cerebellum with shorter parallel fibers produced by early immobilization of kittens. With

36 A. PELLIONISZ AND J. SZENT,~GOTHAI

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parallel fibers of half length (1 mm) and double density of synapses 14 one would certainly expect gross changes of function, as shown also by the living animals. As apparent in Fig. 9 (the mode of display is here the same as in Fig. 8) the effect of immobilization in the basic circuit (Fig. 9, F) is a virtual isolation of the fields of active Purkinje cells that develop over the input foci. This isolation, however, is considerably lessened by the action of the two inhibitory interneuron systems (Fig. 9, C). The Golgi inhibition acts obviously by merging the several foci through its so called 'leveling effect' on granule cell activity. In addition to this, the basket cells act by a drastic reduction of massive Purkinje cell activities at the two ends of the selected column (Fig. 9, CT). As a result the central area between the foci shows almost the same Purkinje cell activity (in CT) as over the excited foci in spite of the crude changes made in the structural model.

Returning to the question of the individual behavior of Purkinje cells, the simulation analysis shows that by introduction into the basic circuit of the specific inhibitory interneuron systems, individuality is enhanced. This can be demonstrated in Fig. 10 where the unit activity of 3 closely neighboring Purkinje cells is shown. Such excessive variation in firing patterns could have hardly been expected under such highly simplified circumstances.

The spatial distribution of Purkinje cells showing these variations in behavior can be compared in Fig. 11 in the 3 cases of the basic circuit (A), in complete circuit with inhibitory systems (B) and the complete circuit when modified structurally by shortening the parallel fibers (C). The differences are most significant in the spatial distribution of integrative type cells (asterisks). Integrative type cells occur mainly as results of neighborhood interactions between the input foci: mainly in the direction of the parallel fibers (vertically in Fig. 11) in the case of basic circuit (A). The field of integrative cells becomes greatly expanded into the central zone in the complete circuit (B). This merging-effect can be attributed mainly to the Golgi inhibition. In the case of the cerebellum damaged by early immobilization, the fields of responding Purkinje cells become drastically isolated from each other, and the number of integrative cells falls to a negligible number.


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DISCUSSION

In trying to answer the questions raised in the Introduction we have first to realize that most of these are closely interrelated, so that in many cases no straight- forward answer can be given to the separate questions.

The problem of highest practical significance (paragraph 1 of Introduction) introduced by the curious coincidence that every fifth to sixth Purkinje cell stands in register with its dendritic tree (in the longitudinal direction of the folium) and that the average parallel fiber also establishes a synapse with every sixth Purkinje cell, (the dendritic tree of which it crosses), receives a rather clear answer by the simulation study. There would be no appreciable difference (or advantage) in a strictly preaddressed parallel fiber-Purkinje cell connectivity system with synapses contacting the Purkinje cells that stand in register, against a 'non-addressed' system in which Purkinje cells out of register are contacted with equal probability. It would make little sense to assume that the formidable problem of finding or selecting from 5-6 possible choices the cells always standing in register was solved by the nervous system when nothing could be gained. This may also increase confidence in the value of this kind

38 A. PELLIONISZ AND J. SZENT.~GOTHAI

of approach that enables the researcher to discard quasi a priori possibilities that could be tested otherwise only with considerable effort and time.

On the contrary the simulation experiments are giving quite strong hints in favor of the importance of dendritic geometry. While the results of the models considering the Purkinje cells as simple algebraic summators of simultaneous parallel fiber impulses (S) do not represent many of the varieties of Purkinje cell behavior that are experienced in recent physiological studies3, s, the models (D) considering - - albeit with crude simplifications - - the basic geometry of the dendritic trees of Purkinje cells, give considerable individuality to the behavior of even closely neighboring units. I f nothing more, this may certainly indicate, that the dendritic geometry, in the sense of the concepts developed by Ral116,17 ought to be incorporated into considerations of neural network functions. Our simulation results certainly support the intuitive conclusion (drawn from electrophysiological investigations 5) that dendritic spikes in a single Purkinje dendritic tree correspond to an inherent, delicate process of summation in which vertical and transversal integration should be thoroughly analysed according to the micromorphological features of dendritic arborization.

