potential cannot be considered to be constant. (Received 25 August 1969) potential of calcium current was estimated to be about + 60 mv in normal

Transcription

1 J. Physiol. (1970), 207, pp With 10 text gurem Printed in Great Britain MEMBRANE CALCIUM CURRENT IN VENTRICULAR MYOCARDIAL FIBRES BY G. W. BEELER JR. AND H. REUTER* From the Section of Physiology and Biophysics, Mayo Clinic, Rochester, Minnesota, U.S.A. and the Department of Pharmacology, University of Berne, Switzerland (Received 25 August 1969) SUMMARY 1. A slow inward current in ventricular preparations of the dog heart can be measured by the voltage clamp method without interference from the initial rapid sodium current if the sodium system is inactivated by conditioning depolarization. 2. The slow inward current is very sensitive to variation in [ca]0. it occurs above the equilibrium potential of INa immediately after changing the bathing fluid to a sodium-free solution and persists under this condition for a long time without much alteration, while INa is rapidly abolished. Tetrodotoxin and [Mg]o have no effect on this current component. These results strongly support the view that the slow inward current in cardiac tissue is carried by calcium ions. 3. The threshold for initiation of the calcium current is around -35 mv in Tyrode solution and is shifted to more negative potentials by either increasing [Ca]0 or reducing [Na]0. 4. Calcium sensitive inward current tails associated with repolarization are assumed to represent a proportional measure of calcium conductance activated during the preceding depolarization. Calcium conductance declines rapidly with time in the inside negative potential range and slowly at positive potentials. The time constants for this 'inactivation' process vary between 40 and 700 msec in the potential range -35 to + 50 mv. 5. By using instantaneous current-voltage relations the reversal potential of calcium current was estimated to be about + 60 mv in normal Tyrode solution. As shown in the Appendix, however, the calcium equilibrium potential cannot be considered to be constant. 6. The importance of the calcium current for the plateau of the cardiac action potential is discussed. * Reprint address: Dr H. Reuter, Pharmakologisches Institut, Friedbiihlstrasse 49, Bern, Switzerland. 7 PHY 207

2 W. BEELER AND H. REUTER INTRODUCTION There is much evidence now that in cardiac muscle preparations calcium ions contribute a component of the total membrane current during the plateau of the action potential. In Purkinje fibres a slow calciumsensitive inward current has been shown to flow in the absence as well as in the presence of extracellular sodium during depolarization of the membrane (Reuter, 1966, 1967, 1968). Although in this cardiac tissue most of the currents measured in the potential range of the plateau do not seem to be carried very selectively by single ions species (Noble & Tsien, 1969 a, b; Peper & Trautwein, 1968), the small but rather well maintained calcium conductance is one of the factors determining the plateau. In addition, Carmeliet & van Bogaert (1969) were able to demonstrate action potentials of rather long duration in Purkinje fibres soaked in sodium-free, strontium-rich solution. Recently a slow inward current, apart from the fast excitatory current, has also been described by Rougier, Vassort, Garnier, Gargoull & Coraboeuf (1969) in frog auricular preparations. As already suggested by Niedergerke & Orkand (1966) this current is at least partially carried by calcium ions and influences greatly the plateau of the action potential in frog heart. Moreover, in mammalian ventricular fibre bundles kept in sodium-free solution calcium-dependent regenerative membrane voltage oscillations have been measured by Reuter & Scholz (1968). Reuter & Beeler (1969b) and Mascher & Peper (1969) presented further evidence that calcium ions are rather specific charge carriers for slow inward current in ventricular fibres from dog and sheep hearts during depolarization. In the preceding paper (Beeler & Reuter, 1970a) we gave a general description of ionic currents flowing through the membrane during stepwise changes of the membrane potential in dog ventricular fibres (voltage clamp technique). In the work described in the present paper we have studied the ionic requirements and the kinetics of the slow inward current more extensively. In a preliminary report (Reuter & Beeler, 1969b) it was shown that the slow inward current could be accurately separated from the large, rapid sodium current only if the sodium system was inactivated. Moreover, complete inactivation of the sodium current, INa, could be achieved under all conditions if the membrane potential was as low as -45 mv (Reuter & Beeler, 1969a; Beeler & IReuter, 1970a). Therefore, when the membrane was depolarized sufficiently long in a first step from the resting potential to about -40 mv, or when the holding potential was set to this level, the slow inward current could be investigated without interference from INa*

