depend on the proportion of the total concentration of X which is combined From the Department of Biophysics, University College London

Transcription

1 434 J. Physiol. (I957) I38, THE NATURE OF THE ANTAGONISM BETWEEN CALCIUM AND MAGNESIUM IONS AT THE NEUROMUSCULAR JUNCTION BY D. H. JENKINSON From the Department of Biophysics, University College London (Received 24 May 1957) Calcium and magnesium ions are known to have specific and opposite effects at the prejunctional nerve terminals of several cholinergic synapses. A nerve impulse releases more acetylcholine (ACh) if the concentration of Ca is raised, within limits, or if that of Mg is lowered (del Castillo & Stark, 1952; del Castillo & Engbaek, 1954; Hutter & Kostial, 1954). del Castillo & Katz (1954 a, b) have discussed this antagonism and have put forward tentatively the hypothesis that Ca and Mg compete for some site or carrier molecule, X, in the nerve endings: on the arrival of an impulse, the calcium compound alone breaks down to give Ca and an active form of X, X', which can release or allow the passage of ACh. Thus the output of ACh should depend on the proportion of the total concentration of X which is combined with calcium. In the present experiments, end-plate potentials (e.p.p.'s) in curarized frog muscle have been measured over a range of Ca and Mg concentrations, and the results have been compared with the predictions of this hypothesis. METHODS The experim ents were performed on the sartorius nerve-muscle preparation of the frog (Rana temporaria) during the months October to February at a room temperature which varied between 19 and 230 C. Measurement of e.p.p.'s The movable liquid electrode (Fatt, 1950) was used to measure the e.p.p. amplitudes in the way described by del Castillo & Engbaek (1954). During a determination the nerve was stimulated at a frequency of 20/min. The time course of a typical experiment is shown in Fig. 1. The muscle was bathed alternately in Ringer's solution and in variants of this, being washed at least twice with each new solution. The amplitude of the e.p.p. in a critically curarized muscle was usually about 3 mv. Other e.p.p. amplitudes were expressed as a percentage of this, except where otherwise stated. Solutions. The Ringer's solution used had the following ionic composition: (mm) Na, 115; K, 2.1; Ca, 1.8; all the salts were used as chlorides. All solutions were isotonic, alterations in the Ca and

2 Ca AND Mg AT NERVE ENDINGS 435 Mg concentrations being compensated by adjustments in the amount of Na in the solutions. The resulting change in electrical conductivity was never greater than 4% and its effects could be neglected. Neostigmine methylsulphate (Roche Products) was used in several experiments in a concentration of 1 x 10-6 g/ml. Tubocurarine chloride (Burroughs Wellcome and Co.) was used in a concentration just sufficient to block transmission. In twenty experiments this varied between 1-4 and 2*0 x 10-6 g/ml. IR Ca 045 mm Ca 1-8 mm 4 40 mm M Mg 8C mm E 4 IR 02 E Mg 20 mm Ca 72 mm Mg 1-0 mm/ o I ' I Time (hr) 7 8 Fig. 1. Time course of typical experiment. The effect on the e.p.p. amplitude of several concentrations of Ca and Mg is shown. Ordinate, amplitude of e.p.p. (mv); abscissa, time in hours from completion of curarization. 0, e.p.p.'s in Ringer's solution; O, in solutions of the composition indicated. 1-8 x 10-6 g/ml. tubocurarine chloride present throughout. RESULTS End-plate potentials in curarized muscle Table 1 shows the effect of a range of Ca and Mg concentrations on the amplitude of the e.p.p. in curarized muscle. del Castillo & Stark (1952) and del Castillo & Engbaek (1954) have shown that the changes are due for the most part to the effect of Ca and Mg on the release of ACh. Before any conclusions about prejunctional events can be drawn from the quantitative action of these ions, several small post-junctional effects must be allowed for. These are discussed below and the values of Table 1, altered by the appropriate amount so as to make them comparable, have been plotted in Fig. 2. The first is due to Mg which, in the presence of curare, is known to increase the depolarization produced by ACh applied in the bathing solution (del Castillo & Engbaek, 1954). It has been assumed that the depolarization which follows the release of ACh from the nerve endings is affected in the same way and, in order to allow for this, e.p.p. amplitudes measured in solutions containing Mg have been diminished by a small amount, calculated from the quantitative results of del Castillo & Engbaek. With 8 mm-mg this is 16 %. Fatt & Katz (1952) have shown that the amplitude of the e.p.p. is altered by changes in the sodium content of the bathing solution. In the present work

