Effects of recurrent collateral inhibition on Purkinje cell activity in the immature rat cerebellar cortex - an in vivo electrophysiological study

Effects of recurrent collateral inhibition on Purkinje cell activity in the immature rat cerebellar cortex - an in vivo electrophysiological study

234 Brain Researth, !~2~(1993) 234-25~; ~ 1993 Elsevier Science Publishers B.V. All rights reserved 1101t6-8993/93/$06.1~0 BRES 19349 Effects of re...

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234

Brain Researth, !~2~(1993) 234-25~; ~ 1993 Elsevier Science Publishers B.V. All rights reserved 1101t6-8993/93/$06.1~0

BRES 19349

Effects of recurrent collateral inhibition on Purkinje cell activity in the immature rat cerebellar cortex - an in vivo electrophysiological study C. Bernard

a H. Axelrad b,,

'~ Department of Physiology and Pharmacology, Southampton University, Bassett Crescent East, S 0 9 3TU Southampton, UK h Laboratoire de Neurophysiologie, Facult~ de M~decine Piti~-Salp~tri~re, 91 bd de l'H~pital, 7.5013 Paris, France (Accepted 8 June 1993)

Key words: Purkinje cell; Recurrent collateral; Inhibition; Cerebellum; New-born rat; System analysis; Cooperativity; Entropy

We present here a study on the effects of inhibitory recurrent collaterals of Purkinje cell (PC) axons on the activity of the immature rat cerebellar cortex. Simultaneous extracellular recordings of pairs of PCs were performed in rat pups aged 5-8 days postnatal. Bicuculline was applied to the surface of the cortex in order to functionally antagonize PC recurrent collaterals. At this early developmental stage these are the only inhibitory links in the network. Dye marks from the microelectrode tips and 3D serial-section reconstruction of the structure allowed the exact determination of the distance separating recorded cells and of their respective orientation in the cortex. Standard statistical tests and an informational entropy index were used to calculate levels of cooperativity. By comparing PC activity under control conditions and after

bicuculline superfusion it is shown that recurrent collateral inhibition has a structurating effect on the PC activity and that it increases the informational content of the network. Inhibition decreases the activity of the cells by 35% and drastically changes the interspike interval histograms. This leads to a more constrained state of the system. Three types of coupling via recurrent collaterals are present: symmetrical, asymmetrical or non existent. The exact type of coupling follows a simple vicinity rule and strongly influences the cooperativity level between the recorded cells. This cooperativity was also found to be spatially compartmentalized. Several pairs were driven by common inputs via climbing fibers or parallel fibers. Using the predictive value of a theoretical model of this immature structure 16 we propose a complementary explanation of the role of the recurrent collaterals at this stage of development: that of a spatial and temporal filter, specific to each different microzone.

INTRODUCTION T h e s t r u c t u r e a n d function o f the m a m m a l i a n cereb e l l a r cortex (CbCx) have b e e n extensively s t u d i e d by means of experimental protocols and theoretical models (see Ito 42 for a g e n e r a l review). D e s p i t e t h e w e a l t h of d a t a at o u r disposition it is still not p o s s i b l e to d e t e r m i n e the exact r e s p o n s e function of this n e u r o n a l network. This is m a i n l y d u e to o u r lack o f k n o w l e d g e about: (1) t h e way i n f o r m a t i o n is c o d e d in this p a r t i c u lar C e n t r a l N e r v o u s System s t r u c t u r e a n d (2) t h e way the different constituents of the CbCx quantitatively i n t e r a c t in o r d e r to t r e a t i n c o m i n g i n f o r m a t i o n . T h e i n t r o d u c t i o ~ o f t h e C b C x m i c r o z o n e c o n c e p t 42'58'59 s t r e s s e d t h e i d e a o f local p r o c e s s i n g o f i n f o r m a t i o n as first p u t f o r w a r d a n a t o m i c a l l y by R a m 6 n y Caja167 a n d physiologically by Eccles a n d c o l l a b o r a t o r s 31. Such 10-

*Corresponding author. Fax: (33) (1) 45.82.95.31.

cal circuits a r e b e l i e v e d to e n c o m p a s s a small v o l u m e o f cortex c o m p o s e d , in t h e p r e s e n t case, o f a r e s t r i c t e d n u m b e r o f P u r k i n j e cells (PCs), inhibitory i n t e r n e u r o n s ( B a s k e t cells, S t e l l a t e cells a n d G o l g i cells) and t h e i r specific inputs, C l i m b i n g (CFs), Mossy ( M F s ) a n d granule cell p a r a l l e l fibers. Being t h e sole o u t p u t o f this s t r u c t u r e the PCs will b e very sensitive to any c h a n g e s in the e x c i t a t o r y / i n h i b i t o r y b a l a n c e they receive. A l t h o u g h s o m e a s p e c t s of t h e inhibitory effects of i n t e r n e u r o n s in the m o l e c u l a r layer on n e a r b y PC activity have b e e n s t u d i e d ~2'31 no d i r e c t analysis has b e e n c a r r i e d out on t h e way the inhibition b r o u g h t a b o u t by the P C axonal r e c u r r e n t c o l l a t e r a l s ( R C ) influence t h e activity of o t h e r PCs. T h e few a n a t o m i c a l a n d physiological s t u d i e s 17Js'zt'44,55,56, t h a t have b e e n p u b l i s h e d on this q u e s t i o n e n h a n c e the functional imp o r t a n c e of t h e s e R C s on t h e n e u r o n s of the s u r r o u n d ing area. In t h e a d u l t s t r u c t u r e such a study is very difficult as inhibition d u e to B a s k e t cells, S t e l l a t e cells a n d R C s m e r g e at the P C level 32'33'34'37 w h e r e they can not b e easily d i f f e r e n t i a t e d . T h e v a r i a b l e s are so nu-

235 merous and their nonlinear integration so complex that it is not possible to specify the role played by each different constituent impinging on the PC somatodendritic membrane in the firing of the cell. To get an insight into the exact role of the RC system it is necessary to analyze its effect in isolation and compare the activity of neighbouring PCs in presence and absence of the specific inhibition. From the differences between the two active states of the local network it should be possible to extract some knowledge about the RC function. As mentioned above, this approach is not possible in the adult CbCx because of the intrication of too many inhibitory phenomena. Fortunately the rat CbCx has an essentially postnatal (PN) development and the maturation of the different elements follows a well known morphological and physiological calendar 7-1°'23'64'65'71-73. This allows a sort of natural, ontogenetical, dissection. In particular, in the earliest stages it is possible to study some of the elements of the structure such as the RCs in isolation. Indeed, between 5 and 8 days PN only some elements of the adult structure are present: the PCs, already spatially arranged in a monolayer, with a profuse RC system; the climbing fibers (CFs) and a few parallel fibers (PFs). In such a simple system it is possible to study the effect of RC inhibition on nearby PC activity. To do so we recorded the ongoing activity of pairs of neighbouring PCs in immature rats and used bicuculline to anatagonize the effect of GABA, the PC neurotransmitter. Using a terminology derived from the artificial neural network field, the 5 to 8 PN days cerebellar cortex can be viewed as a poorly connected monolayer neural network. This network can be characterized by two functional modes: the mode where the RCs are fully functional (Control mode) and the mode where the inhibitory action of the RCs is blocked by bicuculline (Bi mode). In the Bi mode the local circuits will process the ongoing information (here the spontaneous activity) without the inhibitory action of the RCs. The recorded spike trains were studied with three statistical techniques, namely: interspike interval histograms, crosscorrelograms and an informational entropy index method, which we introduced and described in a companion, theoretical, report 16. We show that: (1) RC inhibition has a significant effect on PC activity, inducing important changes in the characteristics of the spike trains; (2) RC inhibition also changes the dynamics of the network and significantly increases the informational entropy index, as superfusion of bicuculline leads to the disappearance of many states of the system;

(3) there is a topological relationship characterizing the type of coupling of the recorded cells in respect to their RCs; (4) in some instances a strong coupling via PFs or CFs is present; (5) the informational entropy index efficiently measures the cooperativity existing between the recorded cells and can thus be used to determine a scale of cooperativity. In a complementary approach to this study a theoretical model of the same structure was built and simulations run so as to calculate the cooperativity between the artificial neurons in the network 16. Comparison between theoretical and experimental results shows fairly good concordance, allowing some predictive consideration about the behaviour of the whole network. We propose that the RC system can be viewed as a dynamical spatial filter constraining the output of a given set of PCs in certain limits. This action would be complementary to the classical inhibitory/ disinhibitory action of R C ' s 44.

