Brain Research, 107 (1976) 275-289
275
© ElsevierScientificPublishingCompany,Amsterdam- Printed in The Netherlands
SOME PROPERTIES OF THE TRANSMITTER RELEASE MECHANISM AT THE RAT GANGLIONIC SYNAPSE DURING POTASSIUM STIMULATION
OSCAR SACCHI AND VIRGILIO PERRI
Institute of General Physiology, University of Pavia, Pavia and Institute of General Physiology, University of Ferrara, Ferrara (Italy) (Accepted September 29th, 1975)
SUMMARY
In the present investigation a study has been made using intracellular recordings in the rat superior cervical ganglion of the mode of transmitter release induced by raised external potassium ion concentration (40 mM), after acetylcholine synthesis has been blocked by hemicholinium-3. It is shown that the progressive decline in the rate of acetylcholine output from the ganglion is related to a decrease in the number of quanta being released. Furthermore, under these conditions there is no evidence for a reduction in the size of the transmitter quantum. The statistical foundations of the quantal release process at the rat ganglionic synapse have been investigated by comparing the distribution of the number of miniature EPSPs during successive constant time intervals in the tracings with the corresponding Poisson and binomial predictions. Analyses have shown that the probability for a quantum to be released is so small as to produce a binomial distribution of responses indistinguishable from the corresponding Poisson distribution, both at the beginning of the potassium-induced quantum discharge and when transmitter release level is low after exhaustion of acetylcholine tissue content.
INTRODUCTION
As has been previously reported 19, the EPSPs evoked in the neurones of the rat superior cervical ganglion (SCG) during prolonged stimulation of a single preganglionic fibre progressively decline in amplitude provided hemicholinium-3 (HC-3) is present to prevent the synthesis of new acetylcholine (ACh) in the nerve terminals. This effect is due to a decrease in the number of quanta in the EPSPs, without there being any modification in the size of individual quanta. Furthermore, the EPSP
276 amplitude fluctuations, at both low and high transmitter release levels, proved to be satisfactorily described by Poisson statistics. In the present investigation a study has been made using intracellular recordings in the rat SCG of the mode of transmitter release induced by raised external potassium ion concentration after ACh synthesis has been blocked by HC-3. It is, in fact, well established that potassium-induced depolarization of the nerve terminals causes a major increase in the release frequency of quanta 16 which, in the presence of HC-3, results in the exhaustion of the transmitter tissue content. It was felt to be of interest to find out whether the transmitter release process is affected in the same way by either chemical or electrical stimulation. The statistical foundations of the quantal release mechanism at the rat ganglionic synapse have been further elucidated by counting directly the individual quantal units present in successive constant time intervals in the tracings during the potassiuminduced quantum discharge6,10. The actual distribution of the numbers of quanta released m each interval has therefore been compared with the theoretical distributions based both on Poisson and binomial predictions. Since present analytical techniques do not allow direct measurement of probability (P) of release, P has been obtained indirectly from the mean (m) and the variance (a2) of the number of quanta counted in each interval using the relation 7 based on binomial statistics: P := 1 - - a2/m. The second binomial term n can easily be derived from n ~= m/P. Alternatively, n and P have been estimated by the method of maximum likelihood 18. The principle of maximum likelihood has been applied to the present analyses by accepting as the best estimate of n and P for a given mEPSP distribution those values of n and P which maximize the likelihood for that mEPSP distribution to be described by a binomial process. METHODS
Experiments were performed in vitro on isolated SCG excised from rats (Wistar strain) weighing 80-100 g. The preparation was superfused at 37 °C with a basic bathing solution of the following ionic composition (mmole/l): NaCI 136; KCI 5.6; CaC12 2.2; MgC12 1.2; NaH2PO4 1.2; NaHCOz 14.3; glucose 5.5. Hemicholinium-3 6 × 10-6 M was present in all cases. The fluid was bubbled with 95 % 02 and 5 % CO2 and flowed continuously at a rate of 2-4 ml/min. The pH of the solution in the bath was 7.3-7.4. Intracellular recordings were performed by conventional glass microelectrodes filled with 2 M potassium citrate, using the methods and precautions previously described17,10. In order to accelerate the quantal release of transmitter, the normal bathing solution was slowly replaced with a modified solution in which the potassium concentration was raised to 40 raM. The changes in potassium concentration were usually accompanied by appropriate reductions in NaC1 concentration to keep the solution isoosmolar. In a few experiments the potassium level was increased by adding small amounts of a concentrated KCI solution directly to the bathing medium : in this case the osmotic compensation was obviously omitted.
277 The following procedure was adopted in 11 experiments. A neurone was impaled while exposed to the normal solution and once it was gauged that the recording conditions were stable, the high potassium solution was gradually introduced into the bathing chamber. In 7 experiments the microelectrode was successfully left in the cell until the mEPSP discharge frequency levelled off; in two experiments it was possible to reimmerse the preparation in normal solution and follow the recovery of the neurone membrane potential until its final value was in satisfactory agreement with the initial value (Fig. 2). Intracellularly monitored potentials from the neurones were amplified and recorded on FM magnetic tape (Ampex SP-300). Simultaneously with the recordings of the miniature potentials, the neurone membrane potential was also noted. Signals were subsequently displayed on an oscilloscope screen, from which they could be photographed; oscilloscope traces of mEPSPs were enlarged with a film reader and measured by hand. The average frequency of groups of between 100 and 200 mEPSPs were determined at 2-10 min intervals during stimulation. Nine series of mEPSPs from 3 different experiments were further processed by analysing the distribution of individual mEPSPs in successive time intervals of constant duration 6,1°. The theoretical mEPSP distribution for each sample was computed using the Poisson and binomial model. If the discharge of quanta is a Poisson process, then the probability of finding intervals containing × (0, 1, 2, 3 . . . . . . . n) mEPSPs can be derived from the Poisson equation: m x
P(x) = e -m"
x!
'
where m is the mean number of quanta per interval. On the assumption that the release mechanism can be described by binomial statistics, probability P for a quantum to be released from the presynaptic terminals was obtained from the relationT: G2
P=I----,
m
where m is the mean and or2 the variance of the number of quanta per time interval. In the first case x is assumed to be a Poisson random variable and the simple mean m of the number of mEPSPs per interval generates the expected distribution. In the second case x is considered a binomial random variable and m is thus separated into its n and P components (m = n.P). The expected frequency distribution was thus computed from the relation: P(x) --
n! ( n - - x ) ! x!
px (1 - - p)n-x .
The observed mEPSP distribution in a series was therefore compared with the theoretically expected distributions based either on Poisson or binomial relation and the validity of the predictions quantitatively evaluated by use of the g2 test. The details of this procedure are given by Johnson and Wernig 11 and Zucker ~a. The Yates correction for continuity was not however applied. The standard error of P was determined from the expression (Zucker, personal communication):
278
0 .2
S.E.p ....
I
m
cr 2
2P 2 --- 1
-b~-(2 + mS- q
.... -~,;--
)'
where N is the total number of intervals into which the mEPSP sequence was fractionated. A maximum likelihood estimate of the binomial parameters n and P was also attempted xs. On the assumption of binomial distribution of the mEPSPs, the likelihood of observing nx times x events in an interval is: [P(x)]nx. The likelihood of observing a given distribution of x events is: n
A :
II x=O
[px]nx
Under the binomial hypothesis, one obtains: n
A =
II x=0
n!
. px(1 __p)n-x. x! (n - - x)!
The values of n and P which maximize A are called the maximum likelihood values of these parameters. In practice, the likelihood equation used is: L :
lnA
and this is the quantity which is maximized. In the present case: n
L = n o n l n ( 1 - - P) +
Z
'x--1
nxl
x = l
+ xlnP + ( n -
=Z" i
[ln(n--i)--ln(i+l)] 0
x ) l n ( 1 - - P) }.