3 436 D. H. JENKINSON TABLE 1. Effect of Ca and Mg ions on the amplitude of the e.p.p. in curarized frog muscle. Amplitudes have been expressed in arbitrary units, relative to that in Ringer's solution which is taken as 100. The mean values, ± s.e. ofthe means, are given in the table: * 3determinations, t 4 determinations. mm-ca *90 1*80 3*60 7*20 No Mg 7-3±1* 40±2* ±3t 221 ±6t 1 mm-mg 2.8±1* 21 ±1* 75±3* 149± 7* 208±11* 2 mm-mg 4 mm-mg 8 mm-mg 16±0.6* 57±2* 136±3* 180 ± 16* 4.2±0.2* 38±3* 109±1* 176± 12* 13±1* 77±3* 163±5* Calcium concentration (mm) Fig. 2. Effect of Ca and Mg ions on the e.p.p. amplitude of curarized frog sartorius muscle. The amplitudes have been expressed in arbitrary units, that in Ringer's solution, with 1-8 mm-ca and no Mg being taken as 100. The results are those of Table 1, altered by a small amount to allow for post-junctional effects (see text). The symbols refer to the following concentrations of Mg (mm). *, no Mg; E, 1; 0, 2; E, 4;, 8. Each point is the mean of several determinations and ± the S.E. of the mean has been shown where this exceeds the size of the symbol.

4 Ca AND Mg AT NERVE ENDINGS 437 the concentration of this ion was adjusted in order to maintain tonicity, and the observed amplitudes must be altered by a small amount in order to distinguish between the changes due to Ca and Mg and those produced by sodium. In the most extreme case, with 7-2 mm-ca and 8&0 mm-mg the e.p.p. must be increased by 19%. Hutter & Trautwein (1956) have shown that stretching a muscle not only increases the amount of ACh released by a nerve impulse but also lowers the relative increase produced by raising the calcium concentration. In the present work, the degree of stretch, although constant during an experiment, no doubt varied from preparation to preparation. The moderate reproducibility of the results showed that this did not introduce a great error except perhaps in those solutions which contained either a very high or a very low concentration of Ca: with these, the relative variability of successive determinations was larger than was observed with more nearly physiological concentrations. With three out of nine muscles tested it was found that immersion in a solution containing 7-2 mm-ca caused the e.p.p. amplitude first to rise, as expected, but then to fall to a very low value. This phenomenon was not examined further; however, it was noticed that Mg accentuated the effect, suggesting that it is due to the onset of inexcitability in the finer nerve branches. Such results were rejected. Fatt & Katz (1952) observed a seasonal variation in the e.p.p. response to low calcium concentrations and thus it seems that less weight should be placed on those results obtained with the two extremes of Ca concentration. The results shown in Fig. 2 can be compared to the scheme put forward by del Castillo & Katz. There are two equilibria: Ca +X= CaX, Mg + XCMgX. If it is assumed that the total concentration of X, bound and unbound, is [X0] and also that X reacts according to the law of mass action, then [Ca] {[X0] - [CaX] - [MgX]} = K. [CaX], [Mg] ([X0] - [CaX] - [MgX]} = KII [MgX], where K, and KII are the dissociation constants of the complexes CaX and MgX respectively. Hence, [CaX] [X-] (1) The relationship between [CaX] and the amplitude of the e.p.p. is unknown, but it is possible to derive some information about the antagonism from the concentrations of Ca and Mg which will maintain the e.p.p. amplitude at any 28 PHYSIO. CXXXVIII