MATERIALS AND METHODS Experiments were carried out on 5- to 8-day-old male SpragueDawley rats (date of birth = day 0; time of birth known within 12 h). Animals were anesthetized with 35 mg/kg Nembutal injected intraperitoneally. Local analgesia of the wounds and pressure points was currently used and renewed every hour. All animals were curarized with 60 mg/kg Flaxedil and put under artificial respiration. Animal temperature and cardiac frequency were kept constant.

Experimental protocol The vermis was exposed and its condition was always checked by watching the blood stream on the cerebellar surface. In some experiments a fine bipolar metallic electrode insulated except for its tips (tip separation: 0.3 mm) was used for juxtafastigial (JF) stimulations. Fig. 1 is a diagram showing the experimental setup. Extracellular recordings of nearby PCs was performed with 2 glass microelectrodes filled with 2 M NaC1 and Methyl blue solution (DC resistance: 5-20 MO). The 2 microelectrodes were mounted on 2 independent micromanipulators. The tip separation and depth in the sagittal and transverse planes was controled under high magnification binocular vision. A large tip micropipette filled with a 1% solution of bicuculline in 1 M NaCl was placed over the surface of the cortex between the recording microelectrodes. A 2 atm pressure during 50 msec expelled a drop whose diameter was determined to be about 3 mm. This volume, approximated to that of a sphere (V--~-d3/6), corresponds to about 0.1/.,g of bicuculline. We tested the dose effect of the drug by varying the quantity of bicuculline applied to the surface. High concentrations of bicuculline ( > 0.5 /~g) induced a drastic increase of the discharge frequency of the recorded PCs, shortly followed by the death of the neuron (30 s after the superfusion of the drug). Below this 0.5/.~g threshold (-t-0.1/zg) the changes induced by the drug were stable and reproducible. The lower limit for which no effect could be recorded was found to be approximately 0.01 /zg. All experiments were carried out with a dose well inside these limits (0.1/~g). PCs were identified by their antidromic response36 as well as by their climbing fiber responses (CFRs) 23,35,64,74 usually recognised, in these immature rats, by their long duration bursts (time between two

236 .I~_3

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iML P
Fig. 1. Schematic drawing of the experimental setup. The superficial part of a folium is shown. The cerebellar cortex under the translucid pia-matter is made of the External Granular Layer (EGL) and the incipient Molecular Layer (iML), the Purkinje Cell Layer (PCL) and the Internal Granular Layer (IGL). Two Methyl-blue filled micropipettes (1 and 2) are lowered with independent micromanipulators. A third large-tip micropipette, filled with a bicuculline solution, is lowered between the recording electrodes. A drop of the solution is rapidly ejected under pressure in order to superfuse the whole area between the recording pipettes. In some cases a bipolar electrode is inserted at the juxtafastigial level in order to stimulate antidromically the axons of the PCs (not illustrated). Standard amplification and recording techniques are used.

successive spikes < 35 ms). Once the recorded cells were identified as PCs the analog signals were recorded, after amplification, on video tape for further treatment. The recorded spike trains were then passed through Schmitt triggers, the output of which were fed to a data acquisition card of a M A S S C O M P 5400 computer. Two files containing the time of occurence of the discharges of the two recorded PCs were thus created.

Determination of the distance between recorded cells Whenever possible, recordings were carried out in the medial part of folium VI. At the end of each experiment Methyl blue was iontophoretically ejected from the tips of the microelectrodes. As the depth of the Purkinje cell layer below the pial surface is small in these preparations, the ejection of the two blue points could be clearly checked by observing the structure under the binocular. In each experiment a drawing was made of the relative positions of the microelectrodes tips to adjoining blood vessels and their mutual distance and spatial orientation was estimated. The cerebellum was then removed, cut with a freezing cryostat in serial 40-/zm-thick sections and processed with neutral red. In consequence there is no shrinkage of tissue and the distances can be directly computed. A semi-automatic procedure has been designed in our laboratory to store on a computer the outlines of the molecular, PC and granular layers for each section, as drawn u n d e r the microscope. The exact locations of the dye markings were also stored in the file. The whole structure can then be reconstructed in 3D by visualizing the succesive serial sections (Fig. 4). The exact distance between the two recorded PCs as well as their respective orientation in both saginal and parasagittal planes can thus be computed TM. These computed values were confronted with the estimations obtained by the eyedrawing procedure. It appears that differences between both procedures were less than 20 ~ m for the tip separation and 10° for the spatial orientation. This allows the use of the former procedure only, in the cases were dye electrophoresis did not succeed.

Analysis of data The experimental results that were kept for further treatment were those for which: (1) each spike train contained at least 500 spikes; (2) the processes describing the spike trains were renewal

ones < and (3) the distance separating the lwo recorded P('s could bc determined. The general principle used to analyse the effect of RC inhibition on the network dynamics is the comparison of two different functional modes: with and without inhibition. As statcd previously these will be termed Control and Bi modes, respectively. This comparison has been achieved by m e a n s of histogram and crosscorrclogram techniques ~c~2 as well as the informational entropy index technique introduced elsewhere I~'. A more detailed description of this entropy index analysis will be given in the relevant Results section. To establish the baseline for a crosscorrelogram, the interspikc intervals of both spike trains were shuffled so as to destroy any kind of correlation between the recorded PCs. This shuffling technique was also used to get the uncorrelated values of the entropy index, providing thus a reference value. To decide it peaks and troughs in crosscorrclograms were significant we systematically used a Kolmogorov test (this test determines if a distribution is uniform within 95~} confidence limit). In the Control mode inhibitory connections will be characterized by troughs in the corresponding crosscorrelograms. In the Bi mode. where inhibition becomes uneffective, these troughs should disappear leaving only the excitatory coupling due to CFs a n d / o r PFs. However, in some experiments data could be collected in the Control mode only. In these cases il was not possible to compare the crosscorrelograms with those corresponding to the Bi mode in order to decide if observed troughs corresponded to inhibitory links. Wc then used the data obtained from the shuffled spike trains as a comparison. Several crosscorrelograms were characterized by an important central peak due to correlated CFRs. This p h e n o m e n o n could be distinguished from a common input via PFs by controling, at the spike train level, the presence of synchronized CFRs. In the Bi mode the central peak subsisted as the drug did not influence CF discharges. Because of their specificity it was easy to withdraw CFRs by program from the files. This lead to new files with sole spontaneous simple spike activity. The withdrawal of the central peak in the erosscorrelograms characterized by common CFRs enhanced the visibility of inhibitory interactions. The same procedure was used for the informational entropy, when needed. RESULTS

Characterization of the recorded PCs At this stage of development the immature CbCx is quite fragile and as we recorded only in the most superficial part of the folium, one or both PCs could die, thereby preventing long duration recordings. In 41 experiments data were obtained in the Control mode only and in 26 other experiments in both Control and Bi modes. Three methods were used to ascertain that the recorded neurons were PCs. (1) JF stimulations (duration 50 /xs, intensity 0 - 1 0 mA) were used to identify PCs. In adults rats such antidromic PCs responses are characterized by a short latency and a capacity to sustain high frequency stimulations 36. In immature rats the latency is much longer (between 10 and 35 ms) and cells can not follow a stimulation frequency higher than 20-30 Hz (Fig. 2A). (2) PCs were also identified by their typical C F R s 23'35'64'74 a s can be seen on Fig. 3. (3) The recording of PCs was confirmed a posteriori by the presence of the dyes at the level of the PC layer. In all the results we show, the distance separating the recorded PCs could be evaluated.

237

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Fig. 2. Antidromic activation of an immature Purkinje cell. 7 days PN old rat. Two superimposed high-frequency ( > 10 Hz) traces before (A) and after (B) bicuculine superfusion. Note that the antidromic spike has a long, fixed, latency and that neither latency or spike form are changed by the drug superfusion.

