J. Phy8iol. (1977), 266, pp. 435-451 With 5 text-figurew Printed in Great Britain
435
FACILITATION OF TRANSMITTER SECRETION FROM TOAD MOTOR NERVE TERMINALS DURING BRIEF TRAINS OF ACTION POTENTIALS
BY RON J. BALNAVE AND PETER W. GAGE
From the School of Physiology and Pharmacology, University of New South Wales, Kensington, N.S. W. 2033, Australia (Received 25 Augnst 1976) SUMMARY
1. End-plate potentials produced by brief trains of action potentials (5-7 at 50-100 Hz) were recorded at toad sciatic-sartorius neuromuscular junctions. When transmitter secretion was depressed in solutions containing magnesium, the increase in amplitude (growth pattern) of successive end-plate potentials was greater than could be accounted for by arithmetic summation of facilitation (arithmetic model) as proposed by Mallart & Martin (1967). 3. With e.p.p.s of normal quantal content or in solutions in which the calcium concentration was lowered, growth patterns were occasionally reasonably close to those predicted by the arithmetic model but there was always some degree of disparity. 4. A simple, two-step, kinetic model is described which is more consistent with the varied growth patterns of end-plate potentials that have been recorded. The model can predict growth patterns of e.p.p.s with high or with low quantal content. INTRODUCTION
At amphibian neuromuscular junctions in which the average number of quanta of acetylcholine secreted in response to an action potential has been depressed, a short train of impulses applied to the motor nerve elicits a train of end-plate potentials (e.p.p.s) which increase in amplitude as a result of facilitation of transmitter secretion (Feng, 1940, 1941; Eccles, Katz & Kuffler, 1,941; Braun, Schmidt & Zimmermann, 1966; Braun & Schmidt, 1966; Mallart & Martin, 1967, 1968; Maeno, 1969; Younkin & Erulkar, 1970; Magleby, 1973). The pattern of growth of e.p.p.s has been
R. J. BALNA VE AND P. W. GAGE 436 studied quantitatively by Mallart & Martin (1967) at the neuromuscular junction of the frog. They formulated a simple and attractive model which fitted the pattern of increase in transmitter secretion that they observed during a short train of impulses. Briefly, it was proposed that each action potential was followed by the same increment in 'facilitation' which decayed exponentially with time, and that facilitation observed at any time was due to linear (arithmetic) summation of decaying facilitatory effects left by preceding action potentials. This model we have called here the 'arithmetic model'. Growth patterns of trains of e.p.p.s in reasonable agreement with such a model have been observed at amphibian neuromuscular junctions (Mallart & Martin, 1967; Younkin & Erulkar, 1970; Magleby, 1973). However, in some initial experiments on facilitation at magnesium-depressed neuromuscular junctions in the toad, growth patterns were observed that could not be fitted by the arithmetic model (Balnave & Gage, 1973 a). Some growth patterns recorded from amphibian neuromuscular junctions by other workers (e.g. Barrett & Stevens, 1972) also appear to be inconsistent with the arithmetic model. Certainly growth patterns in some crustacean preparations do not fit the simple arithmetic model (Linder, 1973; Zucker, 1974b). In the experiments reported here we have examined the pattern of growth of e.p.p.s produced by short trains of impulses at curarized and Mg-depressed neuromuscular junctions in the toad, in an attempt to test the general applicability of the arithmetic model. It was found that only under conditions of high quantal content did the growth patterns tend to approach predictions from this model. A preliminary report of some of these results has been published previously (Balnave & Gage, 1973a). METHODS The preparation used was the sciatic nerve-sartorius muscle preparation from the toad, Bufo marinu8. Animals were obtained from Queensland and used in summer months from September to Marcb. The standard toad solution contained (m-mole/i.): NaCi, 115; KCl, 2-5; CaCl2, 1.8 and Na2HPO4+NaH2PO4, 3, with their ratio adjusted to give a pH of 7 1-7-2. To obtain lower e.p.p. quantal contents, MgC12 was added to this solution in varying concentrations (5-30 mM) (del Castillo & Katz, 1954; Jenkinson, 1957) and the concentration of NaCl was then adjusted to maintain constant osmotic pressure. However, with concentrations of MgCl above 8 mm the NaCl concentration was kept at 90 ImM so that the solutions were somewhat hypertonic. In all experiments except where specifically stated otherwise, Ca concentration was kept at 1-8 mM. When quantal content was relatively high, D-tubocurarine (Curare, Drug Houses of Australia) was used at concentrations from 1-4 to 7' ums to prevent twitching and to reduce errors introduced by non-linear summation of e.p.p.s (Martin, 1955). Temperature was maintained at 20 ± 0.50 C.
HIGH-FREQUENCY FACILITATION
437
The sartorius muscle was pinned out on Sylgard (Dow Corning) set into the bottom of a Perspex bath and the nerve was stimulated with short trains of supramaximal, brief (< 0 5 msec) pulses. Intervals and repetition rates were set with a Digitimer (Devices). The frequency of stimulation within a train was normally 100 Hz and the interval between trains was normally kept longer than 20 sec to allow recovery. No trains longer than 70 msec were used (normally no longer than 50 msec) so that the later phase of facilitation (Mallart & Martin, 1967) was avoided. E.p.p.s and spontaneous miniature e.p.p.s (m.e.p.p.s) were recorded intracellularly using conventional micro-electrode recording techniques. Because of the statistical fluctuations in e.p.p. amplitudes in successive trains, the responses obtained from a number of trains (10-300) were averaged using a minicomputer on-line (Lab 8 system, Digital Equipment Corporation). An average wave form with 95 % confidence limits was displayed on an oscilloscope in some experiments and photographed. Experiments in which regression of mean e.p.p. amplitude occurred in the course of an experiment were discarded. The amplitudes of e.p.p.s after the first were measured from their peaks to the extrapolated tails of preceding e.p.p.s. When average e.p.p. amplitude was greater than 5 mV (only obtained in solutions containing no Mg) a correction was made for non-linear summation (Martin, 1955). Quantal contents were determined by one of several methods listed in order of preference; from the ratio of mean e.p.p. amplitude to mean m.e.p.p. amplitude, from the percentage of 'failures' of e.p.p.s, and from the coefficient of variation of e.p.p. amplitudes (see Martin, 1966). The Advanced Averager program for the Lab 8 system computes the average wave form and the 95 % confidence limits (2 s.E. of mean) from which the quantal contents were calculated assuming Poisson statistics. For technical reasons, this program was not always used so that quantal contents could not always be calculated. Use of Poisson statistics may give an over-estimate at higher quantal contents (Christensen & Martin, 1970; Bennett & Florin, 1974; Wernig, 1975; Miyamoto, 1975; Branisteanu, Miyamoto & Volle, 1976) but the method was considered adequate to indicate approximate quantal contents. As the size of m.e.p.p.s and presumably the amplitude of a quantal response were not significantly different before, during and after the trains, the growth pattern of e.p.p.s was taken as a good representation of the growth pattern of quantal contents and hence of transmitter secretion. RESULTS
Growth patterns of e.p.p.s with low quantal contents At neuromuscular junctions bathed in a solution containing 30 mMMg9l2 which was added to depress transmitter secretion, a short train of stimuli applied to the motor nerve at 100 Hz elicited a train of e.p.p.s of progressively increasing amplitude. The pattern of increase in the amplitude of seven successive e.p.p.s recorded in one experiment can be seen in Fig. 1 A (average of 200 trains). It is clear that the increment in amplitude of successive e.p.p.s became greater during the train. A plot of e.p.p. amplitude (V, triangles) against position in the train (n) is shown in Fig. 1 B (e.p.p.s measured from the average trace shown in A). The amplitudes of successive e.p.p.s appeared to increase exponentially rather than arithmetically. This type of growth pattern was found in ten experiments with solutions containing 30 mM-MgCl2.