5 438 D. H. JENKINSON one value: this should correspond to a certain [CaX]. If the concentration of Ca which will give this value of [CaX], in the absence of Mg, is [Ca'], then [XO] [XO] K 1+ [Ca'] [Ca] [ g KII therefore [Ca] -1+[Mg] (2) [Ca'] KI 6 - (a) E0 C 0 C 0 C C~~~~ (b) Mg concentration (mm) [Ca'] (mm) Fig. 3. (a) Relationships between the concentrations of Ca and Mg ions in solutions which will maintain the amplitude of the e.p.p. at any one value; data taken from Fig. 2. The number associated with each line shows the level of e.p.p. amplitude, on the ordinate of Fig. 2, for which the relationship has been plotted. (b) Initial slope of curves in (a) plotted against [Ca'], the intercept which these lines make with the ordinate. The two values shown by the symbol C are from data obtained in the absence of tubocurarine (0, Fig. 5). Thus if the amount of Ca in the bathing solution is increased, and if sufficient Mg is also added to keep the e.p.p. amplitude at its original value, [Mg] should be proportional to [Ca]. In Fig. 3 a the relationship between [Ca] and [Mg] has been plotted for several values of the amplitude using the data of Fig. 2. The initial slope of these lines is shown as a function of [Ca'] in Fig. 3 b, and it is seen that the relationship is fairly linear, as would be expected from Equation (2). The slope of this line suggests that KII, the dissociation constant of MgX, is about 4 x 10-3M. The intercept which this line makes on the abscissa of Fig. 3 a may arise from the small standing concentration of Ca near the

6 Ca AND Mg AT NERVE ENDINGS 439 nerve endings which will result from the slow loss of this ion which takes place from muscle fibres immersed in low-ca solutions. The lines of Fig. 3a deviate markedly from linearity with high concentrations of Ca and Mg. The explanation of this is uncertain, but may be due to the fact that, in this range, the allowances made for the post-junctional effects of Mg, and the displacement of Na, become rather large and these effects may not be independent of each other, as has been assumed. However, this should not affect appreciably the initial slopes o 150 a¼00 E < 50 olj~~~~~ / Ca concentration (mm) Fig. 4. Amplitudes of e.p.p.'s in arbitrary units, plotted with the concentration of Ca on a linear scale. Data from Fig. 2 (different scale). 0, points measured in Mg-free solutions; 0, solutions with 8 mm-mg. Equation (2) does not depend on any particular quantitative relationship between the output of ACh and [CaX] (and thus on [Ca], from Equation (1)). It was hoped that some simple connexion between the two might be found. Two of the curves of Fig. 2 have been replotted, with [Ca] on a linear scale, in Fig. 4. It is seen that the slope increases initially and that there is a point of inflexion. This type of relationship could be explained in several ways: it would be expected if the entity X normally reacted with two atoms of Ca: 2Ca + X= Ca2X. Mg might be expected to react similarly: 2Mg + X=Mg2X. 2&-2

7 440 D. H. JENKINSON If this were the case the relationship [Ca] -1+ [Mg]2 [Ca']2 KII should hold in place of Equation (2), for any one value of the e.p.p. amplitude. However, the data fit Equation (2) more closely. In an attempt to distinguish between other alternative explanations for the initial increase of slope of the curves of Fig. 4 a few experiments were made to see if the relationship between e.p.p. amplitude and Ca was altered when (1) the solution contained notubocurarine, and (2) when the acetylcholinesterase was inhibited. The results are given in the next main sections. Since the primary action of ACh at the end-plate is to produce an increase in membrane conductance, it would be expected that this increase (AG) would be more closely related to the output of ACh than would be the resulting depolarization (AE); for Martin (1955) has shown that only small values of AG and AE are linearly related. However, if the conductance changes are estimated, in the way shown by Martin, the relationship between the concentration of Ca and AG has a similar initial increase of slope, and point of inflexion, so that some other explanation for these features must be sought. End-plate potentials in the absence of tubocurarine Neuromuscular block was established using a modified Ringer's solution with 0-90 mm-ca and 8-0 mm-mg. When the e.p.p. had come to a steady value this solution was alternated with others which also maintained the block without tubocurarine and the effect on the amplitude of the e.p.p. was found. The results are shown in Table 2. TABLE 2. E.p.p. amplitudes measured in muscles in which transmission has been blocked by using low Ca, with or without Mg; each point is the mean of three determinations and the e.p.p.'s have been expressed relative to the value, taken as 100, in a solution containing 0-90 mm-ca and 8-0 mm-mg, ±S.E. of the mean. mm-ca No Mg 1 mm-mg 2 mm-mg 4mM-Mg 8 mm-mg ± ±4 125± ± In three out of four muscles tested a solution with 0-90 mm-ca and 4-0 mm- Mg maintained block. Since the reduction of e.p.p. amplitude produced by a solution of this composition had been measured in a curare-blocked muscle it was possible to relate the results of Table 2 to those of Table 1. Both sets of values have been plotted in Fig. 5 after the appropriate allowances for postjunctional effects had been made. After scaling the curare-free results so as to make them fit the curare-blocked results with 4-0 mm-mg, the other points agree well with their appropriate curves, suggesting that the relative effects of Ca and Mg are little changed by the presence of tubocurarine.