Localization of the recorded PCs Pairs of nearby PCs were usually located in the medial part of the folium VIb + c at a depth, under the pia matter, ranging from 60/zm to 160/~m. Fig. 4A shows a computer reconstruction of folia VI a and VIb+ c of a single section in a 6-day-old cerebellum. The PC layer (PCL) is clearly outlined, just beneath the external granular layer. Note that, at the superficial part of the folia, the PCs are located at a small distance beneath the surface. Fig. 4B and C show two examples of 3D reconstructions. In these cases we have illustrated only the PC layer in adjacent serial sections, so as to show the location of the dye markings ejected from the tip of the micropipettes at the end of the experiments. In Fig. 4D is shown a photomicrograph of one of the sections from which Fig. 4C was reconstructed. Distances separating the microelectrode tips varied between 40 and 280 /zm. They were subdivised in 3 orientation classes: (1) longitudinal if dye spots were aligned along the longitudinal axis of the folium (18 out of 67 pairs),

(2) transversal if dye spots were aligned perpendicularly to the axis of the folium in a parasagittal plane (Figs. 4C and D) (11 out of 67 pairs) and (3) diagonal in all the other cases (Fig. 4B) (38 out of 67 pairs).

General considerations on spike activity and on the effect of bicuculline Two types of spike activity are easily recognizable: (1) the simple spike firing, the modulation of which is due to the integration of the excitatory/inhibitory balance impinging at the membrane level. This background ongoing activity was of rather slow frequency, in comparison with the adult, and irregular (Fig. 5A). As previously stated in the litterature TM doublets could be found in 5-6 days old rats. (2) the complex spike activity, of very low frequency, which is due to the excitatory input of CFs. As was described previously by other groups in newborn 28 as well as in adults 13 we found correlations between pairs of spontaneous CF discharges. Such correlations were detected by the simultaneous advent of complex spike discharges on both spike trains of the recorded PCs of a pair. An example is illustrated in Fig. 3. Correlated CFRs were not necessarily exactly time locked but could be separated by a small delay (up to 20 ms). Such a strong correlation is also clearly demonstrated by the existence of an important central peak on the corresponding crosscorrelogram as in Fig. 11, C1-C3. In all cases where common CFRs were present, the recorded PCs have a transverse orientation relative to the axis of the folium. Bicuculline superfusion clearly modifies the activity of the network. The background activity is more regular and significantly shifted towards a net increase in

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that there are no differences in the latency, in the spike shape, duration or amplitude. The capacity to sustain high frequency stimulations was not altered either. This seems to be as good as possible an indication, in extracellular recordings, that the applied quantity of drug does indeed have a purely specific effect. The spontaneous level of CF activity (about 0.2 Hz) as well as correlations existing between pairs of PCs by means of CFRs were maintained in the Bi mode.

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Quantitative analysis of PC spike trains General statistics. Table I lists the values of the mean

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the discharge frequency. This can be seen by comparing the spike trains in Fig. 5B with the ones in Fig. 5A. Such an effect was fully effective and constant about one minute after superfusion. To test wether this effect was solely due to the blocking of the RC inhibition by the drug and not by a change in the general m e m b r a n e properties of the PCs we compared the responses to antidromic JF stimulations in both Control and Bi modes. This is illustrated in Fig. 2A,B. It can be seen

interspike interval, the corresponding standard deviation and the median as a function of the age class of the new-born rat in the Control case. Fig. 6 illustrates this evolution for the 134 recorded PCs (2 x 26 in the Control + Bi set and 2 x 41 in the Control only set). In all cases there appears to be an important variability of the mean firing frequency between cells of a same age class as well as between age classes. This observation may be interpreted as the functional counterpart of the different degree of morphological maturation of neighbouring PCs in a restricted area 66. Nevertheless, a statistical analysis shows that there are no significant differences between classes in the values of Table I. We therefore considered that all recorded neurons could be pooled in a single class. The study of the different statistical parameters gives an insight on what happens in the network after superfusion of bicuculline. Table II compares, for each age class, the values of the mean interspike interval, the corresponding standard deviation and the median for those neurons for which data are available in both Control and Bi modes. This is, in turn, illustrated in Fig. 7. As can be seen from Table II and Fig. 7, the comparison between Control and Bi modes indicates that the blocking of RC inhibition induces a 35% decrease in the median of the interspike interval. This

Fig. 4. 3D reconstruction of recording sites after dye electrophoresis from the tip of the recording microelectrodes and serial parasagittal sectioning of the vermis. A computer program was designed to draw the outline of the different layers of the cerebellar folia from a given section (A). It also allows 3D visualization of a number of aligned serial sections (B). To avoid blurring, only the PC layer is represented here. Note the location of the two dye markings, which are diagonally oriented in respect to the axis of the folium. In (C) another example is given with the dye marks more transversally oriented. A photomicrograph of the corresponding section is illustrated in (D). The two dye markings are indicated by arrows. P6 and P7 indicate the postnatal age of the animal. Note differences in scale. Scale in D is 100/xm.

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much higher firing frequency also appears to be more regular (see standard deviation). lnterspike interval histograms. All our recorded spike trains are renewal processes and the following statistics are therefore valid. The shape of an interspike interval histogram gives an indication on the frequencies of the different states a neuron can take. Any changes in the shape of the histogram under two different functional conditions will indicate the modification in the successive, time-dependent, states of the cell. The exact determination of the mathematical function describing a distribution of interspike intervals is a very complex task. As a first approximation, the distribution func-

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tions of the recorded cells correspond to various combinations of uniform distributions, Gaussian distributions and Poisson processes, with one or the other being prevalent. Therefore we classified the 134 interspike interval histograms in two classes inside which histograms shared common characteristics: 'Gaussianlike' processes and 'Poisson-like' processes, examples of which are illustrated in Figs. 8 and 9, respectively. All 134 interspike interval histograms in the Control mode are characterized by a main peak between 35 and 400 ms as well as a slowly decreasing slope of long lasting intervals on the right side of the histogram. Fig. 8 shows the changes of the interspike interval histograms of a pair of PCs recorded in both Control and Bi modes (8 PN days old rat). The histograms of both cells in the Control mode (Figs. 8 A1 and 8 B1) may be described as 'Gaussian-like' distributions, centered on 150 ms and 275 ms respectively. Both are characterized by a slowly decreasing slope towards long lasting intervals on the right side of the histogram. In contrast to real Gaussian distribution the envelop is not symmetrical. In one case, CFRs can be detected on the histogram by the presence of a peak near the origin (Fig. 8 A1). This peak, which corresponds to short

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242 intervals, is due to the fact that CFRs are usually constituted by burst responses• Indeed, if the signal to noise ratio of the recording is good enough, secondary

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Fig. 9• A,B: as Fig. 8. Note that in one of the PCs the interspike interval histogram shape shifts from a 'Gaussian-like' distribution function in the Control mode (A1) to a 'Poisson-like' process in the Bi mode (A2). For the other on'e the shape is a constant 'Poisson-like' process (B1,B2). In both cases long-lasting intervals are nearly suppressed in the Bi mode and the peak is shifted torwards short lasting intervals. Note the presence of a peak of very short lasting intervals (around 40 ms) in the Bi mode. They characterize doublet discharges (see text). The analysis of the crosscorrelogram in the Control mode (C1) reveals a trough on the left side of the histogram which indicates an asymmetric inhibition. In the Bi mode (C2) and for both shuffled spike trains (C3 and C4) the distributions are uniform. In this and following figures arrows indicate the presence of inhibitory troughs.

243 events. Although CFRs were present, there is no peak near the origin on the second histogram (Fig. 8 B1) because the signal to noise ratio of the recording, in this case, was not good enough to allow the detection of secondary and tertiary spikes. Fig. 9 illustrates another experiment. A pair of PCs were recorded in both Control and Bi modes at 6 PN days, one of the neurons having a 'Gaussian-like' distribution centered around 175 ms (Fig. 9 A1), whereas the other one (Fig. 9 B1) shows a 'Poisson-like' process with long lasting intervals. The analysis of the interspike interval histograms in the Bi mode confirms that inhibition drives the network in a different space of states. Indeed, new features appear: (1) the main peak of the histogram is shifted, in all cases, towards shorter intervals: from 275 ms to 225 ms (Fig. 8 B2), from 175 ms to 50 ms (Fig. 9 A2) and from 45 ms to 40 ms (Fig. 9 B2). (Fig. 8 A2 is the only atypical case where the peak is delayed by 100 ms and becomes centered around 250 ms). In consequence, as described in the previous section, for a same recording time in both Control and Bi modes, the number of spikes is in average 1.5 times higher in the Bi mode (increase in discharge frequency). Notice that the peak at the origin due to CFRs does not change in the Bi mode (Fig. 8 A2), as the drug does not modify the CF discharge. (2) Long lasting intervals tend to disappear. As can be seen on Figs. 8 A2, 8 B2, 9 A2 and 9 B2, not only does the total number of long lasting intervals decrease but there is also a shorter slope on the right side of the peak. Figs. 8 A2 and 8 B2 are particularly illustrative as we obtain, after superfusion of bicuculline, nearly 'pure Gaussian' distributions, symmetric around the peak. (3) In most cases (90%) the rough shape of the histogram, does not change in the Bi mode. However, in 10% of the cases the shape of the histogram does change drastically. Such a case is illustrated in Fig. 9 A2 where the shape of the distribution becomes a 'Poisson-like' process in the Bi mode, whereas in the Control mode it was a 'Gaussian-like' distribution (Fig. 9 A1). This experiment (Fig. 9) also illustrates the presence of doublet discharges that were shown to exist in young animals TM. No climbing fiber responses were present for either PC. Although no doublet spikes were present in the Control mode, they appear in the Bi mode (Figs. 9 A2 and 9 B2) where they are evidenced by an important peak near the origin. Usually, the mean interval between the 2 spikes of such doublets is in the range of 40 ms. This distinguishes them from complex spikes which have interspike intervals in the order of 10-20 ms. Because such doublet discharges seem to appear more often in the Bi mode only, it may be