R. J. BALNA VE AND P. W. GAGE
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Fig. 1. A, growth pattern of e.p.p.s in a solution containing 30 mM-MgCl2. The middle trace shows the average of 200 trains of end-plate potentials elicited at 100 Hz every 20 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 0-25 mV; horizontal, 4 msec (200 C). B, amplitudes (V, mV) of averaged e.p.p.s shown in A (triangles) plotted according to position in the train (n), i.e. at 10 msec intervals. The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
HIGH-FREQUENCY FACILITATION
439 In solutions containing 30 mM-MgCl2, the quantal content of the first e.p.p. was generally less than 1. In the experiment illustrated in Fig. 1 the quantal content of the first e.p.p. (measured from failures) was 0-58. Possible complications in these experiments were that the sodium concentration was lowered to 90 mm and that the addition of 30 mM-MgCl2 increased the ionic strength and osmotic pressure of the solution. However, in two experiments, 1-8 mM-MnC12 was added to the standard solution instead of MgCl2 to reduce the average quantal content of e.p.p.s (Meiri & Rahamimoff, 1972; Balnave & Gage, 1973b). The growth patterns obtained in these two experiments (quantal contents 3-5 and 2.8) were very similar to those recorded in solutions containing 30 mM-MgCl2. This suggested that the changes in ionic strength and osmotic pressure in the high Mg solutions, and the lowering of Na concentration, had not affected growth patterns.
The growth patterns are inconsistent with the arithmetic model The arithmetic model described by Mallart & Martin (1967) is based on the assumptions that the new facilitatory effect produced by any action potential is independent of previous history and adds linearly to any residual facilitatory effects remaining from preceding action potentials. Facilitation produced by a second action potential t msec after a preceding action potential is defined by F(t) =
(V2-V1)fV1,
(1)
where V1 and V2 are the amplitudes of the first and second e.p.p.s produced by the two action potentials. Facilitation decays exponentially (Mallart & Martin, 1967; Balnave & Gage, 1974) so that after t msec F(t) - F(0) et/lT,
(2)
where r (msec) is the time constant of decay of facilitation. If successive action potentials (interval t msec) in a train each produce an equal increment (F(0)) of facilitation, and if the decay of each increment of facilitation is exponential with time constant r, then the amplitude of the nth e.p.p. (Vn) will be given by tfr En = Vn_1 + V1. F(0) e (3) Using V1 and V2 recorded in the experiment illustrated in Fig. 1 and a value of 40 msec for r (average value at 20° C; Balnave & Gage, 1974) e.p.p. amplitudes for subsequent e.p.p.s were calculated according to eqn. (3). The predicted growth curve is shown as a continuous line in Fig. 1B for comparison. It can be seen that the observed growth pattern is not as predicted from eqn. (3)
R. J. BALNA VE AND P. W. GAGE 440 It was thought that these growth patterns, which are very different from those reported by Mallart & Martin (1967), might be a characteristic of e.p.p.s with low quantal content. However, e.p.p. growth patterns obtained at higher quantal contents again could not be fitted by eqn. (3).
Growth patterns of e.p.p.s with higher quantal contents Less depression of transmitter secretion was obtained in another series of experiments by using 5-10 mm rather than 30 mM-MgCl2. Curare (14-2-1 /SM) was added to these solutions to reduce e.p.p. amplitude. When neuromuscular junctionswere exposedto these solutionsthe average quantal content of 'first' e.p.p.s (calculated from failures and variance) ranged from 2 to 14. It was found that growth patterns were still inconsistent with the arithmetic model. The average of twenty trains of 5 e.p.p.s at 100 Hz recorded in one of these experiments is shown in Fig. 2A and the amplitudes of e.p.p.s are plotted against position in the train (n) in Fig. 2B (triangles). In the experiment illustrated the solution contained 5 mM-MgCl2 and 2*1 /M curare. The first four e.p.p.s show a steep increase in amplitude as seen with lower quantal contents but the fifth e.p.p. in the train shows signs of 'roll-off' in amplitude. This was only slight but was found in all nine junctions tested in these low Mg solutions. The growth of e.p.p.s predicted from eqn. (3) is shown by the continuous line in Fig. 2B. The experimental observations are clearly inconsistent with the arithmetic model.
Growth patterns of e.p.p.s with 'normal' quantal contents Growth patterns of e.p.p.s produced by brief trains of stimuli were studied further at junctions bathed in standard solution to which 147 EM curare had been added to reduce the amplitude of the post-synaptic response. The growth patterns in a few of these experiments approached growth patterns predicted from eqn. (3), especially when quantal contents were relatively high. A series of six e.p.p.s recorded in one experiment in which the quantal content of the first e.p.p. was eighteen is shown in Fig. 3A. After the first three e.p.p.s there was clearly a decline in the successive increments in e.p.p. amplitude. The growth patterns of e.p.p. amplitudes in experiments in which the average quantal contents of the first e.p.p.s were estimated as 30 (squares) and 150 (triangles) are shown in Fig. 3B. These two experiments were chosen for illustration because the first and second e.p.p.s had similar mean amplitudes but the quantal contents of the first e.p.p.s were very different. The increase in e.p.p. amplitude predicted from eqn. (3) (using the amplitude of the first two e.p.p.s) is shown as a continuous line in Fig. 3B for comparison. It was apparent that the agreement of e.p.p. growth curves with the arithmetic model was much better at high than at low quantal contents. Similar growth patterns were
441 HIGH-FREQUENCY FACILITATION recorded in seven experiments in which quantal contents were not adjusted but e.p.p. amplitude was reduced with curare. For some reason, the quantal content of 'normal' e.p.p.s was often as low as ten to fifty (Balnave & Gage, 1974). This appeared to be especially so from October to January but there was not a sufficient number of observations to be sure
of this. A
A
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12 1*0
08
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04 _02 _ o
L1
3
4
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Fig. 2. A, growth pattern of e.p.p.s in a solution containing 5 mM-MgCl2 and 2-1 FM curare. The middle trace shows the average of 200 trains of e.p.p.s elicited at 100 Hz every 8 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 0-25 mV; horizontal, 2 msec (19-50 C). B, amplitudes (V, mV) of averaged e.p.p.s shown in A, plotted according to position in the train (n), i.e. at 10 msec intervals. The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
R. J. BALNA VE AND P. W. GAGE
442
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Fig. 3. A, growth pattern of e.p.p.s in normal solution (no MgCl2) containing 5X3 pM curare. The middle trace shows the average of 20 trains of e.p.p.s elicited at 100 Hz every 20 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 1 mV; horizontal, 3 msec (20.50 C). B, the average amplitude of end-plate potentials, recorded in standard solution containing curare, plotted according to position in the train (n). The average quantal contents of first e.p.p.s were 30 (squares) and 150 (triangles). The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
443 HIGH-FREQUENCY FACILITATION The average growth patterns of e.p.p.s in the three solutions containing 30 mM-MgCl2 (circles), 5-10 mM-MgCl2 (triangles) and no MgCl2 (squares) are shown in Fig. 4 together with standard errors of the means (vertical lines) where they extend beyond the symbols. A growth curve predicted from eqn. (3) is shown as a continuous line. All three average growth curves clearly deviate from the growth curve predicted from the arithmetic model. 15
n 100 E
c4 0
5
1
3
2
4
5
n
Fig. 4. The average growth patterns of the first five e.p.p.s (normalized with respect to the first) elicited by repetitive stimulation at 100 Hz in solutions containing 30 m.m (circles), 5-10 mm (triangles) and no (squares) MgCl2. The vertical bars denote ± 1 s.E. of mean where they are longer than the symbols. The continuous line shows the growth pattern of e.p.p.s predicted from the amplitude of the first two e.p.p.s according to the arithmetic model.
A kinetic model Although Mallart & Martin (1967) presented a mathematical description of growth patterns based on a simple physical model, the description would apply equally well to a single-step rate process such as A
k.,
B.
k-,
where k, is very small except during an action potential (A remains essentially constant), k-1 is a rate constant controlling the rate of decay of facilitation and transmitter secretion is proportional to the concentration of B. However, as shown above, our results are inconsistent with such a model.