8 Ca AND Mg AT NERVE ENDINGS 441 -o >1.0 cl 1- & cl 0 2) Ca concentration (mm) Fig. 5. Effect of Ca and Mg ions on the e.p.p. amplitudes of frog sartorius muscle. E.p.p.'s again in relative units with that in Ringer's solution taken as 100 (log-log scale). The five curves from left to right correspond to magnesium concentrations of 0, 1, 2, 4 and 8 mm respectively. Each value shown is the mean of three or four determinations and is from the results shown in Tables 1-3, adjusted slightly to allow for post-junctional effects as described in the text. 0, points measured in the presence of tubocurarine (data also plotted in Fig. 2); C, with tubocurarine and 1 x 10-6 g/ml. prostigmine; 0, in a tubocurarine-free solution. In order to relate the values measured in the absence of tubocurarine to the others, the e.p.p. amplitude in a tubocurarine-free solution containing 0-90 mm-ca and 4-0 mm-mg has been assumed to be 4-2; this value has been chosen as it is the e.p.p. amplitude (relative to that in Ringer's solution, taken as 100) observed in a similar solution which also contained tubocurarine; see Table 1. This procedure was used because only at this point do the two sets of data, which have been measured on the sartorii of different frogs, overlap.

9 442 D. H. JENKINSON End-plate potentials measured in the presence of prostigmine In order to inhibit the cholinesterase, prostigmine was added to the bathing solution in a concentration of 1 x 10-6 g/ml., together with sufficient tubocurarine to produce block. The effects of several concentrations of Ca and Mg are shown in Table 3 and these results, altered by small amounts to allow for post-junctional effects, are also plotted in Fig. 5. It is seen that the form of the curves relating the concentrations of Ca and Mg to the e.p.p. does not depend to a great extent on the activity of the cholinesterase. TABLE 3. E.p.p. amplitudes measured in the presence of 1 x 10-6 g/ml. prostigmine and sufficient tubocurarine to produce block. Each value is the mean of three determinations; the 8.E. of the mean is also given. The amplitudes are expressed relative to that in Ringer's solution (containing the same concentration of tubocurarine and prostigmine) which is taken as 100. mm-ca No Mg 8 mm-mg ± L1 3*60 187t6 68±3 DISCUSSION The results show that the e.p.p. is very sensitive to a wide range of Ca and Mg concentrations. It is known that summer frogs contain twice the blood Ca of winter frogs (de Boer, 1918) and also that the plasma Mg varies with the season. The number of muscle fibres in which the e.p.p. amplitude exceeds threshold may thus vary under physiological conditions, e.g. with the time of the year. The hypothesis tested in Fig. 3, which seems to fit the data reasonably well, involves the assumption that Ca and Mg act competitively at nerve endings. If Mg acts by deactivating the CaX compound, that is, if there is no competition between the ions, a different relationship should hold. The two equilibria are Ca+X= CaX, Mg + CaX CaMgX Then [CaX]= [X0] [XO] (inactive) K, [M] [Ca'] [Ca] Ki,, KEI, is the dissociation constant of the Ca-Mg-X complex and [Ca'] is as defined previously. Then 1 1 [Mg] [Ca'] - [Ca] K,,,K,1 This predicts that [Mg] should be linearly related to the reciprocal of [Ca] under conditions where it has been shown (see Fig. 3a) that the two concentrations are more nearly directly proportional. If Mg and Ca combined with different points or groups on X so as not to compete directly with one another, and if the molecules combined with Mg were again inactive, another relationship should be followed.