It is remarkable how clearly the simulation results support, even in the basic circuit lacking the specific inhibitory interneurons (Golgi and basket cells), the observation of individual behavior of closely neighboring Purkinje cells. One has to realize that what we were modeling here as the 'basic circuit' is essentially a frog-type cerebellar cortex. Although the frog cerebellum lacks Golgi and basket cells, it has one kind of interneuron: stellate cells 6. Since we have not incorporated the stellate cells at this stage into the model we cannot predict how much refinement or modifi- cation they might add to the operations of the 'basic circuit' as revealed by this simulation. However, as can be judged from the results when incorporating the two specific interneuron types (Golgi and basket cells), certain refinements and perhaps a trend towards more individuality in behavior of the Purkinje cells can be expected to be added by the stellate cells to the basic circuit.

The significance of the two specific inhibitory interneuron systems (Golgi and basket cells), according to this simulation study, could be envisaged as giving refinement both in spatial and in temporal respects to the activation of the Purkinje cells. Spatially the Golgi cells act by controlling the transmission from the mossy terminals to granule cells in the foci of high input density and promote transmission in the surround of single and in the neighborhood of multiple foci. This 'leveling effect' or with other words 'defocusing' has been observed already in the earlier study 15 (occurring after a very brief transient focusing effect), but its consequences become apparent only in the behavior of Purkinje cells in the zones between different loci of input. Temporally the Golgi cells seem to be responsible for a more phasic character of the Purkinje cell response by introducing a sharp very short latency 'on' response (Fig. 7, P) during emergence and a similar 'off' response during waning of the input.

The basket cells appear to separate the central field of active Purkinje cells, brought about by the Golgi cells, from the fields over the centers of the foci by blotting out Purkinje cell activity in the peripheral parts of the foci (Fig. 8, C). In


the absence of Golgi inhibition the basket cells would seem to abolish virtually all Purkinje cell activity in the central field between the input loci (Fig. 8, F). Hence, basket cell inhibition alone, would not improve but rather prohibit any integration between neighboring foci. The effect of basket cell inhibition appears now to be a much more delicate mechanism than assumed hitherto18,10.

The simulation study shows above all that neighborhood interactions over parallel fibers activated from different foci of input might be the really significant part of the processing in the cerebellar cortex. This has been felt already by the pioneers of this field, notably by J. C. Eccles who has tried to visualize what might happen in regions if various degrees of overlap exist between activities set up by smaller foci of mossy input (Fig. 123 in Eccles e t al. a and Fig. 4-13 in Eccles2). The results of the simulations go well beyond these expectations in showing not only that a quite considerable degree of interaction occurs already in the basic circuit (Fig. llA), but that the inhibitory interneuron system seems to enhance specifically the interactions in the central field between the input foci, while putting a certain check on Purkinje cell activities over the foci (Fig. 11B).

The experimental model prompted by the observations of shorter parallel fibers developing in the cerebellar cortex after early immobilization in kittens 14 shows very impressively (Fig. 11C) that these neighborhood interactions break down almost completely if the length of the parallel fibers is reduced to one-half. It must be mentioned additionally that the remaining small amount of interaction between the foci is ensured only by the presence of the specific inhibitory interneurons.

It is worthwhile to compare this inference with the important anatomical finding of Voogd z0 on the subdivision of the anterior lobe into about 7 sagittal compartments both with respect to the main afferent and efferent pathways. These compartments are visibly separated from one another by so called 'raphes'. Since the total width of one-half of the anterior lobe is around 7-8 mm in the adult cat, practi- cally each granule cell of any compartment would penetrate large portions of its two neighboring compartments if the parallel fibers were running for 1.1 mm from the points of their bifurcation. However, they could not possibly reach the next again compartment. With parallel fibers only half as long, interaction between neighboring compartments would, obviously, have to break down.

As a more general conclusion these studies would point towards the importance to move away from the 'localistic' views of neural operations - - a natural consequence of the microelectrode methods - - towards a more 'pluralistic' approach, e.g. by multielectrode recordings 1 which might open up new ways to look at and to under- stand network operations.