444 R. J. BALNA VE AND P. W. GAGE It was suggested to us by Professor R. Golding (Department of Physical Chemistry, University of N.S.W.) that a two-step reaction might give good fits to the S-shaped growth curves we had observed. The two-step reaction that we have considered can be written k,
ks
k-1
k_,
A -,Bt---C~ ,
and it is proposed that transmitter secretion (in) is proportional to the concentration of C. Such a model can indeed generate patterns of C similar to the growth patterns of e.p.p.s that we have observed. The way in which the model was used and mathematical expressions for A, B and C are described in an Appendix. Essentially the reaction above was driven from A to C for 1 msec to simulate the effect of an action potential and to build up C. This was done by giving k1 and k2 selected values and setting k-1 and k-2 to zero. Then the reaction was driven from C to A for 9 msec so that C decayed. This was done by setting k1 and k2 to zero and giving k-1 and k2 values which produced a decay of C at a rate appropriate for the decay of facilitation. Rate constants were set to zero where specified only to simplify the equations. This scheme was used in an attempt to mimic the 'pulsed' secretion of transmitter during stimulation at 100 Hz. In comparing results from analysis of the kinetic model with experimentally obtained growth patterns of e.p.p.s, it was assumed that the amplitude of e.p.p.s (V) was linearly related to the number of quanta secreted which in turn was linearly related to the concentration of C. That is, V = bC, where b is a proportionality constant. With an appropriate choice of rate constants and initial steadystate values for C, it was found that the growth curves of e.p.p.s recorded under a variety of conditions could be fitted reasonably well. To allow comparison of growth patterns generated under different conditions, values for C were normalized with respect to C, and, because of the assumed linear relationship between C and V, this gave predicted normalized values for V also. Two sets of variables which gave good fits to two different types of recorded growth patterns are given in Table 1. In both, the initial value of A was set at 10-3 mole (the actual value made no difference to normalized growth patterns if the ratio AOCO was kept constant). The maximum value of C1 was much higher with the lower set of values than with the upper. Therefore the upper and lower sets of variables may be related to conditions of low and high quantal content respectively. The average growth pattern of normalized e.p.p.s recorded under conditions of low quantal content (ml1 < 1) is shown in parentheses for comparison, as is the growth pattern showing least growth in e.p.p. amplitude recorded in a
HIGH-FREQUENCY FACILITATION
445
TABLE 1. Normalized e.p.p. amplitudes ( V) calculated from the kinetic model assuming that V is directly proportional to the peak value of C during phase 1 (see Appendix). The rate constants (k, sec-1) and initial values of C (mole) were chosen to obtain good fits to experimental results (initial values of A and B were 10-3 and 0 respectively). T (msec) was calculated by varying the interval between the first two pulses (see Appendix). The average growth pattern obtained with low quantal contents (mil < 1) and a growth pattern obtained with a high quantal content (ml = 150) are shown in parentheses for comparison. Below is shown a pattern of e.p.p.s which would be predicted by the arithmetic model from V1 = 1 and V2 = 2-53
ini1
k2 kL
k1 1
103
2
2
k-2
V1
Co
23 5 5 x 10-10
15
5 x 10-8
38
15
(1(1
150
(11 Arithmetic model
1
2*56
V3 4*79
2*3 2*53 2-3 2*53
V2
Vs 10*31
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Fig. 5. Predicted growth patterns of e.p.p.s according to the kinetic model under conditions of low quantal content (circles) and high quantal content (triangles). Parameters were chosen as indicated in Table 1. Compare with experimental results shown in Fig. 4. The growth pattern predicted from the first two e.p.p.s according to the arithmetic model is shown as a continuous line.
preparation with high quantal content (ml = 150). The values obtained for V from the kinetic model in Table 1 are shown graphically in Fig. 5 to illustrate the similarity to recorded e.p.p. patterns and the reasonably good correspondence that could be obtained between the kinetic (triangles) and arithmetic (continuous line) models with suitable choice of variables.
R. J. BALNA VE AND P. W. GAGE When the interval between VJ and V2 was increased in these two examples, F(t) was found to decay essentially exponentially (Mallart & Martin, 1967; Balnave & Gage, 1974) for t < 50 msec, with the single time constant r given in Table 1, so satisfying an important criterion for facilitation. Thus this simple kinetic model can successfully mimic the growth patterns we have recorded, including some which appeared consistent with the arithmetic model. It therefore appears a more general model with greater 'truth content' than the arithmetic model. It also satisfies the criterion of giving an exponential decay of facilitation with appropriate time constant. No attempt has been made here to introduce steps to account for other known characteristics of transmitter secretion: a more complicated model which is based an the scheme outlined above will be described elsewhere. 446
PISCUSSION It is clear that some growth patterns of e.p.p.s recorded at the toad neuromuscular junction are inconsistent with the arithmetic model of cumulative facilitation originally proposed by Mallart & Martin (1967). Other investigators have also found that growth patterns of excitatory junctional potentials recorded at crustacean neuromuscular junctions cannot be described by the simple arithmetic model either (Linder, 1973; Zucker, 1974a, b) but it could be suggested that this is due to the difference in experimental animals. However, growth patterns in the toad at low quantal contents are strikingly similar to those recorded by Zucker (1974 b) in the crayfish, whereas at higher quantal contents they can approach growth patterns recorded in the frog (Mallart & Martin, 1967; Magleby, 1973). It seems reasonable to assume that the two types of growth pattern are expressions of the same basic mechanism. We have described a simple kinetic model which will predict both the steep S-shaped growth patterns and the apparently arithmetic growth patterns, with suitable choice of rate constants and steady state concentrations. The model is almost cetainly an oversimplified representation oftrue events and does not pretend to account for many other aspects of transmitter secretion. However, it may serve as a simple kinetic description of facilitation at a variety of synapses and is proving useful as a basis for a more complex model of transmitter secretion which will appear elsewhere. In spite of these reservations, it is tempting to speculate about the possible nature of A, B and C in the simple kinetic model presented here. The large increase in transmitter secretion following an action potential is thought to be caused by a transient influx of Ca ions (for a review of evidence, see Katz, 1969). The reaction A k- B could well represent an
447 HIGH-FREQUENCY FACILITATION influx of Ca. For example, under the influence of the change in membrane field k1 could transiently assume a relatively large value. The one millisecond used to obtain the growth curves (Table 4, Fig. 9) would not be
unreasonable duration for this event. The reaction B k, C could represent the conversion of Ca from form B to an activated form C (presumably a Ca complex) which is a necessary co-factor for transmitter secretion. The rate of this reaction was also assumed to be affected by membrane field. The decay of C would be responsible for the decay of facilitation (Balnave & Gage, 1974). There is little information about the reactions C a B A which determine the decay of facilitation. It seems very unlikely that the decay of C represents simple diffusional loss of free Ca ions (or other activator) as the decay of facilitation is very temperature sensitive (Eccles et al. 1941) having an activation energy of about 100 kJ . mol-1 (Balnave & Gage, 1970, 1974), which is too high to be accounted for by a simple diffusional process. It has been suggested that the decay of facilitation may be due to dissociation of Ca from an active site because the rate is much slower when Sr substitutes for Ca as an activator of acetylcholine secretion (Balnave & Gage, 1974). We obtained a good fit to e.p.p. growth patterns with the kinetic model when C had an initial value of 5-5 x 10-10 mole in high Mg solutions and 5 x 10-8 mole in normal solution (Table 1, Fig. 5). This would suggest that magnesium reduces the resting concentration of C perhaps by competing with Ca for an active site. It was also necessary to raise k, (Table 1) to obtain the growth patterns recorded in solutions in which Ca influx during an action potential was presumably normal and certainly higher than in the raised-magnesium solutions (Katz & Miledi, 1969; Blaustein, 1971). If the rate constant k, represents the rate of Ca influx, it should indeed be higher when the quantal content is higher, if the Ca hypothesis (Katz, 1969) is correct. Several other factors such as a change in the amplitude of action potentials or a 'power' relationship between some linearly increasing intracellular activator concentration and acetylcholine secretion could conceivably have given the recorded growth patterns. It seems improbable that an increase in the amplitude of action potentials could have contributed to the steep growth patterns. In ten experiments there was either a small decrease or no change in the amplitude of extracellularly recorded action potentials in motor nerve terminals during repetitive stimulation, never an increase. In other preparations in which the possibility has been carefully investigated, facilitation is unaccompanied by an increase in action potential amplitude (Hubbard & Schmidt, 1963; Katz & Miledi, 1965; Martin & an