3 Ca CURRENT IN CARDIAC MUSCLE 193 METHODS The experiments were performed with thin ventricular trabeculae or papillary muscles excised from dog hearts. The apparatus and general experimental procedure have been extensively described in the preceding paper (Beeler & Reuter, 1970a) and need no further comment. Tyrode solution was used as the normal solution. In sodium-free solutions sodium chloride was replaced by isosmotic amounts of sucrose, choline chloride or Tris- (hydroxymethyl)-aminomethane (Tris) chloride. These solutions were buffered to ph 7-4 with Tris-buffer + HCl when oxygenated with 100% 02. The other constituents were the same as in Tyrode solution (cf. Beeler & Reuter, 1970a). Choline chloride solution contained atropine sulphate (5 x 10-6 g/ml.). In all solutions calcium chloride was sometimes varied between 0 and 7-2 mm. RESULTS The effects of [Ca]o and [Na]o on the slow inward current. In a previous report (Reuter & Beeler, 1969b) it has been shown that a slow inward current can be activated in dog ventricular fibre bundles at a membrane potential of about -30 mv when the rapid, large sodium current is inactivated by a conditioning depolarizing clamp step. This slow inward current occurs as net inward current even at inside positive potentials up to + 20 mv. Fig. 1 shows three series of depolarizing clamp steps recorded from a dog trabecula in Tyrode solution with and without calcium chloride. The membrane potential was first constantly displaced from the -81 mv resting potential to -40 mv, the holding potential, in order to inactivate the sodium system completely (Beeler & Reuter, 1970a). After a surge of capacitative outward current, increasing peaks of inward current were produced by stepwise changes of the membrane potential in the potential range -33 to -25 mv (series I and III). During stronger depolarizations thecurrent amplitude decreased again, and at potentials more positive than about + 25 mv it was not possible to separate the slow inward current accurately from delayed outward current which increases in this potential range (Beeler & Reuter, 1970a). Therefore, the equilibrium potential of this current could not be determined precisely in the conventional way (Hodgkin & Huxley, 1952a). Net inward current, however, was recorded in this experiment up to + 8 mv. This indicates clearly that the equilibrium potential of the slow inward current is in the inside positive potential range. Another approach to estimating the equilibrium potential, using the instantaneous current-voltage relations, will be described later (p. 202). Fig. 1 shows the effect of [Ca]0 on the slow inward current. In nominally calcium-free solution (series II) the slow inward current virtually disappeared within several minutes. The steady-state conductance at the end of the 570 msec pulse increased only to a small extent. The 7-2

4 W. BEELER AND H. REUTER abolishment of the slow inward current was immediately reversible in calcium-containing solution while the steady-state conductance was still slightly increased (series III). Fig. 2 shows the results of another experiment with different [Ca]0 (0.2, 1b8 and 7-2 mm) plotted as current-voltage relations. Here the membrane potential was changed in two steps in order to inactivate INa. The plotted values are the maximum inward current or minimum outward current flowing during the variable, second voltage step, V2. Since inward current cannot be separated easily from the outward current, especially 11 III 20/iA [ -33 m msec. Fig. 1. Effect of external calcium on membrane currents (upper traces) recorded from a dog ventricular trabecula during voltage clamp steps (lower traces). Tyrode solution with 1'8 mm-cacl2 (series I), 0 mm-cacl2 (series II) and 1P8 mm-cacl2 again (series III). The holding potential was set to -40 mv from a resting potential of -81 mv in order to inactivate 'Na. The figures beside voltage records indicate membrane potentials during displacement from the holding potential in this and subsequent Figures; inward current is shown downwards.

