J. Physiol. (1976), 257, pp. 597-620 With 6 text-figure. Printed in Great Britain

597

THE EFFECT OF CALCIUM IONS ON THE BINOMIAL STATISTIC PARAMETERS THAT CONTROL ACETYLCHOLINE RELEASE AT PREGANGLIONIC NERVE TERMINALS

By M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW From the Neurobiology Laboratory, Department of Physiology, University of Sydney, Sydney, N.S.W, Australia

(Received 11 August 1975) SUMMARY

1. A study has been made of the effects of changing [Ca]. and [Mg]. on the binomial statistic parameters p and n that control the average quantal content (hi) of the excitatory post-synaptic potential (e.p.s.p.) due to acetylcholine release at preganglionic nerve terminals. 2. When [Ca]0 was increased in the range from 0-2 to 0 5 mM, p increased as the first power of [Ca]0 whereas n increased as the 0-5 power of [Ca]0; when [Mg]0 was increased in the range from 5 to 20 mm, p decreased as the first power of [Mg]o whereas n decreased as the 0 5 power of [Mg]0. 3. The increase in quantal release of a test impulse following a conditioning impulse was primarily due to an increase in n; the increase in quantal content of successive e.p.s.p.s in a short train was due to an increase in n and p, and the increase in n was quantitatively described in terms of the accumulation of a Ca-receptor complex in the nerve terminal. 4. The decrease in quantal content of successive e.p.s.p.s during long trains of impulses over several minutes was primarily due to a decrease in n. These results are discussed in terms of an hypothesis concerning the physical basis of n and p in the release process. INTRODUCTION

The evoked release of acetylcholine at the motor end-plate increases with the external calcium concentration, [Ca]0, in such a way as to suggest that transmitter release is dependent on the formation of a Ca-receptor complex in the nerve terminal (Jenkinson, 1957; Dodge & Rahamimoff, 1967; Miledi, 1973). This quantal release can be described by binomial statistics (Bennett & Florin, 1974; Wernig, 1975) in which the probability parameter p is linearly dependent on [Ca]0 whereas the quantal release parameter n is dependent on the third power of [Ca]o (Bennett, Florin &

598 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW Hall, 1975). Although it is known that the evoked quantal release of acetylcholine at preganglionic nerve terminals can be described by binomial statistics (McLachlan, 1975), the calcium dependence of this release and of the binomial statistic parameters is not known. The aim of the first part of the present work is to determine the dependence of p and n on [Ca]. at preganglionic nerve terminals. At the motor end-plate, the facilitated release of acetylcholine by a test impulse following a conditioning impulse (Mallart & Martin, 1967) is due to an increase in n (Bennett & Florin, 1974; Bennett et al. 1975) whereas the potentiated release of acetylcholine (Magleby, 1973a, b) is due to an increase in p (Bennett et al. 1975). If facilitation and potentiation are due to the accumulation of residual Ca-receptor complexes in the nerve terminal (Katz & Miledi, 1968), and n and p are dependent on the third and first power of their respective Ca-receptor complexes ([CaX] and [CaY]), then facilitation should increase as the third power of residual [CaX] and potentiation with the first power of residual [Ca Y], which is the case (Barrett & Stevens, 1972; Younkin, 1974; Magleby & Zengel, 1975a, b). The dependence of facilitation and potentiation on n and p at preganglionic nerve terminals has been determined, and a quantitative study made of whether facilitation increases in a manner consistent with the residual Ca-receptor hypothesis. METHODS The statistics of transmitter release were studied in the guinea-pig (150 g) superior cervical ganglion. The ganglion with its nerve supply was removed from the animals as previously described (Bennett & McLachlan, 1972a), and mounted in a Perspex organ bath of about 10 ml. capacity. This was perfused with a modified Krebs solution of the following composition (mM): Na+, 151; K+, 4-7; Ca2+, 1-8; Mg2+, 1-2; Cl, 142; H2PO4, 1-3; SO,, 1-2; HCO3, 16-3; glucose, 7-8; and gassed continuously with 95 %' 02 and 5 0O CO2. Solutions were maintained at 28-30° C and flowed continuously through the bath at a high rate (about 10 ml. min'). Excitatory postsynaptic potentials (e.p.s.p.s) were recorded in the ganglion cells in response to stimulation of the cervical sympathetic trunk, the stimulus parameters being adjusted so that only a single axon was excited. The intracellular recordings were made with glass microcapillary electrodes filled with 2 M-KC1, and the e.p.s.p.s were led through a high impedance unity gain pre-amplifier, displayed on an oscilloscope and photographed on moving film. Changes in [Ca]0 and [Mg], were made by changing the CaCl2 or MgG12 present in the reservoir supplying the organ bath. The total divalent cation concentration was always in excess of 0 7 mmt so as to avoid possible changes in impulse conduction (Frankenhauser & Hodgkin, 1957). In general changes in [Ca]. or [Mg]o were made by progressively increasing CaCl2 or MgCl2 so as to keep the time taken for the average quantal content of the e.p.s.p.s to reach a new steady state to a minimum, which was generally about 15 min. In experiments in which m-, p and n were determined in different [Ca]. or [Mg]0, the nerves were stimulated at 3 0 Hz. and long