k-+
448 R. J. BALNA VE AND P. W. GAGE Pilar, 1964; Braun & Schmidt, 1966; Linder, 1973; Zucker, 1974 a). It would probably be possible to fit the steeper growth patterns of e.p.p.s by assuming that there is a linear increase in an activator during repetitive stimulation and that transmitter secretion is proportional to some power of the activator concentration. Unless the power were unity, the model would need to be modified again to give the exponential decay of facilitation with a single time constant which has been unequivocally found (Mallart & Martin, 1967; Balnave and Gage, 1974). Such complicated models would lose the attractiveness of the original arithmetic model and would be more complex than the simple kinetic model outlined here. It is interesting that Magleby (1973) recorded e.p.p.s greater than predicted from the arithmetic model when 'high' stimulation rates (31.2 and 50 sec-1) were used in frogs. The stimulation frequency used in the present experiments (100 sec1) may have served to accentuate the inconsistency and make it apparent earlier during a pulse train. It is also possible that the growth patterns that we have observed are more prominent in toads which often have e.p.p.s with low quantal contents in normal solution, perhaps more so in summer months. However, it is difficult to imagine that the basic mechanisms of transmitter secretion should differ greatly between frogs and toads, or with season. In order to account for divergence from the arithmetic model Magleby (1973) separated facilitation into two components with different characteristics. The alternative explanation we present here has the advantage of greater simplicity and wider applicability. In the light of these observations, there seems little value in trying to modify the arithmetic model in an ad hoc fashion to fit the wide range of growth curves which has been recorded. The kinetic model is more consistent with the experimental results and may be found to fit growth patterns in a wide variety of synapses. Facilitation is obviously a mechanism of some importance in the central nervous system where it seems to have many of the characteristics (cf. Porter, 1970) of facilitation at neuromuscular junctions (Mallart & Martin, 1967, 1968; Balnave & Gage, 1974). Patterns of increase in the amplitude of excitatory post-synaptic potentials have appeared to be similar at both sites and it has been suggested, after Mallart & Martin (1967), that facilitation in the central nervous system is due to arithmetic summation of a calcium complex which decays slowly and exponentially. While the arithmetic model may provide an adequate mathematical description of many patterns which have been observed, it clearly becomes very inappropriate under certain conditions at neuromuscular junctions and it may also be found to be inappropriate at some central synapses. If the kinetic model survives the gauntlet of new experimental data, it
449 HIGH-FREQUENCY FACILITATION may eventually be possible to identify A, B and C and to interpret the increase in transmitter secretion produced by bursts of action potentials in terms of underlying molecular events. APPENDIX
The kinetic scheme analysed was kl
k2
k-,
k_,
A It rB
Ca
The reaction was considered to go from A to C during an action potential (phase 1) and from C to A following an action potential (phase 2).
Phase 1 The rate constants k1 and k2 were given values to simulate activation of the secretion mechanism for 1O-3 sec. During this time, k1c and k12 were considered to be negligible and were set at zero for convenience. With these conditions, A, B and C are given by A =AO exp (-klt), B = Bo exp ( - k2t) + k 1
C=
Ao (exp (-Ikct)-exp (-k2t)),
AO+Bo+CO-A-B,
where AO) Bo and C0 are the initial values of A, B and C at the beginning of this phase.
Phase 2 Then for the next 9 x 1O-3 sec, AO, Bo and C0 were initially set equal to the final values of A, B and C during the preceding phase 1, k, and k2 were set at zero while k-, and k12 were given real values. With these conditions, C = Coexp(-k12t), B
=
Bo exp (- k-1t) + k
k-1= Ao+Bo+Co-B-C.
-2
Co (exp (-k-20- exp, (-k1t)),
A Phase 1 was repeated five times, followed by phase 2 each time except the last. C1, C2, C3, C4 and C5 were the maximum values of C during successive phase is. To examine the influence of duration of phase 2 on C2, the duration of phase 2 was increased to 19 x 103 sec, 29 x 1O-3 sec and 39 x 10-3 sec. The increase in C produced by the second phase 1 (C2 - C1), was found
450 R. J. BALNA VE AND P. W. GAGE to decrease exponentially as the duration of phase 2 increased. The relationship could be reasonably fitted by
C2 - C1 = Q exp (- d/T), where Q was a constant, d the duration of phase 1 plus phase 2, and r was the time constant of decay of C2 Cl. -
We are grateful for the assistance of C. Prescott, E. Bowler, R. Malbon and J. Oliver. The minicomputer was [provided by the National Health and Medical Research Council of Australia. REFERENCES
BALNAVE, R. J. & GAGE, P. W. (1970). Temperature sensitivity of the time course of facilitation of transmitter release. Brain Ree. 21, 297-300. BALNAVE, R. J. & GAGE, P. W. (1973 a). Early facilitation at the toad neuromuscular junction. Proc. Au8t. Phyaiol. Pharmac. Soc. 4, 192-193. BALNAVE, R. J. & GAGE, P. W. (1973b). The inhibitory effect of manganese at the neuromuscular junction of the toad. Br. J. Pharmac. 47, 339-352. BALNAVE, R. J. & GAGE, P. W. (1974). On facilitation of transmitter release at the toad neuromuscular junction. J. Phyaiol. 239,657-675. BARRETT, E. F. & STEVENS, C. F. (1972). The kinetics of transmitter release at the frog neuromuscular junction. J. Physiol. 227, 691-708. BENNETT, M. R. & FLORIN, T. (1974). A statistical analysis of the release of acetylcholine at newly formed synapses in striated muscle. J. Phyaiol. 238, 93-107. BLAUSTEIN, M. P. (1971). Preganglionic stimulation increases calcium uptake by sympathetic ganglia. Science, N.Y. 172, 391-393. BRANISTEANU, D. D., MIYAMOTO, M. D. & VOLLE, R. L. (1976). Effects of physiologic alterations on binomial transmitter release at magnesium-depressed neuromuscular junctions. J. Phyaiol. 254, 19-37. BRAUN, M. & SCHMIDT, R. F. (1966). Potential changes recorded from the frog motor nerve terminal during its activation. Pfluiger8 Arch. ge8. Physiol. 287, 56-80. BRAUN, M., SCHMIDT, R. F. & ZIMMERMANN, M. (1966). Facilitation at the frog neuromuscular junction during and after repetitive stimulation. Pfluger8 Arch. ges. Physiol. 287, 41-55. CHRISTENSEN, B. H. & MARTIN, A. R. (1970). Estimates of probability of transmitter release at the mammalian neuromuscular junction. J. Physiol. 210, 933-945. DEL CASTILLO, J. & KATZ, B. (1954). Quantal components of the end-plate potential. J. Physiol. 124, 560-573. ECCLES, J. C., KATZ, B. & KUFFLER, S. W. (1941). Nature of the endplate 'potential' in curarized muscle. J. Neurophysiol. 4, 362-387. FENG, T. P. (1940). Studies on the neuromuscular junction. XVIII. The local potentials around N-M junctions induced by single and multiple volleys. Chin. J. Physiol. 15, 367-404. FENG, T. P. (1941). Studies on the neuromuscular junction. XXVI. The changes of the end-plate potential during and after prolonged stimulation. Chin. J. Physiol. 16, 341-372. HUBBARD, J. I. & SCHMIDT, R. F. (1963). An electrophysiological investigation of mammalian motor nerve terminals. J. Physiol. 166, 145-165. JENKINSON, D. H. (1957). The nature of the antagonism between calcium and magnesium ions at the neuromuscular junction. J. Physiol. 138, 434-444.
