Naunyn-Schmiedeberg's
Archivesof Pharmacology
Naunyn-Schmiedeberg'sArch. Pharmacol. 295, 103- 108 (1976)
9 by Springer-Verlag1976
Quanta1 Parameters of Transmission at the Frog Neuromuscular Junction* R O B E R T L. V O L L E and D I M I T R I E D. B R A N I S T E A N U Department of Pharmacology, University of Connecticut, Health Center, Farmington, Connecticut 06032, U.S.A.
Summary. Estimates of quantal release parameters at frog neuromuscular junctions showed that alterations in [Ca2+]0 affected m (number of quanta), p (probability of quantal release) and n (stores of quanta available for release). The effect of [Ca2+]o depended upon the initial value for p. When p was low, raising [Ca2+]o increased m and p, but not n. However, when p was large, raising [Ca 2 +]o had no further effect on p but increased m and n. During prolonged repetitive nerve stimulation to cause a decrease in m, n was decreased and p was increased. This finding was attributed to a failure of transmitter mobilization to maintain the stores of transmitter available for release. Key words: Transmitter release - Neuromuscular junction - Quantal parameters of release - Probability of release - Transmitter mobilization.
INTRODUCTION The quantal hypothesis holds that transmitter release at the neuromuscular junction occurs in the form of discrete units (quanta) and that the number of quanta (m) released by the nerve terminal action potential is directly proportional to the stores of transmitter available (n) for release and the mean probability of release (p) for the quantal units (del Castillo and Katz, 1954). Alternative statistical models of release suggest that the quantal parameter n is related to the number of release sites in the terminal membrane (Zucker, 1973; Rahamimoff and Meiri, 1975) and that p is a compound probability involving both the activation of release sites and the probability of release for the Send offprint requests to: R. L. Volle at the above address * Supported by grant NS-07540-08 from the Institute of Neurological Diseases and Stroke, N.I.H., U.S.P.H.S.
available quanta (Zucker, 1973). There is good evidence to show that n is related to the length of the nerve terminal being activated and has a value similar to the number of vesicle attachment sites (Wernig, 1975). Because transmitter release during long trains of stimulation is distributed according to binomial law, reasonable estimates can be made of the quantal parameters of release (Bennett and Florin, 1974; Miyamoto, 1975; Wernig, 1972, 1975; Branisteanu et al., 1976). Therefore, the relationship between the statistical quantal parameters and the physical process of transmitter release can be studied by determining the changes in the parameters when transmitter release is increased or decreased. In the experiments described here altered [Ca 2+ ]0 and prolonged repetitive stimulation were used to modify transmitter release under conditions where the quantal parameters of release could be estimated from a statistical analysis of voltage fluctuation of endplate potentials (EPPs) and miniature EPPs (mepps). Bennett et al. (1975), Miyamoto (1975) and Rahamimoff and Meiri (1975) have already reported that alterations in [Ca2+]0 affect the statistical parameter n. Branisteanu et al. (1976) found that [Ca 2 + ]0 had only a slight effect on n. It now appears that the effect of [Ca 2 + ]o on n depends upon the initial value for p. METHODS Sciatic nerve-sartorius muscles were removed from Rana pipiens
and equilibrated in a Ringer solution containing (raM): NaC1 97; KC12.5; CaC120.7-1.7; MgC125-10; NaH2PO4 0.85; NazHPO4 2.15, and neostigmine (3 x 10 6 M). In those experiments where 5 mM MgCt2 was used to depress transmission, an osmotically equivalent amount of sucrose was added to maintain osmotic strength of the Ringer solution and to maintain the ratio of Caz+/ Na +. In some instances the Ca2+/Mg2+ was expressed(Dodge and Rahamimoff, 1967)as eft Ca2+ =
[Ca2+] 1 + [Ca2+] + [Mg2+]/3 "
104
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976)
Solutions were used at room temperature (20-22 ~C) and perfused through the bath (2 ml) at a rate of 6 ml/min. Osmolarities of the solutions were checked by measurement of the depression of the freezing point of water. Only the fibers in the superficial layer were used. Rectangular wave pulses of supramaximal voltage and 0.5 ms duration were delivered to the sciatic nerve. Electrical activity was monitored using glass microelectrodes filled with 3 M KC1 ( 5 - ] 5 megohms). Potentials were displayed on an oscilloscope. The appearance of mepps and EPPs with rise times of 1.5-2.0 ms was used to locate the endplates. A direct estimate of quantal content (m) was made by measuring EPPs and mepps at the same junction, correcting for nonlinear summation (Martin, 1966) and determining the ratio of mean EPP to mean mepp. At least 150 consecutive EPPs evoked at a rate of 0.5 Hz and 100 mepps were used for each estimate of m. In the cells studied here, transmitter release was described by the binomial probability distribution. Therefore,
p
=
1
--
var EPP EPP. y
n~ _
/"
-40
/"
-30
m
. . . . . ax. . . . . - d
-20
1.0'
-10
0.5/"
0.4 /
/"
. lJ--- m ----o P
/"
it"
0'31 0.2 k
72
where var EPP is the variance of corrected EPPs, y is the mean amplitude of the mepps and az the variance of the mepps (Bennett and Florin, 1974; Miyamoto, 1975). Estimates of n were obtained from n = m/p. Using experimentally determined values for n and p, the release process was tested for conformity to binomial probability distribution by comparing observed parameters of transmitter release with those predicted by the binomial term p:,
60 ~50
/ .,~ n /~/./ /./"
pXq(.- x~
(n -- x) !x! where Px is the expected frequency of EPPs with x quanta, and q is (1 - p), the average probability that a quantum will not be released. The goodness of fit between observed and expected data was tested by the chi-square method. The degrees of freedom used was N-3 (cf. McLachlan, 1975). Data were included in the study only when the following conditions were satisfied: (1) there was no change in the amplitudefrequency distribution of the mepps, (2) a stable resting membrane potential was maintained through several changes of solutions, (3) the S.E.M. for the statistical parameters was less than 2 0 ~ of the mean (Zucker, 1973), and (4) values for p were greater than 0.25 (Bennett et al., 1975).
