Quantal parameters of ?minimal? excitatory postsynaptic potentials in guinea pig hippocampal slices:...

Exp Brain Res (1992) 89:248 264

E.rn Br n Research �9 Springer-Verlag 1992

Quantal parameters of "minimal" excitatory in guinea pig hippocampal slices: binomial approach

postsynaptic potentials

L.L. Voronin 2, U. Kuhnt 1, G. Hess 3, A.G. Gusev 2, and V. Roschin 4

1 Max-Planck-Institute for biophysical Chemistry, Department of Neurobiology, P.O. Box 2841, W-3400 G6ttingen, Federal Republic of Germany 2 Brain Research Institute, Academy of Medical Sciences, CIS-103064 Moscow, Russia a Jagiellonian University, Institute of Zoology, PL-30-060 Krakow, Poland 4 Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences, CIS-103064 Moscow, Russia

Received April 15, 1991 / Accepted December 31, 1991

Summary. Binomial distributions of amplitudes of excitatory postsynaptic potentials (EPSPs) mixed with Gaussian noise were simulated. The objective of Monte Carlo simulations was, firstly, to study influences of sam- piing size (N) and noise standard deviation (Sn) on estimates of mean quantal content (m), quantal size (v) and binomial parameters (n and p) by four methods of quantal analysis (histogram, variance, failures and combined method) based on the binomial model and, secondly, to modify these methods on the basis of comparison of estimated with simulated parameters. Reliable estimates (within + 10% of the simulated values) were obtained for large sample sizes (N= 500-1000) with Sn<v by the histogram (deconvolution) method and with Sn < 2v by the other three methods. Similar results were obtained by averages from about 10 simulations if smaller samples were used (N= 50-200). In electrophysiological experiments on slices, "minimal" EPSPs were recorded from CA1 pyramidal cells after low-intensity stimuli to stratum radiatum or stratum oriens. Amplitudes of minimal EPSPs fluctuated in a manner predicted by the quantum hypothesis. Amplitude distributions of EPSPs in the nonfacilitated state were adequately described either by binomial statistics with an average p equal to about 0.4 (a range of 0.3-0.7) and an average n of about 3 (range 2 6) or by Poisson statistics with m of about 1. The quantal analysis suggests that typical values o fm and v for a single activated fibre in stratum radiatum might be about 0.5 1 and 300-400 ~tV, respectively, with low p (0.1-0.3) and n (2-4). However, the estimates of binomial parameters should be considered as coarse approximations in view of the simulation results and a possible nonuniformity of parameter p. The comparison of results of various methods based on the binomial model, in both simulation and physiological experiments, indicates the reliability of estimates of basic quantal parameters (m and v) under realistic conditions of physiological experiments. The methods are considered to be sufficiently sensitive to make

Offprint requests to: U. Kuhnt

use of them for studies on mechanisms of long-term synaptic plasticity.

Key words: Quantal analysis - Computer simulation - Hippocampus In vitro - Guinea pig

Introduction

A known electrophysiological approach to a quantitative analysis of synaptic transmission is based on the quantum hypothesis (Del Castillo and Katz 1954a, b). The hypothesis and its applications were described extensively (Katz 1966, 1969; Martin 1966, 1977; Kuno 1971; Wernig 1975; Kandel 1976; McLachlan 1978; Voronin 1979; Standaert 1982; Korn and Faber 1987; Redman 1990; cited below as Revs.). Briefly, the quantum hypothesis is based on the assumption that a postsynaptic potential (PSP) at a synapse with chemical transmission consists of a whole number of fixed units ("quanta"), i.e

Ei =xv, (1)

where E i is the amplitude of a single PSP, v is "quantal size" or "unit PSP", and x is the number of quanta in a given PSP ("quantal content"), x being an integer (x =0, i, 2 . . . ) . Approximate fulfillment of the relation (1) was confirmed many times with recordings from neuromuscular junctions and neuro-neuronal synapses (see Revs.). If n is the constant number of "available release units" (Del Castillo and Katz 1954a) or "release sites" (Zucker 1973; Korn et al. 1982) and p is the probability of the release of a single quantum (the same for each release site) then the mean number of quanta released per presynaptic impulse, i.e. the mean quantal content

m = np, (2)

the mean PSP amplitude

E = m v , (3)

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and the number of PSPs with x quanta is given by binomial coefficients with parameters p and n (see Revs. for formulae).

This traditional variant of the quantal hypothesis assumes that the synaptic release can be described by the binomial process (or its Poisson approximation when parameter p is negligible if compared with 1). The quantal analysis was initially used in studies of neuromuscular junctions although attempts have been made since the early sixties to apply this theory to "minimal" (evoked by low-intensity stimulation) PSPs of spinal motoneurones (Katz and Miledi 1963; Kuno 1964a, b). The application of quantal analysis to neurones of the vertebrate central nervous system (CNS) met many difficulties. One of the difficulties is related to the multiple inputs impinging on central neurones. This difficulty might be partially over- come by recording unitary PSPs (i.e. PSPs evoked by activity of a single presynaptic axon) following either stimulation of isolated afferent fibres (Mendell and Henneman 1971) or intracellular stimulation of presynaptic neurones (Shapovalov 1980; Shapovalov and Shiriaev 1979, 1980; Korn et al. 1982, Grantyn et al. 1984). How- ever, this situation is not practical for studies of many kinds of central neurones. For example, earlier attempts to record simultaneously from two hippocampal neurones in vivo were only successful in a few cases (Baskys et al. 1980). Even in hippocampal slices, the success rate of simultan- eous recordings from synaptically connected neurones in CA1/CA3 was found to be very low (Friedlander et al. 1990; Sayer et al. 1989, 1990). In addition, several other problems are not resolved for CNS neurones. Among them is the difficulty of directly determining v from spontaneous activity because of multiple synaptic inputs (see as an exception data of Korn et al. 1987, Korn and Faber 1990 for the Mauthner neurone and also recent developments of Bekkers et al. 1990 based on the patch clamp technique for hippocampal neurones). Additional problems are created, firstly by the high noise level due to both high electrode resistance and background synaptic activity, secondly by small sample sizes because of the short time of intracellular recording from healthy cells, and also by the necessity of "stationarity" for a reliable statistical analysis. The limita- tion of sampling sizes might be illustrated by the study of unitary inhibitory PSPs in the fish Mauthner cell (Korn et al. 1982) with the average number of counts equal to 161 and with less than 70 counts in some cases. All these problems common for most neurones of the CNS are heavily aggravated for recordings from higher CNS levels of the mammalian brain (e.g. cortical structures).

Attempts were made previously to apply the quantum hypothesis to study both short-term and long-term synaptic plasticity in the mammalian brain by recording minimal excitatory postsynaptic potentials (EPSPs) from the hippocampus of unanaesthetized rabbits (Baskys et al. 1978; Voronin 1981-1988b). A more favourable situation for the statistical analysis is provided by the hippocampal slice preparation (Hess et al. 1987). Initial attempts along this line were made by Brown et al. (1979) with recordings of spontaneous PSPs in CA3 and by McNaughton et al. (1981) with recordings of minimal EPSPs in the dentate gyrus. At present data on quantal analysis were published

on presumably unitary EPSPs from pyramidal neurones in area CA3 (Yamamoto 1982; Higashima et al. 1986; Yamamoto et al. 1987), on unitary EPSPs of inhibitory cells in area CA3 (Miles 1990), as well as on spontaneous (Ropert et al. 1990) and evoked (Edwards et al. 1990) inhibitory currents in area CA1 and in dentate gyrus, respectively. Before we started the present experiments, only preliminary data on statistical analysis of EPSPs recorded in region CA1 were published (Andersen et al. 1985). The related full publications appeared recently (Sayer et al. 1989, 1990; Friedlander et al. 1990),

In the present study, we attempted to obtain estimates of quantal parameters of synaptic transmission in the hippocampal area CA1 in the context of the binomial model. The final aim was to use the estimates to clarify the neuronal mechanisms of long-term synaptic plasticity in the hippocampus (see accompanying papers, Kuhnt et al. 1992; Voronin et al. 1992b). The application of a less restrained quantal model will be considered in the last paper of this series (Voronin et al. 1992a, see also Voronin et al. 1991). As a first step, we evaluated the performance of statistical procedures based on the binomial model in both computer and physiological experiments. Monte Carlo simulations were performed with variations of model parameters in a broad range of physiologically realistic situations. In physiological experiments different methods based on the binomial model were applied to analyse minimal hippocampal EPSPs evoked by low-intensity afferent stimulation. Parts of the results were reported (Voronin et al. 1988b, 1990a).

