211

J. Physiol. (1978), 276, pp. 211-226 With 10 text-figure8 Printed in Great Britain

QUANTAL ANALYSIS OF THE SIZE OF EXCITATORY POST-SYNAPTIC POTENTIALS AT SYNAPSES BETWEEN HAIR CELLS AND AFFERENT NERVE FIBRES IN GOLDFISH

BY T. FURUKAWA, Y. HAYASHIDA AND S. MATSUJRA From the Department of Physiology, Tokyo Medical and Dental University, School of Medicine, Yushima, Bunkyo-ku, Tokyo, 113 Japan, and the Department of Physiology, Osaka City University Medical School, Abeno-ku, Osaka, 545 Japan (Received 13 June 1977) SUMMARY

1. A statistical analysis has been made of the transmitter release at the hair cell afferent fibre synapse in the sacculus of the goldfish, using the amplitude of the excitatory post-synaptic potentials (e.p.s.p.s) in response to stimulus tone as a measure of the transmitter release under application of tetrodotoxin. 2. Application of binomial statistics allowed a direct calculation of the mean probability of release (p) and the readily available store (n), and the X2-test showed that the binomial predictions fitted fairly well with the observed distribution of the responses. 3. Adaptive rundown of e.p.s.p.s during sound stimulation, i.e. the successive rundown in the size of the mean quantal content (m), was found to be associated with a reduction in the size of parameter n, but not of p. 4. A marked negative correlation was demonstrated between the amplitude of two consecutive e.p.s.p.s, supporting the depletion hypothesis of the adaptive rundown of e.p.s.p.s. 5. The increase in the e.p.s.p. amplitude and the increase in the mean quantal content, m, brought about by an increase in the tone intensity were found mostly explicable in terms of an increase in the statistical parameter n. The probability parameter p was found largely invariable, although in certain instances the increase in m was also accompanied by a slight increase in the parameter p. INTRODUCTION

A discrete quantal release of transmitter, which was originally proposed by Del Castillo & Katz (1954a) for the neuromuscular junction, has been demonstrated to be applicable to many other synapses (Boyd & Martin, 1956; Dudel & Kuffler, 1961; Blackman, Ginsborg & Ray, 1963; Martin & Pilar, 1964; Kuno, 1964; Martin, 1966; Johnson & Wernig, 1971; Ishii, Matsuura & Furukawa, 1971). In most of these analyses, Poisson statistics were employed to describe the distribution of the quantum content of post-synaptic potentials. But a recent trend is to apply binomial statistics to a variety of cases (Johnson & Wernig, 1971; Wernig, 1972; Zucker, 1973;

T. FURUKA WA, Y. HAYASHIDA AND S. MATSUURA Bennett & Florin, 1974; Miyamoto, 1975; Wernig, 1975; McLachlan, 1975). This trend stems from the fact that Poisson statistics are applicable only to those cases where the statistical parameter p is small (Del Castillo & Katz, 1954a, b; Martin, 1955; Branisteanu, Miyamoto & Volle, 1976), and that under normal conditions the value of p rather commonly exceeds 0O2 and is often much larger. Binomial statistics should show a much better fit with the experimental results under such conditions. The present study was undertaken to see whether binomial statistics are applicable for a description of the distribution of quanta at the hair cell afferent fibre synapse in the sacculus of the goldfish (Furukawa & Ishii, 1967). A quantal analysis of the transmission at this synapse has been carried out by Ishii et al. (1971). They demonstrated that an analysis based on Poisson statistics showed a fairly good fit in certain cases. More often, however, the prediction from Poisson statistics deviated from the actual distribution of e.p.s.p. sizes. It will be shown in the present study that an analysis with binomial statistics better fits the actual distribution under a variety of conditions. In applying binomial statistics, however, it is required that, beside m, the value of release parameters n and p be determined, while only the value of m has to be found with Poisson statistics. It is of some interest to know how these parameters are changed when the transmitter release is modified. In the present study, special emphasis was placed on the phenomenon of adaptive rundown in the size of e.p.s.p.s during the sound stimulation and on the changes in the transmitter output due to changes in the sound intensity (Furukawa & Matsuura, 1978). It will be shown in the present study that a change in the size of the statistical parameter n appears to be mainly responsible for the adaptive rundown and also for the change in the transmitter output due to changes in the sound intensity. On the other hand, the value of p, i.e. the average probability of release, remained almost unchanged. 212