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KATZ, B. (1969). The Relea8e of Neural Transmitter Sub8tances. Liverpool: Liverpool University Press. KATZ, B. & MILEDI, R. (1965). The effect of calcium on acetylcholine release from motor nerve terminals. Proc. R. Soc. B 161, 496-503. KATZ, B. & MILEDI, R. (1969). Tetrodotoxin-resistant electric activity in presynaptic terminals. J. Physiol. 203, 459-487. LrNDER, T. M. (1973). Calcium and facilitation at two classes of crustacean neuromuscular synapses. J. gen. Phyoiol. 61, 56-73. MAENO, T. (1969). Analysis of mobilization and demobilization processes in neuromuscular transmission in the frog. J. Neurophysiol. 32, 793-800. MAGLEBY, K. L. (1973). The effect of repetitive stimulation on facilitation of transmitter release at the frog neuromuscular junction. J. Physiol. 234, 327-352. MIALLSART, A. &; MARTIN, A. R. (1967). An analysis of facilitation of transmitter release at the neuromuscular junction of the frog. J. Phy8iol. 193, 679-694. MALLART, A. & MARTIN, A. R. (1968). The relation between quantum content and facilitation at the neuromuscular junction of the frog. J. Phy8iol. 196, 593-604. MARTIN, A. R. (1955). A further study of the statistical composition of the end-plate potential. J. Physiol. 130, 114-122. MARTIN, A. R. (1966). Quantal nature of synaptic transmission. Phy8iol Rev. 46, 5166. MARTIN, A .R. & PnIAR, G. (1964). Presynaptic and postsynaptic events during P.T.P. and facilitation in the avian ciliary ganglion. J. Physiol. 175, 1-17. MEtal, U. & RAHAMIMOFF, R. (1972). Neuromuscular transmission: inhibition by manganese ions. Science, N. Y. 176, 308-309. MILEDI, R. & SLATER, C. R. (1966). The action of calcium on neuronal synapses in the squid. J. Physiol. 184, 473-498. MIYAMOTO, M. D. (1975). Binomial analysis of quantal transmitter release at glycerol treated frog neuromuscular junctions. J. Phygiol. 250, 121-142. PORTER, R. (1970). Early facilitation at corticomoto-neuronal synapses. J. Phy.iol. 207, 733-745. WERNIG, A. (1975). Estimates of statistical release parameters from crayfish and frog neuromuscular junctions. J. Phyaiol. 244, 207-221. YOuNKIN, S. G. & ERULKAR, S. D. (1970). A quantitative study of primary potentiation of the frog neuromuscular junction. Phypiologidt, Wa8h. 13, 353. ZUCKER, R. S. (1974a). Crayfish neuromuscular facilitation activated by constant presynaptic action potentials and depolarizing pulses. J. Phy8iol. 241, 69-89. ZUCKER, R. S. (1974b). Characteristics of crayfish neuromuscular facilitation and their calcium dependence. J. Physiol. 241, 91-110.
435
FACILITATION OF TRANSMITTER SECRETION FROM TOAD MOTOR NERVE TERMINALS DURING BRIEF TRAINS OF ACTION POTENTIALS
BY RON J. BALNAVE AND PETER W. GAGE
From the School of Physiology and Pharmacology, University of New South Wales, Kensington, N.S. W. 2033, Australia (Received 25 Augnst 1976) SUMMARY
1. End-plate potentials produced by brief trains of action potentials (5-7 at 50-100 Hz) were recorded at toad sciatic-sartorius neuromuscular junctions. When transmitter secretion was depressed in solutions containing magnesium, the increase in amplitude (growth pattern) of successive end-plate potentials was greater than could be accounted for by arithmetic summation of facilitation (arithmetic model) as proposed by Mallart & Martin (1967). 3. With e.p.p.s of normal quantal content or in solutions in which the calcium concentration was lowered, growth patterns were occasionally reasonably close to those predicted by the arithmetic model but there was always some degree of disparity. 4. A simple, two-step, kinetic model is described which is more consistent with the varied growth patterns of end-plate potentials that have been recorded. The model can predict growth patterns of e.p.p.s with high or with low quantal content. INTRODUCTION
At amphibian neuromuscular junctions in which the average number of quanta of acetylcholine secreted in response to an action potential has been depressed, a short train of impulses applied to the motor nerve elicits a train of end-plate potentials (e.p.p.s) which increase in amplitude as a result of facilitation of transmitter secretion (Feng, 1940, 1941; Eccles, Katz & Kuffler, 1,941; Braun, Schmidt & Zimmermann, 1966; Braun & Schmidt, 1966; Mallart & Martin, 1967, 1968; Maeno, 1969; Younkin & Erulkar, 1970; Magleby, 1973). The pattern of growth of e.p.p.s has been
R. J. BALNA VE AND P. W. GAGE 436 studied quantitatively by Mallart & Martin (1967) at the neuromuscular junction of the frog. They formulated a simple and attractive model which fitted the pattern of increase in transmitter secretion that they observed during a short train of impulses. Briefly, it was proposed that each action potential was followed by the same increment in 'facilitation' which decayed exponentially with time, and that facilitation observed at any time was due to linear (arithmetic) summation of decaying facilitatory effects left by preceding action potentials. This model we have called here the 'arithmetic model'. Growth patterns of trains of e.p.p.s in reasonable agreement with such a model have been observed at amphibian neuromuscular junctions (Mallart & Martin, 1967; Younkin & Erulkar, 1970; Magleby, 1973). However, in some initial experiments on facilitation at magnesium-depressed neuromuscular junctions in the toad, growth patterns were observed that could not be fitted by the arithmetic model (Balnave & Gage, 1973 a). Some growth patterns recorded from amphibian neuromuscular junctions by other workers (e.g. Barrett & Stevens, 1972) also appear to be inconsistent with the arithmetic model. Certainly growth patterns in some crustacean preparations do not fit the simple arithmetic model (Linder, 1973; Zucker, 1974b). In the experiments reported here we have examined the pattern of growth of e.p.p.s produced by short trains of impulses at curarized and Mg-depressed neuromuscular junctions in the toad, in an attempt to test the general applicability of the arithmetic model. It was found that only under conditions of high quantal content did the growth patterns tend to approach predictions from this model. A preliminary report of some of these results has been published previously (Balnave & Gage, 1973a). METHODS The preparation used was the sciatic nerve-sartorius muscle preparation from the toad, Bufo marinu8. Animals were obtained from Queensland and used in summer months from September to Marcb. The standard toad solution contained (m-mole/i.): NaCi, 115; KCl, 2-5; CaCl2, 1.8 and Na2HPO4+NaH2PO4, 3, with their ratio adjusted to give a pH of 7 1-7-2. To obtain lower e.p.p. quantal contents, MgC12 was added to this solution in varying concentrations (5-30 mM) (del Castillo & Katz, 1954; Jenkinson, 1957) and the concentration of NaCl was then adjusted to maintain constant osmotic pressure. However, with concentrations of MgCl above 8 mm the NaCl concentration was kept at 90 ImM so that the solutions were somewhat hypertonic. In all experiments except where specifically stated otherwise, Ca concentration was kept at 1-8 mM. When quantal content was relatively high, D-tubocurarine (Curare, Drug Houses of Australia) was used at concentrations from 1-4 to 7' ums to prevent twitching and to reduce errors introduced by non-linear summation of e.p.p.s (Martin, 1955). Temperature was maintained at 20 ± 0.50 C.