Ca AND ACh RELEASE

599

trains of at least 50 e.p.s.p.s recorded. During stimulation at 0-3 Hz there is a slight increase in the quantal content of the e.p.s.p. (McLachlan, 1975). However this rate was used as it frequently allowed sufficient time for data to be collected for two different solution changes during the one impalement (Zucker (1974) has shown that the [Cal] dependence of the quantal content of synaptic potentials at the crayfish neuromuscular junction is independent of the frequency of stimulation). For long trains (> 50) at least 5 min was left between periods of stimulation. Amplitude-frequency histograms were constructed for the e.p.s.p.s and these compared with the predictions of binomial statistics (Bennett & Florin, 1974); miniature excitatory post-synaptic potentials, m.e.p.s.p.s, recorded in a cell during and for a few sec after repetitive stimulation were taken to originate from the stimulated nerve terminal (Sacchi & Perri, 1971), and were used to obtain a measure of the mean and variance of the quantal size (very large multi-model m.e.p.p.s were excluded from the analysis). The binomial probability distribution of e.p.s.p. amplitudes (and therefore quantal contents) has been predicted from

P(x) =

ACi prq'- P(-kr) e-Aktl

r=0

derived by Robinson (1975) where P(x) is the expected frequency of e.p.s.p.s with an amplitude of x mV; r (= 0, 1, 2 ... n) is the possible quantal content value for -- + -, where m and S2 are the mean and variance of the each e.p.s.p.; p = 1- my y" e.p.s.p. amplitudes, y and a. are the mean and variance of the spontaneous e.p.s.p. amplitudes; r is the gamma function and A = y/f'2 and k = -2/cr2. At those junctions where the changes in p and n during a short train were studied, the nerve terminal was stimulated by a train of six to seven impulses and these trains repeated about twenty times, with an interval of 1 min between trains to avoid any effects due to potentiation (McLachlan, 1975); at the end of the impalement the nerve was generally stimulated continually for at least 20 see and about fifty e.p.s.p.s collected for determination of the binomial statistic parameters in the steady state; amplitude-frequency histograms were constructed for the e.p.s.p.s for each impulse over the twenty or so trains as well as for the fifty e.p.s.p.s collected during the steady state and these compared with the predictions of binomial statistics. At those junctions at which p and n were determined during continual high frequency stimulation over several min, the average quantal content of groups of fifty to a hundred e.p.s.p.s were collected at intervals of 1-2 min, and amplitude frequency histograms of these were also constructed and compared with the predictions of binomial statistics; nerve terminals were only subjected to one continual high frequency stimulation. For all amplitude-frequency histograms collected in these experiments, the 'goodness of fit' of the binomial distribution to the observed distribution was determined by a x2 test. The statistical methods employed in determining the s.E. of the means of ir, p and n are given in Bennett & Florin (1974) and in Robinson (1975). In all experiments the e.p.s.p.s used in the statistical analysis were less then 10 mNT, so as to avoid serious corrections for non-linear summation (Martin, 1955). The criteria used in determining the quality of an impalement during the collection of data for statistical analysis were: a shift in the resting potential; a shift in the amplitude of action potentials evoked by current injection from the micro-electrode and any trend in the average e.p.s.p. quantal content at the end of data collection compared with that at the beginning. The derivation of the mass action equation describing the competitive actions of

600 M. R. BENNETT, T. FLORIN AND A. 0. PETTIOREW Ca and Mg at a point or points in the release process are given by Jenkinson (1957), Dodge & Rahamimoff (1967) and Bennett et al. (1975), as is the general method for determining the dissociation constants in the equation. The derivation of the equation describing the relationship between the increase in quantal content of successive synaptic potentials during a train and the accumulation of Ca-receptor complexes in the terminal, according to the residual Ca-receptor hypothesis, is given by Linder (1973), Younkin (1974) and Zucker (1974). The facilitated increase in mi, p and n for successive impulses in a train has been defined according to Mallart & Martin (1967). In those few cases in which the amplitude of the e.p.s.p. was greater than 5 mV, and therefore mW greater than about 8 (see Tables 1 and 2), the e.p.s.p. -was corrected for non-linear summation according to the procedure given in the Appendix. The present results are subject to a number of errors. The recording system noise contributes to the variance of both the evoked and spontaneous potentials; the root mean square value of membrane potential fluctuations in the frequency range of the synaptic potentials (that is the S.D. of the noise, Erxb,.) was such that the noise variance was less than 10 % of the variance of either the spontaneous or evoked amplitude-frequency distributions and no correction was made for this; noise variance contributes equally to the variance of both the spontaneous and evoked amplitude-frequency distributions (i.e. to a-2 and S2) and as these are of opposite sign in the expression for p, the effect of the noise variance tends to cancel out for p and when m = y to exactly cancel out. It is very likely that p varies between the different members making up n, thus giving an over-estimate of p according to the (72 var p P, where p5 and var p are the mean and variance of p; relation 1 --82 +- = P+ my y2 P and therefore do not know to what extent we have no means of correcting for we have over-estimated p, although var p cannot be too large compared with ip or the binomial predictions of the observed amplitude-frequency distributions would not have been good (over 70 % of all amplitude-frequency distributions were fitted by the binomial prediction with a X2 test of the 'goodness of fit' possessing P > 0 -50). Finally, the present analysis assumes that the spontaneous potentials collected during stimulation allow an estimate of the mean and variance of the quanta participating in impulse-evoked release; it is unlikely that significant differences occur between the mean and variance of the size of the evoked quanta and that of the spontaneous potentials, because of the good-fit of the binomial prediction to the observed amplitude-frequency distributions. RESULTS

The effects of changes in [Ca]0 and [Mg]. on the statistical paramneers governing transmitter release In most ganglion cells impaled the e.p.s.p. due to stimulation of a single axon was subthreshold for initiation of the action potential, so that the effects of changes in [Ca]0 from the normal concentration of 1-8 mm down to 0-3 mm on the quantal content of the e.p.s.p. and hence on p and n could be determined. Fifty to one hundred e.p.s.p.s. were collected for analysis after a steady-state mean release had been reached during continual stimulation at low frequencies (0-3 Hz) in different [Ca]0; .n, p and n