5 Ca CURRENT IN CARDIAC MUSCLE 195 in the positive potential range, we did not try to subtract the currents from each other in order to get the true values for inward current as has been done on other occasions (Fig. 9; Reuter & Beeler, 1969b). Therefore, the total inward current is underestimated in this plot and the crossover of the curves at the voltage axis indicates only the disappearance of net inward current and is not the equilibrium potential of the slow inward current. Outward current (#A) V2 (mv) I I EItx-I S I I I I \ V2 (mv) -10 V1 V2 Inward current (ua) Fig. 2. Current-voltage relations of slow inward current measured in a dog ventricular fibre in Tyrode solution with three different calcium concentrations (0.2 mm, filled circles; 1-8 mm, crosses; 7-2 mm open circles). The first potential step, V1, was always from the resting potential (-75 mv) to -44 mv in order to inactivate IN. at the variable potential step V2 (inset). Plotted are maximum inward (negative) or minimum outward current (positive; ordinate) flowing at the variable potential step V2 (internal potential; abscissa). In some preparations the current-voltage relation obtained with 7*2 mm- [Ca]0 crossed the voltage axis at more positive potentials than the one recorded with 1-8 mm-[ca]0. Fig. 2, however, shows clearly that net inward current at V2 increases with increasing [Ca]0. Furthermore, it demonstrates that the voltage dependence of the slow inward current up to its maximum amplitude at -20 mv is smoothly graded and that the threshold for initiation of this current is shifted to more negative potentials when [Ca]0 is increased. An interesting feature of this plot is the marked increase in steepness of the slopes of the current-voltage relations in the positive potential range as [Ca]0 is raised. This effect is more pronounced later in

6 196 G. W. BEELER AND H. REUTER the time course of the current records and makes an accurate separation of inward current from outward current even more difficult. The steep increase in net outward current at high [Ca]0 could explain the shortening of the action potential under comparable conditions (e.g. Hoffman & Cranefield, 1960). Effects of [Ca]0 on the slow inward current similar to those shown in Figs. 1 and 2 have been observed in each of eleven preparations. The dependence of this inward current on [Ca]0 suggests that it is carried by calcium ions. Mascher & Peper (1969) found a similar dependence of the second inward current on [Ca]o in sheep ventricular trabeculae and therefore also interpreted this current as a calcium current. It could be argued, however, that the second inward current is another sodium current since it is known that the availability of the sodium system is also dependent on [Ca]0 (Weidmann, 1955; Frankenhaeuser & Hodgkin, 1957; Beeler & Reuter, 1970a). Tetrodotoxin in a concentration (1.5 x 10-5 g/ml.) which greatly reduced or abolished INa (Beeler & Reuter, 1970a) had no effect on the slow inward current. The strongest evidence against this argument, however, are the results obtained in sodium-free solution (cf. Reuter & Scholz, 1968; Reuter & Beeler, 1969b; Mascher & Peper, 1969). Fig. 3 shows the result of an experiment in which the voltage clamp measurements were started very soon after the bathing fluid had been changed from Tyrode solution to sodium-free, choline chloride solution. There was still a small sodium inward current at -45 mv (panel a) which had changed its sign, becoming outward current, at -26 mv (panel b). Stronger depolarization to -20 mv (panel c) induced the slow inward current to occur above the equilibrium potential of the initial sodium current. This excludes the possibility that both inward currents are carried by the same ion species. Similar results have been obtained in four experiments. They indicated further that the slow inward current cannot be generated by sodium ions in unstirred extracellular clefts since the current was immediately affected by changes in [Ca]0 (cf. Fig. 1).The persistence of the slow inward current after a longer time in sodium-free solution is demonstrated in Fig. 4. Similar results were consistently obtained in many preparations no matter whether sodium was replaced by sucrose, choline or Tris. The initial INa was always rapidly abolished, while the slow inward current persisted until the preparation started to deteriorate after min in sodium-free solution. In a few experiments the slow inward current was slightly reduced in amplitude after withdrawal of [Na]0. However, this effect was inconsistent and is not considered to be the consequence of specific contribution of sodium ions to this current (Mascher & Peper, 1969) but rather is thought to be due to an accumulation of internal calcium in the fibres in the absence of [Na]0 (Reuter & Seitz, 1968). On the

7 Ca CURRENT IN CARDIAC MUSCLE 197 b c 30,A [ 50mV [ 520 msec Fig. 3. Membrane currents during voltage clamp steps. Measurements were started immediately after changing the bathing fluid from Tyrode solution to sodium-free (choline chloride) solution. Resting potential (= holding potential) -83 mv; voltage clamp step to -45 mv (a), -26 mv (b) and -20 mv (c). Note occurrence of slow inward current (c) above the reversal potential of initial fast inward current (b). 30ulA [ 57mV msec 510 msec Fig. 4. Membrane currents (upper traces) during depolarizing voltage clamp steps (lower traces) recorded from a dog ventricular trabecula in sodium-free solution (NaCl replaced by sucrose; 1-8 mm-cacl2). Holding potential (= resting potential) -85 mv. Note slow net inward current.