considered that inhibition masks this type of discharge in normal conditions. Other examples of the histograms obtained from pairs of PCs recorded before and after bicuculline superfusion are illustrated in Figs. 10 A,B, 11 A,B and 12 A,B. No obvious relationships could be found between the age of the animal and the shape of the distribution function of the interspike interval histograms of the recorded cells (see, nevertheless, Discussion).

Summary of the effect of inhibition on the states of the network, as deduced by the changes in the interspike interval histograms. As stated previously, the changes that occur in the shape and numerical characteristics of an histogram under two different conditions of the system are an indication of the constraints that lie on the neuron under study. The results described above show that RC inhibition imposes indeed a strong modulation on the activity of the network. (1) Some states tend to disappear (short lasting intervals and doublet discharges). (2) There is a shift of the peak of the histogram towards longer intervals. (3) New states appear (very long lasting intervals). (4) More complex changes in the firing characteristics of the neurons are also present as, in somes cases, the shape of the histogram shifts from 'Gaussian-like' to 'Poisson-like' after bicuculline superfusion. It must be stressed then that, if the cerebellar cortex is considered from the point of view of system analysis, the constraints brought about by the RC inhibition can be understood as a modification of the number of states available for the network. Indeed when inhibition is blocked the standard deviation and the median decrease as well as the mean values of the interspike intervals. This means that there are many more different states effectively scanned by the neurons in the network, the network seeming to evolve in a non-constrained state. When inhibition is present the system, on the contrary, evolves in a more confined space of states, each different neuron being submitted to particular constraints. Thus, in the present case, the shift in the space of states seems essential in building up cooperativity between the neurons of this system, as it will be demonstrated further on.

Study of the network with correlation techniques We will now analyze the effects of the RC inhibition on the cooperativity between PCs with correlation techniques: crosscorrelograms and informational entropy index. Crosscorrelograms. Crosscorrelograms are useful in determining the kind of correlation existing between two

244 neurons 5~'~2, be it mutual excitation a n d / o r inhibition or a c o m m o n input• T h e analysis of crosscorrelograms is sometimes very c u m b e r s o m e as it may be difficult to ascertain it' a p e a k or a trough is statistically significant.

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Fig. 10. As in Fig. 9, for another pair of PCs. The same general remarks concerning the effect of inhibition on the interspike interval histograms can be applied as in the preceding figures. The crosscorrelogram in the Control mode (CI) is characterized by troughs on both sides of the histogram, indicating symmetric inhibition of the pair of recorded neurons•

245

pier as we already have an idea of the local connectivity of the neuronal network: we know that at this stage

of development the 0nly excitatory inputs are due to CFs and very few functional PFs and that the only inhibitory ones are due to the RCs of the PCs. Thus, if one cell of the pair inhibits the other, there should be a trough in the corresponding side of the crosscorrelogram. If they inhibit themselves reciprocally there should be a trough on both sides. If they share a common excitatory input there should be a central peak in the case of correlated CFRs a n d / o r a peak or a plateau in the case where on line PCs receive common inputs through PFs. If no correlation exists the distribution of the crosscorrelogram should be uniform. The determination of the kind of connectivity which exists between two ceils is also important for the following as we will be able to relate it to the values of the informational entropy index. This index measures an absolute value of cooperativity between cells, the informational transfer between them. It can thus give us an indication about the structuring effect of inhibition. Concerning RC inhibition we found three kinds of relationships: (1) non-existent (no inhibition), (2) asymmetrical (one cell of the pair inhibits the other one) and (3) symmetrical (reciprocal inhibition). Table III lists the number of cases obtained for each of these in both the Control + Bi mode and the Control only mode. Apart from the correlations due to inhibitory interactions we also found several cases where correlations were due to excitatory inputs. We will now detail all these different cases: (1) No correlation at all. Figs. 8 C1 and 8 C2 are an illustration of the absence of correlation in the Control and in the Bi mode respectively. Both crosscorrelograms are characterized by uniform distributions. Figs. 8 C3 and 8 C4 are the corresponding crosscorrelograms of the shuffled spike trains. Their distribution is uniform and is comparable, in this case, to the Control and Bi mode ones. (2) Asymmetrical coupling. Fig. 9 C1 clearly shows on the left side of the crosscorrelogram a net decrease in the dischage probability of cell 1 after cell 2 has discharged. Inhibition seems to be efficient as soon as 10 ms after the discharge of cell 2 and lasts up to 400 ms after the discharge. In the Bi mode the trough disappears (Fig. 9 C2) and the distribution is uniform. As in the following, the corresponding shuffled spike train crosscorrelograms are drawn as controls (Figs. 9 C3 and 9 C4). (3) Symmetrical coupling. On Fig. 10 C1, 2 troughs clearly appear on both sides of the crosscorrelogram showing that the 2 PCs inhibit each other. The charac-

TABLE III

Inhibitory link

Non-existent Asymmetrical

Symmetrical

Control + Bi mode Control only Total

8 (30%) 18 (44%) 26 (39%)

9 (35%) 16 (39%) 25 (37%)

9 (35%) 7 (17%) 16 (24%)

teristics of the troughs are the same as in the previous case: early inhibitory onset and long lasting effect. The troughs disappear after superfusion of bicuculline (Fig. 10 C2). (4) Correlations due to common CFRs. This case is more complex as inhibitory interaction may be superimposed to common excitatory inputs due to synchroneous CF discharges. All cases were encountered in the experimental set: common CFRs superimposed with no inhibitory interaction (2 cases), asymmetrical (5 cases) coupling or a symmetrical one (7 cases). The case we illustrate in Fig. 11 corresponds to the superposition of common excitatory inputs due to CFs and an asymmetrical inhibitory coupling. We chose this case as it also possesses a particular interest: a very long lasting recording after bicuculline superfusion. Fig. 11 C1 shows the typical broad peak due to shared CF inputs. The broadness of the peak may be explained by the the combination of two phenomena: (1) the presence of several spikes in the CF burst and (2) the fact that they are not perfectly synchronized (if we take the onset of the cell 1 burst as a reference for the onset of cell 2 burst we get a window of +_25 ms wide). Superimposed on this phenomenon a trough seems to exist on the left part of the crosscorrelogram. As this phenomenon may be masked by the common CFRs we retrieved (as indicated in Materials and Methods, Analysis of data) all CFRs from the files containing the spike trains. The treated crosscorrelogram (Fig. 11 D1) clearly shows a trough on the left side of the crosscorrelogram (cell 2 inhibits cell 1) with the same previous characteristics concerning the onset and the duration of inhibition. Notice that in this case the trough is solely due to the background simple spike activity of cell 2 as all CFRs are retrieved. This method is thus quite reliable as it allows the detection of the underlying relationship due to simple spike activity. In the Bi mode (Fig. 11 C2) the peak is still present as CF activity is not affected by the drug but it is however broader. This is due to the fact that more spikes appear in the CFR because of the absence of inhibition. Indeed, a decrease in the level of inhibition implies an increase in the number of spikes of the CFR 35'38. The two sides of the crosscorrelogram, apart the central peak, seem to be at level, indicating that the asymmetrical inhibition has disappeared. This is