601 Ca AND ACh RELEASE were determined for each such collection and a comparison made between the predicted and the observed amplitude-frequency distributions of e.p.s.p.s, which on a x2 test of the 'goodness of fit' had to possess a P > 0-50 or the results were rejected. The quantal content of the e.p.s.p.s increased with the 1-5 power of [Ca]. over the concentration range from 0-3 to 0-5 mM (Fig. 1 A), and this was mainly due to a 1 0 power dependence ofp A

p

'ii

10-0

n

41

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0-3

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1-0

0-1

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0-3

1-0

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2-0-

1-0 0-40.2 0.1

1

3

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1

3

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1

Fig. 1. Dependence of the statistical parameters describing transmitter release on [Ca]. and [Mg].. A, the effect of changing [Ca]. in a fixed [Mg]. of 1-2 mm on the quantal content (mi) of the e.p.s.p. and on p and n is shown on log.-log. co-ordinates. B, the effect of changing [Mg]o in a fixed [Ca]. of 1-8 mM on iii, p and n is shown on log.-log. co-ordinates. Each point is the mean + one SE. of the mean of a binomial statistic parameter determined at four to eight synapses, at each of which at least fifty e.p.s.p.s were used in the statistical analysis; if the S.E. of the mean of a parameter determined at a synapse was greater than 15 % of the mean value it was not included. In A, log mi, log p and log n increased initially along gradients of 1-5, 1 -0 and 0- 5 respectively with an increase in log [Ca]0. In B, log im, log p and log n finally decrease along gradients of 1-5, 1-0 and 0-5 respectively with an increase in log [Mg].. Least-square regression lines to the data in the linear range are shown in each of the graphs.

602 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW on [Ca]0 as n only changed as the 0 5 power of [Ca]. (Fig. 1 A). The decrease in the slope of the curve relating mi with [Ca]. at higher [Ca]0 (> 0*6 mM) was due to p reaching saturation (i.e. 1 0) at [Ca]o above 0*6 mm (Fig. 1 A). Elevating the external magnesium concentration [Mg]0, depressed the quantal content of the e.p.s.p. in a manner consistent with a competitive inhibition between Ca and Mg at some point in the release process (Fig. 1 B), as it does to transmitter release at the motor end-plate (Jenkinson, 1957; Dodge & Rahamimoff, 1967). As the [Mg]o was increased to high concentrations (> 6 mM) the quantal content of the e.p.s.p. decreased as the 1-5 power of [Mg]o and this was due to a 10 power decline in p and a 0*5 power decline in n with [Mg]o at high concentrations (Fig. 1B), as would be anticipated if Mg acts to block the effects of Ca in elevating p and n during an impulse.

Dissociation constants of the statistical parameters governing transmitter release The dissociation constants both for the effects of Ca in enhancing mn, p and n (KI) and of Mg in antagonizing this action (K2) were determined in expressions of the form n =

LnjCaXj = Ln 1[;]o[Mg]o '

(1)

where R. is the slope of the relationship between log [Ca]o and log n, and Ln is a proportionality constant; the values for Ri, RP and Rp (from Fig. 1) were 1-5, 1-0 and 0 5 respectively. K2n was determined as before (Dodge & Rahamimoff, 1967; Bennett et al. 1975), by considering two different [Ca]o/[Mg]o solutions for which n is constant and equating the right hand side of eqn. (1) for each of the solutions; the data in Fig. 1 gave values for K2g, K2p and K2. of 0-8, 0 4 and 0-8 mm respectively. KIn was also determined as before by arranging eqn. (1) so that a double-reciprocal plot (Lineweaver & Burk, 1934) of n-'-I'n against [Ca]-1 gave a straight line allowing an estimate of - [Ca*]-1 from the inter[a] cept of this line with the abscissa, so that K1n = + [Mg]o could be

K2n obtained; such double-reciprocal plots for m, p and n obtained from the data in Fig. 1 are given in Fig. 2, and these allowed estimates for K1I,K1P and Kln of 0-8, 0-8 and 2-0 mm respectively. In order to check the applicability of eqn. (1) to transmitter release at preganglionic nerve terminals a comparison was made between the predictions of this eqn. and the changes in m, p and n in different. [Mg]0;

Ca AND ACh RELEASE

603

[Ca]-'

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-1

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1

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3

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[Ca]-' Fig. 2. Double reciprocal plots for the relationship between: /1 1-0 1 1 i 1/1-5 1 V1 1/0-5 and [C and M F~~Ca-]0 \p and [Ca]0' [Ca].' nLinear co-ordinates. [Mg]. in all cases is 1-2 m The data shown in Fig. 1 have been re-plotted on these co-ordinates and lines of best fit drawn. The lines intercept the abscissa at [Ca]. of 2-0, 3-3 and -5 mm for the fm, p and n plots respectively. .

-

-

604 M. B. BENNETT, T. FLORIN AND A. G. PETTIGREW B

A

1000

2-5

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i

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0

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0

5

10

[mg] 0

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Fig. 3. Comparison between the predicted and observed results for the dependence of the statistical parameters describing transmitter release on [Mg]o. A, mi, p and n plotted against [Mg]o on linear co-ordinates; the values are those given in Fig. 1 B; the theoretical curves have been drawn according to eqn. (1) with the appropriate dissociation constants and R values given in the text, with a [Ca]0 of 1-8 mM and with L values (see text) which gave a best fit to the points; L equals 44-6, 6-6 and 9-3 for mii, p and n respectively. B, im, p and n plotted against (1 + [Caj/K1 + [Mg]O/K2) on log.-log. co-ordinates; the values given in Fig. 1 B have been re-plotted on these co-ordinates; the lines have been drawn through the points with the same slopes as those in Fig. 1, namely 1-5, 1-0 and 0-5 respectively; the appropriate dissociation constants given in the text have been used with a [Ca04 of 1-8 M .