RESULTS As illustrated in Figures I and 2, estimates of m, n andp agreed well with those reported by Wernig (1975) and Branisteanu et al. (1976) for Mg-depressed junctions. However, a complex pattern of changes in the quantal release parameters was observed when [Caz + ]0 was altered (Figs. 1 and 2). As expected, raising [Ca2 + ]0 caused a marked increase in the value for m. By contrast, the changes in n and p produced by raising [Ca2 + ]o depended upon the initial rate of transmitter release. When release was relatively low, raising [Ca2 + ]o increased the values for m and p, but not n. On the other hand, when transmitter release was relatively high, raising [Ca2+]o increased the values for m and n, but not p.
0.1
I
0.8
I
0.9
1.0
I
I
1.1
1.2
[co Fig. 1. Statistical parameters of transmitter release plotted semilogarithmically as a function of [Ca2+]0. Transmitter release was depressed throughout by 5 mM Mg2 +. The rate of stimulation was 0.5 Hz and the same endplate was used for each [Ca2+]o. The right ordinate indicates numbers of quanta and refers to m and n; the left ordinate indicates the values for p. Lines are drawn by inspection
9200 j-"
.....;-" l.O"
/k--.~.~
.1"1"I ~'~"~"I I " / / ,i.~ . ~ f - -
......om
/ -/~ --0 . . . . .
-100
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50
0.4
40
0.3
30
0.2-
20
0.1
111
'
1.'3
'
1',5
'
117
10
[ce +,r.M] Fig.2. Experimental conditions the same as those of Figure 1 except that transmitter release was depressed by 10 mM Mg~+
Mean values for m, n and p were obtained by pooling results from 6 endplates of different muscles and normalizing the values around those obtained when eft Ca 2+ was 0.23 mM (10 mM Mg2+). The
R. L. Volle and D. D. Branisteanu: Transmitter Release
105
between the frequency distribution of the observed quantal content of the EPPs and that predicted by binomial law. For example, the frequency histograms for the data of Figure 1 are given in Figure 4 and
power relationship between eft Ca 2§ and m for the data given in Figure 3 was 3.6 when calculated by y
=
ax b
where x is effCa 2§ and y is m or by the slope of the line formed by a double logarithmic plot of m v s eft Ca 2 § (Dodge and Rahamimoff, 1967). In contrast to m which showed a single power relationship to eft Ca 2 § of about 4, n and p did not appear to follow a single power relationship. Between 0.17 and 0.23 mM eft Ca 2+, the power relationship was estimated to be 3.4 for m and 3.5 forp (Fig. 3). The value for n did not change. However, between 0.23 and 0.28 mM eft Ca 2+, the power relationship was estimated to be 3.9 for m and 3.4 for n. There was only a small increase in p. Thus, over the lower range of [Ca2+]0, the increase in m was due to an increase in p but, over the upper range of eft Ca 2 +, the increase was due to an increase in n. The critical concentration of eft Ca a+ for the break in the power relationship for n and p was 0.23 mM for the cells of Figure 3. For the cell described in Figure 1, the critical concentration of effCa 2+ (5 mM Mg 2+) was 0.27 mM. For these cells, the chi-square test was used to determine if the release of transmitter followed a binomial distribution over the range of eft Ca 2 § used in the study. Comparisons were made at each [Ca 2 § ]o
m uJ
3228-
A ?
O ./
1,0-
0.504 I
0.3" 0.1 0.15
0;7 o19 o.i
o)3 015 0?7 019
Lrco++ .fql Figi 3. Parameters of release plotted as a semi-logarithmic function o f e f f C a 2+ (10 m M Mg z+ throughout). The data were pooled from 6 endplates and normalized by setting the values obtained at 0.23 m M eft Ca 2+ as unity. The mean (_+ S.E.M.) values obtained at 0.23 m M effCa 2+ were: m; 44.7 _+ 7.4 (quanta); n, 79.6 _+ 14.6 (quanta) andp, 0.575 _+ 0.039
B
21-
t~'
16-
Z
.12f"
~
20 -
~E
2.0'
~
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t
'i 2
4 6 8 QUANTAL
.c~ 24 u.i
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g Z
r
I0 12 14 16 18 20 CONTENT
i
2
4
,
,
,
i
,
i
,
i
6 8 10 12 14 16 18 20 QUANTAL CONTENT
o
~
~
6
8 10 12 14 16 18 20 22 2'4 QUANTAL CONTENT
D
20
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,
,
,
,
,
,
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,
,
,
,
,
10 12 14 16 18 20 22 24 26 28 30 32 QUANTAL
CONTENT
0
14 16 18 20 22 24 26 28 30 32 34 36 38 QUANTAL
CONTENT
F i g . 4 A - E . Frequency histograms of the quantal contents of EPPs evoked at a rate of 0.5 Hz in Ringer solution containing 5 mm Mg2 + and 0.8 (A), 0.9 (B), 1.0 (C), 1.1 (D) and 1.2 (E) m M Ca 2+. The data are derived from the experiment described in Figure 1. The dashed lines show the distribution of quantal contents of EPPs predicted by binomial statistics. The chi-square and P values, respectively, were: (A), 13.44, > 0.3; (B) 4.1, 0.99; (C) 3.5, 0.99; (D) 3.1, 0.99 and (E) 3.3, 0.99
106
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976)
- 200
~
1.0-
0.5-
-100
P
50 m
0.2-
20
0.I
10
EPP
NUMBER
(10 3 )
Fig.5. Changes in quantal release parameters during repetitive stimulation at a rate of 5 Hz. The Ringer solution contained 12 mM Mb~ + and 1.4raM Ca z§ The data are plotted semi-
logarithmically as a function of EPP number. The right ordinate indicates the number of quanta the left ordinate, the values for p
2.0-
15
6
1.0
6
~6
6
fq
,
bq
b
b
6
b
6 m
0.5
0
i
i
i
i
5r
J
i
i
i
101
i
i
EPP, the values for m, n a n d p were 53.6, 120 and 0.44, respectively; at the 24x 103 EPP, the values for m, n and p were 32.2, 50.6 and 0.63, respectively. Mepps were recorded before and after the period of stimulation. There were no changes in mean amplitude of mepps. The values obtained from 7 endplates of different muscles were pooled and expressed as the mean ratio of the values obtained for the 300th EPP (Fig. 6). The Ringer solution contained 12raM MgZ + and 1.4 m M Ca 2+. The mean ratios (_+ S.E.M.) for m, n, a n d p at the 103 EPP were 1.04 +_ 0.017, 0.97 + 0.067 and 1.04 _+ 0.102, respectively. For the 20 x 103 EPP, the mean ratios were 0.57 + 0.039 (m), 0.36 _+ 0.068 (n) and 1.56 + 0.146 (p).