8 W. BEELER AND H. REUTER other hand a component of slowly inactivating or persisting INa cannot be excluded when the sodium system is fully activated (cf. Reuter, 1968). Due to the limitations of the clamp during the flow of INa (Beeler & Reuter, 1970a) this problem could not be resolved accurately. The threshold for initiation of the slow inward current was significantly more negative in sodium-free solution ( mv; mean + S.E. of mean) than in Tyrode solution ( mv). A plot of a current-voltage relation for slow inward current and for steady-state outward current of a fibre Outward current (,ua) mv I- I-\--I-I -+I I mv Inward current (ja) Fig. 5. Current-voltage relations of slow inward current and steady-state outward current obtained from dog ventricular trabecula in sodium-free solution (NaCl replaced by sucrose, 1-8 mm CaCl2). Slow inward current (x) is plotted as maximum inward or minimum outward current and is not subtracted from steady-state outward current; 'steady-state' outward current (*) was measured at the end of the 500 msec clamp step. Holding potential (= resting potential) was -81 mv. Abscissa: membrane current in jua; ordinate: membrane potential in mv. bundle in sodium-free solution is shown in Fig. 5. Here, as in Fig. 2, inward current is not subtracted from outward current but rather the initial current minima (crosses) and the current maxima at the end of a 500 msec depolarization (filled circles) are plotted. The outward current at the end of the pulse showed inward-going rectification exhibiting a negative slope in the voltage range from -50 to -30 mv, much the same as in Tyrode solution (Beeler & Reuter, 1970a). Net inward current occurred in the voltage range -25 to + 4 mv. The effect of changes of [Ca]0 on inward current was the same in fibres soaked in sodium-free as in sodium-con-

9 Ca CURRENT IN CARDIAC MUSCLE 199 taining solutions. Alterations of [Mg]o between 0 and 10 mm had no effect on the slow inward current. From these experiments it is concluded that the slow inward current which can be measured in ventricular myocardial fibres is a calcium current (ICa). The time course of IC. at various potentials. One of the major kinetic characteristics of a membrane current is its time course at different potential levels. The time dependent changes of calcium current in dog ventricular fibre bundles were analysed in detail by a conventional method introduced by Hodgkin & Huxley (1952 b). The method depends on the fact that the tails of inward current which are associated with repolarization immediately after a depolarizing pulse are a proportional measure of calcium conductance, provided that calcium is the only ion carrying positive charge into the fibre. It depends further on the assumption that the driving force (Em - Eca), does not change or that a possible change does not affect conductance. The theoretical discussion in the Appendix including computations on this subject, shows clearly that the latter assumption is not valid during the activation time of ICa since the equilibrium potential, E0a may shift appreciably due to the flow of ICa. Therefore, an accurate estimation of the time constants for activation of ICa was not obtainable, although the observed rate of activation became consistently more rapid with increasing depolarization (cf. Mascher & Peper, 1969). Nevertheless, during the decay of ICa, the current tails upon repolarization are a proportional measure of calcium conductance activated during the preceding depolarization. Therefore, the time constants of decay of I.C at different potential levels could be resolved accurately. In these experiments, which were performed in Tyrode solution, the holding potential was always clamped to about -40 mv in order to inactivate 'INa. Depolarizing clamp steps of varying amplitude and duration were applied and the inward current tails occurring upon repolarization were measured. These inward current tails were dependent on [Ca]0 in the same way as the slow inward current. The variation of inward current tails with the duration of the depolarizing pulse are illustrated by Fig. 6. In this experiment the membrane potential was clamped stepwise for varying durations to -23 mv where ICa was fully activated. The inward current tails decreased with increasing pulse duration. The maxima of these tails were obtained bv correction for the capacitative current and extrapolation to the end of the initial depolarization. Generally the inward current tails were measured at a higher time resolution than in Fig. 6. This allowed a more accurate estimation of the capacitative part of the inward current. The current maxima after the corrections were plotted on a semilog scale and could be fitted by straight lines. The time constants of these exponen-