HIGH-FREQUENCY FACILITATION
437
The sartorius muscle was pinned out on Sylgard (Dow Corning) set into the bottom of a Perspex bath and the nerve was stimulated with short trains of supramaximal, brief (< 0 5 msec) pulses. Intervals and repetition rates were set with a Digitimer (Devices). The frequency of stimulation within a train was normally 100 Hz and the interval between trains was normally kept longer than 20 sec to allow recovery. No trains longer than 70 msec were used (normally no longer than 50 msec) so that the later phase of facilitation (Mallart & Martin, 1967) was avoided. E.p.p.s and spontaneous miniature e.p.p.s (m.e.p.p.s) were recorded intracellularly using conventional micro-electrode recording techniques. Because of the statistical fluctuations in e.p.p. amplitudes in successive trains, the responses obtained from a number of trains (10-300) were averaged using a minicomputer on-line (Lab 8 system, Digital Equipment Corporation). An average wave form with 95 % confidence limits was displayed on an oscilloscope in some experiments and photographed. Experiments in which regression of mean e.p.p. amplitude occurred in the course of an experiment were discarded. The amplitudes of e.p.p.s after the first were measured from their peaks to the extrapolated tails of preceding e.p.p.s. When average e.p.p. amplitude was greater than 5 mV (only obtained in solutions containing no Mg) a correction was made for non-linear summation (Martin, 1955). Quantal contents were determined by one of several methods listed in order of preference; from the ratio of mean e.p.p. amplitude to mean m.e.p.p. amplitude, from the percentage of 'failures' of e.p.p.s, and from the coefficient of variation of e.p.p. amplitudes (see Martin, 1966). The Advanced Averager program for the Lab 8 system computes the average wave form and the 95 % confidence limits (2 s.E. of mean) from which the quantal contents were calculated assuming Poisson statistics. For technical reasons, this program was not always used so that quantal contents could not always be calculated. Use of Poisson statistics may give an over-estimate at higher quantal contents (Christensen & Martin, 1970; Bennett & Florin, 1974; Wernig, 1975; Miyamoto, 1975; Branisteanu, Miyamoto & Volle, 1976) but the method was considered adequate to indicate approximate quantal contents. As the size of m.e.p.p.s and presumably the amplitude of a quantal response were not significantly different before, during and after the trains, the growth pattern of e.p.p.s was taken as a good representation of the growth pattern of quantal contents and hence of transmitter secretion. RESULTS
Growth patterns of e.p.p.s with low quantal contents At neuromuscular junctions bathed in a solution containing 30 mMMg9l2 which was added to depress transmitter secretion, a short train of stimuli applied to the motor nerve at 100 Hz elicited a train of e.p.p.s of progressively increasing amplitude. The pattern of increase in the amplitude of seven successive e.p.p.s recorded in one experiment can be seen in Fig. 1 A (average of 200 trains). It is clear that the increment in amplitude of successive e.p.p.s became greater during the train. A plot of e.p.p. amplitude (V, triangles) against position in the train (n) is shown in Fig. 1 B (e.p.p.s measured from the average trace shown in A). The amplitudes of successive e.p.p.s appeared to increase exponentially rather than arithmetically. This type of growth pattern was found in ten experiments with solutions containing 30 mM-MgCl2.
R. J. BALNA VE AND P. W. GAGE
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Fig. 1. A, growth pattern of e.p.p.s in a solution containing 30 mM-MgCl2. The middle trace shows the average of 200 trains of end-plate potentials elicited at 100 Hz every 20 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 0-25 mV; horizontal, 4 msec (200 C). B, amplitudes (V, mV) of averaged e.p.p.s shown in A (triangles) plotted according to position in the train (n), i.e. at 10 msec intervals. The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
HIGH-FREQUENCY FACILITATION
439 In solutions containing 30 mM-MgCl2, the quantal content of the first e.p.p. was generally less than 1. In the experiment illustrated in Fig. 1 the quantal content of the first e.p.p. (measured from failures) was 0-58. Possible complications in these experiments were that the sodium concentration was lowered to 90 mm and that the addition of 30 mM-MgCl2 increased the ionic strength and osmotic pressure of the solution. However, in two experiments, 1-8 mM-MnC12 was added to the standard solution instead of MgCl2 to reduce the average quantal content of e.p.p.s (Meiri & Rahamimoff, 1972; Balnave & Gage, 1973b). The growth patterns obtained in these two experiments (quantal contents 3-5 and 2.8) were very similar to those recorded in solutions containing 30 mM-MgCl2. This suggested that the changes in ionic strength and osmotic pressure in the high Mg solutions, and the lowering of Na concentration, had not affected growth patterns.
The growth patterns are inconsistent with the arithmetic model The arithmetic model described by Mallart & Martin (1967) is based on the assumptions that the new facilitatory effect produced by any action potential is independent of previous history and adds linearly to any residual facilitatory effects remaining from preceding action potentials. Facilitation produced by a second action potential t msec after a preceding action potential is defined by F(t) =
(V2-V1)fV1,
(1)
where V1 and V2 are the amplitudes of the first and second e.p.p.s produced by the two action potentials. Facilitation decays exponentially (Mallart & Martin, 1967; Balnave & Gage, 1974) so that after t msec F(t) - F(0) et/lT,
(2)
where r (msec) is the time constant of decay of facilitation. If successive action potentials (interval t msec) in a train each produce an equal increment (F(0)) of facilitation, and if the decay of each increment of facilitation is exponential with time constant r, then the amplitude of the nth e.p.p. (Vn) will be given by tfr En = Vn_1 + V1. F(0) e (3) Using V1 and V2 recorded in the experiment illustrated in Fig. 1 and a value of 40 msec for r (average value at 20° C; Balnave & Gage, 1974) e.p.p. amplitudes for subsequent e.p.p.s were calculated according to eqn. (3). The predicted growth curve is shown as a continuous line in Fig. 1B for comparison. It can be seen that the observed growth pattern is not as predicted from eqn. (3)
R. J. BALNA VE AND P. W. GAGE 440 It was thought that these growth patterns, which are very different from those reported by Mallart & Martin (1967), might be a characteristic of e.p.p.s with low quantal content. However, e.p.p. growth patterns obtained at higher quantal contents again could not be fitted by eqn. (3).
Growth patterns of e.p.p.s with higher quantal contents Less depression of transmitter secretion was obtained in another series of experiments by using 5-10 mm rather than 30 mM-MgCl2. Curare (14-2-1 /SM) was added to these solutions to reduce e.p.p. amplitude. When neuromuscular junctionswere exposedto these solutionsthe average quantal content of 'first' e.p.p.s (calculated from failures and variance) ranged from 2 to 14. It was found that growth patterns were still inconsistent with the arithmetic model. The average of twenty trains of 5 e.p.p.s at 100 Hz recorded in one of these experiments is shown in Fig. 2A and the amplitudes of e.p.p.s are plotted against position in the train (n) in Fig. 2B (triangles). In the experiment illustrated the solution contained 5 mM-MgCl2 and 2*1 /M curare. The first four e.p.p.s show a steep increase in amplitude as seen with lower quantal contents but the fifth e.p.p. in the train shows signs of 'roll-off' in amplitude. This was only slight but was found in all nine junctions tested in these low Mg solutions. The growth of e.p.p.s predicted from eqn. (3) is shown by the continuous line in Fig. 2B. The experimental observations are clearly inconsistent with the arithmetic model.