605 Ca AND ACh RELEASE Fig. 3A shows that there was reasonable agreement between the two over the range of [Mg]o for which the eqn. may be expected to hold, that is over the entire range for n but only up to the saturation ofp in the case of p and mi. When the values of mi, p and n in different [Mg]. were plotted

their respective (1+ K + K2) on log.-log. co-ordinates (Fig. 3B), they fell on lines with slopes of 1-5, 1.0 and 0-5 respectively as expected from eqn. (1) and the results in Fig. 1A. These observations suggest that p is dependent on the first power of a Ca-receptor complex in the nerve terminal (i.e. p =-Lp [CaY]10) and n is dependent on the 0 5 power of a Ca-receptor complex (i.e. n = Ln [CaXr05).

against

Changes in the statistical parameters governing transmitter release during short trains of impulses If the increase in quantal content of a test e.p.s.p. (mi) following a -Mo (Mallart & Martin, = conditioning e.p.s.p. (mi) is defined as 1967), then ff followed a time course with at least two components (Fig. 4), the longest of which had a time constant of about 8 sec. If the 2-0 10

LL 0-2

0-1

7 5 6 3 4 Interval (sec) Fig. 4. The effect of a conditioning impulse on the quantal content of the e.p.s.p. evoked by a subsequent test impulse. The log. ordinate gives the facilitation of quantal content (fw, filled circles) and of n (f,,, open circles) determined at various intervals after the conditioning impulse given on the linear abscissa. Each point is the mean + 1 S.E. of the mean of the results from six synapses, at each of which fA and f, were determined by applying binomial statistics to a test and conditioning e.p.s.p. in twenty trials; if the s.E. of the mean of a parameter determined at a synapse was greater than 15 % of the mean that value was not included. The curve (a least-square regression line to the data) has a time constant of 8 sec. Note that f,. is close to fm at the various intervals, indicating that there is little facilitation of p (f,) by a single conditioning impulse. Expressions Af, fi, and f, are defined in the text. 0

1

2

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608 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW increase in the binomial statistical parameters during a test e.p.s.p. (n, p) following a conditioning e.p.s.p. (no, po) are defined as n= -no and no P P0, then Fig. 4 shows that the increase in fm was primarily due = fp Po to an increase infi, although there was also a small increase infp (Table 1). Changes in the binomial statistic parameters were also determined for successive impulses in short trains at different frequencies. At all frequencies of stimulation studied (0.2 Hz < frequency < 10 Hz) the increase in quantal content of successive e.p.s.p.s during the first few impulses was due to increases in both n and p (Figs. 5 and 6; Table 1). During the 2.0

I0 _

0.5 0. "

0-5_ 0-25

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0 I F0

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2

3

4 5 Time (sec) Fig. 5. Changes in the statistical parameters describing transmitter release during short trains of impulses at low frequency (1 Hz). The changes in fjf, andf. (defined in the Text) are shown for each of the first six impulses in a train, together with the steady-state values reached after about 15 see of stimulation. Each point is the mean + 1 s.E. of the mean of results from six synapses, at each of which fE, f, and fy were determined by applying a binomial statistic analysis to the successive e.p.s.p.s in at least twenty trains; if the s.E. of the mean of a parameter determined for a particular impulse number in a train at a synapse was greater than 15% of the mean, that value was not included. The mean values + s.E. of mean of m5, p and n for the first impulse at the six synapses were 2-46 ± 064, 0-525 ± 0-065 and 5-00 ± 1-30 respectively. The continuous line gives the theoretical predictions for the increase in Af according to the residual [CaX] hypothesis (eqn. (2), see Text). 1

Ca AND ACh RELEASE 2-0

609

T

1*5

IE ±-

I

0-5 I

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0-5 0*

0

01

0-2 03 04 0.5 0-6 0-7 0-8 09 Time (sec)

Fig. 6. Changes in the statistical parameters describing transmitter release during short trains of impulses at high frequency (10 Hz). The changes in f, and f. (defined in the Text) are shown for each of the first eight fj, impulses in a train. Each point is the mean + 1 S.E. of the mean of results from six synapses, at each of which fW, f, and f,, were determined by applying a binomial statistic analysis to the successive e.p.s.p.s in at least twenty trains; if the s.x. of the mean of a parameter determined for a particular impulse number in a train at a synapse was greater than 15 % of the mean, that value was not included. The mean values + s.x. of mean of fin, p and n for the first impulse at the six synapses were 3-11 ± 0-48, 0-651 + 0-062 and 4-85 + 0-69 respectively. The continuous line gives the theoretical predictions for the increase in f,, according to the residual [CaX] hypothesis (eqn. (2), see Text).

first few impulses p increased to a maintained high value whereas n continued to increase with a time constant of about 8 see (Fig. 5; Table 1). An attempt was made to predict transmitter release during trains of impulses by applying the residual Ca-receptor hypothesis to the growth of the binomial statistic parameters during a train. If no= L.{CaX}RM and po = LP{Ca Y}RP, then the quantal content of a conditioning impulse

MO

=

nopo

=

LnLp [CaX]R_ [Ca Y]PP,

610 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW whereas the quantal content of a subsequent test impulse m = np = LnLp [Ca X + Ca Xr]RP [Ca Y + Ca Yr]Rp, where CaXr and Ca Yr are the residual Ca-receptor complexes, which control n and p, that remain after the conditioning impulse. Thus

Ca Yr]Rp CaXrh r1+ ~1+ [ =[1+ CaY] -1 Jm CaXJ

A

=

(2)

(fn+1) (fp+t)-1.