Methods

Simulation experiments

A program was written to simulate firstly normally distribfited noise values with standard deviation (SD) equal to Sn and secondly binomial amplitude distributions convolved with this normally distributed, additive, and independent noise according to the following formula (see Baskys et al. 1979; Matteson et al. 1979, 1981; Voronin 1982):

~ / n \ 1 N(E) = N ~....~ / ]pX(1 -p) n-x -

• o \ x J w/2~z(S2 + xS 2)

F (E-xv)~ -I x exp ~ ,

L2(S, +xS~,J (4)

In Eq. (4), N is the number of measurements, Sv is the SD of v, the other terms were defined above. In most computer and physiological experiments, Sv was assumed to be equal to 0.05v. We believed that a finite Sv value is more realistic than Sv = 0 as was assumed by other authors for spinal (Jack et al. 1981; Kullmann et al. 1989; Walmsley et al. 1988) and hippocampal neurones (Sayer et al. 1989, 1990). Estimates for hippocampal (Baskys et al. 1979) and other central synapses (Korn et al. 1987, 1990; Redman 1990; Walmsley et al. 1988) indicated that the upper limit of the coefficient of variation might be of the order of 0.05-0.15. Sv values of 0.4-0.5v, given recently by Bekkers et al. (1990) might be overestimates probably due to an occasional release of multiple quanta. In fact, an Sv of this order would be inconsistent with the histograms with distinct regular peaks that have been observed in spinal (Walmsley et al. 1988) and hippocampal neurones (Hess et al. 1987; see also Fig. 9B, D). For

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neuromuscular synapses, the value of Sv was traditionally assumed to be about 0.3v (see Revs.) but in the original publication (Fatt and Katz 1952) this value actually included S,. "Subunits" of miniature end-plate potentials were reported to have a coefficient of variation of the order of 0.1 (Kriebel et al. 1982). In our simulation experiments, v was generally fixed (v = 100), while the other parameters from Eq. (4) were varied to study their influence on the estimate of "basic" (m, v) and binomial (p, n) parameters by several methods listed below.

Electrophysiological experiments

Adult guinea pigs (400 600 g) were killed by a blow to the neck and then decapitated. Transverse hippocampal slices (400-500 #m thick) were cut on a vibratome and placed in the recording chamber on a thin perforated platinum sheet. The slices were covered by a silk net to keep them in a submerged state (see Kuhnt et al. 1988 for additional details). The perfusion fluid in the chamber contained 124 mM NaCI, 5 mM KC1, 2 mM CaC12, 2 mM MgSO4, 1.25 mM NaHCO 3, and 10 mM glucose. O2/CO2 (95%/5%) was continu- ously bubbled through the medium. The volume of the chamber was 0.4 ml and the flow rate of the medium was 0.5 ml/min. The temperature in the recording chamber was kept at 35_+ 0.5~

The intracellular glass recording electrode (4 M K-acetate, 20 100 M~) was inserted in stratum (str.) pyramidale of CA1. Two stimulation electrodes (tungsten in glass, 0.1 1 M~)) were inserted in str. radiatum (tad.) and/or oriens (or.). Each of two inputs (either from str. rad. and str. or. or both from str. rad.) was tested every 8-10 s with one input following the other by 4 s. In some experiments, only one input (from str. tad.) was tested (every 5-10 s). An impaled neurone was accepted for recording if it had no spontaneous discharges and a resting membrane potential that was more negative than 60 inV. Stimulus intensity (0.7-1.5 V, 20-40 ps) was set to evoke "minimal" EPSPs with average amplitudes < 1 mV and with failures in response to single stimuli (Fig. 4A C). Extra- cellular control responses were routinely recorded after withdrawal of the electrode from the neurone. No field potentials were detected in averaged records which could significantly influence amplitude measurements. The recorded activity was stored on a computer system for off-line analysis, high frequencies were usually cut at 300 Hz (Fig. 4B). The filtering did not influence EPSP amplitudes (compare averages in Fig. 4A and B) but significantly diminished noise (compare noise before the calibration pulses in Fig. 4A and B, upper sweeps; note also changes of the calibration pulse and o( the stimulus artifacts which have faster rise times than EPSPs).

Data from two series of physiological experiments will be analysed. In the first series, an attempt was made to record at least 500 responses under stable recording conditions (Fig. 4D). The aim was to compare quantal parameters estimated by different methods at various sample sizes. The recording was stopped if the neurone was deteriorating as judged by a deviation of the resting membrane potential level by more than 5 mV or by the appearance of spontaneous spikes. Otherwise either tetanic stimulation was applied after about 500 testing stimuli (about 1.5 h of recording) or the recording was continued as long as possible. In the second series, after recording about 100-200 responses at stable conditions, tetanic stimulation was delivered and as many post-tetanic responses as possible were collected. In one cell, two conditioning tetani were given during the recording period. The conditioning tetanic pattern typically consisted of 10 trains at 100 Hz for 200 ms with a stimulus duration equal to 3 to 5 times of the testing stimulus duration. Intertrain intervals were equal to that between testing stimuli (8 10 s).

The off-line analysis comprised response averaging to determine fixed time points ( a time "window", see below), subsequent measurement of amplitudes from single responses, and calculation of quantal parameters. Two kinds of measures were used: the amplitude difference between two fixed points of the window and the "mean window

amplitude" (Hess et al. 1987). The first point of the window was set at the onset of the averaged EPSP (Fig. 4A-C, dotted lines) and the second point near the EPSP maximum (or 1-6 ms before it) at a time (window width) 3-10 ms from the first point. Both measures provided highly correlated values (Hess et al. 1987). The background noise was measured before the stimulus artefact with the same window width. Data presented here are based on measurements of the "mean window amplitude" which will be referred to as "amplitudes" for simplicity. No corrections were made for nonlinear summation of these small ( < 5 mV) EPSPs which presumably origin- ate from axo-spinal synapses (Harris and Stevens 1987).

"Quasi-stationary" plateau regions (see Kandel 1976; Voronin 1979, 1982) were determined from plots of means of 16 to 64 amplitude measurements (Fig. 4D). The region was defined as a continuous part of a record with means not significantly different from each other (P>0.01, Student's t-test). Two procedures to estimate the number of failures (No) were compared in physiological experiments. According to the first ("subjective") procedure, N o was determined for every plateau region by visually comparing single sweeps with the average over the region. All doubtful cases (if any) were repeatedly averaged in order to exclude non-failures from averages of failures (Castellucci and Kandel 1974). Figure 4C shows the averaged failures with no significant response corresponding in time to the averaged EPSP1, i.e. the EPSP evoked by the first pulse in the paired-pulse paradigm (see Fig. 4A, B). Only a small late hyperpolarization is visible in Fig. 4C well after the time corresponding to the peak of EPSP1. A similar late hyperpolarization was observed in one more neurone recorded in this study.

The determination of N o was usually repeated by two observers and as a rule it provided parameters (v and m) similar within _+ 10%. In cases of disagreement, the mean value of two determinations was taken as final N o estimate. According to the second ("objective") procedure (Nicholls and Wallace 1978; Pawson and Chase 1988), No was estimated as the double number of negative amplitude values.

Calculation of quantal parameters

In peripheral synaptic junctions, v can be estimated from the amplitude of the spontaneous "miniature" EPSP. More indirect methods were used for CNS neurones with multiple synaptic inputs. For the estimate of v and other parameters in the present study, a simple binomial model was assumed (see Discussion and the accompanying paper Voronin et al. 1992a for consideration of less restrained models). The model implies that EPSP amplitudes are distributed according to Eq. (4) with uniform probability p for all release sites. The following methods were applied to estimate quantal parameters in both simulation and physiological experiments.

Histogram ("deconvolution") method. To estimate the quantal parameters by the histogram method (indexed by 1), we searched for the best fit binomial distribution for the observed (experimental) histogram by using a simplified variant of the "noise deeonvolution" procedure. The deconvolution technique was developed by Edwards et al. (1976a,b) for the analysis of fluctuations of EPSP amplitudes in spinal motoneurones. It allows the extraction of the noise-free EPSP fluctuation pattern from a noisy experimental histogram (Bart et al. 1988; Korn et al. 1982; Kullmann 1989; Redman 1990; Wong and Redman 1980). In principle, no constraints can be imposed upon the parameters of the noise-free EPSP distribution (Edwards et al. 1976a; Jack et al. 1981; Kullmann et al. 1989; Sayer et al. 1989, 1990), except that the distribution is discrete, that EPSPs add linearly and that noise and EPSPs are statistically independent. However, several authors (Bart et al. 1988; Korn et al. 1982; Wojtowicz and Atwood 1986) used more restrained deconvolution procedures assuming the traditional binomial model for synaptic release. The variants based on the binomial model have the advantage that statistically reliable parameter estimates despite less strict requirements for Sn/v and N. A systematic description of the optimization methods based on

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deconvolution was recently made by Redman (1990). The details of the deconvolution procedures were given by Jack et al. (1981), Wong and Redman (1980), and Kullmann et al. (1989) for the unrestrained deconvolution procedures and by Bart et al. (1988), Korn et al. (1982), and Wojtowicz and Atwood (1986) for the deconvolution procedure based on the binomial model.

In our variant, EPSP amplitude and noise amplitude histograms were constructed typically with the number of bins set to 30. To estimate the "basic" (v 1 and ml) and binomial parameters (nl and Pl), the computer algorithm searched for a "best-fitted" binomial distribution. To this aim, the value of Vl was systematically changed in a given range which started typically from the value equal to the maximal amplitude down to 20 #V by steps of 1 or 2 #V. At every given vl, the histogram was divided into classes corresponding to different quantal contents (x). The mean quantal content was calculated as m~ =E/v1. Parameter p was calculated from the known lormula based on the binomial distribution (see Revs.):

p, = 1 -S~/Ev~ + S2/v~ (5)

where S~ is the variance of quantal contents. Parameter n~ was estimated from Eq. (2). The expected propor-

tion of responses for each bin was then calculated from Eq. (4) and the expected distribution was compared with the experimental one using the Chi-square test. From the range of the tested v~ (and the corresponding m~, nl and p~), those values which gave the maximal probability from the Chi-square table were taken as final estimates by the histogram method. The value of S. (for Eq. (4) and Eq. (5)) was either directly calculated from measured noise amplitudes (see Fig. 4F, Sn = 85 ~V) or it was extracted from the noise distribution using a similar procedure based on the Chi-square test (see Fig. 4F, S .=87 #V in brackets). The values of S, found with these two procedures never differed by more than 5% and estimates of the basic quantal parameters based on these two procedures were practically identical. The Chi-square test showed that in no case was the noise histogram significantly different from a Gaussian distribution (P > 0.05).