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247

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confirmed by the crosscorrelogram corresponding to the Bi mode with the CFRs retrieved from the files (Fig. 11 D2). The distribution is now uniform. In the experiment illustrated here we were able to keep the two PCs in fairly good conditions for a long period of time. We could then compute the different data a long time (10 min) after the superfusion of bicucculline. The CFR peak is still present (Fig. 11 C3) but less broad than just after the superfusion of the drug. The trough on the left side reappears and is more clearly visible once the CFRs are retrieved (Fig. 11 D3). These results show that the effect of bicuculline had disappeared and that the inhibitory effect of the RCs was restored. As we get the same numerical values and the same histograms as in the Control mode, we may conclude that the network returned to its previous state, with fully functional inhibition. (5) Correlations due to common PF inputs. This phenomenon could only be found in the Control + Bi mode set of experiments as it appeared after superfusion of bicuculline (n = 8 cases out of 26). In the Bi mode, when inhibition was blocked, several crosscorrelograms were characterized by an excitatory plateau on a single side of the histogram. This was found only for pairs of PCs aligned along the longitudinal axis of the folium and is therefore certainly due to afferent volleys carried by functional, although immature, PFs. This phenomenon starts at 7 days PN (apart from one case at day 6). This in keeping with published results that indicate the end of the first PN week as being the

period when PCs respond constantly to an electrical stimulation of the PFs at the surface of the folium65'7°'73. As can be infered from anatomical data this type of connectivity is independant of the RC connectivity. Indeed, correlation by PFs was found for 2 PCs pairs with no inhibitory coupling, 3 pairs with asymmetrical coupling and 3 pairs with symmetrical coupling. Fig. 12 C1 illustrate an example of such a superposition of symmetrical inhibitory interaction with shared PF inputs. The time courses are different as we note on the right side of the histogram a slower decreasing slope. As inhibition disappears in the Bi mode the crosscorrelogram is characterized by an excitatory plateau Qn the right side (Fig. 12 C2, arrowhead). The interspike interval histograms confirm an important increase in the discharge frequency (Fig. 12 A1,A2,B1, B2). Our explanation of this phenomenon is the following: the two cells being aligned along the longitudinal axis of the folium share a certain amount of common PFs. Spikes are traveling along the PFs from cell 1 to cell 2. In the Bi mode the PF spikes that induce discharges in cell 1 will also contribute to the discharge of cell 2. Hence an increase of the probability of discharge of cell 2 once cell 1 has fired. In the Control mode this plateau can not be detected, because of the inhibitory action of the RCs that prevents cell 2 to fire after cell 1. We did not find cases where the parallel fibre excitatory coupling was present in both directions, although the existence of such cases is theoretically plausible.

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249

To summarize five classes of functional correlations were present in the network: (1) Absence of inhibition, (2) RC inhibition (symmetrical or asymmetrical), (3) Correlations due to CFRs (with or without RC inhibition), (4) Correlations due to PF activity after uncoupling (with or without inhibition) (5) A mixture of cases 3 and 4. No clear correlations were found between the different parameters of the recorded PCs. In particular there seems to be no relationship between: (1) the frequency of discharge of the PCs of a pair and their mutual inhibitory relationship; (2) the shape of the distribution function of the interspike intervals of a PC and the kind of inhibitory input it receives from the other cell of the pair and (3) the kind of inhibitory relationship and the age of the newborn rat. This last point enforces our choice of pooling all the data. Informational entropy technique. In a companion, theoretical, paper 16, that will be discussed in section IV, we define an informational entropy index derived from information theory 69. This index can detect any kind of correlation among any number of neurons. A scale of cooperativity can be set up and the index is sensitive enough to detect the slightest cooperativity. This is true even in the cases where the crosscorrelogram will appear uniform, i.e. if all excitatory and inhibitory phenomenon merge themselves into a seeming noise. Another advantage is that it can measure cooperativity between theoretically any number of neurons whereas the crosscorrelogram technique, in its classical sense, is limited to the simultaneous study of three neurons 63. On the other hand, the limit of this index is that it gives an absolute value and can therefore not indicate wether correlations are due to external/internal a n d / or excitatory/inhibitory actions in the pool of neurons, as a crosscorrelogram may. We will briefly recall here the technique used to calculate the entropy index termed AS. Let us consider

two spike trains corresponding to simultaneously recorded PCs and a fixed time window (let us say 300 ms). We now move this window step by step along the two spike trains. At each step we calculate the number of spikes present inside the window (let us say i spikes for cell number 1 and j spikes for cell number 2). We then calculate the frequency of appearance Pi (Pj) of i (j) spikes for cell 1 (2 respectively) as well as the joint f r e q u e n c y Pij for both cells during this time window. The informational entropy index is defined by: ~_~Pi log Pi + E P j log pj - EPij log Ply AS=

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If there is no correlation we get theoretically AS = 0. With this mathematical tool we can thus specify the level of cooperativity existing between 2 cells. The higher the value of the index the more structurated is the system and the more stringent are the constraints on its active elements. We distinguish four indices: AS c in the Control mode, ASBi in the Bi mode, AScs in the Control mode after shuffling the spike trains and ASBis in the Bi mode after shuffling the spike trains. As shown in the theoretical study the values obtained after shuffling indicate the level of statistical fluctuations ~6. As all correlations disappear with the shuffling technique we should get AScs = ASBis whereas if correlations exist in the Control mode (Bi mode) we should get AS c > AScs (ASBi > ASBis).

In the previous section we saw that we could distinguish five classes of functional correlation existing between pairs of PCs. Typical values for AS obtained in each class are listed in Table IV. The significance level takes into account the first decimal only. These values correspond to the set of data obtained in both Control + Bi mode. Note that in all cases AScs = ASBis, indicating the effectiveness of the shuffling technique in obtaining uncorrelated data. The

T A B L E IV

no inhibition (0) asymmetric inhib (1) symmetric inhib (2) common CFRs + 0 common CFRs + 1 common CFRs + 2 common PFRs + 0 common PFRs + 1 common PFRs + 2

AS c

ASBi

AScs

ASBi s

0.006 0.164 0.308 1.054 2.266 7.097 0.024 0.106 1.817

0.052 0.009 0.018 1.075 0.803 4.588 0.147 0.084 0.761

0.047 0.026 0.034 0.014 0.032 0.018 0.030 0.035 0.042

0.045 0.027 0.029 0.002 0.047 0.046 0.038 0.029 0.053

CFRs are retrieved from the files AS C ASBi AScs

~lSBiS

0.005 0.132 0.327

0.009 0.020 0.015

0.011 0.019 0.034

0.023 0.033 0.022

250 differences correspond to statistical fluctuations. When the cells are independent (no correlation) we get AS( =AS~] = d S c s =ASBi s. When the cells are coupled asymmetrically we get a significative value, AS c = 0.164 whereas the other values are equal (ASB] = a S c s = ASBis). In the case of a symmetrical coupling we get a higher value of AS c (0.308) which is in keeping with the fact that the cells show more cooperativity than when they are asymmetrically coupled. Again we see that (ASBI = AScs = ASBis). When common CFRs are present we get higher values of AS depending on the level of inhibitory coupling. Indeed, there is a cumulative effect of both inhibition and excitation on the value of the index. For example, compare, in Table IV, AS c = 1.054 for common CFRs with no inhibition with the case A S c = 7.097 for common CFRs with symmetrical inhibition. In the corresponding Bi modes the values decrease because of the blocking of inhibition, but remain high due to the strong excitatory coupling (AS = 1). If the CFRs are retrieved, leaving only inhibitory correlations, we obtain the same values as the ones obtained for ceils not coupled with common CFRs (0.327 compared with 0.308 for a symmetrical coupling and 0.132 compared with 0.164 for an asymmetrical one). The case where common PFs are present gives intermediary values and the resulting coupling seems less efficient than the one due to common CFRs. This coupling appears when inhibition is blocked and the resulting values range from 0.084 to 0.761. The coupling due to inhibition is prevalant as the values obtained in the Control mode are greater than in the Bi mode. On Fig. 13 we plotted all the values of AS c for 59 pairs of recorded PCs (complete and non complete set). Values corresponding to pairs with common PF inputs (n = 8) are not plotted because the coupling due to common PFs can not be withdrawn from the files as it was the case for common CFRs. In order to study the sole inhibitory effect we withdrew from the files common CFRs when they were present. The index value was represented as a function of the ratio between the two corresponding mean interspike intervals so as to illustrate its independance in respect to the activity level of the different neurons. Three distinct zones can be distinguished. (1) The first one contains values of AS c ranging from 0.0 to 0.06 and corresponds to the cases where no direct inhibitory link exists between the 2 PCs of the recorded pair. The values of the entropy index in the Control mode and in the Bi mode are of the same range as those obtained after shuffling the spike trains i.e. AS c = ASB~ = 0 as is theoretically expected.