Growth patterns of e.p.p.s with 'normal' quantal contents Growth patterns of e.p.p.s produced by brief trains of stimuli were studied further at junctions bathed in standard solution to which 147 EM curare had been added to reduce the amplitude of the post-synaptic response. The growth patterns in a few of these experiments approached growth patterns predicted from eqn. (3), especially when quantal contents were relatively high. A series of six e.p.p.s recorded in one experiment in which the quantal content of the first e.p.p. was eighteen is shown in Fig. 3A. After the first three e.p.p.s there was clearly a decline in the successive increments in e.p.p. amplitude. The growth patterns of e.p.p. amplitudes in experiments in which the average quantal contents of the first e.p.p.s were estimated as 30 (squares) and 150 (triangles) are shown in Fig. 3B. These two experiments were chosen for illustration because the first and second e.p.p.s had similar mean amplitudes but the quantal contents of the first e.p.p.s were very different. The increase in e.p.p. amplitude predicted from eqn. (3) (using the amplitude of the first two e.p.p.s) is shown as a continuous line in Fig. 3B for comparison. It was apparent that the agreement of e.p.p. growth curves with the arithmetic model was much better at high than at low quantal contents. Similar growth patterns were
441 HIGH-FREQUENCY FACILITATION recorded in seven experiments in which quantal contents were not adjusted but e.p.p. amplitude was reduced with curare. For some reason, the quantal content of 'normal' e.p.p.s was often as low as ten to fifty (Balnave & Gage, 1974). This appeared to be especially so from October to January but there was not a sufficient number of observations to be sure
of this. A
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Fig. 2. A, growth pattern of e.p.p.s in a solution containing 5 mM-MgCl2 and 2-1 FM curare. The middle trace shows the average of 200 trains of e.p.p.s elicited at 100 Hz every 8 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 0-25 mV; horizontal, 2 msec (19-50 C). B, amplitudes (V, mV) of averaged e.p.p.s shown in A, plotted according to position in the train (n), i.e. at 10 msec intervals. The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
R. J. BALNA VE AND P. W. GAGE
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Fig. 3. A, growth pattern of e.p.p.s in normal solution (no MgCl2) containing 5X3 pM curare. The middle trace shows the average of 20 trains of e.p.p.s elicited at 100 Hz every 20 sec. The outside traces show 95 % confidence limits. Calibrations: vertical, 1 mV; horizontal, 3 msec (20.50 C). B, the average amplitude of end-plate potentials, recorded in standard solution containing curare, plotted according to position in the train (n). The average quantal contents of first e.p.p.s were 30 (squares) and 150 (triangles). The continuous line shows the amplitude of e.p.p.s predicted from the first two e.p.p.s according to the arithmetic model.
443 HIGH-FREQUENCY FACILITATION The average growth patterns of e.p.p.s in the three solutions containing 30 mM-MgCl2 (circles), 5-10 mM-MgCl2 (triangles) and no MgCl2 (squares) are shown in Fig. 4 together with standard errors of the means (vertical lines) where they extend beyond the symbols. A growth curve predicted from eqn. (3) is shown as a continuous line. All three average growth curves clearly deviate from the growth curve predicted from the arithmetic model. 15
n 100 E
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5
1
3
2
4
5
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Fig. 4. The average growth patterns of the first five e.p.p.s (normalized with respect to the first) elicited by repetitive stimulation at 100 Hz in solutions containing 30 m.m (circles), 5-10 mm (triangles) and no (squares) MgCl2. The vertical bars denote ± 1 s.E. of mean where they are longer than the symbols. The continuous line shows the growth pattern of e.p.p.s predicted from the amplitude of the first two e.p.p.s according to the arithmetic model.
A kinetic model Although Mallart & Martin (1967) presented a mathematical description of growth patterns based on a simple physical model, the description would apply equally well to a single-step rate process such as A
k.,
B.
k-,
where k, is very small except during an action potential (A remains essentially constant), k-1 is a rate constant controlling the rate of decay of facilitation and transmitter secretion is proportional to the concentration of B. However, as shown above, our results are inconsistent with such a model.
444 R. J. BALNA VE AND P. W. GAGE It was suggested to us by Professor R. Golding (Department of Physical Chemistry, University of N.S.W.) that a two-step reaction might give good fits to the S-shaped growth curves we had observed. The two-step reaction that we have considered can be written k,
ks
k-1
k_,
A -,Bt---C~ ,
and it is proposed that transmitter secretion (in) is proportional to the concentration of C. Such a model can indeed generate patterns of C similar to the growth patterns of e.p.p.s that we have observed. The way in which the model was used and mathematical expressions for A, B and C are described in an Appendix. Essentially the reaction above was driven from A to C for 1 msec to simulate the effect of an action potential and to build up C. This was done by giving k1 and k2 selected values and setting k-1 and k-2 to zero. Then the reaction was driven from C to A for 9 msec so that C decayed. This was done by setting k1 and k2 to zero and giving k-1 and k2 values which produced a decay of C at a rate appropriate for the decay of facilitation. Rate constants were set to zero where specified only to simplify the equations. This scheme was used in an attempt to mimic the 'pulsed' secretion of transmitter during stimulation at 100 Hz. In comparing results from analysis of the kinetic model with experimentally obtained growth patterns of e.p.p.s, it was assumed that the amplitude of e.p.p.s (V) was linearly related to the number of quanta secreted which in turn was linearly related to the concentration of C. That is, V = bC, where b is a proportionality constant. With an appropriate choice of rate constants and initial steadystate values for C, it was found that the growth curves of e.p.p.s recorded under a variety of conditions could be fitted reasonably well. To allow comparison of growth patterns generated under different conditions, values for C were normalized with respect to C, and, because of the assumed linear relationship between C and V, this gave predicted normalized values for V also. Two sets of variables which gave good fits to two different types of recorded growth patterns are given in Table 1. In both, the initial value of A was set at 10-3 mole (the actual value made no difference to normalized growth patterns if the ratio AOCO was kept constant). The maximum value of C1 was much higher with the lower set of values than with the upper. Therefore the upper and lower sets of variables may be related to conditions of low and high quantal content respectively. The average growth pattern of normalized e.p.p.s recorded under conditions of low quantal content (ml1 < 1) is shown in parentheses for comparison, as is the growth pattern showing least growth in e.p.p. amplitude recorded in a
HIGH-FREQUENCY FACILITATION
445
TABLE 1. Normalized e.p.p. amplitudes ( V) calculated from the kinetic model assuming that V is directly proportional to the peak value of C during phase 1 (see Appendix). The rate constants (k, sec-1) and initial values of C (mole) were chosen to obtain good fits to experimental results (initial values of A and B were 10-3 and 0 respectively). T (msec) was calculated by varying the interval between the first two pulses (see Appendix). The average growth pattern obtained with low quantal contents (mil < 1) and a growth pattern obtained with a high quantal content (ml = 150) are shown in parentheses for comparison. Below is shown a pattern of e.p.p.s which would be predicted by the arithmetic model from V1 = 1 and V2 = 2-53
ini1
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Fig. 5. Predicted growth patterns of e.p.p.s according to the kinetic model under conditions of low quantal content (circles) and high quantal content (triangles). Parameters were chosen as indicated in Table 1. Compare with experimental results shown in Fig. 4. The growth pattern predicted from the first two e.p.p.s according to the arithmetic model is shown as a continuous line.
preparation with high quantal content (ml = 150). The values obtained for V from the kinetic model in Table 1 are shown graphically in Fig. 5 to illustrate the similarity to recorded e.p.p. patterns and the reasonably good correspondence that could be obtained between the kinetic (triangles) and arithmetic (continuous line) models with suitable choice of variables.