10 W. BEELER AND H. REUTER tials were strongly dependent on the membrane potential during the preceding depolarization. This is illustrated by Fig. 7, which summarizes the results of seven similar experiments. The reciprocal time constants (rate constants) of the decay of the inward current tails are plotted as functions of the membrane potential during the depolarizing pulse. The voltage 201i A[ msec Fig. 6. Dependence of inward current tails associated with repolarization on the duration of the preceding depolarization. The amplitude of the depolarizing pulse was 17 mv; the holding potential was -40 mv and the resting potential was -81 mv; figures below each record indicate the duration of depolarizing clamp pulses. Ventricular trabecula in Tyrode solution. The envelope of inward current tails after correction for capacity current could be fitted by [1 - exp ( - t/tr)] in this and similar records. The time constant (r) depends on the strength of the preceding depolarization _- A _ v k 5.0 _- u r W 0 o x + o I +? *if o *o o.i I I I a Em(mV) Fig. 7. Variation of the decay rates of slow inward current (IC.) with membrane potential. Abscissa: membrane potential (Em) during depolarizing clamp steps; ordinate: rate constants of decay of slow inward current measured as reciprocal time constants (7-1; cf. Fig. 6). Results of seven experiments with different trabeculae in Tyrode solution are plotted. 82

11 a Ca CURRENT IN CARDIAC MUSCLE 201 dependence of the rate constants is very steep in the potential range from -35 to 0 mv. This means that Ica is inactivated rapidly at negative potential levels and slowly in the positive potential range, with time constants increasing up to 700 msec. This voltage dependence of the time constants of inactivation of ICa is of great significance for the plateau of 20/iA [ -18 mv msec Fig. 8. Membrane currents (upper traces) recorded from a dog ventricular trabecula in Tyrode solution during double-step voltage clamps (lower traces). The first potential step (40 msec) was always from the holding potential (-40 mv) to - 18 mv, the second step (470 msec) was varied in amplitude. Note that the decay rate of inward current measured at the second potential step decreases greatly as the membrane potential becomes more positive. the cardiac action potential as well as for the voltage- and time-dependent changes of activation of contraction described in the following paper (Beeler & Reuter, 1970b). Another experiment which provides an independent, qualitative confirmation of this result is shown in Fig. 8. Here the membrane potential

12 202 G. W. BEELER AND H. REUTER was changed in two steps. The first step had a duration of 40 msec and clamped the membrane potential always from -40 to -18 mv in order to activate ICa to its maximum. The second step was varied in amplitude and displaced the membrane potential between -51 and + 40 mv. The deflexion of the current tails which occurred at the second potential step was always in the inward direction after the capacitative surge. Net inward current could be measured up to + 8 mv. These current tails declined exponentially when corrected for the capacity and extrapolated to zero time, but the rate of decline decreased greatly as the membrane potential became more positive much the same as shown in Fig. 7. Identical results were obtained with three other preparations. Instantaneous current-voltage relation of Ica* From the result shown in Fig. 8 we felt justified in tentatively plotting the difference between maximum inward current at the beginning and maximum outward current at the end of the second potential step as total ICa in order to get information about the instantaneous relation between ICa and membrane potential (cf. Hodgkin & Huxley, 1952b). Such information appeared particularly desirable to us since it could give an estimation of the reversal potential of ICa. The condition for this approach is that ICa is always activated to the same extent at a first potential step (V1) and the driving force is changed by varying the potential at a second clamp step (JV2) as illustrated by Fig. 8. The total amplitude of the instantaneous inward current, ICa occurring at V2 should be large during hyperpolarization and it should decrease during depolarization. In Fig. 9 the results of such an experiment are plotted. The relation between instantaneous total ICa and membrane potential is shown in curve a (crosses). This instantaneous current-voltage relation for total ICa shows a marked curvature in the potential range between - 15 and + 5 mv, but it is almost straight on either side of this range. At potentials above + 40 mv the steepness of the delayed outward current (Beeler & Reuter, 1970a) increased, thus preventing subtraction of inward current from outward current. Because of the linearity of the instantaneous current-voltage relation between + 5 and + 40 mv, however, it seemed reasonable to extrapolate to the voltage axis in order to get an estimation of the calcium equilibrium potential, ECa. This would be at + 60 mv in this experiment. The second current-voltage relation (b) in Fig. 9 was obtained from the same preparation. In this case the differences between peak inward current and maximum outward current measured during single clamp steps are plotted. As predicted theoretically (cf. Hodgkin & Huxley, 1952 b), both current-voltage relations diverge appreciably at potentials more negative than -15 mv and run together at more positive potentials. Similar results were obtained with three other preparations. The average ECa estimated by this method was mv