METHODS

Experiments were carried out on the hair cell-afferent fibre synapses at the sacculus (inner ear) of the goldfish about 12 cm long. General experimental methods, including sound stimulation, recording techniques, correction for non-linear summation of the e.p.s.p. size and others have been described previously (Furukawa & Ishii, 1967; Furukawa & Matsuura, 1978). The nerve responses and the monitored sound wave were displayed on an oscilloscope (Tektronix Type 532) and photographed on 35 mm film. The measurements were made on enlarged prints of these records. Miniature excitatory post-synaptic potentials (m.e.p.s.p.s) were also recorded when possible and their amplitude was measured. E.p.s.p.s were preferably recorded from the large afferent fibres which respond either to compression or to rarefaction phases of the sound only (Furukawa & Ishii, 1967) for a precise measurement of individual e.p.s.p. size. Tetrodotoxin (10- g/ml.) was applied locally to abolish spike potentials in most instances. To estimate the release parameters n, m and p in binomial statistics and to construct an

amplitude-frequency histogram of e.p.s.p.s, the fluctuation in the size of e.p.s.p.s were measured for a series of trials. The bin size used for measuring the amplitude of the evoked e.p.s.p.s was 0. 1-0 4 mV. The sound stimulus was repeated more than 80 times in each experiment. The parameters needed for a binomial analysis were the mean y and standard deviation o- of the quantal size, and those of the evoked e.p.s.p. size (mean, x; standard deviation, 8). As estimates of y and oc, those values for the spontaneous m.e.p.s.p.s were employed. However, the size of spontaneous m.e.p.s.p.s was often comparable to the noise level of the recording system. When the number of m.e.p.s.p.s obtained were less than 40, the data for the fibre were discarded. To calculate P(x), i.e. the probability distribution of the evoked e.p.s.p.s, one must know the

QUANTAL ANALYSIS AT SENSORY SYNAPSE

213

distribution of the quantal size. The distribution of the quantal size was fitted with a normal distribution in the present study (Del Castillo & Katz, 1954a; Boyd & Martin, 1956; Bennett & Florin, 1974; Miyamoto, 1975), although there is a report that gamma distribution showed a better fit at certain junctions (McLachlan, 1975). The values of binomial parameters, such as m, p and n were calculated using the following formulae: mn = -,

82

ay

m.y y22 m Up The binomial probability distribution of the evoked e.p.s.p.s has been predicted from I P(x) = Gpq1X t-

and

n=-.

r=O

)(2orr)

(

y)2r J2r

where P(x) is the expected frequency of the e.p.s.p.s with an amplitude of x mV, and r (= 0, 1, 2, ... n) is the possible quantal content of each e.p.s.p. (Bennett & Florin, 1974). The distribution predicted from statistical analysis was compared with the observed amplitudefrequency histogram of the e.p.s.p.s. The goodness of fit of the binomial distribution to the observed histograms was determined by X2-test. For estimation of P value of the goodness of fit by the X2-test, some bins were collected together into one group not less than four or five in size, and the number of the bins collected minus three was used as a degree of freedom. Statistical analysis was facilitated by a computer (FACOM 270-30, Fujitsu Co.). The results in this paper were obtained from eleven fibres which filled the above described criteria. RESULTS

The e.p.s.p.8 produced by tone stimuli E.p.s.p.s recorded from a single eighth nerve fibre in response to tone stimuli usually show successive decline in their amplitude as has been described in Furukawa & Matsuura (1978). An additional feature of the sound-evoked e.p.s.p.s is the random fluctuation in their size which was more marked when a low level of stimulation was used. When the fluctuation in the size of e.p.s.p.s was very marked, the trend of their successive rundown often became less clear. For example, in the case shown in Fig. 1, large e.p.s.p.s comparable in size to the first or second e.p.s.p.s appeared even in the latter phase of sound stimulation (see Fig. 1, N and Q). However, even in such cases a clear trend of rundown was demonstrated when many responses were averaged (Fig. 1 A). When strong sound stimuli were applied and the release took place at higher levels, however, the rundown in the size of e.p.s.p.s was very clearly observed in each trial (Furukawa & Matsuura, 1978). It is evident from these observations that there exists an unvaried trend of rundown in the transmitter output for a wide range of sound intensities.

Binomial analysis of the quantal release Quantal size. In this analysis, it was assumed that the quantal units in soundevoked e.p.s.p.s and in spontaneously evoked m.e.p.s.p.s can be described by a normal distribution with the same mean and other statistical parameters. Namely, the amplitude-frequency distribution of the spontaneous m.e.p.s.p.s is assumed to

T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA 214 be the same as that for the unit e.p.s.p.s obtained by delivering a weak sound. In other words, the mean amplitude and variance of the unit e.p.s.p.s (r = 1) should be the same as those for the spontaneous m.e.p.s.p.s. A X2-test was conducted to find out whether observations may fit the above assumption. First, it was tested whether the amplitude-frequency histogram of the spontaneous m.e.p.s.p.s could be described by the normal distribution. The P values were greater than 0-5, indicating a fairly good fit. Next, the mean amplitude and standard deviation of the soundevoked e.p.s.p.s were compared with those of the spontaneous m.e.p.s.p.s (Table 1).