i
i ]51
i
i
J
i 210
EPP NUMBER (103)
Fig. 6. Normalized values for m, n and p during repetitive stimulation at a rate of 5 Hz. T h e data were pooled from 7 endplates and were normalized with the values for the first 300 EPPs set at unity. The mean ( + S.E.M.) values for m, n and p at 300 EPPs were 41.2 + 4.01,147.0 _+ 26.0 and 0.31 _+ 0.057, respectively; at 20 x 103, the values were, 25.4 _+ 3.29, 64.6 _+ 6.48 and 0.48 _+ 0.069, respectively. O n the graph, the vertical lines indicate the S.E.M. of the m e a n ratios
show good agreement with predicted binomial distribution at all [Ca 2 + ]o. The values for m and n were decreased and the value for p increased during prolonged repetitive stimulation at a rate of 5 Hz (Fig. 5). At the 300th
DISCUSSION As started by Martin (1966), " . . . the parameters n and p must be considered to be just as 'real' as the directly measurable quantity m." Manifestly, the problem has been to relate the statistical parameters to the physical process of transmitter release. Thus far, complex results have been obtained whenever attempts have been made to correlate transmitter release with the binomial parameters of release. Stated in its simplest form, transmitter release is thought to occur after a synaptic vesicle has fused with a specific membrane attachment site. However, the relationship between synaptic vesicles, vesicle attachment sites (Couteaux and Pecot-Dechavassine, 1970) and the parameters n and p, remains to be determined. Hubbard and Kwanbunbumpen (t968) concluded that n and p reflect membrane events and are unrelated to the number of vesicles adjacent to membrane release sites. On the other hand, Christensen (1976), combining electrophysiotogical and ultrastructural studies, defined n as the number of vesicles available for release from the total junctional content of synaptic vesicles. Alternatively, Wernig (1975) like Zucker (1973) and Rahamimoff and Meiri (1975), suggested that since n has the same value as the number of synaptic vesicle attachment sites, n is a measure of the number of membrane release sites. Unfortunately, rigorous evidence to support or reject any of these possibilities is unavailable. This much is clear. The statistical parameters of release were changed in a complex way by prolonged repetitive nerve stimulation or [Ca2+]o. If the assumption is made that Ca 2 + have more than one action on transmitter release, the complex responses to elevated [Ca2+]o can be explained in terms of the model proposed originally by del Castillo and Katz (1954).