Fig. 4 shows that fn fm, so that Fig. 4 can be used to determine the time CaXr] R. CaXr CX I1 when fp is small. If it is [ course of decline of Ca asfw K a CaX assumed that the same amount of CaX is formed due to the entry of Ca with each impulse, and that the time constant of decline of CaX is the same for each impulse and can be calculated from Fig. 4, then the increase in n with successive impulses during short trains (s< seven impulses) could be predicted (Figs. 5 and 6) by the residual Ca-receptor hypothesis according to the eqn. (Linder, 1973; Zucker, 1974): -

-

A Ui) =

(1 +fn(AtU - 0)) IM - 1]+1

-1

(3)

where fn (j) is the value of fn for the jth impulse, At is the interval between impulses, fn (At(j - i)) is the value offn for the interval At(j - i) from Fig. 4 and Rn is the slope of the curve relating log n to log[Ca]o in Fig. 1 A. The predictions of eqn. (3) shown in Figs. 5 and 6 were determined usingf,, (At(j - i)) from Fig. 4 rather than f. (At(j - i)) as the former was more accurately determined than the latter. Asf. is consistently smaller thanfw in Fig. 4 it is likely, as mentioned above, that there is a small increase in f,, (Table 1); thus the predictions of eqn. (3) give an over-estimate of the effects of residual Ca X on the increase in n during trains: If RR, is made equal to 1-0 instead of 0-5, there is no agreement between the predictions of eqn. (3) and the observed increases inf, following about the third impulse in a train at frequencies from 1-0 to 10 Hz; the predicted steady-state value of fR at 1 Hz is 2-5 for R., = 1 -0 compared with the observed value of 1-15 (Fig. 5), and this discrepancy between the predicted and observed values becomes greater at higher frequencies. An interesting consequence of the residual CaX hypothesis applied to the binomial statistic parameters is that given R. and R. in eqn. (2) are 0-5 and 1-0 respectively, and CaY are 1 -0, then the maximum and that the maximum possible values of CaX Ca-Y Ca X valuesf; can take in a test-conditioning trial is 1-82.

No attempt was made in the present work to predict the increase in p with successive impulses according to the residual Ca Y hypothesis, as the amount by which p increases is clearly dependent on the value of p during the conditioning impulse (i.e. whether it is close to 1-0 or not), a problem which did not arise with n, and which has not yet been quantitatively

611 (a AND ACh RELEASE studied. Furthermore, p seemed to increase in a more complicated way than n during successive impulses (Figs. 5 and 6; Table 1), perhaps reflecting that the time constant of decline of the CaY introduced by each impulse increases with successive impulses as it does at the motor endplate (Magleby & Zengel, 1975a, b), rather than remaining constant as does the decline of CaX introduced by each impulse.

Changes in the statistical parameters governing transmitter release during long trains of impulses If the preganglionic nerve terminals were stimulated for long times (20 see) at low frequencies ( < 1 Hz) both the increase in n which accompanies the increase in quantal content during a train as well as the steadystate release reached after about 12 sec of stimulation were close to that predicted by eqn. (3) (Fig. 5; Table 1); thus at 0-5 and 1 0 Hz the predicted steady-state fn is 0*9 and 1-45 respectively whereas that observed was 0-7 and 1-25. However, if the nerves were stimulated for long times (20 see) at high frequencies (> 1 Hz), the increase in n which accompanies the increase in quantal content at the beginning of the train is predicted by eqn. (3) (Fig. 6; Table 1), whereas the steady-state release reached after about 12 see of stimulation is not; thus at 5 Hz the predicted steadystate f, is 4-5 whereas the observed was only 3 0. It is probable that this departure of the measured f, from that predicted is due to a gradual depletion of quanta in the nerve terminal during high frequency stimulation (see below). If the nerve terminals were stimulated continually at high frequencies for periods greater than 30 sec, the quantal content of the e.p.s.p. decreased over several min (Table 2) until a new steady-state quantal release rate was reached and this was maintained for at least 45 min (Bennett & McLachlan, 1972a). This decrease in quantal content was mainly due to a decrease in n (Table 2), as it is at the end-plate (Bennett & Florin, 1974), for after p reached its ffaximum value during the first few sec of stimulation (Fig. 6) it remained close to this value throughout the remaining period of stimulation (Table 2). The decline in n and therefore mi during continual stimulation is accompanied by a similar proportional decline in the number of synaptic vesicles in cholinergic terminal varicosities (during continual stimulation at 10 Hz for periods greater than 5 min, n declined by 52 + 10 % (Table 2) whereas synaptic vesicle numbers decline by 50 % in sympathetic ganglia (Pysh & Wiley, 1974; Fig. 6) and 40 % in striated muscle (Heuser & Reese, 1973; Table 1)). However, if either motor or preganglionic nerves are stimulated continually at high frequencies in the presence of hemicholinium, the amplitude and quantal content of the synaptic potentials decline to a

