membrane, is dependent on the concentrations of ions, such as Ca and protons,

Transcription

1 J. Physiol. (1978), 282, pp With 6 text-figurew Printed in Great Britain DISPLACEMENT OF ACTIVATION THRESHOLDS IN CARDIAC MUSCLE BY PROTONS AND CALCIUM IONS BY R. H. BROWN JR. AND D. NOBLE From the Univereity Laboratory of Physiology, Park Road, Oxford (Received 24 February 1977) SUMMARY 1. The Na current threshold in sheep cardiac Purkinje fibres and in frog atrium is shifted in a positive direction by protons and Ca2+ ions. The titration curves for Purkinje fibres are consistent with a surface potential of -18 mv at ph 7*4 and 1-8 mm-ca. 2. In Purkinje fibres, the pacemaker K current activation curve, 8w,, is shifted in a positive direction by Ca2+ ions. The results are consistent with a surface potential of -16 mv in normal physiological solutions. 3. The results on so during ph changes are unexpected. As also shown by Van Bogaert, Vereecke & Carmeliet (1975) the voltage shifts are usually in the opposite direction to that expected from titration of external surface negative charges. 4. Acid solutions reduce the magnitude Of ik, when fully activated. Alkalinity has little effect on ik2. 5. Acidification and alkalinization are both capable of arresting spontaneous activity in Purkinje fibres. The effects of acidity are usually irreversible. The effects of alkalinity are reversible. INTRODUCTION Since Frankenhaeuser & Hodgkin's (1957) experiments on the influence of Ca2+ ions on the conductance mechanisms of squid nerve, considerable evidence has accumulated to favour the view that part of the electrical field within the membrane controlling the gating of ionic channels depends on the presence of a surface negative potential. The magnitude of this potential, and hence the electrical field across the membrane, is dependent on the concentrations of ions, such as Ca and protons, that may shield or bind to surface negative sites. For reviews of the experimental evidence the reader is referred to Hille (1968, 1970) and Gilbert (1971). The electrical effects of calcium and protons are of importance in cardiac electrophysiology, partly because variations in the plasma level of Ca2+ and H+ are of clinical interest. Both high Ca2+ and low ph produce toxic effects by themselves and greatly increase the toxic actions of cardiac glycosides. The possible mechanisms of these toxic effects will be discussed in a following paper (Brown, Cohen & Noble, 1978). The purpose of the present paper is to measure the changes in conductance thresholds that may be attributable to variations in surface charge. Weidmann (1955) has shown that high Ca2+ displaces the Na inactivation curve (h.) in a positive

2 334 R. H. BROWN AND D. NOBLE direction on the voltage axis and increases the excitation threshold. We have extended these results by using the voltage clamp technique to measure Na threshold changes with variations in Ca2+ concentrations and ph. We have also investigated Ca-induced displacement of the activation curve (8w) for the pace-maker K current. Hecht & Hutter (1965) have investigated the influence of ph on Purkinje fibres. We have confirmed some of their observations on the influence of acid and alkali on pace-maker activity. We have also studied the influence of H+ on the pace-maker K current, tk,. METHODS Our experiments were performed on sheep Purkinje fibres obtained from local slaughterhouse using the two micro-electrode voltage clamping technique as outlined by Brown (1973) or Cohen, Daut & Noble (1976). Our solutions were modified by substituting for the bicarbonatephosphate buffers a buffer consisting of 2 ml each of maleic acid, acetyl glycine and TRIS, according to the method of Hutter &_ Warner (1967). ph adjustments were made by adding NaOH without correcting for the added Na (which at ph 9.5 was only 7 mx). The buffering capacity of the solution was linear over the range ph *0 with a value of one Slyke. According to Hutter & Warner, this buffer system does not complex with ions in the solution. They estimated that at ph 10-0 this buffer solution in Ringer solution reduced the calcium concentration by only 3 %. The frog atrial experiments were performed using the sucrose gap method of H. F. Brown & S. J. Noble (1969) with reduction of the bicarbonate to 1P2 mx and inclusion of 2 mx of one of the above buffers in both the control solution at ph 7-3 