R. L. Volle and D. D. Branisteanu: Transmitter Release
At low initial levels of Ca z +, raising [Ca 2+ ]o can be viewed as increasing m by increasing the mean probability that a transmitter release site in the membrane (Couteaux and Pecot-Dechavassine, i970) will be activated. If the pool of quanta is large and maintained by an adequate level 6f mobilization, no measurable change in the number 6f quanta available for release occurs. With increasing [Ca2 + ]o, the mean probability of activating such sites would be expected to approach a maximum. Under these conditions, a further increase in m could occur only if a marked increase in the number of quanta available for release takes place. This increase in available quanta should be reflected by an increase in n. Since it is known that raising [Ca2+]0 increases transmitter mobilization (Wilson, 1973), it may be by this mechanism that raising [Ca 2+ ]o increases n. Whether or not [Ca2+ ]0 affects transmitter mobilization under the conditions of low frequency nerve stimulation used for estimating binomial release parameters is not known. It is of some interest that tetraethylammonium and guanidine ions enhanced transmitter release at junctions depressed by Mg 2+ by increasing m and n and had little effect on p (Volle and Branisteanu, 1976). Like [Ca 2 + ]0 these drugs also increased the rate of transmitter mobilization. Thus, drugs known to increase transmitter mobilization produced a corresponding increase in n, whereas drugs known to decrease transmitter mobilization decreased n (Volle, 1973; Branisteanu et al., 1975). The gradual decline of transmitter release occurring during repetitive stimulation can be accounted for also by the model proposed by del Castillo and Katz (1954). It is clear that the decrease in m was due to a decrease in n, probably as a consequence of the failure of transmitter mobilization to maintain the stores of transmitter available for release. If this is so, then n reflects the stores of transmitter as proposed originally by del Castillo and Katz (1954). The increase in p occurring during repetitive stimulation may result from an accumulation of C a 2 + by the nerve terminals and, consequently, the activation of release sites (Rahamimoff, 1968). The increased value for p could result both from an increased probability for the activation of release sites and a closer proximity between the quanta available for release and the release sites. Some of .the findings described here can be explained also by the alternative model that n represents the number of release sites (vide supra) rather than the number of quanta available for release (Zucker, 1973; Rahamimoff and Meiri, 1975; Wernig, 1975). According to this model, the effect of raising [Ca2+]o results in increased transmitter release by increasing the number of active release sites. At low
107
initial [Ca 2 + ]o, the effect of raising [Ca2+ ]o on n might be obscured because of the errors inherent in the measurement made when the value for p is low (Zucker, 1973; Bennett et al., 1975). Similarly, the decrease in the value for n during prolonged repetitive stimulation may be due to a loss of activated sites resulting from depleted stores of transmitter and may be more apparent than real. Clearly, estimates of the number of sites depend upon the site being occupied by a quantum of transmitter. Therefore, in those situations where depletion of transmitter occurs but release can be described by binomial statistics, the value for n will be, in fact, an underestimate of the number of activated release sites. There is no method, at present, for discriminating between these two models of transmitter release or for obtaining rigorous evidence to support alternative models. Although n and p can be demonstrated to be independent parameters of release under some circumstances, in most instances it is not possible to alter one parameter without affecting the other. It is not surprising that a certain amount of interdependence exists between the two parameters of release. Estimates of transmitter release depends a priori upon the availability of transmitter and the activation of release sites in the membrane. In any event, the present results show that the effects of drugs or other interventions on the statistical parameters of release depend very much on initial values for p. Similar data have been obtained in sympathetic ganglia (McLachlan, 1975). When p was > 0.5, enhanced release produced by increasing rates of preganglionic stimulation was associated with increases in m and n, but not p; conversely, when p was < 0.5, the increase in release was associated with an increase in m and p, but not n. Finally, some limitations of the methods must be noted (Zucker, 1973; Bennett et al., 1975; Miyamoto, 1975; Wernig, 1975). Inasmuch as estimates of m and var m depend upon measurements of voltage fluctuations of a train of EPPs, consideration must be given to amplitude fluctuations of mepps, membrane potential, background noise, and the correction for non-linear summation (see Martin, 1966). The proper correction for non-linear summation of quanta when EPPs are large has been a particularly nettlesome problem for some (see Wernig, 1975). However, in this laboratory use of the correction factor as described by Martin (1955) has always provided estimates of n and p which satisfy prediction by the binomial law when tested by the chi-square method. Acknowledgement. We want to thank our colleague Dr. M. D. Miyamoto, University of Connecticut for many stimulating hours of discussion and help with this work.
108 REFERENCES Bennett, M. R., Florin, T. : A statistical analysis of the release of acetylcholine at newly formed synapses in striated muscle. J. Physiol. (Lond.) 238, 93-107 (1974) Bennett, M. R., Florin, T., Hall, R. : The effect of calcium ions on the binomial statistical parameters which control acetylcholine release at synapses in striated muscle. J. Physiol. (Lond.) 247, 429 - 446 ( 1975) Branisteanu, D. D., Miyamoto, M. D., Volle, R. L. : Quantal release paramters during fade of endplate potentials. Naunyn-Schmiedeberg's Arch. Pharmacol. 288, 323-327 (1975) Branisteanu, D.D., Miyamoto, M. D., Volle, R. L. : Effects of physiologic alterations on binomial transmitter release at magnesium-depressed neuromuscular junctions. J. Physiol. (Lond.) 254, 19-37 (1976) Christensen, B. N. : Morphological correlates of synaptic transmission in lamprey spinal cord. J. Neurophysiol. 39, 197-212 (1976) Couteaux, M. R., Pecot-Dechavassine, M. : Vesicules synaptiques et poches au niveau des ~(zones actives>) de la jonction neuromusculaire. C.R. Acad. Sci. (Paris) 271, 2346-2349 (1970) del Castillo, J., Katz, B.: Quantal components of the endplate potential. J. Physiol. (Londl) 124, 560-573 (1954) Dodge, F. A., Jr., Rahamimoff, R. : Co-operative action of calcium ions in transmitter release at the neuromuscular junction. J. Physiol. (Lond.) 193, 419-432 (1967) Hubbard, J. I., Kwanbunbumpen, S.: Evidence for the vesicle hypothesis. J. Physiol. (Lond.) 194, 407-420 (1968) Martin, A. R. : A further study of the statistical composition of the end-plate potential. J. Physiol. (Lond.) 130, 114-122 (1955) Martin, A. R. : Quantal nature of synaptic transmission. Physiol. Rev. 46, 51-66 (1966)
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976) McLachlan, E. : An analysis of the release of acetylcholine from preganglionic nerve terminals. J. Physiol. (Lond.) 245, 447- 466 (1975) Miyamoto, M. D. : Binomial analysis of quantal transmitter release at .glycerol treated frog neuromuscular junctions. J. Physiol. (Lond.) 250, 121 - 142 (1975) Rahamimoff, R. ! ~.. dual effect of calcium ions on neuromuscular facilitation. J. Physioll (Lond.)~195, 471 • 480 (1968) Rahamimoff, R., Meiri, H. : The eff'ect of calcium ions on the statistical parameters of transmitter release. Israel J. reed. Sci. 111 68 (1975) Volle, R. L. : Frequency dependent decrease of quantal content in a drug-treated neuromuscular junction. Naunyn-Schmiedeberg's Arch. Pharmacol. 278, 211 - 2 8 4 (1973) Voile, R. L., Branisteanu, D. D. : Statistical parameters of transmitter release at frog neuromuscular junctions treated with guanidine or tetraethylammonium. J. Pharmacol. exp. Ther. 197, 653-661 (1976) Wernig, A. : Changes in statistical parameters during facilitation at the crayfish neuromuscular junction. J. Physiol. (Lond.) 226, 751-759 (1972) Wernig, A. : Estimates of statistical release parameters from crayfish and frog neuromuscular junctions. J. Physiol. (Lond.) 244, 207-221 (1975) Wilson, D. F. : Effects of caffeine on neuromuscular transmission in the rat. Amer. J. Physiol. 225, 862-865 (1973) Zucker, R. S. : Changes in the statistics of transmitter release during facilitation. J. Physiol. (Lond.) 229, 787-810 (1973)
Received April 8~Accepted July 1, 1976
Archivesof Pharmacology
Naunyn-Schmiedeberg'sArch. Pharmacol. 295, 103- 108 (1976)
9 by Springer-Verlag1976
Quanta1 Parameters of Transmission at the Frog Neuromuscular Junction* R O B E R T L. V O L L E and D I M I T R I E D. B R A N I S T E A N U Department of Pharmacology, University of Connecticut, Health Center, Farmington, Connecticut 06032, U.S.A.