13 Ca CURRENT IN CARDIAC MUSCLE 203 with 1-8 mm-[ca]0. This corresponds to an intracellular calcium ion concentration of 1-6 x 10-5 M. However, Eca cannot be considered to be constant since it has to be assumed that there is a continuous shift between free and bound calcium in the cardiac muscle fibre during a contractionrelaxation cycle (cf. Ashley & Ridgway, 1968). Furthermore, as will be shown in the Appendix, the flow of ICa itself might cause an appreciable shift of Era Since 'Ca increases with increasing [Ca]0, ECa is not affected by a change in [Ca]0 in the manner predicted by the Nernst equation mv I imv Y/^7 B-10 xqa - *-20 Inward current (1iA) Fig. 9. Plot a (crosses): instantaneous relation between membrane potential and slow inward current. The results were obtained from an experiment similar to that shown in Fig. 8. The first step had an amplitude of 20 mv and a duration of 35 msec; the second step was variable in amplitude and lasted 500 msec. Holding potential was -43 mv, resting potential -80 mv. The difference between maximum inward current, after correction for capacitative current, at the beginning of the second potential step and outward current at the end is plotted as total inward current (ordinate). Abscissa, membrane potential during the second step. Plot b (same trabecula as in plot a) filled circles: relation between total inward current (ordinate) and membrane potential during single depolarizing pulses (abscissa). Holding potential -43 mv. Further description in text. The effect of membrane potential on ICa- In order to investigate whether peak calcium current is related to the preceding membrane potential in the same way that sodium current is (Hodgkin & Huxley, 1952c; Beeler & Reuter, 1970a), the membrane potential was changed in two steps. Fig. 10 illustrates an experiment in which ICa was always activated at the same potential V2, while the preceding step, Vl, was varied. Peak ICa at V2 decreased only if appreciable ICa was activated at V1. This held true also for longer (1-2 sec) conditioning depolarization steps. Equal results were obtained with five preparations. Therefore, conclusive support for the similarities of the inactivation systems for LNa and ICa could not be obtained, although the relation between peak inward currents and the membrane potential during conditioning clamp steps is sigmoid in both cases.

14 204 20pA [ -11 mv -40 Ul 2. W. BEELER AND H. REUTER msec Fig. 10. Membrane currents (upper traces) during double-step voltage clamps (lower traces) recorded from a ventricular trabecula in Tyrode solution. Holding potential -40 mv, resting potential -81 mv. The conditioning clamp step was varied in amplitude and lasted 470 msec; the second step had an amplitude of 29 mv and a duration of 300 msec. Note that inward current at the second potential step decreases only if inward current is activated during the conditioning clamp step. DISCUSSION The main conclusions to be drawn from the experiments reported in this paper are, first, that the second inward current which can be analysed by the voltage clamp method in ventricular myocardial preparations is a calcium current and, secondly, that the rate of inactivation of this current is strongly voltage-dependent. The evidence for the conclusion that the slow inward current is carried by calcium ions is different from the classical approach of demonstrating a theoretically predicted shift of an ion equilibrium potential (Hodgkin & Huxley, 1952a). On the basis of such an analysis it has been shown that the rapid large inward current in ventricular cardiac muscle is a sodium current (Reuter & Beeler, 1969a; Beeler & Reuter, 1970a). Our main evidence for the assumption of a rather specific calcium current, on the other hand, is merely its ionic dependence. Since the only ionic require-