and the test solution. Acetyl glycine, maleic acid and TRIS were used for the low ( ), intermediate ( ) and high ( ) phs respectively. High Ca solutions were made by adding CaCl3. The surface area of each preparation was estimated from microscopic measurements of the fibre length and diameter (excluding connective tissue). The membrane currents have been expressed with respect to surface membrane area. The cleft is not included in this calculation. Other studies (Mobley & Page, 1972; Hellam & Studt, 1974) suggest that the current densities should be divided by 10 to obtain current/unit area of membrane including clefts. We have not done this since it is not known how this factor varies with the size of the preparation. RESULTS Na threshold In the majority of Purkinje fibres, it is not possible to fully control the Na current using the voltage clamp technique. However, it is possible to make accurate deterninations of the Na threshold. Fig. 1 (top) shows membrane currents in response to depolarizations of 10, 11, 12 and 14 mv from the holding potential (-75 mv). It can be seen that depolarizations of 10 and 11 mv fail to activate any inward current, whereas a large inward current, accompanied by a transient 'escape' of the voltage trace, appears in response to 12 and 14 mv. It is therefore possible to determine the Na threshold to an accuracy of about 1 mv. Fig. 1 (bottom) shows the results of changing the extracellular ph to 4*0, 5*5 and 9-0. It can be seen that acid shifts the Na threshold substantially in a positive direction while alkali produces a small but probably not significant shift in a negative direction. The effects of changes to ph 5*5 or 9 0 were fully reversible but the change to ph 4 0 was accompanied by such a rapid deterioration of the preparation (see Brown et al. 1978) that reversal was impossible. Similar results were obtained using frog atrium. As in the Purkinje fibre, acid produces a positive shift, although the effect is quite small until ph 4 0 is approached. Alkali produces a slight negative shift.

3 Ca AND PROTONS ON PURKINJE FIBRES 335 The influence of Ca2+ ions on the sodium threshold in Purkinje fibres was studied by increasing the concentration of this ion from its normal value, N = 1*8 m, to 1/4, 4 and 16 x N. At sixteenfold increases the bicarbonate buffer system was replaced by 1 mx-tris to avoid precipitation of CaCO3. We also used a conditioning hyperpolarizing pulse to ensure that no Na inactivation was present. Fig. 2 (@) shows the change in threshold plotted as a logarithmic function of the Ca concentration. Over this range there is a slope of 5 or 6 mv per fourfold change in Ca2+ concentration. Fig. 2 also illustrates essentially the same findings in the Na threshold in atrium (U) t ~ ~ [ 25 mv 20 seccm 100 pa cm2 en, 10\ 10 0) 0 v 0\ 0 * /(Ca =0-05 mm Fig. 1. Top: determination of the fast Na current threshold. The membrane potential is clamped from a holding potential of -75 mv to successively more positive potentials. At -63 mv (a depolarization of 12 mv) a large inward current is activated and there is a transient escape of the membrane potential (in these records the trace of the inward current has been retouched. On the current scale used, the K currents are too small to show time dependence). Bottom: effect of ph on the threshold. Changing from 7 3 to 4-1 or 4-2 shifts the threshold by 15 mv in a positive direction. Each point represents a separate fibre. The continuous curve is calculated from eqn. (1) assuming the Ca2+ concentration is 1P8 mm and that the Ca affinity constant of the surface negative charges is 0*05 mm-1. The sensitivity of this curve to changes in Kc. and in Ka is shown in Brown (1974). As shown in the following paper (Brown et al. 1978) ph and Ca changes also produce changes in holding current. In the region of the Na threshold (-60 mv) acidity or high ph usually produces an inward current shift which would, by itself, reduce the apparent Na threshold, rather than increase it, as observed. In the present experiments the background current level did not shift by amounts likely to cause serious error in the threshold determinations, except perhaps at ph 4 0 where the voltage shift may be more unreliable. The use of the Na current threshold to measure changes in surface charge is