Summary. Estimates of quantal release parameters at frog neuromuscular junctions showed that alterations in [Ca2+]0 affected m (number of quanta), p (probability of quantal release) and n (stores of quanta available for release). The effect of [Ca2+]o depended upon the initial value for p. When p was low, raising [Ca2+]o increased m and p, but not n. However, when p was large, raising [Ca 2 +]o had no further effect on p but increased m and n. During prolonged repetitive nerve stimulation to cause a decrease in m, n was decreased and p was increased. This finding was attributed to a failure of transmitter mobilization to maintain the stores of transmitter available for release. Key words: Transmitter release - Neuromuscular junction - Quantal parameters of release - Probability of release - Transmitter mobilization.
INTRODUCTION The quantal hypothesis holds that transmitter release at the neuromuscular junction occurs in the form of discrete units (quanta) and that the number of quanta (m) released by the nerve terminal action potential is directly proportional to the stores of transmitter available (n) for release and the mean probability of release (p) for the quantal units (del Castillo and Katz, 1954). Alternative statistical models of release suggest that the quantal parameter n is related to the number of release sites in the terminal membrane (Zucker, 1973; Rahamimoff and Meiri, 1975) and that p is a compound probability involving both the activation of release sites and the probability of release for the Send offprint requests to: R. L. Volle at the above address * Supported by grant NS-07540-08 from the Institute of Neurological Diseases and Stroke, N.I.H., U.S.P.H.S.
available quanta (Zucker, 1973). There is good evidence to show that n is related to the length of the nerve terminal being activated and has a value similar to the number of vesicle attachment sites (Wernig, 1975). Because transmitter release during long trains of stimulation is distributed according to binomial law, reasonable estimates can be made of the quantal parameters of release (Bennett and Florin, 1974; Miyamoto, 1975; Wernig, 1972, 1975; Branisteanu et al., 1976). Therefore, the relationship between the statistical quantal parameters and the physical process of transmitter release can be studied by determining the changes in the parameters when transmitter release is increased or decreased. In the experiments described here altered [Ca 2+ ]0 and prolonged repetitive stimulation were used to modify transmitter release under conditions where the quantal parameters of release could be estimated from a statistical analysis of voltage fluctuation of endplate potentials (EPPs) and miniature EPPs (mepps). Bennett et al. (1975), Miyamoto (1975) and Rahamimoff and Meiri (1975) have already reported that alterations in [Ca2+]0 affect the statistical parameter n. Branisteanu et al. (1976) found that [Ca 2 + ]0 had only a slight effect on n. It now appears that the effect of [Ca 2 + ]o on n depends upon the initial value for p. METHODS Sciatic nerve-sartorius muscles were removed from Rana pipiens
and equilibrated in a Ringer solution containing (raM): NaC1 97; KC12.5; CaC120.7-1.7; MgC125-10; NaH2PO4 0.85; NazHPO4 2.15, and neostigmine (3 x 10 6 M). In those experiments where 5 mM MgCt2 was used to depress transmission, an osmotically equivalent amount of sucrose was added to maintain osmotic strength of the Ringer solution and to maintain the ratio of Caz+/ Na +. In some instances the Ca2+/Mg2+ was expressed(Dodge and Rahamimoff, 1967)as eft Ca2+ =
[Ca2+] 1 + [Ca2+] + [Mg2+]/3 "
104
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976)
Solutions were used at room temperature (20-22 ~C) and perfused through the bath (2 ml) at a rate of 6 ml/min. Osmolarities of the solutions were checked by measurement of the depression of the freezing point of water. Only the fibers in the superficial layer were used. Rectangular wave pulses of supramaximal voltage and 0.5 ms duration were delivered to the sciatic nerve. Electrical activity was monitored using glass microelectrodes filled with 3 M KC1 ( 5 - ] 5 megohms). Potentials were displayed on an oscilloscope. The appearance of mepps and EPPs with rise times of 1.5-2.0 ms was used to locate the endplates. A direct estimate of quantal content (m) was made by measuring EPPs and mepps at the same junction, correcting for nonlinear summation (Martin, 1966) and determining the ratio of mean EPP to mean mepp. At least 150 consecutive EPPs evoked at a rate of 0.5 Hz and 100 mepps were used for each estimate of m. In the cells studied here, transmitter release was described by the binomial probability distribution. Therefore,
p
=
1
--
var EPP EPP. y
n~ _
/"
-40
/"
-30
m
. . . . . ax. . . . . - d
-20
1.0'
-10
0.5/"
0.4 /
/"
. lJ--- m ----o P
/"
it"
0'31 0.2 k
72
where var EPP is the variance of corrected EPPs, y is the mean amplitude of the mepps and az the variance of the mepps (Bennett and Florin, 1974; Miyamoto, 1975). Estimates of n were obtained from n = m/p. Using experimentally determined values for n and p, the release process was tested for conformity to binomial probability distribution by comparing observed parameters of transmitter release with those predicted by the binomial term p:,
60 ~50
/ .,~ n /~/./ /./"
pXq(.- x~
(n -- x) !x! where Px is the expected frequency of EPPs with x quanta, and q is (1 - p), the average probability that a quantum will not be released. The goodness of fit between observed and expected data was tested by the chi-square method. The degrees of freedom used was N-3 (cf. McLachlan, 1975). Data were included in the study only when the following conditions were satisfied: (1) there was no change in the amplitudefrequency distribution of the mepps, (2) a stable resting membrane potential was maintained through several changes of solutions, (3) the S.E.M. for the statistical parameters was less than 2 0 ~ of the mean (Zucker, 1973), and (4) values for p were greater than 0.25 (Bennett et al., 1975).