The first derivatives of this quantity with respect to n and P are equated to 0 and solved simultaneously giving the values which maximize L. In the present study, we preferred to explore a given range of n and P, trying to find the maximum of L directly, using a computer programme called Minuit which was written at CERN in Geneva. RESULTS
Increasing the concentration of potassium to which the nerve terminals are exposed in the bathing medium has been shown to result in elevated rates of ACh release 16. The discharge frequency of quanta can in fact be raised as a consequence of the potassium depolarization of the presynaptic membrane by a factor of several hundred or more, to a point where the miniature potentials become so frequent as
279 to be unmeasurable. The 40 mM potassium concentration used in the present study was chosen as it gave a high transmitter release rate (a peak frequency of 40-80 mEPSPs/sec) without any excessive reduction in the accuracy of the count of individual mEPSPs. At the same time the ACh discharge level was adequate to achieve depletion of the presynaptic transmitter stores of the ganglion, superfused in the presence of HC-3 to prevent the synthesis of new ACh, with a time constant comparable to the expected duration of a good impalement of the neurone. A depletion of 82 % in ACh ganglion levels has actually been detected in rat SCG as a result of a 30 min stimulation period with 40 mM KCI, performed in the presence of HC-3 6 × 10-6 M (Ladinsky et al., unpublished). According to Birks and Macintosh 1, this implies that virtually all the synaptically located ACh is released by increasing the external potassium concentration. Fig. 1 illustrates some examples of quantal emission at different release rates, recorded intracellularly from a rat ganglion neurone in the course of changing the bathing solution to one containing the desired raised potassium level. HC-3 was present throughout. The frequency of mEPSPs greatly increases, but the individual spontaneous potentials are still clearly distinguishable despite some of them being partially fused. The peak frequency obtained with 40 mM KCI was not maintained and subsequently declined to very low levels. The decrease in mEPSP frequency was real and not secondary to the mEPSPs getting smaller, which would have resulted in a loss in the baseline noise. In fact, in the bottom row, individual miniature potentials are clearly discernible and measurable
|
[
2mV
lOOmsec
Fig. I. Intraccllularly recorded mEPSPs in a rat ganglion neurone evoked by raised potassium ion concentration. Tracings illustrate different transmitter release levels at progressively increasing times during chemical stimulation. HC-3 6 × 10-6M was present throughout. The amplitudes of the mEPSPs in the two bottom lines have to be corrected for changes in the membrane potential of the neurone when compared with those of the first line (correction factor 1.23).
280
Q
Q
L -45 :E O
O
Q a
o
.65
AFTIR WASHING
¸ 40mM
KC!
4O
~ 2O E
0
ao mln
Fig. 2. Time-course of the change in membrane potential amplitude and mEPSP frequency produced by 40 mM KC1 in a rat ganglion neurone in the presence of HC-3 6 × 10-6M. The high potassium solution was progressivelyintroduced into the bathing chamber starting from the arrow. At the end of stimulation the preparation was re-immersed in normal solution and the final value of neurone membrane potential after a 20 min washing period is shown.
despite some increase in background noise due to a rise in electrode resistance, which usually occurred during the long-lasting impalement. Fig. 2 shows the time-course of the change in mEPSP frequency produced by the potassium activation of the presynaptic nerve terminals in the presence of HC-3 6 × l0 -6 M. The potassium-induced depolarization of the postsynaptic neurone is also illustrated. It will be noted that the peak amplitude of the membrane depolarization in 40 m M potassium is 22 mV (a mean of 21 mV in 11 experiments); this figure is less than expected from the Nernst equation and conforms to the view that the neurone is an inaccurate potassium electrode 15. The rate of occurrence of mEPSPs shows a rapid and substantial increase. However, the peak frequency of quanta discharge, attained within 8-10 min, was not stable, but after having reached its maximum immediately began to subside slowly, with the result that approximately one hour after exposure of the preparation to high potassium concentration the transmitter release had virtually levelled off. The failure of high release rates to be sustained, in spite of the rapid achievement of the final potassium concentration in the chamber, reflects depletion of the preexisting pools of ACh in the ganglion 1. The results were very much the same in 11 experiments, in which depression of mEPSP frequency invariably occurred. The time taken for the quanta discharge frequency to run down to 1 0 ~ of the peak value was in the range of 40-90 rain. Fig. 3 shows an example of the amplitude distributions of the same number of sequential mEPSPs recorded in a n experiment in A at the beginning and in B at the end of the potassium-induced transmitter release. The dotted line in B shows the
281 40"
A 20
0
0 Q 0
F 60'
i
|
m
it.-*! I
r "'j i
~ 4o E
2,
B
F 0
" "~.-,..s"~,-,-~..-,-,--,
?
I
2 m l P S P amplitude
mV
Fig. 3. Histograms showing the amplitude distribution of the same number of sequential mEPSPs at the beginning (A) and end (B) of the transmitter release induced on a neurone by increated potassium concentration. The dotted line in B shows the amplitude distribution actually observed; the continuous line that obtained after correcting individual amplitudes for displacement of membrane potential (11 mV) occurring between A and B.
amplitude distribution actually observed, in which no account is taken of the fact that mEPSP amplitude decreases as membrane potential moves towards the equilibrium potential for the transmitter. In comparing mEPSPs in A and B, allowance must in fact be made for the 11 mV displacement of resting potential level occurring between A and B. According to the data by Takeuchi at the frog neuromuscular junction 20, the possible alteration of the equilibrium potential for the transmitter due to the increase in potassium concentration is likely to be compensated by the decrease in the external sodium concentration. On the tacit assumption that the equilibrium potential adopted for ACh (--10 mV) was the same in B as in A and assuming a linear relation between membrane potential and synaptic potential amplitude, the mEPSP amplitudes in B were thus multiplied by factor (EA--10)/ (EB - - 10), where E is the membrane potential at A and B respectively. If this correction is applied, a new amplitude distribution is obtained (continuous line), which fits quite well into the control distribution at A. The profile of the distributions is obviously skewed, since spontaneous potentials arise at all the synaptic sites on the neurone; they will therefore undergo differing dendritic attenuation according to the distance of the site of generation from the recording electrode. Fig. 4 shows the results of a similar experiment, in which small amounts of a concentrated KCI solution were added at two different times to the bathing medium. No alteration in NaCI concentration was thus made when the potassium level was modified, with the result that the outside solution was hypertonic. The pattern of
282
14°1
A
It j L , [
20
r~
i o ISmM
KCI
18mM
6O
KCI
B Q i
80
I
v
L
o e i o
1'o
o
m£PSP amphtude
mV
50 rain
Fig. 4. Changes in the frequency of mEPSPs and comparison of their amplitude distributions in a
rat ganglion neurone, A at the beginning and B at the end of the potassium-induced transmitter release in the presence of HC-3 6 × 10-eM. In this experiment small amounts of a concentrated KC1 solution were added at two different times (arrow) direct to the bathing medium. The indicated figures should be added to the initial level (5.6 m M ) to obtain the actual final potassium concentration.
events is similar to that previously described. Yet it should be noted, when comparing A with B ( A at the beginning of the quantal emission and B one hour later), that the mEPSPs corresponding to amplitude classes larger than 1.3 mV are much more frequent in A than in B. There is, however, no shift to the left in the smallest amplitude classes and this rules out any possibility that a drastic reduction in the size of the transmitter quantum had occurred. The total amount of quanta released by potassium stimulation after blockade of ACh synthesis by HC-3 is an estimate of the presynaptic transmitter store present in all the nerve endings impinging on the neurone under test. This value varied from neurone to neurone in the range of 36,000-120,000 quanta, with an average of 77,300 transmitter quanta in 7 experiments. The mEPSP distribution in the tracings was analysed on the assumption that the fractionation of the mEPSP discharge sequence into intervals of arbitrary duration will not substantially affect the statistical properties of the release process. If this is the case, the analysis then becomes similar to that of discharges evoked by electrical stimulation of the presynaptic fibre 12. To test this p o i n t , the statistical parameters o f the release process were evaluated in 3 sets of data, taken from the same mEPSP series but sampled using time intervals of increasing amplitude. The results of these analyses are listed in Table I. The properties of the mEPSP sequence,
283 TABLE I EFFECT OF INCREASINGTHE AMPLITUDEOF THE TIME INTERVALINTO WHICH THE SAMEm E P S P SEQUENCE IS FRACTIONATEDON THE ESTIMATESOF THE STATISTICALPARAMETERS DESCRIBINGTRANSMITTER RELEASE m, m e a n n u m b e r of mEPSPs per time interval; cr2, variance of the m E P S P distribution; P, probability for a q u a n t u m to be released; P', probability level for the Poisson or binomial model to fit the observed distribution, evaluated by use of the X2 test.