612 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW very low value (Elmqvist & Quastel, 1965; Bennett & McLachilan, 1972a, b), whereas the decline in the numbers of synaptic vesicles in the varicosities is the same as that which occurs in the absence of the drug (Heuser & Reese, 1973; Birks, 1974). We therefore performed a binomial statistic analysis of quantal release at preganglionic nerve terminals during prolonged high-frequency stimulation in the presence of hemicholinium (5 x 10-5 M). In this case the decline in quantal content of the synaptic TABLE 2. Statistical parameters describing transmitter release during continual nerve stimulation. The values of mi, p and n at different times during stimulation at 10 Hz are shown for: A, preganglionic nerve terminals; B, preganglionic nerve terminals in the presence of hemicholinium (5 x 10- M). The s.E. of mean of mi, p and n were calculated using the equation given in Bennett & Florin (1974) and Robinson (1975). Time

< 05

2*0

30

3-74 ± 014 6-96 + 051 7-83 + 0 59 6-56 + 0-44 5.73 + 017 3-81 + 0 19 19-31 + 1-50 5.35 ± 0-21 2*65 + 0-15 6-62+0-38

3.45 + 013 4-89 0-28 5-81± 046 6-30 + 0*39 454+ 0-17 2-49 + 0*15 11-49+ 092 2*49 + 0-16 1-56+ 017 427 +0-24

2-41 + 0*09 4-87±0-35 5-56 + 0-42 6-34 + 0 34 4-22 + 1-38 2-05 + 0-14 8-29 + 0-65 3-58 + 0-22 0 94 + 0 09 3-11 ± 0-18

1-56 ± 0-06 4-24 + 0-26 4-84 ± 0.60 5-15 ± 0-30 1-80 + 0-28 0.44 + 006 3-19+0 19 2-66 ± 0-16 0 54 + 0-07 1-60 + 0-17

0 919 + 0-023 1-005 + 0.055 0-520 + 0-088 0-886 + 0 035 0-804 + 0*030 0-789 + 0-049 0-379 ± 0.111 0-225 + 0*133 0-340 + 0-144 0-484 + 0-081

0-965 ± 0-020 1-022 ± 0-042 0*840± 0-110 0-860 ± 0 040 0-810 ± 0-028 0*234 + 0-096 0-342 ± 0 090 0-362 + 0-095 0-042 ± 0-126 0-250 ± 0-122

5-0

(mi) A

B

1P A

0O896 + 0-026

B

1 109 ± 0-071 0-481 ± 0-098 0-921 + 0-034 0-895 + 0-022 0-899 + 0-029 0 539 ± 0'135 0-813 + 0-047 0 754 + 0-039 0-565 + 0-082

A

4-17+0 19

B

6-03 ± 0-64 16-28 + 3-94 7-12 ± 0 59 6-40 + 0-23 4-23 + 0-26 35-83 + 9-78 6-57 + 0-39 3-52 + 0-27 11-72+ 1*96

0-897 0-025 1-027 + 0-042 0*776+ 0059 0-886 ± 0 034 0-731 ± 0 047 0*641 + 0-058 0-383 ± 0-143 0-452 + 0 093 0-431± 0-085 0-520 + 0 079 3-85 + 0-17

4.74 ++ 0-37 7.49 0-95

7-11 ± 0-56 6-62 + 0-42 3-88± 0-41 29-97 + 11-95 5-52 + 1-13 3-62 + 0-65 8-21 + 1*37

2-62 ± 0.11 4-84 + 0-47 10-69 + 2-23 7*32 + 0 53 5-24 ± 2- 12 2-60 + 0-25 21-85± 7-13 15-69 + 9-00 2-76 ± 1.10 6-43 ± 1-14

1-61 ± 0 07 4-14 ± 0-33 5-76 + 1-22 5-99 + 0 49 2-22 + 0-12 1-88 ± 0 90 9.34 + 2-61 7.34 + 1-93 0 54 + 0 07 6-40 ± 3-24

613 Ca AND ACh RELEASE potentials was due to a decrease in p (Table 2), as well as in n. Thus the quantal content of the synaptic potentials declines to a very low value in the presence of hemicholinium because both p and n decrease, and there is still an approximately proportional decline in n (50 + 17 %; Table 2) with the decline in synaptic vesicles. During continual stimulation of motor nerve terminals in striated muscle in the presence of hemicholinium, p also declines, as well as n, so that there is a similar proportional decline in n and in the number of synaptic vesicles (M. R. Bennett and T. Florin, unpublished). It is possible then that a causal relationship exists between the decline in the number of synaptic vesicles in the terminal varicosities during continual transmitter release and the decline in n, and this would be expected according to the vesicle hypothesis, although the present results do not allow a distinction to be made between whether the time course of loss of synaptic vesicles is due to the decline in n or the decline in n is due to the loss of synaptic vesicles.

DISCUSSION

The effect of changes in [Ca]o and

[Mg]. on statistical

release parameters

At preganglionic nerve terminals, the main effect of Ca entry during the nerve impulse (Hodgkin & Keynes, 1957; Baker, Hodgkin & Ridgway, 1971), which is responsible for transmitter release (Miledi, 1973), is to increase the probability of transmitter release p (Fig. 1). The probability parameter is linearly dependent on [Ca]. as it is at the motor end-plate (Bennett et al. 1975) and the crayfish neuromuscular junction (Wernig, 1972), indicating that a common mechanism exists at these synapses by which Ca increases the probability of quantal release. However, the quantal release parameter n is dependent on only the 0 5 power of [Ca]. at preganglionic nerve terminals, whereas it is dependent on the third power of [Ca]o at the motor end-plate (Bennett et al. 1975); a similar insensitivity of n to changes in [Ca]. is observed at the crayfish neuromuscular junction (Wernig, 1972), indicating that the mechanism by which Ca entry acts to increase the quantal release parameter is at least quantitatively different at different nerve terminals. It is likely that the main action of Mg on the nerve terminal is to block the inward movement of Ca ions (Baker et al. 1971) rather than to enter the nerve terminal (Baker & Crawford, 1972). Thus the antagonism by Mg of the action of Ca in increasing both p and n may be mainly due to Mg blocking Ca entry into the nerve terminal, as has been proposed for the motor end-plate (Bennett et al. 1975), rather than due to Mg entering