RESULTS As illustrated in Figures I and 2, estimates of m, n andp agreed well with those reported by Wernig (1975) and Branisteanu et al. (1976) for Mg-depressed junctions. However, a complex pattern of changes in the quantal release parameters was observed when [Caz + ]0 was altered (Figs. 1 and 2). As expected, raising [Ca2 + ]0 caused a marked increase in the value for m. By contrast, the changes in n and p produced by raising [Ca2 + ]o depended upon the initial rate of transmitter release. When release was relatively low, raising [Ca2 + ]o increased the values for m and p, but not n. On the other hand, when transmitter release was relatively high, raising [Ca2+]o increased the values for m and n, but not p.
0.1
I
0.8
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0.9
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[co Fig. 1. Statistical parameters of transmitter release plotted semilogarithmically as a function of [Ca2+]0. Transmitter release was depressed throughout by 5 mM Mg2 +. The rate of stimulation was 0.5 Hz and the same endplate was used for each [Ca2+]o. The right ordinate indicates numbers of quanta and refers to m and n; the left ordinate indicates the values for p. Lines are drawn by inspection
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[ce +,r.M] Fig.2. Experimental conditions the same as those of Figure 1 except that transmitter release was depressed by 10 mM Mg~+
Mean values for m, n and p were obtained by pooling results from 6 endplates of different muscles and normalizing the values around those obtained when eft Ca 2+ was 0.23 mM (10 mM Mg2+). The
R. L. Volle and D. D. Branisteanu: Transmitter Release
105
between the frequency distribution of the observed quantal content of the EPPs and that predicted by binomial law. For example, the frequency histograms for the data of Figure 1 are given in Figure 4 and
power relationship between eft Ca 2§ and m for the data given in Figure 3 was 3.6 when calculated by y
=
ax b
where x is effCa 2§ and y is m or by the slope of the line formed by a double logarithmic plot of m v s eft Ca 2 § (Dodge and Rahamimoff, 1967). In contrast to m which showed a single power relationship to eft Ca 2 § of about 4, n and p did not appear to follow a single power relationship. Between 0.17 and 0.23 mM eft Ca 2+, the power relationship was estimated to be 3.4 for m and 3.5 forp (Fig. 3). The value for n did not change. However, between 0.23 and 0.28 mM eft Ca 2+, the power relationship was estimated to be 3.9 for m and 3.4 for n. There was only a small increase in p. Thus, over the lower range of [Ca2+]0, the increase in m was due to an increase in p but, over the upper range of eft Ca 2 +, the increase was due to an increase in n. The critical concentration of eft Ca a+ for the break in the power relationship for n and p was 0.23 mM for the cells of Figure 3. For the cell described in Figure 1, the critical concentration of effCa 2+ (5 mM Mg 2+) was 0.27 mM. For these cells, the chi-square test was used to determine if the release of transmitter followed a binomial distribution over the range of eft Ca 2 § used in the study. Comparisons were made at each [Ca 2 § ]o
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F i g . 4 A - E . Frequency histograms of the quantal contents of EPPs evoked at a rate of 0.5 Hz in Ringer solution containing 5 mm Mg2 + and 0.8 (A), 0.9 (B), 1.0 (C), 1.1 (D) and 1.2 (E) m M Ca 2+. The data are derived from the experiment described in Figure 1. The dashed lines show the distribution of quantal contents of EPPs predicted by binomial statistics. The chi-square and P values, respectively, were: (A), 13.44, > 0.3; (B) 4.1, 0.99; (C) 3.5, 0.99; (D) 3.1, 0.99 and (E) 3.3, 0.99
106
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976)
- 200
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Fig.5. Changes in quantal release parameters during repetitive stimulation at a rate of 5 Hz. The Ringer solution contained 12 mM Mb~ + and 1.4raM Ca z§ The data are plotted semi-
logarithmically as a function of EPP number. The right ordinate indicates the number of quanta the left ordinate, the values for p
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EPP, the values for m, n a n d p were 53.6, 120 and 0.44, respectively; at the 24x 103 EPP, the values for m, n and p were 32.2, 50.6 and 0.63, respectively. Mepps were recorded before and after the period of stimulation. There were no changes in mean amplitude of mepps. The values obtained from 7 endplates of different muscles were pooled and expressed as the mean ratio of the values obtained for the 300th EPP (Fig. 6). The Ringer solution contained 12raM MgZ + and 1.4 m M Ca 2+. The mean ratios (_+ S.E.M.) for m, n, a n d p at the 103 EPP were 1.04 +_ 0.017, 0.97 + 0.067 and 1.04 _+ 0.102, respectively. For the 20 x 103 EPP, the mean ratios were 0.57 + 0.039 (m), 0.36 _+ 0.068 (n) and 1.56 + 0.146 (p).