Time interval ( msec )
No. o f intervals
m
a2
P*
P" Poisson
P" binomial
200 400 600
1007 503 335
2.762 5.525 8.278
2.601 5.403 8.009
0.058 -4- 0.041 0.022 -4- 0.061 0.032 4- 0.075
> 0.60 > 0.99 > 0.10
> 0.70 > 0.99 > 0.10
* -4- S.E.
derived from the experiment illustrated in Fig. 4 (time 9-12 min), do not actually seem to be affected by differences in sampling. As mentioned above, an important point in the present study was to elucidate which model will best approximate the transmitter release process and whether the statistical properties of this model are maintained unchanged during the whole observation period, even when the release level of quanta is low after depletion of the presynaptic ACh stores by potassium stimulation. In 3 experiments a total of 9 mEPSP series were thus analysed, 4 of these being at the beginning of the quantal emission and 5 after the release rate had run down to less than 10 ~ of the peak value. The basic criterion for selecting the 9 series was the absence of any apparent drift, within each series, in the rate of quantal secretion as evaluated from the mean number of events in blocks of 30 time intervals. Furthermore, the linear regression of the transmitter release rate over time was never statistically significant; the regression coefficient for the longest of the 9 mEPSP sequences presented (Expt I, 10 min) was + 0.001. Each series was therefore considered to be a stationary section of the entire experiment. The distributions observed and the comparison with the corresponding Poisson and binomial predictions are summarized in Table II. The parameters characterizing transmitter release in the 3 experiments, obtained from the meanvariance method (P = 1 - - tr2/m), are listed in Table III. It is evident from Table II that the distributions observed are approximated closely by both the Poisson and binomial models. Probability (P) of release for a quantum was in fact so small in all cases that both the predictions were similar and indistinguishable from each other. In 4 analyses a negative value of P was obtained. However, this seems more likely to be due to the small value of P and the large systematic statistical errors affecting its evaluation (see Tables I and III for P 4- S.E.) than to a drift in the transmitter release rate occurring within the mEPSP sequence, which would result in an increase in the variance. The estimates obtained by the maximum likelihood fit are similar to those obtained by the mean-variance method. The results are given in Table IV. It will
SEQUENCES CONTAINING X ( 0 , 1, 2, . . . . ,
8) Q U A N T A
65
60
Expt. III 10
71
60
10
Expt. II 5
60
Expt. I 10
Observation time (min)
Observed Poisson Binomial Observed Poisson Observed Poisson Binomial
Observed Poisson Observed Poisson Binomial Observed Poisson Observed Poisson Binomial
Observed Poisson Binomial Observed Poisson
Observation or prediction
39.0 49.1 43.5 39.0 39.0 71.0 75.2 70;9
33.0 28.7 57.0 58.3 55.1 15.5 15.9 5.0 7.7 6.1
64.0 63.6 58.5 62;0 60.4
0
104.0 89.0 89.9 76.0 79.0 105.0 103,3 106.0
35.5 39.4 93.0 95.3 96.4 37.5 35.4 19.0 22.0 20.5
158.0 175.7 171.6 128.0 127.0
1
71.0 80.7 86.7 90.0 80.1 77.0 70.9 74.5
24.0 27.0 82.0 78.0 81.0 38.0 39.6 39.0 31.4 32.5
255.0 242.6 246.3 132.0 133.4
2
58.0 48.8 51.7 49.0 54.1 30.0 3Z5 32.8
12.5 12.3 43.0 42.5 43.5 29.0 29.4 27.5 29.9 32.5
233.0 223.4 230.6 91.0 93.4
3
21.0 22.1 21.3 24.0 27.4 11.0 I 1.2 10.1
7.0 4.2 17.0 17.4 16,7 15.0 16.4 26.5 21.3 23.0
158.0 154.2 158.4 44.0 49.1
4
6.0 8.0 6.4 12:0 11.1 3.0 3.8 2.8
1.0 1.4 7.0 7.3 6.3 9.0 7.3 9.5 12.2 12.2
77.0 85.2 85.1 27.0 20.6
5
2.0 3.2 1.8 3.0 3.8
3.0 2.7 4.0 5.8 5.0
43.0 39.2 37.2 8.0 7.2
6
3.0 1.4
1.0 1.1 2.5 2.4 1.6
13.0 15.5 13.6 2.0 2.9
7
1.0 1.2 0.4
6.0 7.5 5.6
8
• 0.80 ..... 0.90
~= 0.60
-~ 0.10 > 0.t0
: 0.60 0.50
:> 0.99
> 0.97 ~- 0.95
> 0.50
:> 0.80
:-~ 0.60 :> 0.70
P
Where x classes ceased to be observed in a given mEPSP series, the predicted numbers for larger quantal classes were added to that computed for the final observed class of the sequence. Fractional numbers in the observed distributions arise from the mean of two successive counts performed on the same mEPSP sequence. Observation time indicates time after switching to the high potassium concentration at which the mEPSP series was selected. Times up to 10 rain should be considered 'initial', i.e., at the beginning of the quantal emission and times longer than 60 rain 'final', i.e. at the end of the transmitter release, when the presynaptic A C h stores are exhausted. P indicates the probability level for the Poisson and binomial predictions to fit the corresponding observed distribution, evaluated by use of the g 2 test.
OBSERVED A N D EXPECTED DISTRIBUTIONS OF THE NUMBERS OF TIME INTERVALS 1N 9 m E P S P
TABLE II t~ O~
285 be n o t e d t h a t w h e n , in t h e d i r e c t e s t i m a t e , P < 0 t h e n t h e l i k e l i h o o d f u n c t i o n d o e s n o t c o n v e r g e to a m a x i m u m in t h e r a n g e e x p l o r e d . I n Fig. 5 o n e c a n o b s e r v e t h e d i f f e r e n t b e h a v i o u r o f L w h e n P > 0 (A) a n d P < 0 (B). I n this s e c o n d case, c o n v e r gence w o u l d s e e m to b e p o s s i b l e f o r n - - - + c~, w h i c h w o u l d m e a n P -
0. T h i s
i n d i c a t e s t h a t s a m p l i n g a n d e x p e r i m e n t a l a c c i d e n t s result in a strictly P o i s s o n process. T h e b i n o m i a l d i s t r i b u t i o n s p r e s e n t e d in T a b l e II are g e n e r a t e d by n a n d P v a l u e s o b t a i n e d f r o m the m e a n - v a r i a n c e m e t h o d . I n cases in w h i c h a n e g a t i v e v a l u e o f P was o b s e r v e d , it was a s s u m e d o n t h e basis o f the a b o v e e v i d e n c e t h a t it was n o t
TABLE III PARAMETERS CHARACTERIZING TRANSMITrER RELEASE IN NINE
mEPSP
SEQUENCES
Observation time, time after exposing the ganglion to the high potassium concentration; time interval, amplitude of the unit interval into which the mEPSP series was divided; m, mean number of quanta per time interval; cr2, v~iance of the mEPSP distribution; P, probability of release calculated from 1 - - cr~/m.
Expt. I Expt. II
Expt. III
Observation time (min)
Time interval msec
No. o f intervals
m
or2
p*
10 60 5 10 60 71 10 60 65
200 200 400 100 100 150 200 100 100
1007 494 113 299 148 134 301 296 297
2.762 2.101 1.372 1.635 2.233 2.854 1.814 2.027 1.374
2.601 2.148 1.612 1.528 2.775 2.426 1.592 2.135 1.262
+ 0.058 --0.022 --0.174 + 0.066 --0.019 + 0.150 + 0.122 --0.053 + 0.081
:k 0.041 -4- 0.065 ± 0.167 :k 0.0~/5 ± 0.119 ± 0.101 + 0.069 -I- 0.088 -I- 0.073
* ±S.E.
TABLE IV ESTIMATES OF THE BINOMIAL RELEASE PARAMETERS n AND P CALCULATED BY THE MAXIMUM LIKELIHOOD METHOD
Analysis is based on the same data sets as those used in Table III.