4 336 R. H. BROWN AND D. NOBLE subject to various possible errors. The voltage to which the surface membrane must be displaced to trigger an uncontrolled flow of sodium current may depend on the properties of the cleft system and, in particular, on the non-uniformities of potential in this system. Only if these remain unaltered as the threshold is approached will changes in voltage threshold give a reliable indication of changes in membrane surface charge. For this reason it seemed important to check on the results using Na current threshold with experiments on a much more controlled current system. 'E -~~~~~~~~~~~~~U. 20,, Kca= , ems~~~~~'u 0 0 U,, mM I I IlIr I I I log (mm) Fig. 2. Effect of Cal+ concentration on Purkinje fibre (0) and atrial (I) Na threshold. Each fourfold increase in Cal+ concentration (ranging from 0 45 to 28-8 mm) produces a positive shift in the threshold of approximately 5 mv. This figure represents three separate experiments on Purkinje fibres and five separate experiments on the frog atrium. Each point is the result of a single experiment. The continuous curve was calculated from eqn. (1). This curve is included to show that H+ and Ca2+ may be titrating the same surface charges. The experimental points themselves clearly do not necessarily require a sigmoid curve since they all fall on the linear part of the curve. The influence of Ca on ik, in Purkinje fibres Unlike the Na system, the slowly activated K currents may be studied fairly completely under voltage clamp conditions. In the case of the pace-maker current, ix,, we therefore determined full activation curves, s8, as described by Noble & Tsien (1968). The displacements are then measured as shifts on the voltage axis of the entire activation curve rather than just the threshold. Fig. 3 shows the variation in the voltage dependence of sa, with extracellular Ca concentration. Once again the plot is semilogarithmic. A slope of 8 mv per fourfold change in concentration was obtained. Positive shifts in sex, with increased Ca2+ concentration have also been reported by Hauswirth, McAllister, Noble & Tsien (1968, 1969) and by di Francesco & McNaughton (1977). The influence of Ca2+ ions on ik, is restricted to a change in the voltage-dependence of the activation curve. The absolute amplitude of the current 'K, was not significantly changed (see Brown et at. 1978).

5 Ca AND PROTONS ON PURKINJE FIBRES 337 The influence of ph on ik, in Purkinje ftbres The results described so far are consistent with those expected when protons and Ca2+ ions reduce the surface negative potential of the membrane (see Discussion). The results obtained with changes in ph on tk. were more variable, however. In some experiments acid ph produced the unexpected result that the activation curve 8s, was shifted in a negative direction. In others, very little change was observed and in one experiment a positive shift was seen _ E I I I I I i log Ca (mm) Fig. 3. Dependence of the voltage dependence of 8D,, on Ca2+ concentration. The second lowest point is the control case ([Ca]. = 1-8 mm). The other points show the results of three experiments in which [Ca]o was increased to 7-2 and 28-8 mm or decreased to 0-45 mm. There is an 8 mv shift per fourfold change in [Ca]0. The continuous curve is calculated from eqn. (1) assuming Kc. = 0-3 mm-. Fig. 4 shows examples of these results. In part A the fibre was changed from ph 7*3 to 5-5 with no change in the voltage dependence of activation and a net inward shift in the background current level (shown as a downward shift of the whole activation curve). During the experiment shown in Fig. 4B a small increase in inward background current occurred which was unaffected by alkali (ph 9.5) but greatly enhanced by acid (ph 5.5). The normalized activation curves reveal a negative displacement of s, in acid but no shift in alkali. Fig. 4D reveals one run in which acidification to ph 4-2 reversibly shifted the s8, curve in a positive-going direction. Although the results on voltage dependence of as,, were variable, the influence of ph on the absolute magnitude ik, was consistent. As shown in Fig. 5 acid reduces ins whereas alkali has no effect. The influence of ph on Bpontaneou8 activity The effects of ph changes on spontaneously firing Purkinje fibres were also investigated. Fig. 6 presents the effect of ph 5-5 on two fibres. It is seen in Fig. 6A that within 100 see the acidification caused a decrease in the maximum rate of upstroke, a diminution in the most positive plateau potential, and a slight prolongation of the plateau duration. By 2 min loss of spontaneity was imminent and