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Fig. 6. Normalized values for m, n and p during repetitive stimulation at a rate of 5 Hz. T h e data were pooled from 7 endplates and were normalized with the values for the first 300 EPPs set at unity. The mean ( + S.E.M.) values for m, n and p at 300 EPPs were 41.2 + 4.01,147.0 _+ 26.0 and 0.31 _+ 0.057, respectively; at 20 x 103, the values were, 25.4 _+ 3.29, 64.6 _+ 6.48 and 0.48 _+ 0.069, respectively. O n the graph, the vertical lines indicate the S.E.M. of the m e a n ratios
show good agreement with predicted binomial distribution at all [Ca 2 + ]o. The values for m and n were decreased and the value for p increased during prolonged repetitive stimulation at a rate of 5 Hz (Fig. 5). At the 300th
DISCUSSION As started by Martin (1966), " . . . the parameters n and p must be considered to be just as 'real' as the directly measurable quantity m." Manifestly, the problem has been to relate the statistical parameters to the physical process of transmitter release. Thus far, complex results have been obtained whenever attempts have been made to correlate transmitter release with the binomial parameters of release. Stated in its simplest form, transmitter release is thought to occur after a synaptic vesicle has fused with a specific membrane attachment site. However, the relationship between synaptic vesicles, vesicle attachment sites (Couteaux and Pecot-Dechavassine, 1970) and the parameters n and p, remains to be determined. Hubbard and Kwanbunbumpen (t968) concluded that n and p reflect membrane events and are unrelated to the number of vesicles adjacent to membrane release sites. On the other hand, Christensen (1976), combining electrophysiotogical and ultrastructural studies, defined n as the number of vesicles available for release from the total junctional content of synaptic vesicles. Alternatively, Wernig (1975) like Zucker (1973) and Rahamimoff and Meiri (1975), suggested that since n has the same value as the number of synaptic vesicle attachment sites, n is a measure of the number of membrane release sites. Unfortunately, rigorous evidence to support or reject any of these possibilities is unavailable. This much is clear. The statistical parameters of release were changed in a complex way by prolonged repetitive nerve stimulation or [Ca2+]o. If the assumption is made that Ca 2 + have more than one action on transmitter release, the complex responses to elevated [Ca2+]o can be explained in terms of the model proposed originally by del Castillo and Katz (1954).
R. L. Volle and D. D. Branisteanu: Transmitter Release
At low initial levels of Ca z +, raising [Ca 2+ ]o can be viewed as increasing m by increasing the mean probability that a transmitter release site in the membrane (Couteaux and Pecot-Dechavassine, i970) will be activated. If the pool of quanta is large and maintained by an adequate level 6f mobilization, no measurable change in the number 6f quanta available for release occurs. With increasing [Ca2 + ]o, the mean probability of activating such sites would be expected to approach a maximum. Under these conditions, a further increase in m could occur only if a marked increase in the number of quanta available for release takes place. This increase in available quanta should be reflected by an increase in n. Since it is known that raising [Ca2+]0 increases transmitter mobilization (Wilson, 1973), it may be by this mechanism that raising [Ca 2+ ]o increases n. Whether or not [Ca2+ ]0 affects transmitter mobilization under the conditions of low frequency nerve stimulation used for estimating binomial release parameters is not known. It is of some interest that tetraethylammonium and guanidine ions enhanced transmitter release at junctions depressed by Mg 2+ by increasing m and n and had little effect on p (Volle and Branisteanu, 1976). Like [Ca 2 + ]0 these drugs also increased the rate of transmitter mobilization. Thus, drugs known to increase transmitter mobilization produced a corresponding increase in n, whereas drugs known to decrease transmitter mobilization decreased n (Volle, 1973; Branisteanu et al., 1975). The gradual decline of transmitter release occurring during repetitive stimulation can be accounted for also by the model proposed by del Castillo and Katz (1954). It is clear that the decrease in m was due to a decrease in n, probably as a consequence of the failure of transmitter mobilization to maintain the stores of transmitter available for release. If this is so, then n reflects the stores of transmitter as proposed originally by del Castillo and Katz (1954). The increase in p occurring during repetitive stimulation may result from an accumulation of C a 2 + by the nerve terminals and, consequently, the activation of release sites (Rahamimoff, 1968). The increased value for p could result both from an increased probability for the activation of release sites and a closer proximity between the quanta available for release and the release sites. Some of .the findings described here can be explained also by the alternative model that n represents the number of release sites (vide supra) rather than the number of quanta available for release (Zucker, 1973; Rahamimoff and Meiri, 1975; Wernig, 1975). According to this model, the effect of raising [Ca2+]o results in increased transmitter release by increasing the number of active release sites. At low
107