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(2) The second one contains values of AS c ranging from 0.065 to 0.17 and corresponds to the cases where inhibitory relationships are asymmetrical. In this zone the value of AS c is above the base line provided by the shuffling technique and it can be noted that it is intermediate between the one obtained in the absence of inhibitory relationship and the one obtained for a symmetrical relationship (next point). (3) The third one contains values of AS c > 0.18 and corresponds to the cases where inhibition is symmetrical. Here the values are more spread out. This result suggests that the 'strength' of inhibition seems to vary from cell to cell (see Discussion). Note that we found a case where PCs were aligned along the longitudinal axis of the folium and had a crosscorrelogram, in the Control mode, showing an uniform distribution (not illustrated). However, the corresponding value of AS was quite high ( = 1.1). In the Bi mode a plateau could be seen in the crosscorrelogram indicating PF coupling. The value of AS dropped to 0.5. We can conclude that PF coupling was present

251

in the Control mode and that no correlation could be

An immunocytochemical study of the distribution of

detected on the crosscorrelogram because the merged excitatory and inhibitory events balanced each other. However, the entropy index could detect the existence of a coupling between the two neurons. According to our scale of cooperativity those two cells could have been symmetrically coupled via their RCs. This result demonstrates that, in some instances, this technique can bypass crosscorrelogram limitations. The informational entropy technique is thus sensitive enough: (1) to detect different levels of cooperativity between pairs of PCs and (2) establish a scale of cooperativity between neurons. The results are, moreover, consistent with those obtained with the crosscorrelograms.

the PC axon collateral 4] has shown that mabQll3 immunoreactive RCs, in the adult rat, are characterized by mediolateral and antero-posterior polarities in accordance with the developmental features of the CbCx. The relative spatial orientations of the asymmetrically coupled pairs, as deduced from the drawings (see material and methods section) and the 3D reconstructions, show the same polarity. 10 out of 11 asymmetric connections in the transverse orientation are oriented in a latero median direction and 5 out of 5 of the pairs in the sagittal orientation are oriented in a postero-anterior direction. It can be noted too that cells characterized by common CFRs tend to be preferentially oriented along the transversal axis of the folium in keeping with published results 28.

Correlation between the type of inhibitory coupling and the distance and orientation of the recorded PCs The cooperativity of the cells is highly dependent upon the anatomical connectivity. We found a strong correlation between the type of inhibitory relationship of a pair and their mutual distance. On Fig. 14 we give the histograms and numerical values, of the distance separating each cell of the pair for cases where there is no inhibitory coupling (A), an asymmetrical one (B) and a symmetrical one (C). It appears that reciprocal inhibition corresponds to a close neighbourhood whereas far separated cells tend not to be coupled by RCs. Asymmetrical coupling is present for intermediate values.

N

pairs

,,

N pairs

A

COMPARISON OF EXPERIMENTAL RESULTS WITH THOSE OBTAINED BY SIMULATIONS IN A MODEL OF THE IMMATURE CEREBELLAR CORTEX We used known morphological and physiological data as well as some of the above described results to build a model of a portion of the immature CbCx ]6. Data of both experimental and theoretical approaches were analysed with the same techniques, allowing thus a point to point comparison between them. In this section we will briefly recall the main characteristics of

B

N

pairs

C

7_

No coupling N-27 m= 1 8 3 ~ o =~tJm m d . 160,urn

0

40

eo

120 1~0 gO0 2 ~ " 2~0" 3~0" 3~0 " 4(~0 Mm

" b " 4o

1

leo 200 240 280 320 360 400 ,urn

u

40

1

1

2

2 M rn

Fig. 14. Diagram of the distance between members of a pair of recorded PCs for the case where the crosscorrelograms indicate that there is no coupling (A), an asymmetric one (B) and a symmetric one (C). Note the strong relationship between the type of coupling and the distance between cells.

252 the model, the main simulated results and compare them with the experimental ones. The network contains 256 artificial neurons (AN) spread in a 16 × 16 square lattice. As for the case of the in vivo experimental situation, the model can evolve in two different modes: the Connected Mode (CM) where RCs are functional (i.e. equivalent to the Control mode) and the Non Connected Mode (NCM) where all ANs are independent (i.e. equivalent to the Bi mode). In the CM all ANs are connected by RCs to a certain number (between 6 and 10) of their 24 nearest neighbours. The firing frequency of each AN is given by a Random Number Generator driven by uniform, Gaussian distributions or Poisson processes. Once an AN fires a spike it inhibits each of the neighbours it is connected to. The inhibitory action was modeled so as to cancel or delay the predicted spike of the receiving AN. This mimicks the functional effect of physiological inhibition at the PC level 12'3~. In order to simulate the sole inhibitory action of the RCs we decided to disregard any coupling due to common CFR or PF inputs. The results can be summarized as follows. The system appears to be less constrained when the RCs are not functional (NCM or Bi mode). In this case the ANs, as the PCs, are allowed to evolve 'freely', driven only by their intrinsic activity and the excitatory inputs due to CFs and PFs in the biological system and, in the model, by the Random Number Generator. Whatever the system (real or modeled) inhibition has the same effects on the activity of the elements: it structurates the network and induces cooperative relationships between the cells. Indeed: (1) There is a net decrease in the discharge frequency of the cells (35% for the PCs, 40% for the modeled cells). (2) The shape of the interspike interval histogram is changed in the same way: the rough shape of the distribution function is maintained, the main peak is shifted towards longer lasting intervals and a slowly decreasing slope of long lasting intervals appears on the right side of the peak in the CM, as in the experimental Control mode. (3) In the model the duration of the inhibitory effect is longer than in the real system. In the model the trough appears after 25 ms and lasts from 40 to 150 ms according to the parameters characterizing inhibition. In the real system the trough appears as soon as 10 ms and may last as long as 300-400 ms. The strength of inhibition seems thus to be stronger in the real system than in the modeled one. (4) Inhibition spreads in the network beyond the strict connectivity, i.e. a group of cells containing ele-

ments not necessarily connected by RCs is characterized by a certain level of cooperativity. This propagation is anisotropic, the effect being present only in preferential directions. (5) We have shown that the informational entropy index is a powerful tool able to detect cooperative structures in a pool of any number of neurons and that a scale of cooperativity can be established. This was confirmed for a real neuronal network as is shown in the Results section of this study. In the biological system we demonstrated that the informational entropy index was sensitive enough to detect not only cooperativity between a pair of PCs but that it was also able to establish a scale of cooperativity. As could be expected mathematically, according to the theoretical results, the index takes a vanishing value for independent neurons. When they are reciprocally linked by RCs the value of the index is significantly much higher. It corresponds to the values found in the model. An asymmetrical coupling is characterized by a value intermediate between the two. We thus showed three separated levels of the index, corresponding to the absence of direct inhibitory link, an asymmetrical coupling and a symmetrical one. In the model variations of the index for two ANs having the same type of coupling were attributed to the differences in the parameters of their RNGs, or to variations in the neighbouring connectivity. Poisson processes seem to give stronger correlations than uniform distributions, as does a denser connectivity in the surrounding. We tried to see if these kinds of correlations held for the in vivo data but we could not find a clear relationship between the value of the index and the activity of the recorded cells. This may suggest that the strength of the inhibitory connection is variable or that the correlation strongly depends upon the local connectivity.

DISCUSSION AND CONCLUSION In this study we describe how the inhibitory RCs of the PCs axons change the activity of the CbCx neuronal network. Although the inhibitory action of cerebellar interneurons on PC activity has been thouroughly analyzed 32,33"34'37 little attention has been paid to the functional role of RCs inside a microzone. Most available data concern morphological studies about the RC distribution 17"18'2°'21'25'41'48'56'60.Our physiological experiments were done at an immature corticocerebellar stage (5-8 PN days) when a simpler organization of the system is present. This allows an analysis restricted to the effects of the sole inhibitory RCs. By comparing

253 the firing of neighbouring PCs in the case where the RC inhibition is effective (Control mode) and in the case where the inhibition has been antagonized by superfusion of bicuculline (Bi mode) we were able to show that: (1) the RCs in this very immature structure have indeed a functional and specific action; (2) the effect of this type of inhibition leads to an increase in the informational content of the network. Moreover a thourough analysis on the type of cooperativity between neurons lead to (3) specify some of the constraints leading the network in a different functioning mode.