The algorithm enabled the optimization not only of v but also of both v and S,. In this variant, S. was not directly estimated from the noise measurements, but it was a free parameter together with v and it was determined by the algorithm. The variant with S n optimization was tested in a separate series (see Results).

Determination of p as ratio of mean to maximal EPSP amplitude. A method of p determination can be derived from the basic equations of the quantum hypothesis (Eqs. (2) and (3)) and from the relationship Ema x = nv which is obvious for the binomial distribution if Em,~ is the maximal EPSP amplitude. Combining this relationship with Eqs. (2) and (3), we obtain

P2 = E/E~,, (6)

This equation was offered by Balanter (1977) and independently by Baskys et al. (1978). The knowledge of p permits the determination of other parameters from two known methods of the quantum analysis which are based on the binomial distribution (see Revs.): i.e. the variance method where m is calculated from the variance of EPSP amplitudes (S 2)

m 2 = E 2 (1 - P2)/(S 2 _ S~) (7)

and the method of failures where

m o = [ - pz/ln(1 -p2)] ln(N/No) . (8)

Parameters n and v were then calculated from Eqs. (2) and (3), respectively. For these two methods, standard errors (SE) of estimates were calculated by formulae similar to those given by Martin (1966), Robinson (1976) and McLachlan (1978). Parameters estimated by the variance and the failures method are indexed by 2 and 0, respectively.

Combined variance-failures method. If N o is given, Eq. (7) and Eq. (8) can be combined to calculate p. Kuno (1964a, b) used this approach

to determine mean values of p for a group of spinal motoneurones. Here, we applied this method to obtain an independent estimate of quantal parameters for individual cases. The combined equation was solved by iteration. Parameters estimated by the combined method will be indexed by 3. We calculated P3 and m 3 satisfying Eqs. (7) and (8). Parameter v3 was then calculated by Eq. (3) and n 3 by Eq. (2).

Because there are two methods to determine No, two variants ("subjective" and "objective") of the method of failures and of the combined method will be considered.

Results

Computer simulations

Testing o f different methods. F i g u r e 1 shows s i m u l a t e d b i n o m i a l d i s t r i bu t ions wi th large s ample sizes ( N = 1000) and two dif ferent no i se levels. As expec ted , wi th a low noise level (Sn = 0.25V), V can be easi ly e s t i m a t e d v isua l ly as the ave r age d i s t ance b e t w e e n the h i s t o g r a m peaks

A 106.

, - B I N:IO00

l'J s~:25 I FII~,. so=zo, ,11 IL r~:ZO ~,u ~I re:t9

~r~ ~l ~ P,I v:97 t ~ v=103 f L t ] \ l p:o.51 WI ~ p=o.~6

o 500 looo

37 75 200% Sn/v

Fig. 1A-C. Comparison of various methods of quantal analysis in computer experiments. A Example of simulated (columns) and algorithm fitted (interrupted line) amplitude distributions. Abscissa: amplitude (in arbitrary units); ordinate: number of counts per bin. Parameters of the simulated distribution: v=100, p=0.5, n=4, Sn=25. Parameters of the theoretical distribution found by the program as the best fit for the simulated distribution are shown. N: sample size. B Same as (A) but S, = 200 for the simulated distribution. C Mean quantal size values (ordinate in arbitrary units, empty symbols) and standard deviations (ordinate, full symbols) plotted for different S,/v ratios (25, 37, 75, 100 and 200%, indicated under abscissae) and different sample sizes (indicated by N values above each graph). Parameters of the simulated distribution were v = 100, p=0.5, n=4. The experiment was repeated 10 times for every combination of Sn/v ratio and N. Triangles, squares, circles and diamonds represent data calculated by the histogram, variance, failures and combined method, respectively

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(Fig. 1A). The quantal size estimated by the computer program on the basis of the histogram method (Fig. 1A, v) deviated less than 5% from both the visual estimate and the simulated value. More unexpected was a good correspondence (within _+ 10%) between the estimated quantal parameters and the simulated values at larger noise when the histogram did not contain distinct regular peaks (Fig. 1B).

To simulate more typical physiological situations, histograms were constructed with smaller sample sizes (N=50-200) and various Sn/v ratios. Every simulation was repeated 10 times and parameters were calculated by four methods in every computer experiment. The results of such experiments are shown in Fig. 1C for a simulated distribution with v = 100, n =4, p =0.5, and various Sn and N. Empty triangles in Fig. 1C represent mean vl values calculated from 10 computer experiments. The deviation of the mean vl values from the simulated v = 100 was usually less than 10-20% even for the smallest samples (N = 50 100) provided S n < v. The estimated v~ values were significantly different from 0 (P < 0.01, Student's t-test, see full triangles which represent SD). It should be noted that in the range of N = 75-200 (and Sn < v), the deviation of v 1 from the simulated v value was not strongly dependent on N and S,. A larger noise level (Sn=2v) prevented a reasonable determination of v~ at smaller sample sizes (N = 50-200). With Sn = 2v, the deviation increased up to 30% of v even with N = 1000.

With Sn > v, multiples of the simulated values of v were often found by the algorithm as the best fit. This led to a significant increase of SD of v~ (Fig. 1C, compare full triangles at different S,). Similar results as demonstrated in Fig. 1 were obtained in other computer experiments with n equal to 2, 4, 8 or 15 and with p variations from 0.05 to 0.95. Sometimes at S , > v , averages of vl determinations were smaller than the simulated v values.

The estimates of the binomial parameters by the histogram method were less reliable than the estimates of parameters m and v. Both systematic deviations of mean n~ values from the simulated n and large SD were found at small sample sizes. The results were slightly better for parameter pl . It did not deviate systematically from the simulated p values, but at N< 100 , the SD of pl was usually large, so that the estimated mean p value was often not significantly different from 0. Similar to the basic quantal parameters, the correspondence between calculated and simulated binomial parameters did not depend strongly on the noise level, provided Sn < V.

Testin9 Eq. (6)for p estimate. One of the major objectives of the computer experiments was to t.est Eq.(6). The equation is based on the assumption that Ema x is known, which is true only for Sn = 0 and for a sufficiently large p and N. Estimates of the basic quantal parameters both by the variance method and (to a lesser degree) by the methods of failures, are influenced by estimates of P2 (Eqs. (7) and (8)). It is clear that with a small p (at a limited N and small Sn), Ernax will be less than the theoretically predicted value, so that Eq. (6) will overestimate p. The overestimate was confirmed in simulations with various N (100 and 1000) and Sn (from 0.25v to 2v). An example is

given in Fig. 2B (dotted bars). However, the influence of this overestimate on the calculated m 2 (Eq. (6)) was small when p was a small fraction of 1 (Fig. 2C, D). Moreover, with a small N, the difference between the theoretically predicted and the observed Ema x was partially compen- sated by the addition of noise, so that estimated values of P2 were not significantly different from simulated values (Fig. 2A, dotted bars). If p was close to I, the addition of noise led to an underestimate of p. The underestimate was especially prominent with a small n (compare Fig. 2A and B, dotted bars), so that mz differed obviously from the simulated m (Fig. 2C, D, dotted bars). Some of the determinations exceeded the borders of the graph (Fig. 2B, E). Fig. 2E and F demonstrate that Eq. (6) led to both random (Fig. 2E, interrupted lines) and systematic deviations (Fig. 2F, interrupted line) of mz determinations in comparison with simulated m values. Figure 2E and F sum- marize the results of computer experiments with variation of p from 0.05 to 0.95 and variations of n from 1 to 15. Interrupted lines represent differences between simulated

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if,, I , ', : ', / iI~g', , n:l , ~ N=I00

c

,j 2. , iL!i n=4 N=I00

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Fig. 2A-F. Comparison of parameters estimated by Eqs. (6) and (9). A Values of P2 found in computer simulations (ordinate) plotted against parameters p of the simulated distributions (abscissa). Values calculated from Eq. (6) and Eq. (9) represented by interrupted and continuous bars, respectively. The length of each bar is equal to two SEM calculated from 10 experiments. Parameters of the simulated distributions: v=Sn=100, p=0.5, n=4. B As (A), but for the simulated distribution with n = 8. C, D As (A) and (B), but with m2 plotted as ordinate. Note that some m2 values are missing because of large deviations from the simulated values. E Variances of mean differences between m 2 and m (ordinate) for various n (abscissa). Variances were calculated from experiments similar to those illustrated in (C, D). F Mean differences between m2 and m (ordinate) for various n (abscissa). Note a reduction of both variances (E) and mean differences (F) for estimates based on Eq. (9) (continuous lines) as compared to those based on Eq. (6) (interrupted lines)

253

m and m 2 determined from Eq. (6) (Fig. 2F) and squares of these differences (Fig. 2E).

To compensate for these deviations, a new half-empir- ical formula for p evaluation was chosen using a trial-and- error method in simulation experiments with variable parameters. The best results for n = 4 and v = 100 were provided by the equation

P2 = E/{M - 0.3 S,ln [2NE/(M - S,)]}, (9)

where M is the mean value calculated from the three largest amplitudes. Eq. 9 was tested in a broad range of n (from 1 to 15), p (from 0.05 to 0.95), v (from 50 to 500) and S,/v ratios (from 0.25 to 2.00). It significantly improved the estimate of p (Fig. 2A, B, continuous bars and especially of m (Fig. 2C, D, continuous bars). The improvement is evident from the comparison of mean variances (Fig. 2E) and mean differences (Fig. 2F) between the simulated parameter m and m 2 calculated on the basis of Eq. (6) and Eq.(9) (interrupted and continuous lines, respectively). The comparison of continuous and interrupted lines shows that both variability (Fig. 2E) and systematic errors (Fig. 2F) were diminished if Eq. (9) was applied instead of Eq. (6).