initial [Ca 2 + ]o, the effect of raising [Ca2+ ]o on n might be obscured because of the errors inherent in the measurement made when the value for p is low (Zucker, 1973; Bennett et al., 1975). Similarly, the decrease in the value for n during prolonged repetitive stimulation may be due to a loss of activated sites resulting from depleted stores of transmitter and may be more apparent than real. Clearly, estimates of the number of sites depend upon the site being occupied by a quantum of transmitter. Therefore, in those situations where depletion of transmitter occurs but release can be described by binomial statistics, the value for n will be, in fact, an underestimate of the number of activated release sites. There is no method, at present, for discriminating between these two models of transmitter release or for obtaining rigorous evidence to support alternative models. Although n and p can be demonstrated to be independent parameters of release under some circumstances, in most instances it is not possible to alter one parameter without affecting the other. It is not surprising that a certain amount of interdependence exists between the two parameters of release. Estimates of transmitter release depends a priori upon the availability of transmitter and the activation of release sites in the membrane. In any event, the present results show that the effects of drugs or other interventions on the statistical parameters of release depend very much on initial values for p. Similar data have been obtained in sympathetic ganglia (McLachlan, 1975). When p was > 0.5, enhanced release produced by increasing rates of preganglionic stimulation was associated with increases in m and n, but not p; conversely, when p was < 0.5, the increase in release was associated with an increase in m and p, but not n. Finally, some limitations of the methods must be noted (Zucker, 1973; Bennett et al., 1975; Miyamoto, 1975; Wernig, 1975). Inasmuch as estimates of m and var m depend upon measurements of voltage fluctuations of a train of EPPs, consideration must be given to amplitude fluctuations of mepps, membrane potential, background noise, and the correction for non-linear summation (see Martin, 1966). The proper correction for non-linear summation of quanta when EPPs are large has been a particularly nettlesome problem for some (see Wernig, 1975). However, in this laboratory use of the correction factor as described by Martin (1955) has always provided estimates of n and p which satisfy prediction by the binomial law when tested by the chi-square method. Acknowledgement. We want to thank our colleague Dr. M. D. Miyamoto, University of Connecticut for many stimulating hours of discussion and help with this work.
108 REFERENCES Bennett, M. R., Florin, T. : A statistical analysis of the release of acetylcholine at newly formed synapses in striated muscle. J. Physiol. (Lond.) 238, 93-107 (1974) Bennett, M. R., Florin, T., Hall, R. : The effect of calcium ions on the binomial statistical parameters which control acetylcholine release at synapses in striated muscle. J. Physiol. (Lond.) 247, 429 - 446 ( 1975) Branisteanu, D. D., Miyamoto, M. D., Volle, R. L. : Quantal release paramters during fade of endplate potentials. Naunyn-Schmiedeberg's Arch. Pharmacol. 288, 323-327 (1975) Branisteanu, D.D., Miyamoto, M. D., Volle, R. L. : Effects of physiologic alterations on binomial transmitter release at magnesium-depressed neuromuscular junctions. J. Physiol. (Lond.) 254, 19-37 (1976) Christensen, B. N. : Morphological correlates of synaptic transmission in lamprey spinal cord. J. Neurophysiol. 39, 197-212 (1976) Couteaux, M. R., Pecot-Dechavassine, M. : Vesicules synaptiques et poches au niveau des ~(zones actives>) de la jonction neuromusculaire. C.R. Acad. Sci. (Paris) 271, 2346-2349 (1970) del Castillo, J., Katz, B.: Quantal components of the endplate potential. J. Physiol. (Londl) 124, 560-573 (1954) Dodge, F. A., Jr., Rahamimoff, R. : Co-operative action of calcium ions in transmitter release at the neuromuscular junction. J. Physiol. (Lond.) 193, 419-432 (1967) Hubbard, J. I., Kwanbunbumpen, S.: Evidence for the vesicle hypothesis. J. Physiol. (Lond.) 194, 407-420 (1968) Martin, A. R. : A further study of the statistical composition of the end-plate potential. J. Physiol. (Lond.) 130, 114-122 (1955) Martin, A. R. : Quantal nature of synaptic transmission. Physiol. Rev. 46, 51-66 (1966)
Naunyn-Schmiedeberg's Arch. Pharmacol. 295 (1976) McLachlan, E. : An analysis of the release of acetylcholine from preganglionic nerve terminals. J. Physiol. (Lond.) 245, 447- 466 (1975) Miyamoto, M. D. : Binomial analysis of quantal transmitter release at .glycerol treated frog neuromuscular junctions. J. Physiol. (Lond.) 250, 121 - 142 (1975) Rahamimoff, R. ! ~.. dual effect of calcium ions on neuromuscular facilitation. J. Physioll (Lond.)~195, 471 • 480 (1968) Rahamimoff, R., Meiri, H. : The eff'ect of calcium ions on the statistical parameters of transmitter release. Israel J. reed. Sci. 111 68 (1975) Volle, R. L. : Frequency dependent decrease of quantal content in a drug-treated neuromuscular junction. Naunyn-Schmiedeberg's Arch. Pharmacol. 278, 211 - 2 8 4 (1973) Voile, R. L., Branisteanu, D. D. : Statistical parameters of transmitter release at frog neuromuscular junctions treated with guanidine or tetraethylammonium. J. Pharmacol. exp. Ther. 197, 653-661 (1976) Wernig, A. : Changes in statistical parameters during facilitation at the crayfish neuromuscular junction. J. Physiol. (Lond.) 226, 751-759 (1972) Wernig, A. : Estimates of statistical release parameters from crayfish and frog neuromuscular junctions. J. Physiol. (Lond.) 244, 207-221 (1975) Wilson, D. F. : Effects of caffeine on neuromuscular transmission in the rat. Amer. J. Physiol. 225, 862-865 (1973) Zucker, R. S. : Changes in the statistics of transmitter release during facilitation. J. Physiol. (Lond.) 229, 787-810 (1973)
Received April 8~Accepted July 1, 1976