Expt. I Expt. II
Expt. III
Observation time (rain)
P
n
10 60 5 10 60 71 10 60 65
+ 0.060 ----. 0 -----~ 0 q- 0.065 ----~ 0 + 0.140 + 0.120 ----~ 0 + 0.091
46.043 -----~ oo -----~ oo 25.154 -----~ oo 20.377 15.115 ----~ oo 15.099
286
-L
1879-
® j
~
t
0.1 p
1877
0
-L 174J
®
t
0.1 p
0
4'0
SO
120
0
n
Fig. 5. Graphs to show the likelihood function in two experiments. In A (Expt. I, 10 rain) L is maximized by the n and P values indicated by the arrow. In B (Expt. II, 5 min) the convergence of n and P to a maximum of L progressively improves as values of n increase and those of P decrease.
significantly different from 0; the expected binomial distribution could not however be legitimately computed. DISCUSSION
It is well known that sympathetic neurones in the rat SCG receive synaptic connections from multiple converging fibres 4,17. The present data allow a quantitative evaluation of the degree of preganglionic convergence on a single neurone. In a previous study 19 it has been demonstrated that the mean size, expressed in quantal terms, of the presynaptic transmitter store initially present in those terminals on a neurone that are activated by the stimulation of a single afferent fibre is some 8000 transmitter quanta. From this and the present estimate of presynaptic stores for all the synaptic sites on the cell, it is suggested that 9-10 preganglionic fibres may be a fair estimate for the mean input to a rat ganglion neurone, if one accepts the risks inherent in extrapolation from a limited number of observations. The total normal ACh content of rat SCG is 28-30 ng, which is reduced by 85 ~ under either electrical or chemical stimulation performed in vitro in the presence of HC-3 (Ladinsky et al., in preparation). Since the mean number of cells in the rat SCG is 35,200 s,la,14, the average amount of transmitter which can be released upon a single neurone is 2.3 × 109 molecules of ACh. From this and the whole presynaptic store value for a single cell it would appear that the transmitter content of quanta released from the nerve terminals of rat SCG is about 3 × 104 molecules of ACh. Implicit in this procedure is the assumption that the number of molecules building up the quantal packet is constant over the whole observation period. The evidence so far adduced suggests that this is the case in the preparation used in the present study. In fact, the effects of the unit quantum of transmitter, released either
287 at the beginning or at the end of the potassium stimulation, are the same in terms of postsynaptie depolarization. The comparison between the population of quanta initially present in the terminals and those released from the exhausted terminals is based on the fit of the mEPSP amplitude distributions sampled at the beginning and at the end of potassium-induced transmitter release. Despite some uncertainties as to the accuracy of the correction for differences in resting potential level, however, the initial and final EPSP amplitude distributions agree reasonably both in form and range. Hence, the derived conclusion that a significant decrease in quantum size can be ruled out appears to be correct. This would suggest that chemical stimulation in the presence of HC-3 acts at the ganglionic synapse in the same way as electrical stimulation. The similarity of the results provides some support for the hypothesis that transmitter quanta can be released by presynaptic terminals in the rat SCG only when they are full size. Furthermore, the progressive depletion in ACh tissue content occurring in the course of prolonged chemical stimulation after transmitter synthesis has been blocked by HC-3 is associated with a decline in transmitter output from the ganglion. Our data show very clearly that the decrease in ACh output invariably corresponds to a decrease in the number of transmitter quanta being released. Elmqvist and Quastel 5 studied the transmitter release process at the rat and human neuromuscular junctions and they showed that the addition of 20 mM KC1 to the bathing solution caused a gradual increase in mEPP frequency, which grew progressively up to 90 min after the potassium ion concentration was raised. At the same time, in the presence of HC-3 4 × 10-6 M, the amplitude of the mEPPs gradually diminished, until they eventually became so small as to be lost in the base line noise. Thus, the progressive increase in the number of quanta released in the unit time is paralleled by a decrease in the size of the individual quantum. The synaptie equivalent of the reduction in ACh release from the nerve terminals therefore appears to be (1) the release of a constant or increased number of transmitter quanta of progressively smaller size at the neuromuscular junction and (2) the release of a lower number of quanta of unchanged size at the ganglionic synapse. This pattern of events, in perfect mutual opposition, can be explained in our opinion only on the basis of the differences between preparations. These findings, however, should prompt further investigations at other synapses, as they may define whether the possibility of generalization is restricted to some aspects only of the transmitter release process, e.g. quantization, while others, such as the invariance in quantum size, are peculiar to individual release sites. The second principal objective of the present investigation was to determine whether or not mEPSP occurrence preferentially follows either the Poisson or binomial distribution. This question is of interest not only from a sheer analytical point of view, since it may give clues as to the elementary model which describes the release of transmitter from a nerve terminal. At the same time, it should be possible to define the still problematic nature of n and P in more concrete terms. The statistical foundations of some models proposed for the mechanism of quantal release have been accurately described by Vere-Jones 21. The possible functional or morphological
288 role of n and P has recently been discussed by Wernig ')2 and Zucker '~',~.The analytical procedure adopted in the present study suffers from some limitations. In fact a physiological significance cannot unfortunately be attached to m or n, which arise from the division of the mEPSP sequence into intervals of arbitrarily fixed amplitude. Nevertheless, this type of analysis allows P to be estimated and the binomial distribution to be predicted. In a previous study at the rat ganglionic synapse 19 it has been demonstrated that the amplitude fluctuations of evoked EPSPs are well described by Poisson statistics, both when the quanta are released initially from the terminals and after exhaustion of the presynaptic transmitter stores by prolonged stimulation in the presence of HC-3. The latter condition was tested since it was felt that the release process could deviate from the Poisson hypothesis in the manner of a binomial when the number of preformed quanta in the terminal is drastically reduced. The present experiments, in which reliable estimates of P have been obtained, show that P remains low despite the fall in the number of quanta available. Furthermore, the evidence presented indicates that the release probability P at the ganglionic synapse is always sufficiently low to generate a binomial distribution of responses indistinguishable from the corresponding Poisson prediction. The use of binomial statistics to describe the transmitter release mechanism in the rat SCG does not therefore appear to be justified under the present circumstances, since the binomial model is accurately approximated by the Poisson model if the probability of quantal emission is low. The process governing the release of quanta at the ganglionic synapse is unaffected by the amount of transmitter actually present in the presynaptic terminal. The original suggestion z,3, therefore, that the Poisson character of the release mechanism may arise from random collision with the nerve terminal membrane of single quanta sampled from a large population of quanta, each with a small probability of release, is not consistent with the present findings since the Poisson model holds good even when the terminal is depleted of preformed quanta. As a consequence, the source of 'Poissonicity' is likely to be associated with other functional or anatomical structures irrespective of quantal population. The release of quanta from a finite number of release sites opening independently from one another will generate a Poisson distribution 7. A similar result also arises if replenishment of the store of releasable quanta follows a Poisson process 21. The solution of this problem, however, is beyond the scope of this study. ACKNOWLEDGEMENTS
We thank Dr. I. Barrai for his advice on the maximum likelihood analysis of the data. We are also grateful to Dr. S. Boffi for providing the computer programs and for useful discussion. This work was supported in part by Grants 73.00718.04 and 74.00241.04 from the Consiglio Nazionale delle Ricerche, Italy.