_m Fig. 1. Fluctuation in the response (e.p.s.p.s) to low intensity sound stimulation. A, averaged record of twenty-one trials. B to V, individual records. Sound frequency, 640 Hz; intensity, 60 dB SPL. TABLE 1. Mean amplitude and standard deviation of spontaneous miniature e.p.s.p.s and sound-evoked e.p.s.p.s with low quantal contents (r = 1), and the test for goodness of fit between the observed amplitude distributions of the spontaneous and sound-evoked e.p.s.p.s

Spontaneous Fibre

IV

V

V1

m.e.p.s.p.s or e.p.s.p. order s.m.e.p.s.p. 11Ith e.p.s.p. 12th e.p.s.p. 13th e.p.s.p. 14th e.p.s.p. s.m.e.p.s.p. 1st e.p.s.p. 11Ith e.p.s.p. 12th e.p.s.p. 13th e.p.s.p. s.m.e.p.s.p. llIth e.p.s.p. 21st e.p.s.p. 22nd e.p.s.p. 23rd e.p.s.p. 24th e.p.s.p.

Mean amplitude and S.D.

(mY) 0-39 ± 0-10 0-35 + 0-12 0-37 + 0-11 0-36 ± 0-10 0-38±+ 0-11 0-47 + 0-12 0-45±+ 0-15 0-49 ± 0-14 0-46 + 0-14 0-45 + 0-14 0-40+ 0-13 0-41± 0-13 0-37 + 0-15 0-38 + 0-12 0-40 + 0-14 0-39 + 0-14

No. of observations 55 47 48 47 49 40 22 40 41 35 71 38 35 43 31 35

X2-test value 0-88 (2)* 5-87 (5) 2-35 (5) 2-54 (4) 3-42 (5) 1-59 (3)* 4-09 (6) 3-65 (6) 1-62 (6) 2-74 (5) 1- 17 (4)* 1-17 (6) 6-35 (6) 5-11 (6) 3-04 (6) 2-83 (6)

Goodness of fit (P value) > > > > > > > > > > > > > > > >

0.5* 0-3 0-7 0-5 0-5 0.5* 0-5 0-7 0-95 0-7 0-8* 0-95 0-3 0-5 0-8 0-8

The abbreviation, s.m.e.p.s.p. represents spontaneous miniature e.p.s.p., and the figures with an asterisk show the results of tests for a validity of assuming a normal distribution of the s.m.e.p.s.p.s. Figures in parentheses show the degrees of freedom.

215 QUANTAL ANALYSIS AT SENSORY SYNAPSE Means and standard deviations were calculated for e.p.s.p.s of the same order of occurrences from the start of sound stimulation. E.p.s.p.s in a quasi-steady state were mostly selected for the calculation. It is clearly shown in the table that these e.p.s.p.s distributed around the means of the spontaneous m.e.p.s.p.s of the same fibres. Results of the X2-test indicated that the values of P for the goodness of fit between the amplitudes of spontaneous m.e.p.s.p.s and the evoked e.p.s.p.s were usually larger than 0.5 except for two instances in which the value was about 0'3.

Fig. 2. Spontaneous m.e.p.s.p.s and the e.p.s.p. responses to a low frequency sound. Sound frequency, 330 Hz; intensity, 64 dB SPL. Triangles and asterisks indicate spontaneous m.e.p-s-p.s recorded before the start of the sound and at the out-of-phase position between the sound-evoked e.p.s.p.s respectively. Stimulus sound is monitored at the bottom of each column.

These results seem to support the postulate that the quantal units in soundevoked e.p.s.p.s are the same in size and distribution to those of the spontaneous m.e.p.s.p.s. It was also shown that the size of the quanta in e.p.s.p.s does not change appreciably during the maintained sound stimulation. From these findings, it is suggested that the adaptive rundown in the size of the e.p.s.p.s is produced by a successive decrease in the mean number of quanta released by the sound wave and there is no sign of desensitization in the post-synaptic meiibrane. A further support for the absence of the post-synaptic desensitization was obtained in an experiment in which occurrences of m.e.p.s.p.s were observed at the out-of-phase position between the e.p.s.p.s produced by the maintained sound stimulus (asterisk in Fig. 2).