The mean quantal parameters estimated by both the variance and the failures methods based on Eq. (9) were close to the simulated values even at small N and large S, (Fig. 1C, squares and circles). The method of failures (Fig. 1C, open circles) gave better average estimates than the variance method (Fig. 1C, squares) with smaller SD (Fig. 1C, full circles).

Values v3 estimated by the combined method also corresponded reasonably with the simulated v values (Fig. 1C, rhombus). However, the combined method gave only coarse estimates of p and parameter n was estimated even less precisely. It should be noted that in the simulations shown theoretically predicted N O were used in Eq. (8).

Testing the "objective" method of failures determination. It is evident that the "objective" No determination is influenced by the noise level. In the last series of simulations, we tested the estimates derived by this method at different values of Sn/V. The method gave correct N o only at small Sn/v when separated peaks were visible in the histogram (see Fig. 1A as example). With Sn/v>0.4 the method overestimated No, evidently due to the "tails" from peaks with quantal contents more than 0. The overestimate o fN o led to an underestimate of m and consequently to an overestimate of v. Figure 3 represents data obtained with simulations of distributions with parameters n equal to 2, 4 or 8, p ranging from 0.1 to 0.9, and N = 1000. For Sn/V =0.25 (Fig. 3, full squares), m o (Fig. 3, ordinate) corresponded with the simulated values (Fig. 3, abscissa). Eight distributions with a mean m = 1.58 _+ 0.27 (+ SD) ranging from 0.6 to 3.2 were simulated with Sn/v=0.25 (Fig. 3, squares). The determined m o ranged from 0.70 to 2.91 with a mean value and SD (1.58_+0.31) which was practically identical to the simulated m. With Sn/v=0.5 (Fig. 3, full circles), underestimates were less than 15%. A good correlation between the estimated m o and the simulated m was evident for all Sn/v values tested (Fig. 3, regression

X3 (b +~ cg

o 63 (J

4.0

3.0

2.0

1.0

0.0 0.0

//" / / /

/ , / �9

I / / /0 [] 0

/,/ ~ o

S O , , i

1.0 2.0 3,0 4.0 m t h e o r e t i c a l

�9 Sn- -O.25v

�9 S n - O . 5 O v

[] Sn= 1 .00v

o Sn= 1 .50v

Fig. 3. Testing the method of failures based on the objective estimation of the number of failures at different noise levels. The mean quantal content calculated by the method of failures (ordinate) plotted against the mean quantal content of the simulated distribution (abscissa). Different symbols represent simulations with different Sn/v ratios (see insert). The equality line (interrupted line) is very close to the linear regression (not shown) for cases with S, =0.25v (full squares). Continuous lines represent linear regressions for other Sn/V ratios (see insert)

lines; the coefficient of correlation ranged between 0.97 and 0.99, P<0.0001 for all Sn). However, the underestimate increased with larger Sn/v (Fig. 3, empty squares and circles), so that at Sn = 1.5v, the calculated m o was only about half of the simulated m (Fig. 3, empty circles).

Physiological experiments

General description. The results of two series of experiments will be presented. The aim of the first series was to compare quantal parameters estimated by different methods at various sample sizes. In this series, responses to paired-pulse stimulation (Fig. 4A, B) were either recorded as long as possible (Fig. 4D and 5C) or the tetanic stimulation was applied (Fig. 5A, B, arrows) after about 500 testing stimuli. In the second series, the tetanic stimulation was delivered after 100-200 testing stimuli under stable conditions. All responses were divided into groups de- pending on whether they were evoked by the first or the second stimulus (EPSP1 and EPSP2, respectively) and whether they were recorded before or after tetanic stimulation (pre- and post-tetanic EPSP, respectively). Here we shall compare estimates obtained by different methods at different sample sizes and consider the parameters of the nonfacilitated EPSP (i.e. pretetanic EPSP1). For some comparisons, data from various groups irrespective of the recording conditions will be combined (i.e. pre- and post- tetanic EPSP1 and EPSP2).

Testing the stability of EPSP amplitudes. During a period from 50 min to more than 2 h, 300 to about 1800 responses were recorded. Altogether 21 sets of EPSPs from 8 neurones (14 inputs) were analysed. Figure 4A-C illustrates minimal EPSPs recorded in the experiment with the

254

~A !! i & > D E.v 4E t

++ + :.r V L !i :/'x~x N:100 ~z,oo + +++ + 15o4

+ "

�9 B r: i . ~ IlmV u~ 1+ ++

STIMULUS NUMBER "SUBREGfON" NUMBER

i

i i i I ,' , [ "X No=19

FN=500f ~ E:-4t4~uV W 60

sn :ss 6o ~~Tbuv ii b

- 200 200 Z

? AV

h )0 ~ E=230 • ~J/~ Sn= 85juV ~'~N f m=2.71(1.97)

F ~]~\ v= 85(117)yV

' 1000

EPSP

:H ' N 1OO Yq E=2/*3-+17~V i . . . . . ~ S n = 88/JV

,04 Iq / 'X m:338{,.7 ) v=72(140)/aV

5 1

J~,zT, I [ ' ~ , - -~ , 0 1000

AMPLITUDE ( juV )

Fig. 4A-H. Minimal hippocampal EPSPs and their statistical analysis. A, B Single (upper rows) and averaged (lower rows) non-filtered (A) and high-frequency filtered (300 Hz) (B) responses to double- pulse stimulation. N: number of averaged responses. C Examples of single (upper row) and averaged (lower row) sweeps taken as failures in response to the first stimulus. Note calibration pulses in the beginning of sweeps (A-C). D Changes of mean EPSP amplitudes in the course of the experiment. Ordinate: mean amplitude _+ SEM from 50 consecutive sweeps. Abscissa: stimulus number. Horizontal bar indicates plateau region used for calculations (E-H). E Mean amplitudes (E) and quantal sizes (v) calculated by different methods (vertical axes) plotted for the whole plateau region with 500 measurements (1-5 in brackets under the horizontal axes) and for consecutive smaller "subregions" with 100 measurements (numbers 1 to 5 under horizontal axes). Averages of estimates from small samples are given

as right-hand symbols (AV at horizontal axes). Triangles, squares, full circles, empty circles, full diamonds, and empty diamonds represent values estimated by the histogram (binomial deconvolution), variance, failures subjective, failures objective, combined subjective and combined objective method, respectively. Bars denote _+ SEM for amplitudes and averages (see AV under the horizontal axes) or estimates of standard errors of v in other cases. F-H Experimental (columns) and theoretical (curves) distributions of noise (F) and EPSP (G, H) amplitudes for regions with N=500 (F, G) and with N= 100 (H). Continuous and interrupted curves (G, H) were constructed on the basis of the parameters found by the histogram and variance method, respectively. Arrowheads in G mark three approximately regularly spaced peaks. Parameters for histogram and variance method given in iftserts (values in parenthesis for the latter method)

largest sample (N = 1756). The EPSP amplitude fluctuated (Fig. 4A, B) with occasional failures (Fig. 4C) so that it was possible to apply all described methods of the quantal analysis. The stationarity of the recorded activity was evaluated by consecutively averaging 16 to 64 amplitudes (Fig. 4D). All responses were divided arbitrarily into three groups. Group 1 consisted of EPSPs without significant trends of averaged amplitudes during the major part of the recording period (6 out of 21 EPSPs). An example is given in Fig. 5A where the responses increased initially but showed no significant trend during the major part of the testing period. More than 900 responses were collected for three out of these six EPSPs, the other three EPSPs (from two different inputs in the same neurone) were recorded during 340 stimulus presentations.

In the second group (9 out of 21 EPSPs), amplitudes declined to the end of the experiment. The decline typically occurred after 100 to 300 stimulus presentations (Fig. 5B) and in two cases after about 600 stimuli (Fig. 5C). The decline was not related to the injury of the neurones as judged from the resting membrane potential, the input resistance, and the absence of spontaneous spikes. Fig. 5D, E exemplifies amplitude histograms from the periods before (Fig. 5D) and after (Fig. 5E) the decline of EPSP amplitude. The decline was accompanied by a decrease in both m and v as determined by different methods. Thus, according to the variance method (Fig. 5D, E, inserts), the

twofold decrease in amplitude was due to an approximately similar decrease of about 70% in m and in v. The distance (about 75 #V) from the zero point to the first peak in Fig. 5D (arrow) was larger than the distances between peaks (about 45/~V) in Fig. 5E (arrows). This might also indicate a decrease in v during the course of the experiment.

The last six EPSPs composed a third group with more complicated amplitude variations during the experiments. Typically, the amplitude increased after 200 to 600 stimulus presentations. Figure 4D demonstrates a case with an initial increase in the average EPSP amplitude followed by a stable plateau region with about 500 responses (Fig. 4D, horizontal bar) and subsequent fluctuations of averaged amplitude with a final tendency to an amplitude diminution (Fig. 4D). For the statistical treatment (Fig. 4E-H), only responses from the indicated plateau region were taken.