289 REFERENCES 1 BIRKS, R., AND MACINTOSH,F. C., Acetylcholine metabolism of a sympathetic ganglion, Canad. J. Biochem., 39 (1961) 787-827. 2 DEL CASTILLO,J., AND KATZ, B., Quantal components of the end-plate potential, J. Physiol. (Lond.), 124 (1954) 560-573. 3 DEL CASTILLO,J., AND KATZ, B., Biophysical aspects of neuro-muscular transmission, Progr. Biophys., 6 (1956) 121-170. 4 DUNANT, Y., Organization topographique et fonctionnelle du ganglion cervical sup6rieur chez le rat, J. Physiol. (Paris), 59 (1967) 17-38. 5 ELMQVIST,D., AND QUASI'EL,n . i . J., Presynaptic action of hemicholinium at the neuromuscular junction, J. Physiol. (Lond.), 177 (1965) 463-482. 6 GAGE, P. W., AND HUBBARD, J. I., Evidence for a Poisson distribution of miniature end-plate potentials and some implications, Nature (Lond.), 208 (1965) 395-396. 7 GINSBORG,B. L., The vesicle hypothesis for the release of acetylcholine. In P. ANDERSENAND J. K. S. JANSEN (Eds.), Excitatory Synaptic Mechanisms, Universitetsforlaget, Oslo, 1970, pp. 77-82. 8 HENDRY, I. A., IVERSEN,L. L., AND BLACK, I. B., A comparison of the neural regulation of tyrosine hydroxylase activity in sympathetic ganglia of adult mice and rats, J. Neurochem., 20 (1973) 1683-1689. 9 HUBBARD, J. I., Microphysiology of vertebrate neuromuscular transmission, Physiol. Rev., 53 (1973) 674-723. 10 HUBBARD, J. I., LLINAS, R., AND QUASTEL,n . M. J., Electrophysiological Analysis of Synaptic Transmission, Arnold, London, 1969, 125 pp. 11 JOHNSON, E. W., AND WERNIG, A., The binomial nature of transmitter release at the crayfish neuromuscular junction, J. Physiol. (Lond.), 218 (1971) 757-767. 12 KATZ, B., AND MILEm, R., The effect of temperature on the synaptic delay at the neuromuscular junction, J. Physiol. (Lond.), 181 (1965) 656-670. 13 KLINGMAN,G. I., The distribution of acetylcholinesterase in sympathetic ganglia of immunosympathectomized rats, J. Pharmacol. exp. Ther., 173 (1970) 205-211. 14 KLINGMAN, G. 1., AND KLINGMAN, J. D., Effects of immunosympathectomy on the superior cervical ganglion and other adrenergic tissues of the rat, Life Sci., 4 (1965) 2171-2179. 15 KUFFLER,S. W., AND NICHOLLS, J. G., The physiology of neuroglial cells, Ergebn. Physiol., 57 (1966) 1-90. 16 LILEY,A. W., The effects of presynaptic polarization on the spontaneous activity at the mammalian neuromuscular junction, J. Physiol. (Lond.), 134 (1956) 427-443. 17 PERRI, V., SACCm, O., AND CASELLA,C., Electrical properties and synaptic connections of the sympathetic neurons in the rat and guinea-pig superior cervical ganglion, Pfliigers Arch. ges. Physiol., 314 (1970) 40-54. 18 RAO, C. R., Advanced Statistical Methods in Biometric Research, Wiley, New York, 1952, 150165 pp. 19 SACCHI,O., ANDPERRI,V., Quantal mechanism of transmitter release during progressive depletion of the presynaptic stores at a ganglionic synapse. The action of hemicholinium-3 and thiamine deprivation, J. gen. Physiol., 61 (1973) 342-360. 20 TAKEUCHI,N., Some properties of conductance changes at the end-plate membrane during the action of acetylcholine, J. Physiol. (Lurid.), 167 (1963) 128-140. 21 MERE-JONES,D., Simple stochastic models for the release of quanta of transmitter from a nerve terminal, Aust. J. Stat., 8 (1966) 53-63. 22 WERNIG,A., The effects of calcium and magnesium on statistical release parameters at the crayfish neuromuscular junction, J. Physiol. (Lond.), 226 (1972) 761-768. 23 ZUCKER, R. S., Changes in the statistics of transmitter release during facilitation, J. Physiol. (Lurid.), 229 (1973) 78%810.
275
© ElsevierScientificPublishingCompany,Amsterdam- Printed in The Netherlands
SOME PROPERTIES OF THE TRANSMITTER RELEASE MECHANISM AT THE RAT GANGLIONIC SYNAPSE DURING POTASSIUM STIMULATION
OSCAR SACCHI AND VIRGILIO PERRI
Institute of General Physiology, University of Pavia, Pavia and Institute of General Physiology, University of Ferrara, Ferrara (Italy) (Accepted September 29th, 1975)
SUMMARY
In the present investigation a study has been made using intracellular recordings in the rat superior cervical ganglion of the mode of transmitter release induced by raised external potassium ion concentration (40 mM), after acetylcholine synthesis has been blocked by hemicholinium-3. It is shown that the progressive decline in the rate of acetylcholine output from the ganglion is related to a decrease in the number of quanta being released. Furthermore, under these conditions there is no evidence for a reduction in the size of the transmitter quantum. The statistical foundations of the quantal release process at the rat ganglionic synapse have been investigated by comparing the distribution of the number of miniature EPSPs during successive constant time intervals in the tracings with the corresponding Poisson and binomial predictions. Analyses have shown that the probability for a quantum to be released is so small as to produce a binomial distribution of responses indistinguishable from the corresponding Poisson distribution, both at the beginning of the potassium-induced quantum discharge and when transmitter release level is low after exhaustion of acetylcholine tissue content.
INTRODUCTION
As has been previously reported 19, the EPSPs evoked in the neurones of the rat superior cervical ganglion (SCG) during prolonged stimulation of a single preganglionic fibre progressively decline in amplitude provided hemicholinium-3 (HC-3) is present to prevent the synthesis of new acetylcholine (ACh) in the nerve terminals. This effect is due to a decrease in the number of quanta in the EPSPs, without there being any modification in the size of individual quanta. Furthermore, the EPSP
276 amplitude fluctuations, at both low and high transmitter release levels, proved to be satisfactorily described by Poisson statistics. In the present investigation a study has been made using intracellular recordings in the rat SCG of the mode of transmitter release induced by raised external potassium ion concentration after ACh synthesis has been blocked by HC-3. It is, in fact, well established that potassium-induced depolarization of the nerve terminals causes a major increase in the release frequency of quanta 16 which, in the presence of HC-3, results in the exhaustion of the transmitter tissue content. It was felt to be of interest to find out whether the transmitter release process is affected in the same way by either chemical or electrical stimulation. The statistical foundations of the quantal release mechanism at the rat ganglionic synapse have been further elucidated by counting directly the individual quantal units present in successive constant time intervals in the tracings during the potassiuminduced quantum discharge6,10. The actual distribution of the numbers of quanta released m each interval has therefore been compared with the theoretical distributions based both on Poisson and binomial predictions. Since present analytical techniques do not allow direct measurement of probability (P) of release, P has been obtained indirectly from the mean (m) and the variance (a2) of the number of quanta counted in each interval using the relation 7 based on binomial statistics: P := 1 - - a2/m. The second binomial term n can easily be derived from n ~= m/P. Alternatively, n and P have been estimated by the method of maximum likelihood 18. The principle of maximum likelihood has been applied to the present analyses by accepting as the best estimate of n and P for a given mEPSP distribution those values of n and P which maximize the likelihood for that mEPSP distribution to be described by a binomial process. METHODS
Experiments were performed in vitro on isolated SCG excised from rats (Wistar strain) weighing 80-100 g. The preparation was superfused at 37 °C with a basic bathing solution of the following ionic composition (mmole/l): NaCI 136; KCI 5.6; CaC12 2.2; MgC12 1.2; NaH2PO4 1.2; NaHCOz 14.3; glucose 5.5. Hemicholinium-3 6 × 10-6 M was present in all cases. The fluid was bubbled with 95 % 02 and 5 % CO2 and flowed continuously at a rate of 2-4 ml/min. The pH of the solution in the bath was 7.3-7.4. Intracellular recordings were performed by conventional glass microelectrodes filled with 2 M potassium citrate, using the methods and precautions previously described17,10. In order to accelerate the quantal release of transmitter, the normal bathing solution was slowly replaced with a modified solution in which the potassium concentration was raised to 40 raM. The changes in potassium concentration were usually accompanied by appropriate reductions in NaC1 concentration to keep the solution isoosmolar. In a few experiments the potassium level was increased by adding small amounts of a concentrated KCI solution directly to the bathing medium : in this case the osmotic compensation was obviously omitted.
277 The following procedure was adopted in 11 experiments. A neurone was impaled while exposed to the normal solution and once it was gauged that the recording conditions were stable, the high potassium solution was gradually introduced into the bathing chamber. In 7 experiments the microelectrode was successfully left in the cell until the mEPSP discharge frequency levelled off; in two experiments it was possible to reimmerse the preparation in normal solution and follow the recovery of the neurone membrane potential until its final value was in satisfactory agreement with the initial value (Fig. 2). Intracellularly monitored potentials from the neurones were amplified and recorded on FM magnetic tape (Ampex SP-300). Simultaneously with the recordings of the miniature potentials, the neurone membrane potential was also noted. Signals were subsequently displayed on an oscilloscope screen, from which they could be photographed; oscilloscope traces of mEPSPs were enlarged with a film reader and measured by hand. The average frequency of groups of between 100 and 200 mEPSPs were determined at 2-10 min intervals during stimulation. Nine series of mEPSPs from 3 different experiments were further processed by analysing the distribution of individual mEPSPs in successive time intervals of constant duration 6,1°. The theoretical mEPSP distribution for each sample was computed using the Poisson and binomial model. If the discharge of quanta is a Poisson process, then the probability of finding intervals containing × (0, 1, 2, 3 . . . . . . . n) mEPSPs can be derived from the Poisson equation: m x
P(x) = e -m"
x!
'
where m is the mean number of quanta per interval. On the assumption that the release mechanism can be described by binomial statistics, probability P for a quantum to be released from the presynaptic terminals was obtained from the relationT: G2
P=I----,
m
where m is the mean and or2 the variance of the number of quanta per time interval. In the first case x is assumed to be a Poisson random variable and the simple mean m of the number of mEPSPs per interval generates the expected distribution. In the second case x is considered a binomial random variable and m is thus separated into its n and P components (m = n.P). The expected frequency distribution was thus computed from the relation: P(x) --
n! ( n - - x ) ! x!
px (1 - - p)n-x .