T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA 216 The mean amplitude and standard deviation of the spontaneous m.e.p.s.p.s during the maintained sound stimulation and those of the m.e.p.s.p.s recorded in the silence were 0 47 + 0d12 mV and 0-46 + 0-13 mV respectively, and the X2-test showed that the value of P for the goodness of fit between the two groups was greater than 0 9.

Binomial parameters and the distribution of the size of e.p.s.p.s predicted therefrom As shown in the preceding section, the quantal size in the evoked e.p.s.p.s remained practically unchanged at the start of stimulation and also during the maintained sound stimulation. Parameters for spontaneously occurring m.e.p.s.p.s were taken as a measure of the quantal size for all the sound-evoked e.p.s.p.s. The values

m

A 80 D A1 3. K 40 2

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1 2 3 4 5 6789 1 2 3 4 5 6 7 8 9 10 Order of occurrence of e.p.s.p.s

Fig. 3. Changes of binomial parameters m, n and p during adaptive rundown of the e.p.s.p.s. A-C (640 Hz, 64 dB SPL) and D-F (400 Hz, 96 dB SPL) were obtained from two different fibres.

of m, n and p for successive e.p.s.p.s were calculated during the rundown of their size in six fibres which satisfied the criteria outlined in the Methods of which results on two fibres are shown in Fig. 3. They represent typical examples for a weak and strong sound stimuli respectively. In the Figure, m, n and p were plotted against the order of occurrence of e.p.s.p.s. Indicating an adaptive rundown in the amplitude of e.p.s.p.s, quantal content m decreased successively until stabilized at steady levels. The parameter n showed a decrease which is associated with the change in the value of m, while the parameter p showed no systematic change. Similar results were obtained for all the fibres examined. Once the values of m, 'n and p were determined, the expected number of occurrences of different amplitude of e.p.s.p.s could be calculated for successive e.p.s.p.s (see Methods), and the results were compared with the actual amplitude-frequency histograms of e.p.s.p.s. Fig. 4 shows a case in which e.p.s.p.s in response to weak

QUANTAL ANALYSIS AT SENSORY SYNAPSE 217 sound stimuli (665 Hz, 64 dB SPL) were analysed. In this case, amplitude histograms were constructed with the bin size of 01 mV without correcting for nonlinearity for the first three e.p.s.p.s. Note the progressive leftward shift in the peak position of histograms from A to C and the increased occurrences of failure in C. The P value for the goodness of fit between the observed amplitude-frequency histograms and the binomial predictions were greater than 0-9 for all the three e.p.s.p. groups shown in this figure. The value was greater than 0-5 in most other e.p.s.p. groups analysed (thirty e.p.s.p. groups in five fibres) except for four of them where the value was less than 0-5. A

10

cokH 10

C CU

-825

-

C

0

015

1-0 1-5 2-0 Amplitude of e.p.s.p. (mV)

2-5

3-0

Fig. 4. Amplitude-frequency histograms of the sound-evoked e.p.s.p.s and curves predicted from binomial statistics. A, B and a are for the first, second and third e.p.s.p.s respectively. Stimulus sound: 665 Hz and 64 dB SPL.

E.p.s.p.s set up by giving an increment in the sound intensity during the maintained sound stimulation It was observed during stimulation with a continuous sound that an increment in the sound intensity brought about an immediate increase in the amplitude of the e.p.s.p.s, even when the increment was given after the e.p.s.p.s had declined to a low level or had disappeared almost completely (Furukawa &s Matsuura, 1978). In the experiment shown in Fig. 5A1-A9, a slight increment in the sound intensity was applied at about the middle of the traces (an addition of about 1 to 60 dB). Although the amount of increment was so small that it is barely noticeable in the sound monitor traces, the effect was very clearly observed in the discharge of e.p.s.p.s. However, the increase in the amplitude of the e.p.s.p. was short-lived, for the amplitude of the e.p.s.p. declined in the same manner as at the start of sound stimulation.

T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA The value of m, n and p calculated for a few augmented e.p.s.p.s were compared with the control values before the increment in the sound intensity in three fibres. A typical example is shown in Fig. 6. The results indicated that the increase in the

218

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Amplitude of e.p.s.p. (mV)

Fig. 5. Increase in the size of e.p.s.p.s produced by an increment in the sound intensity. A 1-A9, sample records. Sound intensity was increased at about the middle of the sweep from 60 to about 61 dB SPL. Sound frequency, 640 Hz. B-D, amplitudefrequency histograms and the predicted distributions for the first augmented e.p.s.p.s (B), and for e.p.s.p.s in the steady state before and after the increment of the sound intensity (C and D respectively). 3- A 0

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31 32 33 34 35 36 21 22 23 24 25 26 27 Order of occurrence of e.p.s.p.s Fig. 6. Effects of an increment in the sound intensity during the maintained sound stimulation on the binomial parameters m, n and p. The parameters are plotted against the serial number of e.p.s.p.s. Sound intensity was increased from 60 to 61 dB SPL for the 31st responses and thereafter. Sound frequency was 640 Hz.