REFERENCES

1 BANTLI, H., Multi-electrode analysis of field potentials in the turtle cerebellum: an electrophysiological method for monitoring continuous spatial parameters, Brain Research, 44 (1972) 676-679.

2 ECCLES, J. C., The Understanding of the Brain, McGraw-Hill, New York, 1973, p. 127. 3 ECCLES, J. C., FABER, D. S., MURPHY, J. T., SABAH, N. H., AND TABOP.IKOVA, H., Investigations

40 A. PELLIONISZ AND J. SZENT.~GOTHAI

on integration of mossy fiber inputs to Purkyn6 cells in the anterior lobe, Exp. Brain Res., 13 (1971) 54-77.

4 ECCLES, J. C., Ixo, M., AND SZENT~GOTHAI, J., The Cerebellum as a Neuronal Machine, Springer, Berlin, 1967, p. 224.

5 LLINAS, R., Neuronal operation in cerebellar transactions. In F. O. SCHMlXT (Ed.-in-Chief), The Neurosciences, Rockefeller Univ. Press, New York, 1970, pp. 409-426.

6 LLINAS, R., AND HILLMAN, D. E., Physiological and morphological organization of the cerebellar circuitry in various vertebrates. In R. LLIN~,S (Ed.), Neurobiology of Cerebellar Evolution and Development, Amer. Med. Ass., Chicago, Ill., 1969, pp. 45-73.

7 LLINAS, R., AND NICHOLSON, C., Electrophysiological analysis of alligator cerebellar cortex. In R. LLINAS (Ed.), Neurobiology of Cerebellar Evolution and Development, Amer. Med. Ass., Chicago, I11., 1969, pp. 431--465.

8 LLIN.~, R., PRECHT, W., AND CLARKE, M., Cerebellar Purkinje cell responses to physiological stimulation of the vestibular system in the frog, Exp. Brain Res., 13 (1971) 408-431.

9 PALKOVITS, M., MAGYAR, P., AND SZENT~,GOTHA1, J., Quantitative histological analysis of the cerebellar cortex in the cat: I. Number and arrangemen~ in space of the Purkinje cells, Brain Research, 32 (1971) 1-13.

10 PALKOVITS, M., MAGYAR, P., AND SZENT3~GOTHAI, J., Quantitative histological analysis of the cerebellar cortex in the cat. I1. Cell numbers and densities in the granular layer, Brain Research, 32 (1971) 15-30.

11 PALKOVITS, M., MAGYAR, P., AND SZENX~,GOTHAI, J., Quantitative histological analysis of the cerebellar cortex in the cat. 111. Structural organization of the molecular layer, Brain Research, 34 (1971) 1-18.

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13 PELLIONISZ, A., Computer simulation of the pattern transfer of large cerebellar neuronal fields, Acta biochim, biophys. Acad. Sci. hung., 5 (1970) 71-79.

14 PELLIONISZ, A., PALKOVITS, M., H~.MORI, J., PINTI~R, E., AND SZENT.~GOTHAI, J., Quantitative comparison of the cerebellar synaptic organization of immobilized and normal kittens. In Proc. IV. lnternat. Biophys. Congr. Moscow, 1972, In press.

15 PELLIONISZ, A., AND SZENTAGOTHAI, J., Dynamic single unit simulation of a realistic cerebellar network model, Brain Research, 49 (1973) 83-99.

16 RALL, W., Theoretical significance of dendritic trees for neural input-output relations. In R. F. REISS (Ed.), Neural Theory and Modeling, Stanford Univ. Press., Stanford, Calif., 1964, pp. 73-97.

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18 SZENT.~GOTHAI, J., Ujabb adatok a synapsis funkcion~ilis anat6mifijfihoz, Magy. Tud. Akad. Biol. orv. Tud. Osztal. K6zl., 6 (1963) 217-227. (In Hungarian).

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20 VOOGD, J., The importance of fiber connections in the comparative anatomy of the mammalian cerebellum. In R. LUNGS (Ed.), Neurobiology of Cerebellar Evolution and Development, Amer. Med. Ass., Education and Welfare Foundation, Chicago, Ill., 1969, pp. 493-514.

pellionisz a, szentàgothai j. brain res. 1974 mar 15;68(1 ......dynamic single unit simulation of a...

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