The observed mEPSP distribution in a series was therefore compared with the theoretically expected distributions based either on Poisson or binomial relation and the validity of the predictions quantitatively evaluated by use of the g2 test. The details of this procedure are given by Johnson and Wernig 11 and Zucker ~a. The Yates correction for continuity was not however applied. The standard error of P was determined from the expression (Zucker, personal communication):
278
0 .2
S.E.p ....
I
m
cr 2
2P 2 --- 1
-b~-(2 + mS- q
.... -~,;--
)'
where N is the total number of intervals into which the mEPSP sequence was fractionated. A maximum likelihood estimate of the binomial parameters n and P was also attempted xs. On the assumption of binomial distribution of the mEPSPs, the likelihood of observing nx times x events in an interval is: [P(x)]nx. The likelihood of observing a given distribution of x events is: n
A :
II x=O
[px]nx
Under the binomial hypothesis, one obtains: n
A =
II x=0
n!
. px(1 __p)n-x. x! (n - - x)!
The values of n and P which maximize A are called the maximum likelihood values of these parameters. In practice, the likelihood equation used is: L :
lnA
and this is the quantity which is maximized. In the present case: n
L = n o n l n ( 1 - - P) +
Z
'x--1
nxl
x = l
+ xlnP + ( n -
=Z" i
[ln(n--i)--ln(i+l)] 0
x ) l n ( 1 - - P) }.
The first derivatives of this quantity with respect to n and P are equated to 0 and solved simultaneously giving the values which maximize L. In the present study, we preferred to explore a given range of n and P, trying to find the maximum of L directly, using a computer programme called Minuit which was written at CERN in Geneva. RESULTS
Increasing the concentration of potassium to which the nerve terminals are exposed in the bathing medium has been shown to result in elevated rates of ACh release 16. The discharge frequency of quanta can in fact be raised as a consequence of the potassium depolarization of the presynaptic membrane by a factor of several hundred or more, to a point where the miniature potentials become so frequent as
279 to be unmeasurable. The 40 mM potassium concentration used in the present study was chosen as it gave a high transmitter release rate (a peak frequency of 40-80 mEPSPs/sec) without any excessive reduction in the accuracy of the count of individual mEPSPs. At the same time the ACh discharge level was adequate to achieve depletion of the presynaptic transmitter stores of the ganglion, superfused in the presence of HC-3 to prevent the synthesis of new ACh, with a time constant comparable to the expected duration of a good impalement of the neurone. A depletion of 82 % in ACh ganglion levels has actually been detected in rat SCG as a result of a 30 min stimulation period with 40 mM KCI, performed in the presence of HC-3 6 × 10-6 M (Ladinsky et al., unpublished). According to Birks and Macintosh 1, this implies that virtually all the synaptically located ACh is released by increasing the external potassium concentration. Fig. 1 illustrates some examples of quantal emission at different release rates, recorded intracellularly from a rat ganglion neurone in the course of changing the bathing solution to one containing the desired raised potassium level. HC-3 was present throughout. The frequency of mEPSPs greatly increases, but the individual spontaneous potentials are still clearly distinguishable despite some of them being partially fused. The peak frequency obtained with 40 mM KCI was not maintained and subsequently declined to very low levels. The decrease in mEPSP frequency was real and not secondary to the mEPSPs getting smaller, which would have resulted in a loss in the baseline noise. In fact, in the bottom row, individual miniature potentials are clearly discernible and measurable
|
[
2mV
lOOmsec
Fig. I. Intraccllularly recorded mEPSPs in a rat ganglion neurone evoked by raised potassium ion concentration. Tracings illustrate different transmitter release levels at progressively increasing times during chemical stimulation. HC-3 6 × 10-6M was present throughout. The amplitudes of the mEPSPs in the two bottom lines have to be corrected for changes in the membrane potential of the neurone when compared with those of the first line (correction factor 1.23).
280
Q
Q
L -45 :E O
O
Q a
o
.65
AFTIR WASHING
¸ 40mM
KC!
4O
~ 2O E
0
ao mln
Fig. 2. Time-course of the change in membrane potential amplitude and mEPSP frequency produced by 40 mM KC1 in a rat ganglion neurone in the presence of HC-3 6 × 10-6M. The high potassium solution was progressivelyintroduced into the bathing chamber starting from the arrow. At the end of stimulation the preparation was re-immersed in normal solution and the final value of neurone membrane potential after a 20 min washing period is shown.
despite some increase in background noise due to a rise in electrode resistance, which usually occurred during the long-lasting impalement. Fig. 2 shows the time-course of the change in mEPSP frequency produced by the potassium activation of the presynaptic nerve terminals in the presence of HC-3 6 × l0 -6 M. The potassium-induced depolarization of the postsynaptic neurone is also illustrated. It will be noted that the peak amplitude of the membrane depolarization in 40 m M potassium is 22 mV (a mean of 21 mV in 11 experiments); this figure is less than expected from the Nernst equation and conforms to the view that the neurone is an inaccurate potassium electrode 15. The rate of occurrence of mEPSPs shows a rapid and substantial increase. However, the peak frequency of quanta discharge, attained within 8-10 min, was not stable, but after having reached its maximum immediately began to subside slowly, with the result that approximately one hour after exposure of the preparation to high potassium concentration the transmitter release had virtually levelled off. The failure of high release rates to be sustained, in spite of the rapid achievement of the final potassium concentration in the chamber, reflects depletion of the preexisting pools of ACh in the ganglion 1. The results were very much the same in 11 experiments, in which depression of mEPSP frequency invariably occurred. The time taken for the quanta discharge frequency to run down to 1 0 ~ of the peak value was in the range of 40-90 rain. Fig. 3 shows an example of the amplitude distributions of the same number of sequential mEPSPs recorded in a n experiment in A at the beginning and in B at the end of the potassium-induced transmitter release. The dotted line in B shows the
281 40"
A 20
0
0 Q 0
F 60'
i
|
m
it.-*! I
r "'j i
~ 4o E
2,
B
F 0
" "~.-,..s"~,-,-~..-,-,--,
?
I
2 m l P S P amplitude
mV
Fig. 3. Histograms showing the amplitude distribution of the same number of sequential mEPSPs at the beginning (A) and end (B) of the transmitter release induced on a neurone by increated potassium concentration. The dotted line in B shows the amplitude distribution actually observed; the continuous line that obtained after correcting individual amplitudes for displacement of membrane potential (11 mV) occurring between A and B.
amplitude distribution actually observed, in which no account is taken of the fact that mEPSP amplitude decreases as membrane potential moves towards the equilibrium potential for the transmitter. In comparing mEPSPs in A and B, allowance must in fact be made for the 11 mV displacement of resting potential level occurring between A and B. According to the data by Takeuchi at the frog neuromuscular junction 20, the possible alteration of the equilibrium potential for the transmitter due to the increase in potassium concentration is likely to be compensated by the decrease in the external sodium concentration. On the tacit assumption that the equilibrium potential adopted for ACh (--10 mV) was the same in B as in A and assuming a linear relation between membrane potential and synaptic potential amplitude, the mEPSP amplitudes in B were thus multiplied by factor (EA--10)/ (EB - - 10), where E is the membrane potential at A and B respectively. If this correction is applied, a new amplitude distribution is obtained (continuous line), which fits quite well into the control distribution at A. The profile of the distributions is obviously skewed, since spontaneous potentials arise at all the synaptic sites on the neurone; they will therefore undergo differing dendritic attenuation according to the distance of the site of generation from the recording electrode. Fig. 4 shows the results of a similar experiment, in which small amounts of a concentrated KCI solution were added at two different times to the bathing medium. No alteration in NaCI concentration was thus made when the potassium level was modified, with the result that the outside solution was hypertonic. The pattern of
282
14°1
A
It j L , [
20
r~
i o ISmM
KCI
18mM
6O
KCI
B Q i
80
I
v
L
o e i o
1'o
o
m£PSP amphtude
mV
50 rain
Fig. 4. Changes in the frequency of mEPSPs and comparison of their amplitude distributions in a
rat ganglion neurone, A at the beginning and B at the end of the potassium-induced transmitter release in the presence of HC-3 6 × 10-eM. In this experiment small amounts of a concentrated KC1 solution were added at two different times (arrow) direct to the bathing medium. The indicated figures should be added to the initial level (5.6 m M ) to obtain the actual final potassium concentration.