General considerations All our results were obtained on PCs recorded at a small distance below the surface of the folium. At this developmental stage PCs are morphologically very immature and show a great variability in their development T M . They are also much more sensitive to any changes in their overall environment, be it an approaching microelectrode tip, the CbCx movements due to respiration, any oedema, or dessication. Because of the necessity to superfuse bicuculline in the protocol our experimental setup hinders the use of an Agar gel to protect and stabilise the surface of the cortex. We therefore paid particular attention to the deterioration of the general state of the animal as well as to any increase or decrease in the discharge frequency of the PCs that could not be attributed to the onset or disappearance of the antigabaergic effect of bicuculline. Any doubt about the state of the recorded neurons a n d / o r on the modification of the discharge frequency of one (or both) recorded PCs, during any of the experimental phases (Control or Bi mode), lead to the rejection of the recorded data. The only recordings that were kept for further treatment were those which were homogeneously stable and for which the distribution functions of the interspike intervals were renewal processes 61. We were also very stringent on the criteria used, (1) to ascertain that the recorded neurons were PCs and (2) that the action of the drug had no detectable side-effects which could account for the changes in the firing of the cells (see relevant Sections), We are, naturally, aware of the limitations, in this regard, of extracellular recordings and also that all the evidence we present to support both these assertions are only indirect. Nevertheless, the homogeneity of the results as well as the biological validity of the criteria/tests we used make us quite confident about the nature of the recorded cells and about the specificity of the drug action.

In the adult rat CbCx G A B A is released at the PC level from different sources: either from the RCs of the PCs axons or from the axonal terminations of basket cells 27'49' stellate cells 57'71 and intermediate fusiform cells n. Molecular layer interneurons have been shown to have a powerful inhibitory action on PCs in the adult 32'33'34. In the newborn rat, whose cerebellar development is for the most part postnatal, the situation in this regard is more simple. The ontogenetic development of electrical, enzymatic and histochemical activites as well as the morphological maturation of the different elements of the CbCx have been thoroughly investigated3'7-1°'64'65'67'68'7°'72-74. Several arguments from these studies indicate that between 5 and 8 PN days basket and stellate cells are not functional. These neurons originate from the external granular layer 67, the maximum peak of proliferation appearing to be around 6-7 PN days for basket cells and from 8 to 11 PN days for stellate cells 7. Their maturation seems to be highly dependent upon the maturation of the external granular layer. As the maturation of folium VI, the one in which we recorded the majority of the PCs, is one of the latest to occur 7-~°, the probability to find functional interneurons between 5 and 8 PN days is very low. Histochemical studies have also shown that lactate dehydrogenase (LDH) and succinate dehydrogenase (SDH) activities appear at about PN day 9 in the molecular layer interneurons, and that the G A B A transaminase activity appears just a short time earlier 72'73. Electrophysiologically the basket and stellate cells have been shown to exert a postsynaptic inhibitory effect at PN day 117°. This result is in keeping with the histochemical data as it seems natural that LDH, SDH and GABA-T activities would precede the functional inhibitory mechanisms themselves. The previous arguments are all in favour of a purely RC origin of GABAergic inhibition on the PCs of the immature CbCx in the period we have studied. Moreover, PCs have been shown to be very sensitive to iontophoretically applied G A B A as soon as 1 PN day 72-74. This sensitivity, whose functional significance seemed puzzling to some authors 7°, can be explained by the existence of a very early RC effect. PCs were indeed shown to have spontaneous activity with a functional axon at the same early age 72,73. Since the completion of this work it has been shown that, contrary to what was thought since the tritiated thymidine studies of twenty years ago 1°, the intermediate fusiform neuron of the granular layer 6° appears at its definitive cortical location at about 5 PN days 43. As this neuron also seems to be GABAergic 11 its effect must certainly contribute to the firing of the PCs in the network. Complementary studies will be needed to clarify this point.

254 In the adult, the PC axon usually gives rise to ascending RCs that form an extensive arborization in the depth of the molecular layer and contact the soma and dendrites of neighbouring PCs in a preferentially transverse direction j7'j~2°21,29'3°'4~'55,5~. In the developing cerebellum a phase of hyper-innervation of RCs has been suggested ~7. An H R P intracellular study aiming to understand the PC multi-innervation by CFs 26 has shown that up to 8 PN days PCs usually have between one and four RCs. The arborization is preferentially oriented in the sagittal plane of the folium and there does not seem to be a relationship between the developmental stage of the PC dendritic tree and the collateralization of its axon, as if the developmental timing of both were independant. Our own electrophysiological data are in keeping with these anatomical ones but they also clearly indicate that the PCs in a given area may have symmetrical or asymmetrical relationships through this RC system. This suggests that these collaterals may play a specific function in the properties of a given microzone. In our model we have taken into account all these results and each AN sends between 6 and 10 collaterals to its 24 possible nearest neighbours, in a preferential sagittal direction. To establish a comparison with the biological system, this choice corresponds to two RCs per PC, each giving rise in average to two arborizations spreading in opposite directions and contacting about four PCs each. This model is in keeping with the most recent morphological investigation performed in the adult CbCx 5~'.

Classical statistical analysis of data Analysis of spike train and interspike interval histogram characteristics have shown that in the Control mode the mean frequency of discharge increases with the age of the newborn rat, as already known from previous reports 23'72'73 and that interspike interval histograms can be described by different distribution functions. We not only found 'Gaussian-like' and 'Poisson-like' distributions but also combinations of both. In all the cases histograms have two common features: a single main peak, between 100 and 300 ms, and a slowly decreasing slope of long lasting intervals. We have not found any relationship between the age of the new-born rat and the shape of the distribution functions. However, morphological studies have shown that in a given area there are PCs of different developmental stages 7-m'66. One can then not exclude that there could be a correlation between a given distribution function and a specific maturation state of the neuron. Only a systematic study of PC activity coupled to H R P intracellular labelling might answer such an issue. It

also seems that there is no relationship between the shape of the distribution function and their type ol inhibitory coupling. In the Bi mode the RC inhibition has been antagonized and the constraining effect of inhibition on the network has disappeared. Superfusion of bicuculline induces a net increase in the discharge frequency of the recorded PCs (between 30% and 100%), the disappearance of long lasting intervals as well as an increase in the number of short lasting intervals. This leads to a shift of the main peak towards shorter intervals and a more steady, regular, discharge of the cells. In some cases a drastic change of the distribution law between the two modes is also seen. This phenomenon might be due to complex inhibitory interactions a n d / o r loops that would constrain the PC in a different discharge mode. Crosscorretograms is a potent technique that can reveal the type of relation between two cells. This is true for direct excitatory or inhibitory links as well as for common inputs 62's~. Several drawbacks of the method have been studied ~'2'5'~9'22'4°'53, in particular the fact that troughs and peaks may sometimes be difficult to detect 4'5°. In our study the crosscorrelogram technique was able to detect inhibitory relationships between'PCs and common excitatory inputs. The crosscorrelogram analysis revealed several features of the inhibitory interactions among which the most important is certainely that it is characterized by a prolonged effect, as the decrease in the probability discharge of the cell in contact lasts several tens of mss (up to 400 ms). This may be explained by the fact that the inhibition brought about by the RCs, at least at this stage of development, is functionally very powerful. One may then wonder if in the adult stucture this type of inhibition might not even be more powerful than the inhibition due to the inhibitory interneurons. An alternative/complementary view is that each inhibitory system impinging on the PCs enforces different types of functional constraints on the output of the network. Two types of excitatory correlations between neuron pairs were seen, namely by means of CFs and of PFs. Of the 67 PC pairs we recorded, 14 were characterized by correlated CFRs. This was apparent as an important central peak in the crosscorrelogram. This phenomenon could be due either to the concommitant firing of two collaterals of the same CF impinging on two different PCs, or to the concordance of discharge of neighbouring olivary neurons, electrically coupled by gap junctions (see Ito4Z), whose axons contact the pair of recorded PCs. An alternative explanation could be the multiinnervation of a pool of PCs by a pool of incoming CFs 24"26'45'4°. It is difficult, with the experi-