After recording of about 500 responses, four neurones were tetanized (Fig. 5A, B). In two neurones, a significant post-tetanic depression was evident (Fig. 5A). In the other two neurones, no significant long-lasting changes were induced. Figure 5B illustrates a case with some post- tetanic increase in EPSP amplitude, which, however, was not significant as compared to the initial amplitudes. Therefore, the effect of tetanization looked like a restora- tion of the depressed amplitude.

A 1.0] N =32

7 TET

QS] + + + ++l - / + + % + + m ~a-+ 4- + +4-

]' ++++++++ r-- 0 , , 4-+-I--t-

d 13_

~E

< N=64 B TET

e._ (12 .4 ._t_'-t'-.4._._H i

w -t ----t-''t'- --4- 0/ , , ,

klJ

(D <

n- ,.. D E

> 0.27 N = 324_ . 4-4--F-l-4-, < j++++.l. ++++4.++-P+ T-l-+4-+ ++

0 ~ , , + i

300 600 900 STIMULUS NUMBER

20- D

N = 1 9 A

o

z

r n

~0 13_

cO

mm20- z o [3_ cO

10- Cc2 kU

Z

0 0

Fig. 5A-E. Testing of stability of EPSP amplitude with recording of about 1000 responses in three different neurones. A Amplitude increased during initial testing but was stable for the major period of the initial 500 stimulations before tetanization. After the tetanus (marked by arrow) a prominent depression was evident. B EPSP amplitude declined after about 250 stimuli with no significant change after tetanization relative to the initial level. C EPSP amplitude declined to the end of the experiment after about 600 stimulations. D, E Experimental (columns) and theoretical (curves) amplitude dis-

EPSP

255

14- + 7pV Z.7/uV 1.73 66t.~V 0./.3 /.

- - 1

200 400 AMPLITUDE (~V)

tributions shown for regions without significant trends before (D) and after (E) the decline of EPSP amplitude. These two regions are marked in C by letters D and E, respectively. Experimental distributions built by the "moving bin" method (Rahamimoff and Yaari 1973) with a larger bin equal to 30/~V and a smaller bin equal to 3 #V. Arrow in D marks first distinct peak, arrows in E mark three approximately regularly spaced peaks. Parameters given in inserts were calculated by the variance method

Comparison of parameters calculated from different samples. Figure 4E shows a good correspondence between determinations of quantal size from the whole plateau region (Fig. 4E, left) and averaged determinations from the corresponding five "subregions" (Fig. 4E, AV). Similar comparisons of the mean calculations from small samples (N = 50-100) and the corresponding calculations from large samples (N=300-900) were performed for other cases which included 21 sets of EPSPs that were discussed in the previous section. Altogether 25 EPSPs for the histogram and variance methods and 20 EPSPs for the failures and combined methods were analysed. For all the following calculations plateau regions and subregions were selected according to the criteria which were specified in Methods. The data are summarized in Fig. 6. The similarity of estimated values from small and large samples as well as good correlations between estimates were evident. The coefficient of correlation was 0.90 for the histogram, and more than 0.98 for the other three methods (P < 0.0001 for all methods). The largest difference between the estimates from small and large samples (about 20%) was found for the histogram method (Fig. 6). Note that vl <v2 for the same set of measurements. For the other methods, the difference between determinations from small and large samples was < 8 % and it was smallest ( < 2 % ) and not significant for the combined method (P > 0.12, Wilcoxon test for matched pairs here and below). Objective and

subjective estimates of N o were used for the comparisons given in Fig. 6.

Objective vs. subjective method of failures determination. Simulation experiments (Fig. 3) showed that the objective method for failure determination led to an underestimate of m (and therefore to an overestimate of v) at Sn > 0.4v. The subjective method is advantageous because it is independent from the method of amplitude measurements. Therefore, within the context of the binomial model, this method is completely independent from other methods. Our impression was, that the procedure of subjective determination o fN 0 could be applied to all our recordings independent of the noise level.

For the comparison of subjective and objective N o estimates (and for comparison of different methods in the following Section), 61 plateau regions with recordings of EPSP1 and EPSP2 of 9 neurones (11 tested inputs) before and after tetanic stimulation were pooled. A single region comprised 59 to 119 measurements (90_+ 17, mean_+SD, here and below). The probability of failures varied from 0 to 0.41 or to 0.54 as estimated by the subjective or objective methods, respectively. The mean value for the regions with at least 1 failure was 0.11 +_0.10 (N=45) for the subjective method and 0.13_+0.13 (N=36) for the objective method. For 32 out of 61 regions both methods determined N o > 1. There was an agreement between the

256

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(23 L_ OJ

v

>

~ V 7OO

6OO

5OO

400

3OO

2O0

100

0 0

Me thods :

�9 H i s t o g r a m

o / / / / / / v 1 - 1 3 3 + 1 0 2 ~ V

/0" V 1 - - 1 6 3 +118 r / / / [ ] V a r i a n c e

/6/ ~ / / / v 2 = 1 7 5 +1 2 7 / ~ V

~ / a ~ T2 = 1 8 9 +1 3 2 ~ V

~ : ~ / ~ / ~ 0 Fa i lu res

* ~ / 7 V ~ v�9 = 2 2 3 + 1 7 6 / ~ V ~ ~ To = 2 3 1 +18 lp , V

�9 ~ C o m b i n e d

v~ = 2 7 l •

v3 = 2 6 6 - F 2 6 4 / ~ V

100 200 300 400 500 600 700 L 6 V

( s m a l l e r s a m p l e s )

Fig. 6. Comparison of estimates of quantal size from larger (ordinate) and smaller (abscissa) samples. Different methods are represented by different symbols (see insert). Mean v values (_+ SD) are given for different methods. Equality line shown as interrupted line, linear regression for the histogram method shown as continuous line. Linear regressions for the other methods are close to the equality line

two methods of N o determination within -t-1 for 10 regions and the average N o per one region was exactly the same (13.5 4- 9.6 for subjective and 13.5 _ 11.6 for objective method). Figure 7A shows a strong correlation and the small and not significant difference between mean values of m estimated by two variants of the failures (P > 0.9) and combined methods (P>0.6) . The correlation was even larger for v estimates (Fig. 7B) and the mean values of both Vo and v3 were practically identical for both variants.

Comparison of different methods. Figure 4E illustrates estimates of v by different methods for the same neurone. Amplitude histograms and the best fit theoretical distribution for the plateau region with N = 500 are presented in Fig. 4G. The insert shows quantal parameters calculated by the histogram and variance methods (numbers without parenthesis and in parenthesis, respectively). Theoretical distributions constructed on the basis of these methods (continuous and interrupted lines, respectively) showed only a slight difference for this neurone while m 1 was about 27% smaller than m 2. Figure 4E demonstrates that the most consistent determinations of v from small samples ( N = 1 0 0 ) were obtained by the variance method: values of v 2 (squares in Fig. 4E) estimated for different subregions were not significantly different (P > 0.1). The histogram method gave more variable estimates of v~ (triangles in Fig. 4E). In this experiment, S . /v was comparatively large (about 75% as judged by the estimate of v2). Smaller v~ (and larger m 1 values) if compared with other methods were c o m m o n for most subregions (Fig. 4E, G, H) as well as for other neurones as mentioned above (Fig. 6, Table 1).

A systematic comparison of different methods was made on the basis of estimates for 61 plateau regions from the second series of physiological experiments. Figure 8 represents correlation fields for m calculated by different methods. Despite some differences, the mean values were of the same order of magnitude. The largest difference was

A

0

(b E (b >

4~ �9

0 v

~o

4.0

3.0

2.0

1.0

0.0 0.0

�9 Failures : m�9 (subJ.)= 1.65_+0.56 m'o (obJ.)- 1 . 6 9 • r=0 .75 / /

(P<O.OOO 1, N=32) / / / o o o / /

4>o / / �9 / / /

o �9 o �9 / / o . oR / / / o ~

o �9 o ~ , o �9

~.t~t~.o %~ ~ o 0 Combined :

�9 ~ o m3 (subj.)= 1.74_+0,69 o � 9 ~ o m' s (ob j . )=1 .84•

o / �9 r=O.6 1 ~o4 �9 / / �9 o (P<O.O005, N=32)

1.o 2.0 s.o 4.0

m o , m s ( s u b j e c t i v e m e t h o d )

a ~v 350.0

0 L |

E 262.5 | >

S ~ 175.0 2D �9

v

,}>m 87.5

.>o

0.0 O.O 87.5 175.0

S Failures :

v�9 (subj.) 1 3 0 - - 5 9 ~ V vj ( ob j . ) =131+64 ~,V e / / r = 0 . 8 9 o / / (P<O.O001. N=32) /

o / / Q �9 / / o

/ /

o �9 / / / �9 o

oo o /%/ _~o ~ / 0 Combrned :

o v3 (subj.)= 1 2 9 • ~zV

~ v's (obj.)= 1 2 8 • /~V r=O.SO

/ & o / ~ - - ~ o ( P < O . O 0 0 1, N=32)

/ /

262.5 350.0 LLV

v o , v a ( s u b j e c t r v e m e t h o d )

Fig. 7A, B. Comparisons of the mean quantal contents (A) and quantal sizes (B) calculated by the failures and combined method with objective (ordinates) and subjective (abscissa) procedure of determination of number of failures. The meaning of symbols, mean values (4- SD), coefficients of correlation (r), significance levels for the latter (P), and the number of measured regions (N) are given in inserts. Regression lines for both methods are close to the equality lines (interrupted lines)

found between determinations by the histogram and other methods (Fig. 8A, D). Estimates from different methods were highly correlated, the lowest coefficients of correlation were found for combinations with m 1 (Fig. 8A, D), the highest for the comparisons of failures and combined methods (Fig. 8E, F).