6 338 R. H. BROWN AND D. NOBLE the ph was restored to 7-3 with slow, low voltage oscillations seen transiently thereafter. Fig. 6B shows an experiment in which abrupt cessation of firing occurred in association with shortening of the action potential duration. In every case of acidification to ph 5-5 or lower, firing ceased within 150 see of the ph change and in no case did resumption of normal firing occur, although as shown in 6B, excitability was sometimes recovered. Fig. 6C demonstrates a typical effect of alkalinization on spontaneity. Cessation of firing occurs nearly 10 min after exposure to ph 9'5 and after restoration of N E 0 6 _ A ph * 7.3 x 55 o ,, A' Ad ph a9-5 8,i o73 co ~~~~~~x mv I8 06 0* I 0a,' / ph o/ A After 2 5 I11,At ,.... y~ 0O i-.-. m/ I ( 0-4-~m Fig. 4. Effect of ph on the voltage dependence of s8y. A, three activation curves are shown as determined from a holding potential of -76 mv for ph initially 7.3 (40-0), then 5.5 (x---x), and finally 7-3 (0-0). For the purpose of comparison, the background current is set at zero for potentials at which ik2 s inactivated in the steady state. u Acidification did not alter the voltage dependence in this experiment. It slightly reduced the over-all current which could be activated at this holding potential, from about PsA/cm2 (this is also seen for the potential -76 mv in Fig. 5B from the same experiment). B, these normalized activation curves demonstrate the effect of changing the ph from 7-3 (0 0) to 9-5 (A--- A) with restoration to ph 7-3 (0-0) and then acidification to ph 5.5 (x---x). Alkalinization did not alter the voltage dependence of s8o whereas acidification by two ph units caused an 8 mv hyperpolarizing shift of s.. C, the activation curves determined at ph 7-3 before (0-0) and immediately after (A---A) approximately 21 min exposure to ph 3-5 show a hyperpolarization of the s8 voltage dependence of 8 mv. Acidification caused an increasing net inward background current which rapidly rendered clamping impossible. The hyperpolarizations of 8sO seen here and in the experiment of Fig 4B were irreversible. D, acidification to ph 4-2 (0-0) from 7-3 (A---A) resulted in a 17 mv positive-going shift in the voltage dependenceof8s,, reversed on return to ph 7-3 ( ) Lowering the ph also reduced ik2 and increased the net inward background current at the holding potential, about - 75 mv, effects not shown here. min

7 Ca AND PROTONS ON PURKINJE FIBRES 339 neutral ph a single stimulus elicits spontaneous pacing. The effects of acid and alkali on firing frequency were highly variable. Both changes variably increased and decreased this parameter. 4 -K2 * ph 7 3 initial 3 * x ph9-5 o ph 7-3 final 2 E~~~~ R/ mv IK2 7 Ad ph 7.3 initial 6 - x ph o ph 7 3 final 4 X mv Fig. 5. Effect of ph on ik,. A, alkalinisation from ph 7 3 (v-- - ) to 9 5 (x --- x) with subsequent restoration of ph 7-3 (0--- 0) did not alter the shape or magnitude of iku, nor did it alter the apparent reversal potential. In this experiment, and that in Fig. 5B, the external K concentration was 4 0 mm. B, acidification from ph 7*3 (O---S ) to 5-5 (x --- x ) depressed the magnitude of ik2 at all potentials negative to the holding potential of -76 mv. This effect was partially reversed at some potentials on restoration of ph 7-3 (0-- -0). The effect of loweringph onthereversal potential is discussed in the following paper (Brown et al. 1977). DISCUSSION The influence of Ca and H on the Na threshold Our results suggest that the sodium systems of Purkinje fibres and atrium respond similarly to variation in calcium concentration There are small quantitative differences in the ph responses. The solution pkh for the Purkinje fibre sodium threshold titration is approximately 5 3, whereas in the atrium it is approximately 4*2. The corresponding maximum shifts per unit ph are 15 and 25 mv respectively. Hille (1970) found qualitatively similar results in node of Ranvier titrated with ph over 4-10 ph units. At phs below 5-5 the Na activation parameters m0 and h<,,, showed 25 mv changes per unit ph change, comparable to the atrial results. Hille also reported that fourfold changes in the Ca2+ concentration produced shifts of about 12 mv in the steady-state voltage dependence of m0. and 9 mv in that of h..