QUANTAL ANALYSIS AT SENSORY SYNAPSE 219 size of m, i.e. in the amplitude of the e.p.s.p., was associated with an increase in the value of n. The value of binomial parameter p was not markedly altered. Similar results were obtained in two other fibres analysed. Although the value of p was different from one fibre to another, it stayed largely unchanged in the same fibre. The distribution of the e.p.s.p. size expected from binomial statistics was calculated and compared with the observed distribution (histograms) in Fig. 5. B of this Figure is for the first augmented e.p.s.p.s after the increment in the sound intensity, and C and D are for e.p.s.p.s in the steady state before and after the increment. A fairly good fit was observed between the predicted and actual distributions as indicated by a value of P greater than 0 5 for most of the e.p.s.p. groups analysed (nineteen in a total) but P was not larger than 0 3 for two e.p.s.p. groups. Correlation between the size of two or three consecutive e.p.s.p.s The successive decrease of m in the sound-evoked e.p.s.p. train was attributed in the above to a decline in the value of parameter n, while p remained practically unchanged. Such results seem to support the idea that the rundown in the amplitude of e.p.s.p.s is likely to be related to a depletion of the releasable quanta. To substantiate the reasoning, an attempt was made to correlate the amount of the transmitter released between pairs of successive e.p.s.p.s. It would be expected that if many quanta happened to be released in the first e.p.s.p. of the pair, it would be followed by a smaller release. An example of the results is shown in Fig. 7. In A of the Figure, the amplitude of the second e.p.s.p.s of the pairs is plotted against the amplitude of the first one. Shown with filled circles are results on the first and second e.p.s.p.s at the start of the sound stimulus, while open circles are on the first and second augmented e.p.s.p.s obtained after giving a small increment in the sound intensity during stimulation with continuous sound (see Fig. 5). A similar result was obtained when the amplitude of the third e.p.s.p.s is plotted against the sum of the first and second e.p.s.p.s (Fig. 7B). These results clearly indicate the relationship that the larger the amplitude of the preceding e.p.s.p.s, the smaller the amplitude of the e.p.s.p.s that follow. However, the effect on the succeeding e.p.s.p.s was very weak or absent when the preceding e.p.s.p.s were very small in amplitude, that is there was no sign indicating the presence of facilitatory effect. The reciprocal relationship is more clearly observed in Fig. 8 in which results of repeated trials were classified according to the amplitude of the first e.p.s.p.s. The size of the latter was expressed as multiples of the quantal size. The mean amplitude of the second e.p.s.p.s was calculated separately for each of these classes and was plotted against the amplitude of the first e.p.s.p.s. In this case there was a clear negative correlation between the amplitude of the first and second e.p.s.p.s. A similar relation was usually observed between a preceding e.p.s.p. and the one that follows, even when pairs of successive e.p.s.p.s were randomly collected from a series of e.p.s.p.s during stimulation with a continuous sound. The degree of negative correlation became weaker when the size of the third e.p.s.p.s was plotted against the sum of the first and second e.p.s.p.s (Fig. 8B).

220

T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA

E.p.s.p.s produced by stimulating with different intensities of sound In the experiment shown in Fig. 9, e.p.s.p.s were evoked by three different intensities of sound. Of successive e.p.s.p.s evoked by the sound, only the amplitude of the first e.p.s.p.s were measured and their observed and predicted distributions were 2.0

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illustrated in Fig. 9A-C. When the sound intensity was 64 dB SPL, e.p.s.p.s distributed around the mean amplitude of 1-56 mV with a standard deviation (S.D.) of 0-91 mV (Fig. 9C). The magnitude of the responses (mean + S.D.) increased to 3-92 + 1-33 and 11-15 + 2-08 mV when the intensity was increased to 66 and 71 dB

221 QUANTAL ANALYSIS AT SENSORY SYNAPSE SPL respectively. The mean amplitude of m.e.p.s.p.s of this fibre was 062 mV with a S.D. of 017 mV (Fig. 9D). The quantal content m to the three different intensities of sound was 2-50, 6-28 and 17*88 respectively. These changes in the value of m were largely attributed to changes in n, but, though smaller in degree, there were also concomitant changes of p in this case. The P values of goodness of fit in the X2-test were between 03 and 095, indicating a reasonable agreement. A 1.5 o>E 10

-

> 0

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4 5 10 11 7 6 8 9 First+second e.p.s.p.s (multiples of y) Fig. 8. Correlation in the amplitude of successive e.p.s.p.s. Results of the experiment were plotted after having been classified according to the amplitude of the first e.p.s.p.s (A), or according to the sum of the first and second e.p.s.p.s (B). Filled circles and open circles represent results obtained from two different fibres.