The correlation of the binomial parameters calculated by different methods was generally lower and for some combinations not significant: for example, r=0 .70 for pl and P2; r = 0.24 for P2 and P3-

Optimization of the standard deviation of the noise. In about half of the observed histograms, more or less regular peaks can be distinguished by eye (Fig. 9A, B) including histograms (Figs. 5E, 9D) constructed by the "moving bin" method (Rahamimoff and Yaari 1973). It was a c o m m o n observation that even for these favourable cases, the best fit theoretical distributions were smooth and usually contained no regular peaks (Fig. 9A). This discrepancy between observed and predicted histograms might be due to

257

A

FN 2

PN 2 - - 2 . 1 7 •

m~ = 2 . $ 4 + 1 . 4 0

8.o[ r 0 . 77 / /

( P < 0 . 0 0 0 1 , / J 6.0 N = 6 1 ) / ,

/ / /

�9 o / / o ~ 4,0 0 O///

2.0 ~ , b ~ ~ o�9 ~o

0.0 0.0

f / /

/ /

2.0 4.0 6.0 8.0

m 1

B

m 2

4.0

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1.0

0.0 0.0

m 2 = 1.61+-0.72 m o 1.8 i--+0.67

r = 0 . 8 0 o ," ( P < 0 . 0 0 0 i , /

N = 3 6 ) �9 , , " . ~

1.0 2.0 3.0 4.0

m' o o b j e c t w e

C

m 2

W~ 2 = 1 . 7 8 •

m o =2.02+--0.77 r = 0 . 8 6 o / "

4 0 [ ( P ( 0 . 0 0 0 1 , / /

I ~=45> " / / I o 2.0 // �9 118

o o 0,0 1.0 2,0 3,0 4.0

m o s u b j e c t i v e

D G) >

U XD

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s ~

m o = 2 . 0 2 •

m = 2 . 4 3 • 6.0

r = 0 . 7 5 / / z

( P < 0 . 0 0 0 1 , / / /

N = 4 5 ) ," / /

4.0 /

/ / o

. o ~ o I / o o o o �9 o

/ / 0 .0

0,0 2.0 4.0 6.0

m ~

E @ >

U 23

CO o

5 0

4.0

3.0

2.0

1,0

O.O

m o 2 . 0 2 • F ms = 2 . 1 9 •

q) 4.0 / J }> r 0 . 9 6

( p < o . o 0 0 !, ," U N = 4 5 ) / / ~ s.o

/

~149 o

J !.O

// r/ /

O.O 1.0 2.0 3 . 0 4 . 0 5.0 m s s u b j e c b v e

Fig. 8A-F. Correlation of the mean quantal contents estimated by different methods. A-C Correlations for m 2 (ordinates) with ml (A), m o calculated on the basis of objective (B) and subjective (C) N o determinations (abscissae). D-F Correlation of mo based on sub-

0.0

m' o 1 . 8 1 •

m' s = ~ , 9 3 2 0 , 7 6

r 0 . 95 # ( P < 0 . 0 0 0 1 , ' " ~

J , N = 3 6 ) �9 , , ~

t

0.0 1.0 2.O 3.O 4.0

m' 3 objec%ve

jective (D, F) and objective (E) N o determinations (ordinates) with m 1 (D), m 3 based on subjective (E) and on objective (F) failure determinations (abscissae). See Fig. 7 for other explanations

small samples either of noise or of response measurements or of both. Alternatively, they might indicate a significant reduction of noise during EPSP. We collected larger samples for estimating the noise SD. Not infrequently, the values of Sn determined from large samples ( N = 5 0 0 - 1000) were larger than those from small samples (N = 100). S n was never reduced to a sufficiently low value to account for the appearance of distinct visible peaks in the histograms.

To test the second possibility, we applied a variant of the histogram method which used Sn as a free parameter (see Methods) instead of Sn from real noise measurements. Figure 9 illustrates applications of the two variants of the histogram method to two distributions recorded from the same neurone before and after tetanic stimulation. Theo- retical distributions constructed with the measured Sn (Fig. 9A, B) and with best fit ("optimized") Sn (Fig. 9C, D) are shown. Figure 9 shows that for cases with distinct peaks, the optimized Sn values (Fig. 9C, D, insert, Sn = 45/~V) might be almost two times less than the actually measured value (Fig. 9A, B, Sn = 78 and 77 #V). However, the average difference for all cases analysed was not as large. Figure 10A represents a comparison between opti-

mized and measured S n values for 63 plateau regions. There was a good correlation between measured and optimized S n values (Fig. 10A, insert). However, the correlation line runs below the equality line which reflects an average diminution of optimized values in comparison with measured S, values. The difference was significant at P = 0.003. The mean optimized S, value (equal to 60 #V) was about 13% less than the actually measured S, (69 ffV).

A comparison of Fig. 9A, C reveals an essential difference in estimates of basic quantal parameters for the two variants of the search algorithm: v~ estimated by the first variant (Fig. 9A) was about half of that estimated by the second variant (Fig. 9C). The latter value seems to be more realistic as judged from visual estimates of the mean distances between major peaks in Fig. 9A and results of other methods (see also Fig. 9B, D where v 1 was about the same as for Fig. 9C). However, for Fig. 9B, D, the difference between estimates from the two variants was negligible. Only a very small difference was found for the pooled data from 63 regions (Fig. 10B) and it was statistically not significant: P > 0.4 (t-test for matched pairs) and P > 0.05 (Wilcoxon test for matched pairs). A significant correlation was found between parameters estimated by

258

A N= 101

1 0 l

to

E : 379 • lg/.~V Sn = 78/uV ml: 4.86 vl : 78FV

LU B

N:97, i i i, 'I ' i m= Sn: e=s s 2 % v vl = 166 v 3287 v =

0 Q'5 1.0 EPSP

C

0 A M P L I T U D E [mV)

Q5 1.0

Fig. 9A-D. Optimization of noise standard deviation. A-D Examples of experimental (columns) and theoretical (curves) distributions recorded from the same neurone before (A, C) and after (B, D) tetanic stimulation. Theoretical distributions in A, B constructed by using So measured directly from experimental data while those in C,D were constructed with Sn found by the optimization procedure. Experimental distributions in C, D were built by the "moving bin" method (Rahamimoff and Yaari 1973) with a larger bin equal to 40/~V and a smaller bin equal to 4 #V. Arrows in A, B mark approximately regularly spaced peaks. Prob- ability values for the Chi- square tests (W) given in inserts in addition to amplitude (E), noise SD (Sn), and quantal parameter values (m 1, vl)

the two variants (Fig. 10B, inserts and regression line). Correlations between estimates by different methods were also similar for the two variants.

Mean quantal parameters ofhippocampal synapses. Table 1 summarizes quantal parameters calculated for 16 stable plateau regions (N = 100-500) of nonfacilitated EPSPs for 16 neurones. "Nonfacilitated" means that only EPSPs evoked by the first testing stimulus in the paired-pulse paradigm during control (pretetanic) periods were tal4en from both series of the physiological experiments. Only EPSPs evoked by the stimulation of str. tad. were included in Table 1. We did not find any significant difference between parameters of EPSPs evoked by stimulation of str. rad and str. or. although the number of the latter was considerably less.

Table 1 shows again the similarity of values calculated by different methods. The exception was the histogram method which gave significantly larger m and lower v than the other three methods. Based on our simulation experiments, we might expect that estimates of quantal parameters by the histogram method with Sn >_ Vl would be unreliable. We selected a group of 8 neurones with Sn<0.9v 1. For this group, the histogram method gave parameters more similar to parameters determined by the other methods. For example, the mean value of vl was equal to 152#V (the range from 58 to 390/~V) with v2 = 174 #V (52 to 462 #V), v 0 = 142 #V (50 to 371 #V) and % = 155 #V (60 to 396 #V) for the same group. This is consistent with the suggestion that the histogram method underestimated v for our sample due to a larger sensitivity of the method to the noise level.

In many cases, especially for nonfacilitated EPSPs, p was less than 0.25. In these cases parameter n usually

exceeded 10 and often 25. Predicted distributions calculated on the basis of binomial statistics (Eq. (4)) were not distinguishable from the distributions calculated on the basis of an equation similar to Eq. (4), but with the binomial term substituted for the term based on the Poisson statistics. It is possible to estimate approximately the lower limits of SE of calculated parameters for the histogram method by tentatively suggesting a SE of v equal to the bin size of the histogram. For calculation of the SE of estimates p and n, we used formulae similar to those given by McLachlan (1978). For cases with p < 0.25 and/or n > 2 5 in our conditions, SE of the binomial parameters appeared to be more than half of the estimated values of the binomial parameters themselves. That means the values were not significantly different from 0 at P > 0.05 (Student's t-test). Therefore, the related distributions were considered to be based on the Poisson statistics with uncertain p and n. Corresponding binomial parameters were excluded from the results (see numbers in brackets in Table 1, first row for each method). In general, both simulation and physiological experiments showed that estimates of binomial parameters were less reliable than estimates of the basic quantal parameters v and m.