8 340 R. H. BROWN AND D. NOBLE It is also of interest that Weidman (1955) recorded an average shift of 5-6 mv in the voltage dependence of h.,3 in the Purkinje fibre. It thus appears that with regard to both ph and Ca titration properties the sodium systems of atrium, Purkinje fibre and frog node are similar although Ca has a less pronounced effect on heart than on frog node. o ph sec 2 min -50 -> \ A -100 sec ph AAAA-)A B E _oot v J 9\2 > v 2LL sec t Fibre stimulated ph 7.3-9*5 10 min ph 7-3 Recovery 50E VVVkVVVQ\ c -100 sec Fig. 6. Influence of ph on pace-maker activity in Purkinje fibres. A, ph 5-5 slows the rhythm and induces low voltage irregular oscillations. B, ph 5-5 arrests the rhythm. The fibre may still be excited by applied stimuli but action potential duration is greatly reduced. C, ph 9-5 induces acceleration of rhythm followed by arrest. These effects are reversible. Note: all records are obtained using a pen recorder. Fast upstrokes and overshoots are not recorded. These Ca and ph results may be quantitatively interpreted using surface charge theory. Briefly, this assumes there are negative charges at the membrane surface which help determine the electric field influencing the gating of ionic channels. Cations will screen and possibly bind to these charges, altering the actual transmembrane potential while not altering the potential recorded between the bulk solutions on either side of the membrane. Thus, for example, if there are external surface negative charges influencing Na gating, increasing Ca2+ concentrations will decrease the potential created by these charges and effectively hyperpolarize the membrane, although the bulk membrane potential will be unchanged. The Na+ threshold will appear to be shifted in a depolarizing direction, since greater depolarization will be required for any given degree of activation of the Na system. For the purposes of this analysis it is assumed that the surface charges are divalent and that the following reactions occur: Ca2+ +S2- = CaS, Kic. 2H++S2- = SH2, K11 where S2- is the surface charge density and K is the affinity constant for the surface charge. One can assume further that S2- is either smeared out over the membrane or discretely localized. It will suffice to use the former assumption for which it can be shown (see Brown, 1974) that 1 d[1 + Kca Ca exp (- 2VF/RT) + KHH2 exp (-2VF/RT)] (1) jb (exp (-z1 VIF/RT) - t)

9 Ca AND PROTONS ON PURKINJE FIBRES 341 where o is the surface charge density (esu/a2), cib is the bulk concentration of the ith species with valence z1, m is the total number of ion species present, d is the average interchange spacing, and G is a constant: G = F/N(2RTe0e,)-A = 270 A2 (mole/l.)i. e0 is the permittivity of free space, e,. is the relative permittivity of water, and F, N, R and T have their usual meanings. Using eqn. (1) it can be shown that the effects of Ca and protons on the Na threshold are well reproduced if the average distance per unit charge is 25 A, Kca is 005 mn-1 and pkh = 5-3 for the Purkinje fibre and 4-3 for atrium. That is, it is reasonable to assume that Ca2+ and H+ ions are both titrating the same surface negative charges near the Na channel. For the Purkinke fibre the above parameters predict a surface potential of -18 mv for ph 7-4 and 1-8 mm-ca. For the normal atrium with 1 1 mr-ca the results are essentially the same. As noted, our Na results are in good agreement with those of Hille (1968) in frog node. An analogous surface charge analysis of his data (Gilbert & Ehrenstein, 1969) requires an intercharge spacing of 15 A, somewhat lower than our figure for Purkinje fibres and atria, yet