2

3

In the above-mentioned case the release parameters were calculated only for the first e.p.s.p.s. The parameters n and p were calculated for all the successive e.p.s.p.s, i.e. for the first through the tenth e.p.s.p.s in the fibre of Fig. 10 for five different sound intensities. It was indicated that the increase in the number of quanta released in response to an increase in the sound intensity was largely attributed to an increase in n. There was also some increase in the value of p in the range up to 73 dB in the fibre. Beyond 73 dB, however, there was practically no increase in the value of p. Therefore, the increase in the size of m in the region beyond 73 dB is almost exclusively attributable to the increase in the size of n. In this fibre, the value of p nearly reached 1 0 for sound intensities beyond 73 dB. Binomial analysis and estimation of the values of m, n and p were further

222 T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA conducted in five other fibres for two or three different intensities of sound. It was found that an increase of the value of n was responsible for the increase in the transmitter output produced by increasing the sound intensity. However, the increase in the value of p was much less evident. There were cases in which p did not show any increase at all. 010

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0

5 5 0 Amplitude of responses (mV)

Fig. 9. Amplitude-frequency histograms constructed for the first e.p.s.p.s obtained by stimulating with different intensities of sound. The sound intensity used was 64 (C), 66 (B) and 71 (A) dB SPL. Sound frequency: 650 Hz. Amplitude distribution of m.e.p.s.p.s is shown by filled columns (D). Continuous lines represent release frequency predicted from binomial statistics. Number of observations (N): 247 (A), 267 (B), 226 (C) and 30 (D). The bin size in the histograms is greater for larger amplitude groups, because of the larger bin size used for measuring the amplitude and also because of the correction for non-linear summation which was made afterwards. The arrow in C shows the number of theoretical failures. DISCUSSION

The objects of the present study were to establish the applicability of the binomial analysis to the release of transmitter quanta at the afferent synapses between hair cells and eighth nerve fibres in the goldfish and to lend support to the idea that the adaptive rundown in the size of e.p.s.p.s at these synapses and also the change in their size due to a change in the sound intensity are attributable to a change of

223 QUANTAL ANALYSIS AT SENSORY SYNAPSE the release parameter n. These two objectives were largely attained in the present study under the assumption that n and p are constant spatially as well as temporally. The applicability of the binomial analysis was indicated by a good agreement of the amplitude-frequency histograms of e.p.s.p.s with the distributions expected from the theorem. Also the values of P indicating the goodness of fit in the X2-test were larger than 05 in eighty-six series of e.p.s.p.s out of a total 103. 50

-

20

-

st e.p.s.p.

A

T

------x

x 2nd

4th

10o

V *

1

.9A

0

2

A 8~~~~th n .- 9~ ~ ~ ~th ~~~ 0th *1~~~~~~~~~

:.-+

Oth

Sound intensity (dB SPL)

Fig. 10. Changes of the value of binomial release parameters n and p produced by changes in the sound intensity. Sound frequency: 800 Hz. Stimulus intensity, abscissa, is shown in dB SPL. Number of trials (N): 104, 100, 97, 98, and 106 for 63 dB, 68 dB, 73 dB, 78 dB and 88 dB SPL respectively.

Regarding the adaptive rundown, it was clearly shown that a reduction in the size of n played a major role in the process of the rundown of e.p.s.p.s, while p stayed practically unchanged (Fig. 3). Such a finding seems to indicate the applicability of a depletion model to the process of e.p.s.p. rundown in the present material. Also the presence of a negative correlation between the amplitude of two successive e.p.s.p.s seems to attest to the involvement of a depletion of the transmitter quanta from the release sites (Figs. 7 and 5). Involvement of the postsynaptic desensitization was clearly excluded as a possible cause of the e.p.s.p. rundown.