Discussion

Simulation experiments

Monte Carlo studies allowed us to refine methods used previously for the statistical analysis of synaptic responses recorded from CNS neurones (Voronin 1979, 1982; Hess et al. 1987). Assuming the binomial model (see below), the

259

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7] 160 @ N

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0

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80

Sn(meas. )=G9• ,u,v o,, / / S 'n(opt . )=60• P,V /

/ / / /

o

o o o / / 0 O//{D O0 O/

a ~'oyo

o o / / oo o oOU~ 4 o o ~ o

� 9 1 7 6 o

�9 0 40 80 120 160 ~LV

Sn measured

B A L ~V v~ (Sn m e a s . ) = 1 2 9 • /~V

73 (]] 380 N

- 2 8 5

v ~ 190 >

9 5

v', (S'n op t . )=140-+74 ~ V

o ~

/ r =0 .84

o o ~ / (P<O.O001

o ~ N=63) o

o o o ~ ~ ~

S o 19o 285 38o L6V

v I (Sn m e a s u r e d )

r = 0 . 7 3

(P<O.O00 1

N=63)

0 0 95

Fig. 10A, B. Influence of optimization procedure on standard deviation of noise and on quantal size estimated by the histogram (deconvolution) method. A Plot of standard deviation of noise found by the optimization (deconvolution) procedure (ordinate) against measured standard deviation of real noise (abscissa). B Plot of quantal size found by the variant of the deconvolution procedure with optimized S, (ordinate) against quantal size determined by the deconvolution procedure with measured S, (abscissa). See Fig. 7 for other notations

described methods can be applied under realistic conditions of physiological experiments even with comparatively small samples (N about 100). It was found that low noise levels (Sn/v ratio) were more important than large sample sizes for reliable estimates of quantal parameters.

With comparatively large samples (N = 500-1000), satisfactory estimates of basic quantal parameters (within less than 10-20% deviation from the simulated m and v values) were obtained up to values of S, comparable to v (all four methods) and even exceeding the latter (variance, failures and combined methods). When the large samples are not available, it is possible to obtain similarly satisfactory estimates by repeating experiments with small samples (N=50-100) for about 10 times.

According to both simulation and physiological experiments, the histogram method appeared to be less reliable and more sensitive to noise level and sample size than the other methods. The variance method is more universal than the failures and the combined method,

because it is independent from the presence of failures and does not include subjective procedures like No determinations. The "objective" method of failures estimates (Nicholls and Wallace 1978) was shown to be valid only for comparatively small Sn/v ratios.

Both simulation and physiological experiments demonstrated that the histogram method besides giving more variable estimates tended to give systematic deviations from the simulated values at large noise levels (Sn >v), when estimates of other methods were still reliable. Never- theless, the histogram method was often found to give satisfactory estimates of quantal parameters, even for histograms without distinct regular peaks (Sn > 0.5V). Sim- ilar to other methods, the variability of the mean estimates of v 1 and m 1 did not strongly depend on the sample size.

The general conclusion of our simulation experiments is that relatively small sample sizes (N= 50-100) can be used for the estimates of the basic quantal parameters (m and v) in the context of the binomial model. The variance method is preferable. However, a comparison of results obtained by several methods is useful to evaluate the variability of the estimates of quantal parameters and Sn/V ratios and, therefore, to evaluate the reliability of the estimates.

EPSP measurements and noise reduction

Usually, peak amplitudes measured either at a single point (Korn et al. 1982) or as the average of a short period around the peak (Jack et al. 1981; Redman 1990) were used for statistical analysis. The "mean window amplitude" measurements might be more sensitive to variations in latencies of EPSPs than peak amplitude measurements as used in the following paper (Kuhnt et al. 1992). But on the basis of our previous studies (Hess et al. 1987), we preferred here the "mean window amplitude" rather than amplitude measurements and chose the right margin of the window before the EPSP maximum to exclude possible influences of polysynaptic PSPs and early inhibitory PSPs (Alger and Nicoll 1982; Miles and Wong 1984; Turner 1990). In fact, the averages from failures never showed any significant early hyperpolarization and only occasionally they re- vealed a weak late hyperpolarization well after the right margin of the chosen window. Signs of inhibitory PSPs were sometimes evident in potentiated EPSPs (due to paired-pulse facilitation or/and long-term potentiation, LTP). The late parts of EPSPs were sometimes clearly shortened in these cases (see e.g. Fig. 2B in the following paper, Kuhnt et al. 1992), so that averaging over a period corresponding to the peak of the control (nonfacilitated) EPSP could produce a distortion of the magnitude of the facil.itated EPSP unlike the measurements of the "mean window amplitude" corresponding to the initial EPSP slope.

Another important problem is the noise reduction. Our applied measurement procedures and the electrical filtering were beneficial for essential noise reduction. They give a partial explanation of the more common appearance of histograms with regular peaks in our previous (Hess et al. 1987) and present recordings in comparison

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Table 1. Quantal parameters of nonfacilitated minimal EPSPs (i.e. pretetanic EPSP evoked by the first stimulus in paired-pulse paradigm). Mean 4- SD is presented in the first row for different methods. Minimal and maximal values are given in the second row. The number of neurones was equal to 16. The number of estimates for p and n was less and is given in parenthesis in the first row for every method. Mean EPSP amplitude (• was 1364-53 #V with a range of 41 to 235 ~tV

Method m v (/~V) p n

Histogram 1.54-t-0.84 114_+91 0.43+0.15 3.2_+ 1.7(6) (0.45 3.52) (31-390) (0.27 0.70) (2-6)

Variance 1.13 4- 0.48 147 _+ 100 0.38 4- 0.08 3.2 4-1.0(14) (0.34-2.11) (52 462) (0.28 0.62) (2-6)

Failures 1.21 _ 0.46 130 _+ 86 0.384- 0.08 3.6 4-1.0(14) (0.48 2.08) (50-371) (0.28 0.62) (2-6)

Combined 1.19-}-0.55 1384-91 0.474-0.12 2.84-1.8(9) (0.40-2.09) (60-396) (0.30 0.63) (1-6)

with publications of other authors (Sayer et al. 1989, 1990). Another reason for the difference might be drifts in quantal parameters during the prolonged testing periods used by the cited authors to collect large samples. Except for stochastic drifts, a systematic decrease of v might be suspected on the basis of earlier data obtained with studies of low-frequency depression both in the snail CNS (Logunov et al. 1980) and in the in vivo hippocampus (Voronin 1982, 1985). A decline in EPSP amplitude was often observed in the present study after prolonged testing stimulation. This decline might be similar to the low- frequency depression previously described for EPSPs of the in vivo hippocampus when slightly higher stimulation frequencies were used (Voronin and Kudryashov 1978; Voronin 1985, 1988a). The low-frequency depression is well known for hippocampal field potentials (see Barrion- uevo et al. 1980, Voronin 1982, 1983, 1985 for references and discussion) and can be demonstrated even with interstimulus intervals in the order of 10 s in both in vivo and in vitro preparations (Voronin 1985). Preliminary observations indicated not only a significant diminution of m during the decline in EPSP amplitude but also a decrease of v. A decrease in quantal size will strongly influence the regularity of peaks.

Testin 9 procedure and sample sizes

We only infrequently obtained large samples (N > 500) in steady state conditions. We used comparatively long interstimulus intervals of about 10 s rather than ! or 2 s used by some other authors (Sayer et al. 1989, 1990; Friedlander et al. 1990) having in mind the prominent plasticity of hippocampal responses including frequency facilitation and low-frequency depression mentioned above. Longer interstimulus intervals naturally led to a prolongation of the time necessary to collect large samples but allowed us to record hippocampal responses in presumably more intact conditions. Even with these rather long interstimulus intervals, a decline of EPSP amplitudes was observed several times. In some neurones, spontaneous drifts might take place in different directions so that large samples of EPSPs in steady state conditions are difficult to achieve. Moreover, we had the impression from our experiments, that prolonged low-frequency stimulation or prolonged intracellular recording interfered with LTP induction: we were not able to induce LTP in four

neurones tested with more than 500 stimuli (recording time of more than one hour). The observation is in agreement with recent data of both Krug et al. (1989), who showed that preliminary low-frequency stimulation diminished or even reversed a potentiating action of a conditioning tetanus in the dentate gyrus and of Friedlander et al. (1990), who found that tetanization did not lead to LTP in the majority of unitary and minimal EPSPs in CA1. These authors used prolonged stimulation prior to tetanization. According to our experience, tetanic stimulation after a comparatively short testing procedure (100-200 testing stimuli with about 10s interstimulus intervals) led to LTP of minimal EPSPs in about 75% of the recorded neurones (Voronin et al. 1990c; 1991, 1992a, b).

Both simulation and physiological experiments indicated that it may be possible to substitute estimates of basic quantal parameters from large samples by averages of several estimates from smaller samples in the order of 100. Therefore, this approach might be used for the approximate description of quantal parameters and their basic trends after tetanic stimulation across experiments with successive recordings from several neurones.

Applicability of the quantum hypothesis to minimal EPSPs. Before discussing the results of the calculation of the quantal parameters, we shall consider the applicability of the basic postulates of the quantal hypothesis to the analysis of minimal hippocampal EPSPs induced by extracellular stimulation. In accordance with our previous data (Baskys et al. 1978, 1979; Hess et al. 1987; Voronin 1979-1988b; Voronin et al. 1990c, 1991) and with data from other authors (Foster and McNaughton 1991; Sayer et al. 1989, 1990; Turner 1988), we found that amplitudes of hippocampal minimal EPSPs fluctuated more than could be predicted from the noise variation (see also Bekkers and Stevens 1990; Malinow and Tsien 1990). Moreover, regular peaks were often distinguishable in the EPSP amplitude histograms. This indicates that hippocampal EPSPs may obey the basic postulate of the quantal hypothesis (Eq. (1)).