consistent with the greater shifts of he,, and m. seen with Ca changes. From the known pkks and the surface potentials near the Na channels, surface pkhs of 5.1 and 4-1 can be calculated for the Purkinje fibre and atrium respectively. It is tempting to speculate that this might correspond to a surface fi- or y-carbonyl group which can have a pkh approaching 5 0 (Mahler & Cordes, 1969) particularly if the molecule is in a phase with a dielectric constant less than that of water. The influence of Ca and hydrogen on s0, It is apparent that the influence of Ca on the voltage dependence of sa, can also be readily explained by surface negative charge titration. Ignoring the possible interactions between protons and the surface site, one finds from eqn. (1) that the required average spacing per unit charge is 18 A with a Kca of about 0'3 mm-' and a surface potential of -16 mv for a Ca2+ concentration of 1P8 mm. It is of interest that Mozhayeva & Naumov (1970) subjected the K system of frog node to a somewhat similar analysis and found an interchange spacing of A, with a Kca of mm-'. This spacing is clearly comparable to ours, although the calcium affinity constant is lower than that required by our data. Acidification to ph 5-5 or lower resulted either in no shift ins., or a hyperpolarizing shift with the exception of the single run in which a small depolarizing shift was observed. Van Bogaert et al. (1975) have also shown that the ph effects on ik, generally in the unexpected direction. They find positive voltage shifts following are alkalinization. One possible explanation is that H+ ions influence internal as well as external surface negative charges, and that the net shift recorded depends on which titration predominates. It is not necessary that the postulated internal charge titration be by H+ ions. In a subsequent paper we consider the possibility that H+ ions may depress the Na-K pump (see Brown et al. 1978) which may in turn alter the activity of the Na-Ca pump so as to increase the internal Ca2+ concentration. The increased intracellular Ca2+ concentration may result in titration of internal

10 342 R. H. BROWN AND D. NOBLE surface charges near the ika channels and thereby produce a hyperpolarizing shift of the 8,cc curve. At low phs we observed an increase in net inward background current, also described by Hecht & Hutter (1965), and reduction in the maximum IK2 at any potential. These points will be discussed in the following paper. The effect of ph on pontaneodly firing Purkinje fibres The most consistent effect ofacidification on pacing fibres was rapid and irreversible loss of normal spontaneous pacing, in conjunction with a decrease in the rate of upstroke. This contrasted with the effects of alkalinization, which arrested spontaneous pacing after longer intervals, usually without grossly detectable alterations in the rapid upstroke and with reversal of the effect on restoration of neutral ph. The effects of ph alteration on firing frequency varied with different fibres. In this regard our results show somewhat greater variability than those of Hecht & Hutter (1965) who reported that acidification of spontaneously firing fibres in 2'5 mm-k only decreased the firing frequency. It would appear from the multiplicity of ph effects discussed above on sodium threshold, a8,, K1, and net inward current that such variability of the ph effect on pacing may depend on the relative magnitudes of the individual effects in any one experiment. Further complicating the issue is the fact that H+ ions reduce the magnitude of the slow inward Ca current in Purkinje fibres and atrium, as well as the repolarization current ix1 in Purkinke fibres (Brown, 1973). With the computer reconstruction of the Purkinje fibre action potential (McAllister, Noble & Tsien, 1975) we have demonstrated that the varied effects of ph on spontaneous pacing are consistent with the voltage clamp results noted thus far (Brown, 1973). REFERENCES BROWN, H. F. & NOBLE, S. J. (1969). Membrane currents underlying delayed rectification and pace-maker activity in frog atrial muscle. J. Physiol. 