224 T. FURUKA WA, Y. HA YASHIDA AND S. MATSUURA However, there is a problem to be settled. It is related to the question of whether or not the value of p as a binomial parameter could be regarded as identical with the release fraction f obtained from the initial slope of the e.p.s.p. rundown (Furukawa & Matsuura, 1978). In so far as the exact value of the latter could be determined under the condition where the mobilization from the store could be excluded and the intervention of any special facilitatory or suppressive processes could be neglected, the values of p and f should agree. Actually, however, these conditions could not necessarily be met. In order to see the degree of diversion, calculation of the release fraction was made with the method of Elmqvist & Quastel (1965) on three fibres examined in this experiment. The values obtained in this way were 044, 038 and 034 respectively, while the value of p estimated from binomial statistics was in the range of 0-61-071, 0-16-0-35, and 060-0s92 respectively. Thus, the values from two sources showed a considerable difference. There are at least two major sources of error in measuring the slope of the rundown. The first and possibly more important source of error is the mobilization of the quanta from the larger store. The second cause of error was rather peculiar to our experiment. Due to the mechanical properties of the vibratory system of the loudspeaker, the sound waves at the start may have some transient irregularity in the amplitude. The first sound wave especially was most susceptible to variations of this sort. Moreover, the results shown in the present paper were selected from the point of view that they were amenable to a quantal analysis. Thus, they did not necessarily represent cases suited for estimating the slope of the rundown of e.p.s.p.s. A further interesting observation was made in the present study on the regulation of the transmitter output. There are grounds for believing that changes in the amount of transmitter output brought about by a change in the sound intensity are mediated by a change in the initial size of the available store of transmitter quanta at the presynaptic release sites (Furukawa & Matsuura, 1978). In the present study, support for the above postulate was afforded by the experiments in which the effects of a change in the sound intensity were tested. The changes in the mean quantal content (m) brought about by a change in the intensity of stimulus sound was largely attributable to changes in the size of n. On the other hand, concomitant change in the value of p, if any, was observed only in a limited range. It must be noted here that the value of p obtained from different fibres showed a great deal of variation from fibre to fibre. If a homogeneous property of receptor cells can be assumed, it is as if the release sites of the cell were modified by afferent fibres which synapse on them (Frank, 1973). However, so far as the release parameter p obtained from any one fibre is concerned, its value stays largely unchanged under a variety of stimulus conditions which results in a large change in the value of m. As mentioned above, binomial analysis in the present study was conducted under the assumption that n and p are constant spatially as well as temporally. However, if either is non-uniform or non-stationary, then the calculations would lead to large errors (Brown, Perkel & Feldman, 1976). For example, if p is non-uniform among different release sites, the expression used to obtain p, namely, S2

v2

m.y2+72

QUANTAL ANALYSIS AT SENSORY SYNAPSE

225

becomes var

82

p I p+_= 1-m 2-

T2 2

Thus, if var p/p has a certain value, then p will be over-estimated by this amount. Similar considerations apply to non-uniformity and non-stationarity of n. One must admit, therefore, that in the absence of more detailed information about the release parameters, calculations of their exact value or of changes in their values are of only limited use. Due to possible hazards of calculating release parameters from binomial distributions, interpretation of the present findings in terms of their physiological meanings can only be made in a very limited extent. However, results of the present study in conjunction with the findings obtained from the slope of e.p.s.p.'s rundown (Furukawa & Matsuura, 1978) seem to support a view that the release sites in the receptor cells are divided into many classes according to their voltage sensitivity. If the release sites were assumed to spread over the presynaptic membrane and occupy a certain area of it (Bennett, Florin & Pettigrew, 1976; Heuser & Reese, 1973), it can be said that the area activated for release would vary depending on the magnitude of depolarization. The idea that an increase in the transmitter output is brought about by an enlargement of the activated zone seems in accordance with the independence of quantal action demonstrated on the motor end-plate (Hartzell, Kuffler & Yoshikami, 1975). It has already been shown that the value of n is in a close relationship with the presynaptic terminal size (Kuno, Turkanis & Weakly, 1971; Bennett & Florin, 1974), or with the length of the activated terminal (Wernig, 1975). Our result may be interpreted in line with these findings. This work was supported by grants from the Ministry of Education of Japan.