15 Ca CURRENT IN CARDIAC MUSCLE 205 ment for the existence of the slow inward current is the presence of [Ca]0 we conclude that calcium ions are the charge carriers of this current. In the Appendix of this paper a simple mathematical model is proposed, based on the present results, which indicates a continuous shift of the equilibrium potential of the slow inward current. This shift is presumed to be due to the inward movement of calcium ions. Since only a very small fraction of the total internal calcium concentration is supposed to be in the ionic form in myocardial fibres in the relaxed state (Katz & Repke, 1966), inward movement of calcium ions during depolarization can raise the amount of free internal calcium ions substantially in the vicinity of the membrane. Therefore, the driving force, i.e. the difference between membrane potential, Em, and effective equilibrium potential, Eca, changes drastically during the current flow at a given membrane potential. This makes it extremely complicated to use the change in the equilibrium potential as a measure of the specificity of the slow inward current, as is done in the classical Hodgkin-Huxley system. In the latter system the driving forces are considered to be functions only of the membrane potential since the internal ion concentrations do not change significantly during the current flow. Furthermore, the steady-state activation and inactivation variables for currents are expressed as functions of voltage-dependent rate constants (Hodgkin & Huxley, 1952d). While the initial rapid shift of the equilibrium potential prevents an accurate estimation of the activation rate constants of ICa' there is a strong voltage dependence of the inactivation rate constants. This latter current feature would be in agreement with the Hodgkin-Huxley kinetics. At this stage of our investigation, however, it cannot be definitely decided whether the calcium current in cardiac muscle can be adequately described by Hodgkin-Huxley equations. We hesitate to take such an approach for the following reasons: (i) Eca shifts during the flow of ICa, (ii) this effect obscures the determination of the time constants for activation of this current and (iii) the voltage dependence of the degree of inactivation is subject to much uncertainty. The calcium current carries the main charge in the inward direction during the plateau of the cardiac action potential. The strong voltage dependence of its decay with time is therefore an important kinetic feature. It provides a rather well maintained inward current at the inside positive potential range. If the voltage clamp is suddenly released during the flow of ICa' the membrane potential depolarizes immediately to the plateau level of a normal action potential (cf. Beeler & Reuter, 1970a, Fig. 4). Apparently the much larger and faster sodium inward current is mainly responsible for depolarization of the membrane to potential levels where ICa is rapidly activated, and, therefore, for the conduction of the action potential. If the membrane potential is sufficiently depolarized by

16 W. BEELER AND H. REUTER constant current pulses, calcium-dependent regenerative voltage oscillations can be recorded in sheep ventricular trabeculae soaked in sodiumfree solution (Reuter & Scholz, 1968). In these preparations Mascher & Peper (1969) also demonstrated two components of inward current with the same ionic requirements as in dog ventricular trabeculae. This confirms the conclusion of Reuter & Scholz (1968) that the inward current for these voltage oscillations is carried by calcium ions. The outward current could have kinetics similar to those described recently by Hauswirth, Noble & Tsien (1969) for comparable voltage oscillations in cardiac Purkinje fibres. Evidence that calcium ions contribute current during the plateau of the action potential was previously obtained from experiments performed on Purkinje fibres (Reuter, 1966, 1967, 1968). But in myocardial fibre bundles of mammalian as well as of frog heart the current components can be separated from each other more readily than in Purkinje fibres under voltage clamp conditions (Rougier et al. 1969; Reuter & Beeler, 1969b; Mascher & Peper, 1969; Beeler & Reuter, 1970a; this paper). The shortening of the action potential in cardiac muscle with increasing [Ca]0 is a well known phenomenon (e.g. Hoffman & Cranefield, 1960). This effect could be explained if one or both components of outward current (Beeler & Reuter, 1970a) are affected by [Ca]0. Some indication for this is shown in Fig. 2. The voltage dependence of net outward current is steeper in high [Ca]0 than in low [Ca]0. Furthermore, preliminary results (H. Reuter, unpublished observations) indicate that the delayed component of outward current (Beeler & Reuter, 1970a) is shifted to more negative potentials and rises more steeply if [Ca]0 is increased. If this effect could be confirmed it might be comparable to the influence of [Ca]0 on the availability of the sodium system in cardiac muscle (Weidmann, 1955; Beeler & Reuter, 1970a). Therefore, one must distinguish clearly in heart muscle between the contribution of calcium ions as charge carriers to the total inward current and the effect of these ions on the movement of other ions across the membrane. This work was supported by grants from the American Heart Association (AHA ) and from the National Institute of Health (FR 00007). One of us (H.R.) was a career investigator visiting scientist of the American Heart Association, sponsored by Dr E. H. Wood. APPENDIX In order to calculate the effect of calcium influx on the equilibrium potential for calcium ions in cardiac muscle, a simple mathematical model was adopted. In principle, the model makes use of the current measurements during repolarization described in this paper as a measure of calcium conductance. The digital computer (CDC 3200) was programmed to yield