R. J. BALNA VE AND P. W. GAGE When the interval between VJ and V2 was increased in these two examples, F(t) was found to decay essentially exponentially (Mallart & Martin, 1967; Balnave & Gage, 1974) for t < 50 msec, with the single time constant r given in Table 1, so satisfying an important criterion for facilitation. Thus this simple kinetic model can successfully mimic the growth patterns we have recorded, including some which appeared consistent with the arithmetic model. It therefore appears a more general model with greater 'truth content' than the arithmetic model. It also satisfies the criterion of giving an exponential decay of facilitation with appropriate time constant. No attempt has been made here to introduce steps to account for other known characteristics of transmitter secretion: a more complicated model which is based an the scheme outlined above will be described elsewhere. 446
PISCUSSION It is clear that some growth patterns of e.p.p.s recorded at the toad neuromuscular junction are inconsistent with the arithmetic model of cumulative facilitation originally proposed by Mallart & Martin (1967). Other investigators have also found that growth patterns of excitatory junctional potentials recorded at crustacean neuromuscular junctions cannot be described by the simple arithmetic model either (Linder, 1973; Zucker, 1974a, b) but it could be suggested that this is due to the difference in experimental animals. However, growth patterns in the toad at low quantal contents are strikingly similar to those recorded by Zucker (1974 b) in the crayfish, whereas at higher quantal contents they can approach growth patterns recorded in the frog (Mallart & Martin, 1967; Magleby, 1973). It seems reasonable to assume that the two types of growth pattern are expressions of the same basic mechanism. We have described a simple kinetic model which will predict both the steep S-shaped growth patterns and the apparently arithmetic growth patterns, with suitable choice of rate constants and steady state concentrations. The model is almost cetainly an oversimplified representation oftrue events and does not pretend to account for many other aspects of transmitter secretion. However, it may serve as a simple kinetic description of facilitation at a variety of synapses and is proving useful as a basis for a more complex model of transmitter secretion which will appear elsewhere. In spite of these reservations, it is tempting to speculate about the possible nature of A, B and C in the simple kinetic model presented here. The large increase in transmitter secretion following an action potential is thought to be caused by a transient influx of Ca ions (for a review of evidence, see Katz, 1969). The reaction A k- B could well represent an
447 HIGH-FREQUENCY FACILITATION influx of Ca. For example, under the influence of the change in membrane field k1 could transiently assume a relatively large value. The one millisecond used to obtain the growth curves (Table 4, Fig. 9) would not be
unreasonable duration for this event. The reaction B k, C could represent the conversion of Ca from form B to an activated form C (presumably a Ca complex) which is a necessary co-factor for transmitter secretion. The rate of this reaction was also assumed to be affected by membrane field. The decay of C would be responsible for the decay of facilitation (Balnave & Gage, 1974). There is little information about the reactions C a B A which determine the decay of facilitation. It seems very unlikely that the decay of C represents simple diffusional loss of free Ca ions (or other activator) as the decay of facilitation is very temperature sensitive (Eccles et al. 1941) having an activation energy of about 100 kJ . mol-1 (Balnave & Gage, 1970, 1974), which is too high to be accounted for by a simple diffusional process. It has been suggested that the decay of facilitation may be due to dissociation of Ca from an active site because the rate is much slower when Sr substitutes for Ca as an activator of acetylcholine secretion (Balnave & Gage, 1974). We obtained a good fit to e.p.p. growth patterns with the kinetic model when C had an initial value of 5-5 x 10-10 mole in high Mg solutions and 5 x 10-8 mole in normal solution (Table 1, Fig. 5). This would suggest that magnesium reduces the resting concentration of C perhaps by competing with Ca for an active site. It was also necessary to raise k, (Table 1) to obtain the growth patterns recorded in solutions in which Ca influx during an action potential was presumably normal and certainly higher than in the raised-magnesium solutions (Katz & Miledi, 1969; Blaustein, 1971). If the rate constant k, represents the rate of Ca influx, it should indeed be higher when the quantal content is higher, if the Ca hypothesis (Katz, 1969) is correct. Several other factors such as a change in the amplitude of action potentials or a 'power' relationship between some linearly increasing intracellular activator concentration and acetylcholine secretion could conceivably have given the recorded growth patterns. It seems improbable that an increase in the amplitude of action potentials could have contributed to the steep growth patterns. In ten experiments there was either a small decrease or no change in the amplitude of extracellularly recorded action potentials in motor nerve terminals during repetitive stimulation, never an increase. In other preparations in which the possibility has been carefully investigated, facilitation is unaccompanied by an increase in action potential amplitude (Hubbard & Schmidt, 1963; Katz & Miledi, 1965; Martin & an
k-+
448 R. J. BALNA VE AND P. W. GAGE Pilar, 1964; Braun & Schmidt, 1966; Linder, 1973; Zucker, 1974 a). It would probably be possible to fit the steeper growth patterns of e.p.p.s by assuming that there is a linear increase in an activator during repetitive stimulation and that transmitter secretion is proportional to some power of the activator concentration. Unless the power were unity, the model would need to be modified again to give the exponential decay of facilitation with a single time constant which has been unequivocally found (Mallart & Martin, 1967; Balnave and Gage, 1974). Such complicated models would lose the attractiveness of the original arithmetic model and would be more complex than the simple kinetic model outlined here. It is interesting that Magleby (1973) recorded e.p.p.s greater than predicted from the arithmetic model when 'high' stimulation rates (31.2 and 50 sec-1) were used in frogs. The stimulation frequency used in the present experiments (100 sec1) may have served to accentuate the inconsistency and make it apparent earlier during a pulse train. It is also possible that the growth patterns that we have observed are more prominent in toads which often have e.p.p.s with low quantal contents in normal solution, perhaps more so in summer months. However, it is difficult to imagine that the basic mechanisms of transmitter secretion should differ greatly between frogs and toads, or with season. In order to account for divergence from the arithmetic model Magleby (1973) separated facilitation into two components with different characteristics. The alternative explanation we present here has the advantage of greater simplicity and wider applicability. In the light of these observations, there seems little value in trying to modify the arithmetic model in an ad hoc fashion to fit the wide range of growth curves which has been recorded. The kinetic model is more consistent with the experimental results and may be found to fit growth patterns in a wide variety of synapses. Facilitation is obviously a mechanism of some importance in the central nervous system where it seems to have many of the characteristics (cf. Porter, 1970) of facilitation at neuromuscular junctions (Mallart & Martin, 1967, 1968; Balnave & Gage, 1974). Patterns of increase in the amplitude of excitatory post-synaptic potentials have appeared to be similar at both sites and it has been suggested, after Mallart & Martin (1967), that facilitation in the central nervous system is due to arithmetic summation of a calcium complex which decays slowly and exponentially. While the arithmetic model may provide an adequate mathematical description of many patterns which have been observed, it clearly becomes very inappropriate under certain conditions at neuromuscular junctions and it may also be found to be inappropriate at some central synapses. If the kinetic model survives the gauntlet of new experimental data, it
449 HIGH-FREQUENCY FACILITATION may eventually be possible to identify A, B and C and to interpret the increase in transmitter secretion produced by bursts of action potentials in terms of underlying molecular events. APPENDIX
The kinetic scheme analysed was kl
k2
k-,
k_,
A It rB
Ca
The reaction was considered to go from A to C during an action potential (phase 1) and from C to A following an action potential (phase 2).
Phase 1 The rate constants k1 and k2 were given values to simulate activation of the secretion mechanism for 1O-3 sec. During this time, k1c and k12 were considered to be negligible and were set at zero for convenience. With these conditions, A, B and C are given by A =AO exp (-klt), B = Bo exp ( - k2t) + k 1
C=
Ao (exp (-Ikct)-exp (-k2t)),
AO+Bo+CO-A-B,
where AO) Bo and C0 are the initial values of A, B and C at the beginning of this phase.
Phase 2 Then for the next 9 x 1O-3 sec, AO, Bo and C0 were initially set equal to the final values of A, B and C during the preceding phase 1, k, and k2 were set at zero while k-, and k12 were given real values. With these conditions, C = Coexp(-k12t), B
=
Bo exp (- k-1t) + k
k-1= Ao+Bo+Co-B-C.
-2
Co (exp (-k-20- exp, (-k1t)),
A Phase 1 was repeated five times, followed by phase 2 each time except the last. C1, C2, C3, C4 and C5 were the maximum values of C during successive phase is. To examine the influence of duration of phase 2 on C2, the duration of phase 2 was increased to 19 x 103 sec, 29 x 1O-3 sec and 39 x 10-3 sec. The increase in C produced by the second phase 1 (C2 - C1), was found
450 R. J. BALNA VE AND P. W. GAGE to decrease exponentially as the duration of phase 2 increased. The relationship could be reasonably fitted by
C2 - C1 = Q exp (- d/T), where Q was a constant, d the duration of phase 1 plus phase 2, and r was the time constant of decay of C2 Cl. -
We are grateful for the assistance of C. Prescott, E. Bowler, R. Malbon and J. Oliver. The minicomputer was [provided by the National Health and Medical Research Council of Australia. REFERENCES
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