On the basis of short latencies of averaged responses and their invariance after a several-fold increase in EPSP amplitude resulting from paired-pulse facilitation and LTP (Voronin et al. 1990c; 1991, 1992a), we consider the minimal EPSPs to be monosynaptic. Nevertheless, reservations should be made regarding the interpretation of

statistical parameters of amplitude fluctuations if minimal PSPs rather than unitary (single fibre) PSPs are recorded. In principle, a "non-quantal" interpretation of the amplitude fluctuations might be valid. In terms of the non- quantal interpretation, the amplitude fluctuations of minimal EPSPs can be explained exclusively by intermittent excitation of several afferent fibres or collaterals. In this case, the meaning of estimated statistical parameters is different from that implied in the present study, i.e. m and n will represent the mean and maximal number of excited fibres, respectively, p will be the mean probability of excitation of a single fibre and v will be the average amplitude of unitary EPSP for a given group of fibres. However, the interpretation based on the quantum hypothesis is more consistent with reasonable values of the calculated parameters which are comparable to those known for other CNS synapses (see Revs.) and with several other observations (see McNaughton et al. 198l, Voronin 1982) including changes in statistical parameters during paired facilitation (Hess et al. 1987) as well as LTP (Voronin 1982-1988b, Voronin et al. 1990b, c, 1991, see also the accompanying papers Voronin et al. 1992a,b). The non-quantal interpretation is contradicted by published observations of unitary hippocampal EPSPs evoked by activation of single presynaptic neurones (Baskys et al. 1980, Sayer et al. 1989, 1990, Friedlander et al. 1990, Malinow 1991). Therefore we favour the "quantal" (or more exactly "mixed") interpretation of the statistical parameters calculated here for the minimal hippocampal EPSPs (see also Redman 1990). This interpretation is similar to that implicated by other authors who recorded minimal PSPs of CNS neurones (Kuno 1964; Kuno and Weakly 1972; McNaughton et al. 1981; Sayer et al. 1989; Friedlander et al. 1990). In the frame of this interpretation, m and n reflect the sum of corresponding quantal parameters for all "effective" fibres, i.e. excited fibres with a sufficiently high response probability. The calculated parameter p depends on both the mean probability of fibre excitation and release probability. The estimated p is close to the "true" p value (i.e. quantal release probability) only when the mean probability of activation of the stimulated fibres is close to 1.

261

in v during paired-pulse facilitation might be masked as was shown previously (Baskys et al. 1978; Hess et al. 1987).

In none of the analysed neurones could a theoretical fit based on the binomial law be rejected on the basis of the Chi-square test. Therefore, the present variant of the histogram method (deconvolution) might be considered as a test for the applicability of the simple binomial model. Estimates based on other methods can also not usually be rejected on the basis of the Chi-square test (see Fig. 4E, G interrupted curves, and Fig. 5D, E). However, the good fit between observed data and predicted binomial (or Poisson) distributions (especially with small samples) does not prove that the given solution is unique or the best one. In fact, more complicated models (see Voronin et al. 1991, 1992a for references) may be more adequate. Several authors (Jack et al. 1981; Kullmann et al. 1989; Walmsley et al. 1988) reported that models based on a nonuniform p might give a better description of release statistics at central synapses (see Redman 1990 for more refs.). Never- theless, the agreement with the binomial model as well as the internal consistency of different methods justify the description of the experimental data based on the binomial statistics. It has to be mentioned that in principle two different methods could be similarly biased and therefore, produce a significant correlation. But known estimates of quantal parameters of hippocampal synapses based on the unconstrained discrete model (Sayer et al. 1989, 1990) were not substantially different from predictions of the binomial model. This is considered as another argument for the application of the latter.

The major aim of our experiments was not the estimate of binomial but rather of basic quantal parameters (m and v) in an attempt to distinguish between pre- and postsynaptic mechanisms ofsynaptic plasticity (see Voronin et al. 1990b, c; 1992b, Kuhnt et al. 1992). It should be stressed that in cases with distinct regular peaks, estimates ofv (and consequently m) by the histogram method are not dependent on whether the distribution is binomial with uniform p or compound binomial with nonuniform p. In all cases with distinct peaks, different methods gave very similar v values. This is considered as a further argument in favour of the application of the binomial model as a first approximation for the determination of basic quantal parameters.

Applicability of binomial statistics

We used the binomial model which had been applied to the analysis of PSP amplitude fluctuations by many authors (see Revs.) including those who studied CNS synapses (Bart et al. 1988; Grantyn et al. 1984; Korn et al. 1982). Some authors used methods based exclusively on the limiting form of the binomial statistics, the Poisson statistics (Castellucci and Kande11974; Pawson and Chase 1988; Yamamoto 1982). However, the estimates based on the Poisson statistics can give essential deviations from true parameters of binomial distributions if p is not small enough: for example, they overestimate m 2 (see term 1 - p in Eq. (7)) and underestimate v2. Conclusions related to the mechanisms of plasticity can be distorted in these cases especially if parameter p is modified. For example, changes

Binomial parameters

The determination of binomial parameters is less reliable than that of v and m. Several publications (Barton and Cohen 1977; Brown et al. 1976; Lustig et al. 1986) demonstrated that methods based on the binomial model can estimate seemingly good-fitting (but meaningless) n and p values from simulated data which cannot be described by the binomial statistics (i.e. with spatial or temporal variation of binomial parameters). Moreover, our computer experiments showed that estimates of binomial parameters even from simulated binomial distributions are essentially less reliable than estimates of m and of v. The correlations for binomial parameters estimated by different methods were usually lower (and partially not significant) than for the basic quantal parameters. Therefore, the

262

given values of binomial parameters (Table 1) have to be considered with reservations.

Noise reduction during EPSP

All common methods of the quantal analysis postulate independence of noise from PSP generation (see Revs). However, in many cases the peaks in the observed histograms were more clearly visible than could be expected for the given Sn/v ratios. This might be interpreted as a diminution of the noise level during the generation of EPSPs. The procedure of S n optimization confirmed this suggestion and indicated that the average diminution of Sn can be of the order of 15 %. A similar diminution of Sn has previously been found for unitary inhibitory PSPs recorded from the sensorimotor cortex in vivo (Voronin et al. 1990a). An even larger diminution of S, was reported by Larkman et al. (1991) for CA1 synapses. Own unpublished observations show that a similar diminution occurs when Sv is taken as zero instead of 0.05 v.

Quantal parameters of hippocampal synapses

This study provided some data related to the quantitative description of synaptic transmission formed by str. rad. fibres (presumably Schaffer collaterals) on CA 1 pyramidal cells. Parameters presented in Table 1 are very similar to previously reported parameters of nonfacilitated hippocampal EPSPs calculated by slightly different methods (Hess et al. 1987). Considering the present data, it is necessary to have in mind that here we measured the "mean window amplitudes" with the right window border before the EPSP peak. It means, that quantal sizes measured as peak amplitudes would be 2 to 3 times larger than values presented in Figs. 4-10 and Table 1. Therefore, the mean quantal size for nonfacilitated str. rad. synapses might be estimated as about 350 #V with a large variation from about 100/~V to about 750 #V for different neurones, values which are consistent with data (Kuhnt et al. 1992) derived from peak amplitude measurements. These values are of the same order but larger and with larger ranges compared to values obtained for other excitatory CNS synapses in vertebrates (Kuno 1971; Shapovalov and Shiriaev 1980; see Redman 1990 for more refs.). The present values are consistent with values reported for different hippocampal synapses both in vivo (Voronin 1981-1988b) and in vitro (McNaughton et al. 1981; Miles and Wong 1984; Sayer et al. 1989; see Redman 1990 for rev.) but are on average smaller than quantal sizes reported by Yamamoto (1982) and Higashima et al. (1986) for presumed unitary EPSPs evoked by mossy fibres in CA3. These authors assumed Poisson statistics which might even underestimate quantal size.

Under our experimental conditions, values of m should depend on the number of stimulated fibres. For the cases with the lowest amplitudes in the nonfacilitated state, which correspond presumably to the activation of a single sufficiently efficient fibre (see Voronin et al. 1988a), m was estimated to be in the range of 0.5 to 1. We suggest that in

these cases one or more fibres with low release probabilities might be activated in addition (Voronin et al. 1988a, see also Malinow 1991). Therefore typical values of m for Sehaffer collaterals are probably less than for recurrent collateral (Miles and Wong 1984) and mossy fibre EPSPs (Yamamoto t982; Higashima et al. 1986) of CA3 neurones. About half of the nonfacilitated EPSPs typically had parameter p in the range of 0.4-0.6 and n equal to 1 or 2 for the cases with the smallest m and presumed activation of one sufficiently effective fibre. It is tempting to conclude, that a typical synapse in str. tad. has one or two release sites with variable probability of release from very low to about 0.6. Although this conclusion seems to be reasonable in view of known electron microscopy data (Harris and Stevens 1987), it should be considered as preliminary having in mind the above mentioned reservations concer- ning the determination of the binomial parameters.

Acknowledgements. We thank Dr. M. Mitiushkin and Dr. N. Ivanov for computer programming and participation in the earlier stages of this work, Dr. D. Michael, K. Bauer, L. Ehrenreich and M. Ezrokhi for computer programming, Mrs. S. Schlette, Mrs. A. Tlustochowski, and Mr. S. Lobachev for skilful technical assistance and secretarial help, and Dr. B. Albowitz for improving the English. G.H. was in receipt of DAAD and ESF stipendia. L.L.V., A.G.G. and V.R. were in receipt of MPG stipendia and supported by an agreement between DFG and USSR Acad. of Med. Sci.

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Quantal parameters of ?minimal? excitatory postsynaptic potentials in guinea pig hippocampal slices:...

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