204, BROWN, R. H. (1973). The characterization and functionalsignificance of surface negative charges in cardiac muscle. D.Phil. thesis, Oxford University. BROWN, R. H. (1974). Membrane surface charge: discrete and uniform modelling. In Progress in Biophysic8, vol. 28, Pp , ed. BUTLER, J. A. V. & NOBLE, D. Oxford: Pergamon. BROWN, R. H., COHEN, I. & NOBLE, D. (1978). The interactions of protons, calcium andpotassium ions on cardiac Purkinje fibres. J. Phy~iol. 282, COzEN, I., DAuT, J. & NOBLE, D. (1976). The effects of potassium and temperature on the pacemaker current ik in Purkinje fibres. J. Phy8iol. 260, Di FRANCEsCO, D. & McNAUGHTON, P. (1977). The effects of calcium on outward membrane currents in Purkinje fibres from sheep hearts... Physiol. 270, 47P. FRNAENUuER, B. & HODGKIN, A. L. (1957). The action of Ca+ on the electrical properties of squid axons. J. Physiol. 137, GinBERT, D. L. (1971). Fixed surface charges. In Biophysics and Physiology of Excitable Membranes ed. ADELiAN, W. J. JR. New York: Van Nostrand Reinhold Co. GILBERT, D. H. & ERRENsTEIN, G. (1969). Effect of divalent cations on K conductance of squid axons: determination of surface charge. Biophys. J. 9, HAUSWIRTH, O., McAL8IEI, R. E., NOBLE, D. & TsIEN, R. W. (1968). Measurement of voltage clamp currents and reconstruction of electrical activity in Purkinje fibres under normal conditions and under the influence of adrenaline. J. Physiol. 198, 8-1OP. HAuswnIim, O., McALisTrER, R. E., NOBLE, D. & TsiEN, R. W. (1969). Reconstruction of the actions of adrenaline and calcium on cardiac pace-maker potentials. J. Physiol. 204, P.

11 Ca AND PROTONS ON PURKINJE FIBRES 343 HEc3ir, H. H. & HUTTER, 0. F. (1965). Action of ph on cardiac Purkinje fibres. In The Electrophysiology of the Heart, ed. TACcADI, B. & MAlcHEr'n, G. Oxford: Pergamon. HELIAM, D. C. & STUDT, J. W. (1974). A core-conductor model of the cardiac Purkinje fibre based on structural analysis. J. Phyeiol. 243, HTTTE, B. (1968). Charges and potential at the nerve surface: divalent ions and ph. J. gen. Phyaiol. 51, H.aE, B. (1970). Ionic channels in nerve membranes. In Progre88 in Biophypics, vol. 21, pp ed BUTLER, J. A. V. & NOBLE, D. Oxford: Pergamon. Hurrou, 0. F. & WARNER, A. E. (1967). The ph sensitivity of chloride conductance in frog skeletal muscle. J. Phyeiol. 189, MAHLER, H. R. & CORDES, E. H. (1969). Biological Chemietry. New York: Harper and Row. McALLIsTER, R. E., NOBLE, D. & TsrmN, R. W. (1975). Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Phy8iol. 251, MoBLEY, B. A. & PAGE, E. (1972). The surface area of sheep cardiac Purkinje fibres. J. Phyeiol. 220, MOZHAYEVA, G. N. & NAumov, A. P. (1970). Effect of surface charge on the steady-state potassium conductance of nodal membrane. Nature, Lond. 228, NOBLE, D. & TsIEN, R. W. (1968). The kinetics and rectifier properties of the slow potassium current in cardiac Purkinje fibres. J. Phyeiol. 195, VAN BOGAERT, P. P., VEREECKE, J. & CARMELIET, E. (1975). Cardiac pacemaker currents and extracellular ph. Archer int. Phyeiol. Biochim. 83, WEItD~NN, S. (1955). The effect of calcium ions and local anaesthetics on electrical properties of Purkinje fibres. J. Phyeiol. 129,