events is similar to that previously described. Yet it should be noted, when comparing A with B ( A at the beginning of the quantal emission and B one hour later), that the mEPSPs corresponding to amplitude classes larger than 1.3 mV are much more frequent in A than in B. There is, however, no shift to the left in the smallest amplitude classes and this rules out any possibility that a drastic reduction in the size of the transmitter quantum had occurred. The total amount of quanta released by potassium stimulation after blockade of ACh synthesis by HC-3 is an estimate of the presynaptic transmitter store present in all the nerve endings impinging on the neurone under test. This value varied from neurone to neurone in the range of 36,000-120,000 quanta, with an average of 77,300 transmitter quanta in 7 experiments. The mEPSP distribution in the tracings was analysed on the assumption that the fractionation of the mEPSP discharge sequence into intervals of arbitrary duration will not substantially affect the statistical properties of the release process. If this is the case, the analysis then becomes similar to that of discharges evoked by electrical stimulation of the presynaptic fibre 12. To test this p o i n t , the statistical parameters o f the release process were evaluated in 3 sets of data, taken from the same mEPSP series but sampled using time intervals of increasing amplitude. The results of these analyses are listed in Table I. The properties of the mEPSP sequence,
283 TABLE I EFFECT OF INCREASINGTHE AMPLITUDEOF THE TIME INTERVALINTO WHICH THE SAMEm E P S P SEQUENCE IS FRACTIONATEDON THE ESTIMATESOF THE STATISTICALPARAMETERS DESCRIBINGTRANSMITTER RELEASE m, m e a n n u m b e r of mEPSPs per time interval; cr2, variance of the m E P S P distribution; P, probability for a q u a n t u m to be released; P', probability level for the Poisson or binomial model to fit the observed distribution, evaluated by use of the X2 test.
Time interval ( msec )
No. o f intervals
m
a2
P*
P" Poisson
P" binomial
200 400 600
1007 503 335
2.762 5.525 8.278
2.601 5.403 8.009
0.058 -4- 0.041 0.022 -4- 0.061 0.032 4- 0.075
> 0.60 > 0.99 > 0.10
> 0.70 > 0.99 > 0.10
* -4- S.E.
derived from the experiment illustrated in Fig. 4 (time 9-12 min), do not actually seem to be affected by differences in sampling. As mentioned above, an important point in the present study was to elucidate which model will best approximate the transmitter release process and whether the statistical properties of this model are maintained unchanged during the whole observation period, even when the release level of quanta is low after depletion of the presynaptic ACh stores by potassium stimulation. In 3 experiments a total of 9 mEPSP series were thus analysed, 4 of these being at the beginning of the quantal emission and 5 after the release rate had run down to less than 10 ~ of the peak value. The basic criterion for selecting the 9 series was the absence of any apparent drift, within each series, in the rate of quantal secretion as evaluated from the mean number of events in blocks of 30 time intervals. Furthermore, the linear regression of the transmitter release rate over time was never statistically significant; the regression coefficient for the longest of the 9 mEPSP sequences presented (Expt I, 10 min) was + 0.001. Each series was therefore considered to be a stationary section of the entire experiment. The distributions observed and the comparison with the corresponding Poisson and binomial predictions are summarized in Table II. The parameters characterizing transmitter release in the 3 experiments, obtained from the meanvariance method (P = 1 - - tr2/m), are listed in Table III. It is evident from Table II that the distributions observed are approximated closely by both the Poisson and binomial models. Probability (P) of release for a quantum was in fact so small in all cases that both the predictions were similar and indistinguishable from each other. In 4 analyses a negative value of P was obtained. However, this seems more likely to be due to the small value of P and the large systematic statistical errors affecting its evaluation (see Tables I and III for P 4- S.E.) than to a drift in the transmitter release rate occurring within the mEPSP sequence, which would result in an increase in the variance. The estimates obtained by the maximum likelihood fit are similar to those obtained by the mean-variance method. The results are given in Table IV. It will
SEQUENCES CONTAINING X ( 0 , 1, 2, . . . . ,
8) Q U A N T A
65
60
Expt. III 10
71
60
10
Expt. II 5
60
Expt. I 10
Observation time (min)
Observed Poisson Binomial Observed Poisson Observed Poisson Binomial
Observed Poisson Observed Poisson Binomial Observed Poisson Observed Poisson Binomial
Observed Poisson Binomial Observed Poisson
Observation or prediction
39.0 49.1 43.5 39.0 39.0 71.0 75.2 70;9
33.0 28.7 57.0 58.3 55.1 15.5 15.9 5.0 7.7 6.1
64.0 63.6 58.5 62;0 60.4
0
104.0 89.0 89.9 76.0 79.0 105.0 103,3 106.0
35.5 39.4 93.0 95.3 96.4 37.5 35.4 19.0 22.0 20.5
158.0 175.7 171.6 128.0 127.0
1
71.0 80.7 86.7 90.0 80.1 77.0 70.9 74.5
24.0 27.0 82.0 78.0 81.0 38.0 39.6 39.0 31.4 32.5
255.0 242.6 246.3 132.0 133.4
2
58.0 48.8 51.7 49.0 54.1 30.0 3Z5 32.8
12.5 12.3 43.0 42.5 43.5 29.0 29.4 27.5 29.9 32.5
233.0 223.4 230.6 91.0 93.4
3
21.0 22.1 21.3 24.0 27.4 11.0 I 1.2 10.1
7.0 4.2 17.0 17.4 16,7 15.0 16.4 26.5 21.3 23.0
158.0 154.2 158.4 44.0 49.1
4
6.0 8.0 6.4 12:0 11.1 3.0 3.8 2.8
1.0 1.4 7.0 7.3 6.3 9.0 7.3 9.5 12.2 12.2
77.0 85.2 85.1 27.0 20.6
5
2.0 3.2 1.8 3.0 3.8
3.0 2.7 4.0 5.8 5.0
43.0 39.2 37.2 8.0 7.2
6
3.0 1.4
1.0 1.1 2.5 2.4 1.6
13.0 15.5 13.6 2.0 2.9
7
1.0 1.2 0.4
6.0 7.5 5.6
8
• 0.80 ..... 0.90
~= 0.60
-~ 0.10 > 0.t0
: 0.60 0.50
:> 0.99
> 0.97 ~- 0.95
> 0.50
:> 0.80
:-~ 0.60 :> 0.70
P
Where x classes ceased to be observed in a given mEPSP series, the predicted numbers for larger quantal classes were added to that computed for the final observed class of the sequence. Fractional numbers in the observed distributions arise from the mean of two successive counts performed on the same mEPSP sequence. Observation time indicates time after switching to the high potassium concentration at which the mEPSP series was selected. Times up to 10 rain should be considered 'initial', i.e., at the beginning of the quantal emission and times longer than 60 rain 'final', i.e. at the end of the transmitter release, when the presynaptic A C h stores are exhausted. P indicates the probability level for the Poisson and binomial predictions to fit the corresponding observed distribution, evaluated by use of the g 2 test.
OBSERVED A N D EXPECTED DISTRIBUTIONS OF THE NUMBERS OF TIME INTERVALS 1N 9 m E P S P
TABLE II t~ O~
285 be n o t e d t h a t w h e n , in t h e d i r e c t e s t i m a t e , P < 0 t h e n t h e l i k e l i h o o d f u n c t i o n d o e s n o t c o n v e r g e to a m a x i m u m in t h e r a n g e e x p l o r e d . I n Fig. 5 o n e c a n o b s e r v e t h e d i f f e r e n t b e h a v i o u r o f L w h e n P > 0 (A) a n d P < 0 (B). I n this s e c o n d case, c o n v e r gence w o u l d s e e m to b e p o s s i b l e f o r n - - - + c~, w h i c h w o u l d m e a n P -
0. T h i s
i n d i c a t e s t h a t s a m p l i n g a n d e x p e r i m e n t a l a c c i d e n t s result in a strictly P o i s s o n process. T h e b i n o m i a l d i s t r i b u t i o n s p r e s e n t e d in T a b l e II are g e n e r a t e d by n a n d P v a l u e s o b t a i n e d f r o m the m e a n - v a r i a n c e m e t h o d . I n cases in w h i c h a n e g a t i v e v a l u e o f P was o b s e r v e d , it was a s s u m e d o n t h e basis o f the a b o v e e v i d e n c e t h a t it was n o t
TABLE III PARAMETERS CHARACTERIZING TRANSMITrER RELEASE IN NINE
mEPSP
SEQUENCES
Observation time, time after exposing the ganglion to the high potassium concentration; time interval, amplitude of the unit interval into which the mEPSP series was divided; m, mean number of quanta per time interval; cr2, v~iance of the mEPSP distribution; P, probability of release calculated from 1 - - cr~/m.