17 Ca CURRENT IN CARDIAC MUSCLE 207 values (i) for the calcium current during the clamp step and during repolarization, (ii) for the change in internal calcium concentration during the flow of ICa, (iii) for the effective cicium equilibrium potential and the effective calcium conductance as functions of time. This was achieved by using a Runge-Kutta integration technique to solve eqns. (1) to (6) in small time intervals beginning with t = 0. The inward current tails during repolarization, h, which provide a measure of calcium conductance as a function of time (t) could be approximated by the equation Ir = Irexp (-tlrf)[1-exp (-t/tr)] (1) For each individual experiment the maximum value of the current tails during repolarization (Ir) and the fall time (Ti) were taken from the experimental data. The rise time (Tr) used for all calculations was 15 msec, based on the analysis of a single experiment. Thus eqn. (1) represents the experimental input to the calculations. In order to relate the effective calcium equilibrium potential, Eta, with the calcium concentration in the fibre interior, [Ca]1, the initial internal calcium concentration at t = 0 is assumed to be 104 mm (Katz & Repke, 1966) and [Ca]0 is 1*8 mm. Thus the effective calcium equilibrium potential at the present conditions is given by Eca = -82*5-30 loglo[ca]i (2) The computation of the rate of change of internal calcium concentration involves the calcium current, ICa' flowing during a clamp potential and is derived from A[Ca]1/At = -35 x 10-9 Ica (3) This equation gives the molar change in internal calcium concentration per msec based on the calcium influx measured in,ta. (ICa is negative for inward current.) The constant relating concentration change to current is determined from a combination of the Faraday number with an estimate of the fibre volume within the fibre bundle. The number of coulombs crossing the membrane per mole of calcium is 0.19 x 106, and the fibre volume is estimated at 0O15 x 1O4 ml. This estimate is made by assuming a fibre bundle diameter of 0 5 mm, a fibre bundle length of 1 mm, and a cross-sectional packing density of fibres within the bundle of 80 %. Therefore, the over-all internal calcium concentration at any time, t, during a clamp step is given by [Ca], = Co+j (d[ca]i!dt)dt. (4) where C0 is the calcium concentration in the muscle fibre at rest. Even if one assumes that the distribution of calcium is not uniform in the cross-

18 208 G. W. BEELER AND H. REUTER section of a myocardial cell, because of rapid binding of internal calcium ions, eqns. (3) and (4) should give correct values for [Ca], very close to the inner surface of the membrane. Therefore, the effective calcium equilibrium potential, Ec., can be expected to be reasonably approximated by eqn. (2). Using the value for the inward calcium current during repolarization, Ir, at a given time and holding potential, Eh, and having calculated the effective calcium equilibrium potential, calcium conductance, GCa' can be computed as GCa = Ir/(Eh-ECa) (5) This effective calcium conductance is then used with the value of the clamp potential, Ec, to compute the calcium current, ICa, at the clamp potential as ICa = 00a(Ec E-a) (6) The results of the computations can be summarized briefly. Proposing an initial [Ca]i of 104 mm, the calcium equilibrium potential starts at a value of mv, and then decreases as [Ca], increases. Based on our experiments, the shifting calcium equilibrium potential approximated a steady state after about 30 msec. This steady state value was in the neighbourhood of + 60 mv with 1 8 mm [Ca]0. The apparent decay of calcium current is not determined by a change in the calcium equilibrium potential, but is in fact a decay in the effective membrane conductance for calcium. Moreover, the observed rates of decay of the envelopes of calcium inward current tails were shown to be the same as the rate of decay of the however, was not the same as the rate of rise of the effective conductance owing to alterations in the effective calcium equilibrium potential. calculated calcium conductance. The rate of rise of Ir, REFERENCES ASHLEY, C. C; & RIDGWAY, E. B. (1968). Simultaneous recording of membrane potential, calcium transient and tension in single muscle fibres. Nature, Lond. 219, BEELER, G. W. JR. & REUTER, H. (1970a). Voltage clamp experiments on ventricular myocardial fibres. J. Phy8iol. 207, BEELER, G. W. JR. & REUTER, H. (1970b). The relation between membrane potential, membrane currents and activation of contraction in ventricular myocardial fibres. J. Phy8iol. 207, CARMELIET, E. & VAN BOGAERT, P. P. (1969). Strontium action potentials in cardiac Purkine fibers. Arch8 nt. Phy8iol. Biochim. 77, FRANKENHAEUSER, B. & HODGKIN, A. L. (1957). The action of calcium on the electrical properties of squid axons. J. Phy8iol. 137, HAUSWIRTH, O., NOBLE, D. & TSIEN, R. W. (1969). The mechanism of oscillatory activity at low membrane potentials in cardiac Purkinje fibres. J. Phy8iol. 200,

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