614 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW the nerve terminal and competitively blocking the binding of Ca to the release receptors It may be argued, as for the motor end-plate (Bennett et al. 1975), that as p is linearly dependent on intracellular Ca, [Ca]1 (because of the linear relationship between Ca entry during the nerve impulse and [Cat (Hodgkin & Keynes, 1957; Baker et al. 1971) and the linear relationship between p and [Cat. up to [Cat. of 0 5 mmi (Fig. 1 A)), then the graph of p against [Mg]. (Fig. 1 B) can be read as a graph of normalized [Ca]1 against [MgL; the graph of log n-log [Mg. can then be transposed to the co-ordinates log n-log (normalized [Call). If this is done the experimental points fall on a line of slope 0-5, as for the log n-log [Cat. curve, indicating that the data are consistent with the interpretation that Mg has mainly one action, to block the inward movement of Ca. A possible physical interpretation of the fact that n ac [Ca]5 (Fig. 1 A) is that it is a consequence of a reaction n'o±n + n, in which n' Xc [Ca X]15; that is one must not only consider a reaction governing the formation of CaX (eqn. (1)) but also a reaction by which CaX governs n. However, other equally speculative interpretations are possible at this stage.

Changes in statistical release parameters during short trains of impulses the increased number of quanta released by a motor the At end-plate test impulse, following a conditioning impulse, is due to an increase in n (Bennett & Florin, 1974). The rapid (facilitated) increase in quantal content of the end-plate potential, e.p.p., during the first few successive impulses in a short train is due to n, and can be predicted on the basis that quantal content is dependent on the third power of [CaX] (Barrett & Stevens, 1972; Younkin, 1974) as n is dependent on the third power of [CaX] (Bennett et al. 1975). The relatively slow (potentiated) increase in quantal content of the e.p.p. is only obvious after the facilitated increase is complete (Magleby, 1973a), and this is due to an increase in p (Bennett et al. 1975) as would be expected if facilitaton is due to an increase in: n and potentiation has a multiplicative effect on facilitation (Magleby, 1973 b). Furthermore, as p is dependent on the first power of [CaY] at the end-plate (Bennett et al. 1975), the residual Ca-receptor hypothesis predicts that potentiation should increase as the first power of residual [CaY], and this is the case (Magleby & Zengel, 1975a). Some authors (Mallart & Martin, 1967; Magleby, 1973a) have predicted the increase in facilitation of the e.p.p. during short trains of impulses. according to the residual [CaX] hypothesis, in which there is a linear rather than a third power dependence of quantal release on [CaX]. The basis of this discrepancy with the other authors quoted above is not clear, although it might be related to a saturation of the X receptors with Ca ions early during a train under the conditions of their experiments.

At preganglionic nerve terminals, the facilitatory effect of a conditioning impulse on the number of quanta released by a subsequent test impulse

Ca AND ACh RELEASE 615 was primarily due to an increase in n, although there was also a small increase in p at the intervals studied ( > 100 msec). The increase in quantal content of the e.p.s.p. during the first few successive impulses in a short train was due to both p and n, and therefore could not be simply predicted on the basis of the dependence of n on [CaX] alone, as at the end-plate, as it also involved the dependence of p on [CaY]. The successive increases in n during a train was predicted on the basis of the residual [CaX] hypothesis (within the restrictions of the frequencies and train lengths given) in which n is dependent on the 0-5 power of [CaX]. It is not possible to determine the binomial statistic parameters responsible for the increased release of transmitter by successive impulses at the adrenergic neuromuscular junction because of the syncytial couplings between the cells (Bennett, 1972). However, there is a second power relationship between [Cat. and synaptic potential size, and the residual Ca-receptor hypothesis gives a good prediction of the growth in amplitude of successive synaptic potentials in a short train (Bennett & Florin, 1975).

Changes in statistical release parameters during long trains of impulses If the number of release sites which participate in transmission at a synapse is increased, by allowing the terminals to increase in length (Kuno, Turkanis & Weakly, 1971; Bennett & Florin, 1974) or by activating different lengths of terminal (Wernig, 1975), then n increases with the number of release sites. However, during long trains of impulses at high frequencies there is a decline in the number of synaptic vesicles accumulated throughout a cross-section of the terminals at release sites of both motor (Heuser & Reese, 1973) and preganglionic (Pysh & Wiley, 1974; Birks, 1974) synapses, and this is accompanied by a parallel decline in n (Bennett & Florin, 1974; Table 2), so that n is also proportional to the number of synaptic vesicles at a release site. These observations suggest the simple hypothesis that n is a measure of the number of release sites which each possess a synaptic vesicle available for release by the nerve impulse; the relationship between n and [Ca]o indicates that the number of these active release sites is dependent on about the third power of [Ca]0 at the motor end-plate (Bennett et al. 1975) but not at preganglionic nerve terminals. In this case p, which is largely invariant to changes in nerve terminal size (Bennett & Florin, 1974) or during long trains of impulses, is the average probability that an active release site participates in transmission by releasing the contents of its synaptic vesicle; the relationship between p and [Ca]0 indicates that this is dependent on the first power of [Ca]0 at both motor (Bennett et al. 1975) and preganglionic nerve terminals. According to this hypothesis, the facilitation observed during the first few impulses at both motor and preganglionic nerve terminals is due to an