Expt. I Expt. II
Expt. III
Observation time (min)
Time interval msec
No. o f intervals
m
or2
p*
10 60 5 10 60 71 10 60 65
200 200 400 100 100 150 200 100 100
1007 494 113 299 148 134 301 296 297
2.762 2.101 1.372 1.635 2.233 2.854 1.814 2.027 1.374
2.601 2.148 1.612 1.528 2.775 2.426 1.592 2.135 1.262
+ 0.058 --0.022 --0.174 + 0.066 --0.019 + 0.150 + 0.122 --0.053 + 0.081
:k 0.041 -4- 0.065 ± 0.167 :k 0.0~/5 ± 0.119 ± 0.101 + 0.069 -I- 0.088 -I- 0.073
* ±S.E.
TABLE IV ESTIMATES OF THE BINOMIAL RELEASE PARAMETERS n AND P CALCULATED BY THE MAXIMUM LIKELIHOOD METHOD
Analysis is based on the same data sets as those used in Table III.
Expt. I Expt. II
Expt. III
Observation time (rain)
P
n
10 60 5 10 60 71 10 60 65
+ 0.060 ----. 0 -----~ 0 q- 0.065 ----~ 0 + 0.140 + 0.120 ----~ 0 + 0.091
46.043 -----~ oo -----~ oo 25.154 -----~ oo 20.377 15.115 ----~ oo 15.099
286
-L
1879-
® j
~
t
0.1 p
1877
0
-L 174J
®
t
0.1 p
0
4'0
SO
120
0
n
Fig. 5. Graphs to show the likelihood function in two experiments. In A (Expt. I, 10 rain) L is maximized by the n and P values indicated by the arrow. In B (Expt. II, 5 min) the convergence of n and P to a maximum of L progressively improves as values of n increase and those of P decrease.
significantly different from 0; the expected binomial distribution could not however be legitimately computed. DISCUSSION
It is well known that sympathetic neurones in the rat SCG receive synaptic connections from multiple converging fibres 4,17. The present data allow a quantitative evaluation of the degree of preganglionic convergence on a single neurone. In a previous study 19 it has been demonstrated that the mean size, expressed in quantal terms, of the presynaptic transmitter store initially present in those terminals on a neurone that are activated by the stimulation of a single afferent fibre is some 8000 transmitter quanta. From this and the present estimate of presynaptic stores for all the synaptic sites on the cell, it is suggested that 9-10 preganglionic fibres may be a fair estimate for the mean input to a rat ganglion neurone, if one accepts the risks inherent in extrapolation from a limited number of observations. The total normal ACh content of rat SCG is 28-30 ng, which is reduced by 85 ~ under either electrical or chemical stimulation performed in vitro in the presence of HC-3 (Ladinsky et al., in preparation). Since the mean number of cells in the rat SCG is 35,200 s,la,14, the average amount of transmitter which can be released upon a single neurone is 2.3 × 109 molecules of ACh. From this and the whole presynaptic store value for a single cell it would appear that the transmitter content of quanta released from the nerve terminals of rat SCG is about 3 × 104 molecules of ACh. Implicit in this procedure is the assumption that the number of molecules building up the quantal packet is constant over the whole observation period. The evidence so far adduced suggests that this is the case in the preparation used in the present study. In fact, the effects of the unit quantum of transmitter, released either
287 at the beginning or at the end of the potassium stimulation, are the same in terms of postsynaptie depolarization. The comparison between the population of quanta initially present in the terminals and those released from the exhausted terminals is based on the fit of the mEPSP amplitude distributions sampled at the beginning and at the end of potassium-induced transmitter release. Despite some uncertainties as to the accuracy of the correction for differences in resting potential level, however, the initial and final EPSP amplitude distributions agree reasonably both in form and range. Hence, the derived conclusion that a significant decrease in quantum size can be ruled out appears to be correct. This would suggest that chemical stimulation in the presence of HC-3 acts at the ganglionic synapse in the same way as electrical stimulation. The similarity of the results provides some support for the hypothesis that transmitter quanta can be released by presynaptic terminals in the rat SCG only when they are full size. Furthermore, the progressive depletion in ACh tissue content occurring in the course of prolonged chemical stimulation after transmitter synthesis has been blocked by HC-3 is associated with a decline in transmitter output from the ganglion. Our data show very clearly that the decrease in ACh output invariably corresponds to a decrease in the number of transmitter quanta being released. Elmqvist and Quastel 5 studied the transmitter release process at the rat and human neuromuscular junctions and they showed that the addition of 20 mM KC1 to the bathing solution caused a gradual increase in mEPP frequency, which grew progressively up to 90 min after the potassium ion concentration was raised. At the same time, in the presence of HC-3 4 × 10-6 M, the amplitude of the mEPPs gradually diminished, until they eventually became so small as to be lost in the base line noise. Thus, the progressive increase in the number of quanta released in the unit time is paralleled by a decrease in the size of the individual quantum. The synaptie equivalent of the reduction in ACh release from the nerve terminals therefore appears to be (1) the release of a constant or increased number of transmitter quanta of progressively smaller size at the neuromuscular junction and (2) the release of a lower number of quanta of unchanged size at the ganglionic synapse. This pattern of events, in perfect mutual opposition, can be explained in our opinion only on the basis of the differences between preparations. These findings, however, should prompt further investigations at other synapses, as they may define whether the possibility of generalization is restricted to some aspects only of the transmitter release process, e.g. quantization, while others, such as the invariance in quantum size, are peculiar to individual release sites. The second principal objective of the present investigation was to determine whether or not mEPSP occurrence preferentially follows either the Poisson or binomial distribution. This question is of interest not only from a sheer analytical point of view, since it may give clues as to the elementary model which describes the release of transmitter from a nerve terminal. At the same time, it should be possible to define the still problematic nature of n and P in more concrete terms. The statistical foundations of some models proposed for the mechanism of quantal release have been accurately described by Vere-Jones 21. The possible functional or morphological
288 role of n and P has recently been discussed by Wernig ')2 and Zucker '~',~.The analytical procedure adopted in the present study suffers from some limitations. In fact a physiological significance cannot unfortunately be attached to m or n, which arise from the division of the mEPSP sequence into intervals of arbitrarily fixed amplitude. Nevertheless, this type of analysis allows P to be estimated and the binomial distribution to be predicted. In a previous study at the rat ganglionic synapse 19 it has been demonstrated that the amplitude fluctuations of evoked EPSPs are well described by Poisson statistics, both when the quanta are released initially from the terminals and after exhaustion of the presynaptic transmitter stores by prolonged stimulation in the presence of HC-3. The latter condition was tested since it was felt that the release process could deviate from the Poisson hypothesis in the manner of a binomial when the number of preformed quanta in the terminal is drastically reduced. The present experiments, in which reliable estimates of P have been obtained, show that P remains low despite the fall in the number of quanta available. Furthermore, the evidence presented indicates that the release probability P at the ganglionic synapse is always sufficiently low to generate a binomial distribution of responses indistinguishable from the corresponding Poisson prediction. The use of binomial statistics to describe the transmitter release mechanism in the rat SCG does not therefore appear to be justified under the present circumstances, since the binomial model is accurately approximated by the Poisson model if the probability of quantal emission is low. The process governing the release of quanta at the ganglionic synapse is unaffected by the amount of transmitter actually present in the presynaptic terminal. The original suggestion z,3, therefore, that the Poisson character of the release mechanism may arise from random collision with the nerve terminal membrane of single quanta sampled from a large population of quanta, each with a small probability of release, is not consistent with the present findings since the Poisson model holds good even when the terminal is depleted of preformed quanta. As a consequence, the source of 'Poissonicity' is likely to be associated with other functional or anatomical structures irrespective of quantal population. The release of quanta from a finite number of release sites opening independently from one another will generate a Poisson distribution 7. A similar result also arises if replenishment of the store of releasable quanta follows a Poisson process 21. The solution of this problem, however, is beyond the scope of this study. ACKNOWLEDGEMENTS
We thank Dr. I. Barrai for his advice on the maximum likelihood analysis of the data. We are also grateful to Dr. S. Boffi for providing the computer programs and for useful discussion. This work was supported in part by Grants 73.00718.04 and 74.00241.04 from the Consiglio Nazionale delle Ricerche, Italy.
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