255 mental protocol we used, to distinguish between these possibilities. In our experiments we have found correlated CFRs in PCs separated by as much as 283 tzm in a diagonal orientation with respect to the axis of the folium, therefore not limited strictly in the sagittal orientation as stated by previous investigators28. The second type of excitatory coupling seems to be due to PFs. In the Bi mode, whereas all inhibition had disappeared, crosscorrelograms were characterized, in eight cases, by an important excitatory plateau and not by a uniform distribution. As this phenomenon appeared only for cells aligned along the longitudinal axis of the folium it seems plausible that this coupling is due to activity in PFs that successively fire the PCs of the pair. As previously mentioned PFs are parallel to the longitudinal axis of the folium and deep ones in the incipient molecular layer are functional at this stage of development 65'7°'72'73. The analysis of the spatial localization of the recorded PCs shows that 10 pairs were aligned along the longitudinal axis of the folium and that 3 pairs aligned along a diagonal direction were separated in the sagittal plane by 20/xm. Of the 8 pairs characterized by common PF inputs, 6 were perfectly aligned along the longitudinal axis of the folium and 2 shifted by 20/xm in the sagittal plane. It will be noted that this 20 /~m value corresponds to the precision of our distance measurement. Given the spread of the dendritic tree at this stage of development 2 cells shifted by 20/xm in the sagittal plane may be contacted by a same bundle of PFs. 75% of the PCs (8 cases out of 13) aligned along the longitudinal axis are thus characterized by this type of correlation. The fact that five pairs do not show this correlation may be explained by the fact that PFs at this early age do not always make synaptic contacts with the dendritic trees they cross as they do in the adult 6°. It will be noted that this excitatory link was seen in the Bi mode but could not be detected in the corresponding crosscorrelograms of the Control mode. This can be explained either by the fact that the superposition of excitatory and inhibitory phenomena at the PC level antagonize each other exactly, thus destroying any existing correlation or, more physiologically, that the RC inhibition hinders the activation of one PC following that of the other in the pair. The fact that the correlation between the two neurons is most often a plateau, means that the concordance of signals in the PFs that successively activate the PCs of the pair is not systematic, and that it is superimposed upon the intrinsic activity of the cells. The issues about information transmission by PFs to PCs along a folium have been analyzed in a recent theoretical study ~5.

Informational entropy index The spike train data analysis with the classical statistical techniques has shown that inhibition induces strong constraints on the system, as its overall activity is shifted from a given functional state towards another one. From an information theory point of view it must be proved that the states the network can reach are different and that its informational content has changed. Measuring the informational content of a given system per se has no relevant meaning. It is indeed necessary to compare two different states of the system in order to quantify the change in information content. In the experimental protocol the immature CbCx is recorded under two different functioning modes: Control and Bi modes. Moreover the results obtained with the shuffling technique can be used as a base line, as was demonstrated in a theoretical study 16. When no correlation exists between 2 cells the 4 values of the informational entropy index (Control, Bi, Control shuffled and Bi shuffled modes) are all close to 0, as predicted by the model. If the two cells are reciprocally coupled via RCs the value in the Control mode is in the same range as the one obtained in the model. This further reinforces the analogy between the model and the real network. If they are asymmetrically coupled the value obtained is intermediate between 0 and the one obtained for a symmetrical coupling. An important point is that inside well defined limits the same kind of coupling gives quite scattered values (Fig. 13). This suggests that the overall effect of the RCs is different from cell to cell. Indeed, for symmetrically coupled cells the index values range from 0.2 to 1.0. Three non-exclusive arguments may explain this scale of values: (1) The 'strength' of the inhibitory synapse is different from cell to cell. This phenomenon could be viewed as the manifestation of modifiable synapses that might exist in a system undergoing a phase of development and structuration. If such is the case modifiable synapses should also be looked for at the RC level and not only at the PF-PC synapse level,as suggested by Marr 47 and Albus 6. Our experimental results show that RC inhibition has a powerful effect on the system contributing at a local level to the processing of information. (2) Morphofunctional differences in the local circuit, around the recorded cells, might explain different levels of cooperativity. (3) The intrinsic activity of the cells themselves may contribute to the level of cooperativity. Our model shows that two neurons that are directly coupled have a greater cooperativity if their spike trains are charac-

25(~ terized by Poisson p r o c e s s e s than if they have G a u s s i a n distributions. W h e n PCs are c h a r a c t e r i z e d by a P F c o u p l i n g the value of the index o b t a i n e d in the Bi m o d e is o f the s a m e o r d e r as the one o b t a i n e d for a s y m m e t r i c a l coupling (0.4). T h e s e values show that the c o u p l i n g via P F s is as strong as the inhibitory c o u p l i n g via RCs. T h e c o n t r i b u t i o n of these P F s to the i n f o r m a t i o n a l c o n t e n t of the system thus a p p e a r s to be significant. This finding c o r r o b o r a t e s o u r hypothesis that P F s must be e n c o m p a s s e d as s o p h i s t i c a t e d d i s t r i b u t i o n lines, i.e. that the r e l e v a n t i n f o r m a t i o n c a r r i e d by P F s is dist r i b u t e d to very few cells in the folium a n d t h a t the r e m n a n t activity p r o v i d e s a b a c k g r o u n d noise to neighb o u r i n g PCs ~~. T h e m o d e l forecasts that inhibition p r o p a g a t e s itself in the n e t w o r k b e y o n d the strict a n a t o m i c a l connectivity. W i t h the e x p e r i m e n t a l s e t u p we used, this finding could not be verified in vivo. H o w e v e r , if we c o n s i d e r the values t a k e n by the e n t r o p y index for non directly c o n n e c t e d pairs in the m o d e l , we can forecast a value i n t e r m e d i a t e b e t w e e n the o n e o b t a i n e d for a s y m m e t r i cally c o u p l e d n e u r o n s a n d t h e o n e o b t a i n e d for far s e p a r a t e d neurons. It is thus possible t h a t a p o r t i o n o f the a r e a d e f i n e d by non directly c o n n e c t e d cells in Fig. 13 might c h a r a c t e r i z e n e u r o n s which could be c o u p l e d by a s u r r o u n d i n g n e t w o r k of relay neurons. O n l y an i n t r a c e l l u l a r study with 3 D r e c o n s t r u c t i o n of s t a i n e d R C s could a n s w e r this issue. F o r obvious r e a s o n s the r e c o r d i n g s in t h e s e very i m m a t u r e a n i m a l s w e r e r e s t r i c t e d to two n e u r o n s . W e could not t h e r e f o r e test the evolution of the i n f o r m a tional e n t r o p y index for a large n u m b e r of n e u r o n s as in the model. This might be achieved, in a c u t e a n i m a l p r e p a r a t i o n s , with the d e v e l o p i n g t e c h n i q u e of multin e u r o n recordings. Conclusion

This e x p e r i m e n t a l study is a c o n t r i b u t i o n to the u n d e r s t a n d i n g of t h e effect o f the inhibitory r e c u r r e n t c o l l a t e r a l s o f the P u r k i n j e cells in the i m m a t u r e rat c e r e b e l l a r c o r t e x n e u r o n a l network. A t this early stage of d e v e l o p m e n t t h e s e R C s a p p e a r to be f u n c t i o n a l a n d to i m p o s e strong c o n s t r a i n t s on t h e overall P C activity. In the a d u l t CbCx, R C inhibition is classically b e l i e v e d to be w e a k a n d acting m a i n l y on i n t e r n e u r o n s via i n h i b i t o r y / d i s i n h i b i t o r y processes. M o r e r e c e n t anatomical studies have insisted on the i m p o r t a n c e o f R C c o n t a c t with n e i g h b o u r i n g PCs in a r e s t r i c t e d area. This is in k e e p i n g with o u r results a n d suggests a c o m p l e m e n t a r y i n t e r p r e t a t i o n o f the R C function. Ind e e d , this R C system c o u l d b e v i e w e d as a specific type o f filter (in a g e n e r a l systems p o i n t of view) that acts

on the o u t p u t of a given m i c r o z o n e so as to c o r r e l a t e the activity of its different PCs. In the p r e s e n t study this c o r r e l a t i o n is clearly seen b e t w e e n the ' s p o n t a n e o u s ' or ' o n g o i n g ' activity of the r e c o r d e d neurons. I1 r e m a i n s to be seen if this c o r r e l a t i o n would be stronger. or w e a k e r , in the case w h e r e a 'meaningful" information transits in the network. A s shown in a c o m p a n i o n t h e o r e t i c a l p a p e r , c o o p e r a t i v i t y is still i m p o r t a n t when this R C system is m o r e diffuse, as in the adult. Finally, this study e n h a n c e s the functional import a n c e o f the a n a t o m i c a l a r c h i t e c t u r e for the informational p r o p e r t i e s of any n e u r o n a l network. The authors wish to express their sincere thanks to Mrs. M.E. Marc for expert technical help. This research was supported by Grants: MRT 86JO332-01 and INSERM CRE 899001.

Acknowledgements.

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