616 M. B. BENNETT, T. FLORIN AND A. G. PETTIGREW increase in n, as more release sites are made active with successive impulses; potentiation is then due to an increase in p because the probability that an active release site releases its synaptic vesicle increases. Furthermore, this hypothesis suggests that as [Ca]o is increased n should approach a value which gives a measure of the total number of release sites which a nerve terminal possesses; as it is likely that release sites can be anatomically identified with the nerve terminal varicosities (Heuser & Reese, 1973), n should then have the same value as the number of terminal varicosities. The work of Zucker (1973) and Wernig (1975) suggests that this is likely to be the case at the crayfish and amphibian neuromuscular junctions; in the present case the largest value of n was about 10, which is similar to the number of preganglionic nerve terminal varicosities per ganglion cell estimated by Elfvin (1963, Fig. 32) for the cat's superior cervical ganglion. The question arises that if quantal content (mn) is a random variable which has a binomial distribution with parameters (n,p) is it possible that n is the number of active release sites? Say that the number of such sites is #s and that this is a random variable; furthermore that the probability of one of these active sites releasing a quantum is a. Then the generating function of the binomial distribution of mn (n,p) is U(8) = (I-p +p8)' and if the generating function of the distribution of p is G(8), then U(8) = G(1-a+as) so that (1-p+p8)R= G(1-a+am); thus G(8) = (1-p +p (8-1 so that the distribution of us is also binomial with parameters

(n, P). Now p must always be less than a, but if p = a then u ceases to be a random variable and equals n (this must happen if p = 1) which is the requirement of the above hypothesis concerning the physical basis of n. If p . a, then n cannot be the number of release sites which participate in release during an impulse, this is now i governed by the binomial parameters(n, E), and the problem of proposing a physical basis for n is made much more difficult.

The model of transmitter release proposed here should be distinguished from the binomial model of transmitter release proposed by Vere-Jones (1966) in which quantal content (mi) has a binomial distribution with parameters (N, Zip) where N is the total number of release sites of the , where a is the probability that an terminal, and Zip - 1(1 P (1 empty site becomes re-occupied by a synaptic vesicle between impulses, a is the probability that a site has a synaptic vesicle and p is the probability that such a site releases the contents of the vesicle; the model is developed for the steady state reached during continual stimulation in which there is interaction between the effects of successive impulses. According to this model if there were no interaction between impulses, the output would still be binomial but with parameters (N, acp). In either case N is fixed during facilitation, depression and in different [Cal0, so

Ca AND ACh RELEASE 617 that the model is not applicable to transmission at the motor end-plate or preganglionic nerve terminals. We are very grateful to Dr M. Quine of the Department of Mathematical Statistics and to Mr R. Hall for discussions, to Ms J. Stratford for valuable technical assistance, and to Professor D. Read for access to his PDP-11 computer. This work was supported by the Australian Research Grants Committee.

APPENDIX

Correction of e.p.8.p. amplitudes to allow for non-linear summation of quantal unit The problem is to correct the measured peak amplitude of an e.p.s.p. (v(tV)) occurring at time to after the beginning of an e.p.s.p. for non-linear summation of the m quantal units of peak amplitude 13j(to). Referring to Martin's (1955) Fig. 1 for a circuit diagram of the cell membrane during transmission, but including the cell membrane capacitance (C), vb(t) can be determined from d

d+(t) (+C()) =

(t),

where mg(t) is a time dependent change in shunt conductance due to the release of m quanta, G is the cell membrane conductance and VO is the driving potential (equal to the difference between the membrane resting potential and the equilibrium potential for transmission). This is a standard first order linear differential equation with variable coefficient, which has the solution

f°g(t)

f+m(t) dt) dt+B), exp (fG exp (-fcG+mg(t) dt) ( where B is a constant. If v1(O) = 0, and g(t) is an impulse-like change in conductance of size ge which lasts for 0 < t < to, then the e.p.s.p. peak amplitude is v(t)

=

1v(to) = where Te

=

C/9e, Tm =

-( exp(

and a =

(l+2e )

°)),

For a miniature e.p.s.p.,

VI (to), the peak amplitude at to is

v1(t=

(1-exp ((a0a O

(1)

ToM lexp( -o))

618 M. R. BENNETT, T. FLORIN AND A. G. PETTIGREW so that

re -V()(e

P

(ilm).

(2)

All the factors on the right hand side of eqn. (2) can be determined experimentally, giving r All the factors on the right hand side of eqn. (1) are now determined, so that v1(to) can be graphed for different values of m and therefore the corrected value mi'1 (to) can be read off the graph. This procedure is equivalent to that adopted by Martin (1955), except that it allows for discharging of the membrane capacitance, C; if the time course of the shunt conductance due to the release of m quanta (to) is very long compared with ame then the correction for non-linear summation outlined above is identical to Martin's. In practice average values for to, r. and V0 were used of 2 msec, 10 msec and 50 mV respectively (McLachlan, 1975), whereas 13l (to) was determined from the average value of the m.e.p.s.p.'s amplitude-frequency distribution recorded in each cell during stimulation. For a 131(to) of 0-5 mV, Te from eqn. (2) is 180 msec, and inserting these values into eqn. (1), gives 13(to) for different m; a comparison between this 1v(to) and miv1 (to) shows that 13(t0) need be increased by less than IO % in the range 5-10 mV to correct for non-linear summation, and then this correction is about half that of Martin's correction in which the effects of membrane capacitance are ignored. It should be noted that the present correction is only appropriate for a cell which is uniformly polarized by the synaptic potential. REFERENCES

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