10 Ca AND Mg AT NERVE ENDINGS 443 The concentration of X molecules combined with Ca would be [XO] K'.1 1+ [Ca] regardless in this case of the presence or absence of Mg. Some of these molecules would be combined with Mg as well. The concentration of X molecules in combination with Ca alone, and thus active, would be Klv [XO] [XOI I1+ [Ca]) (KI[Ca] V + [mg]) 1 +[Ct ~~~~[Ca'] where KI V is the dissociation constant of the Mg compound, [Ca'] being as defined before. Hence [Ca] 1 (K1 + [Ca]( [Ca'] +m * K11VK1 (3) If K1>[Ca], [Mg] and [Ca] should be linearly related, and it would be impossible (by this test alone) to distinguish between this type of inhibition and the competitive form (compare Equation (2)). However, the former seems less preferable for the following reason: if the inhibition is not competitive, and if K1> [Ca], KI V is about 4 x 1O-3M. from Fig. 3b. Since the effects of a small amount of Mg can be reversed by an even smaller amount of Ca (see Fig. 2) it is likely that K1 <KI.V Thus KI is probably of the same order of magnitude as [Ca], not much larger, and Equation (3) predicts that if [Ca] is plotted against [Mg], the lines should not only deviate from linearity but should do so in the opposite direction to that found experimentally in Fig. 3a. The shape of the curves (Fig. 4) relating the size of the e.p.p. and [Ca], at a fixed [Mg], does not seem to depend on either the activity ofthe cholinesterase or the presence of tubocurarine (Fig. 5). However, there remain several other possible explanations of the initial increase of slope and point of inflexion; these features would be expected if, for instance, there was a threshold concentration of CaX required to produce an end-plate response, or if the relationship between the total amount of ACh released and the resultant depolarization had the same initial slope increase. The present work supports the hypothesis of a calcium compound (CaX) which controls the nerve impulse-induced release of ACh. It must be pointed out, however, that the evidence is still very indirect and the hypothesis may not survive a more direct experimental test. SUMMARY 1. The effect of a range of Ca and Mg concentrations on the amplitude of the e.p.p. in frog muscle has been measured, using external electrodes. 2. The relationship between those concentrations of Ca and Mg which maintain the e.p.p. amplitude at any one level is in reasonable agreement with what would be expected on the basis of competition between the ions for a receptor molecule which controls the amount of ACh released by a nerve impulse. 3. The dissociation constant of the Mg-receptor complex appears to be of the order of 4 x 10-3 M.

11 444 D. H. JENKINSON The author would like to thank Professor B. Katz for his advice and encouragement, Dr H. 0. Schild for helpful criticism of the manuscript, and also Mr J. L. Parkinson, Miss A. Painton and Mr K. Copeland for technical assistance. The experiments were made during the tenure of a grant from the Medical Research Council. REFERENCES DE BOER, S. (1918). Le liquide de perfusion des coeurs de grenouilles d'et6. Arch. ne'erl. Physiol. 2, DEL CASTILLO, J. & ENGBAEK, L. (1954). The nature of the neuromuscular block produced by magnesium. J. Physiol. 124, DEL CASTILLO, J. & KATZ, B. (1954a). The effect of magnesium on the activity of motor nerve endings. J. Physiol. 124, DEL CASTILLO, J. & KATZ, B. (1954b). Changes in end-plate activity produced by pre-synaptic polarization. J. Physiol. 124, DEL CASTILLO, J. & STARK, L. (1952). The effect of calcium ions on the motor end-plate potentials. J. Physiol. 116, FATT, P. (1950). The electromotive action of acetylcholine at the motor end-plate. J. Physiol. 111, FATT, P. & KATZ, B. (1952). The effect of sodium ions on neuromuscular transmission. J. Physiol. 118, HUTTER, 0. F. & KoSTIAL, K. (1954). Effect of magnesium and calcium ions on the release of acetylcholine. J. Physiol. 124, HUTTER, 0. F. & TRAUTWEIN, W. (1956). Neuromuscular facilitation by stretch of motor nerveendings. J. Physiol. 133, MARTIN, A. R. (1955). A further study of the statistical composition of the end-plate potential. J. Physiol. 130,