REFERENCES BENNETT, M. R. & FLORIN, T. (1974). A statistical analysis of the release of acetylcholine at newly formed synapses in striated muscle. J. Phy.iol. 238, 93-107. BENNETT, M. R., FLORIN, T. & PETTIGREW, A. G. (1976). The effect of calcium ions on the binomial statistic parameters that control acetylcholine release at preganglionic nerve terminals. J. Phy8iol. 257, 597-620. BLAcKEN, J. G., GINsBORG, B. L. & RAY, C. (1963). On the quantal release of the transmitter at a sympathetic synapse. J. Phyaiol. 167, 402-415. BOYD, I. A. & MARTIN, A. R. (1956). The end-plate potential in mammalian muscle. J. Physiol. 132, 74-91. BRANISTEANU, D. D., MIYAMOTO, M. D. & VOLLE, R. L. (1976). Effects of physiologic alterations on binomial transmitter release at magnesium-depressed neuromuscular junctions. J. Physiol. 254, 19-37. BROWN, T. H., PEREEL, D. H. & FELDMAN, M. W. (1976). Evoked neurotransmitter release: statistical effects of nonuniformity and nonstationarity. Proc. natn. Acad. Sci. U.S.A. 73, 2913-2917. DEL CASTILLO, J. & KATZ, B. (1954a). Quantal components of the end-plate potential. J. Phy8iol. 124, 56-573. DEL CASTILLO, J. & KATZ, B. (1954b). Statistical factors involved in neuromuscular facilitation and depression. J. Physiol. 124, 574-585. DUDEL, J. & KuFFLER, S. W. (1961). The quantal nature of transmission and spontaneous miniature potentials at the crayfish neuromuscular junction. J. Physiol. 155, 514-529. ELMQVIST, D. & QUASTEL, D. M. J. (1965). A quantitative study of end-plate potentials in isolated human muscle. J. Physiol. 178, 505-529. PHY 276 8

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FRANK, E. (1973). Matching of facilitation at the neuromuscular junction of the lobster: a possible case of influence of muscle on nerve. J. Phy8iol. 233, 635-658. FURUKAWA, T. & ISHII, Y. (1967). Neurophysiological studies on hearing in goldfish. J. Neurophy8iol. 30, 1377-1403. FURUKAWA, T. & MATSUURA, S. (1978). Adaptive rundown of excitatory post-synaptic potentials at synapses between hair cells and eighth nerve fibres in the goldfish. J. Physiol. 276, 193-209. HARTZELL, H. C., KUFFLER, S. WV. & YOSHIKAMI, D. (1975). Post-synaptic potentiation: interaction between quanta of acetylcholine at the skeletal neuromuscular synapse. J. Physiol. 251, 427-463. HEUSER, J. E. & REESE, T. S. (1973). Evidence for recycling of synaptic vesicle membrane during transmitter release at the frog neuromuscular junction. J. Cell Biol. 57, 315-344. ISHI, Y., MATSUURA, S. & FURUKAWA, T. (1971). Quantal nature of transmission at the synapse between hair cells and eighth nerve fibers. Jap. J. Physiol. 21, 79-89. JOHNSON, E. WV. & WERNIG, A. (1971). The binomial nature of transmitter release at the crayfish neuromuscular junction. J. Physiol. 218, 757-767. KUNO, M. (1964). Quantal components of excitatory synaptic potentials in spinal motoneurones.

J. Phyaiol. 175, 81-99. KuNo, M., TuRKANIs, S. A. & WEAKLY, J. N. (1971). Correlation between nerve terminal size and transmitter release at the neuromuscular junction of the frog. J. Phy8iol. 213, 545-556. McLAcHLAN, E. M. (1975). An analysis of the release of acetylcholine from preganglionic nerve terminals. J. Physiol. 245, 447-466. MARTIN, A. R. (1955). A further study of the statistical composition of the end-plate potential. J. Phy8iol. 130, 114-122. MARTIN, A. R. (1966). Quantal nature of synaptic transmission. Phy8iol. Rev. 46, 51-66. MARTIN, A. R. & PILAR, G. (1964). Quantal components of the synaptic potential in the ciliary ganglion of the chick. J. Phy8iol. 175, 1-16. MIYAMOTO, M. D. (1975). Binomial analysis of quantal transmitter release at glycerol treated frog neuromuscular junction. J. Physiol. 250, 121-142. WERNIG, A. (1972). Changes in statistical parameters during facilitation at the crayfish neuromuscular junction. J. Physiol. 226, 751-759. WERNIG, A. (1975). Estimates of statistical release parameters from crayfish and frog neuromuscular junctions. J. Physiol. 244, 207-221. ZUCKER, R. S. (1973). Changes in the statistics of transmitter release during facilitation. J. Physiol. 229, 787-810.

Quantal analysis of the size of excitatory post-synaptic potentials at synapses between hair cells and afferent nerve fibres in goldfish.

211 J. Physiol. (1978), 276, pp. 211-226 With 10 text-figure8 Printed in Great Britain QUANTAL ANALYSIS OF THE SIZE OF EXCITATORY POST-SYNAPTIC POTE...
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