J. Phyeiol. (1978), 280, pp. 169-191 With 13 text-figures Printed in Great Britain

169

A POTENTIAL- AND TIME-DEPENDENT BLOCKADE OF INWARD RECTIFICATION IN FROG SKELETAL MUSCLE FIBRES BY BARIUM AND STRONTIUM IONS

BY N. B. STANDEN AND P. R. STANFIELD From the Department of Physiology, Medical Sciences Building, University of Leicester, University Road, Leicester LEl 7RH

(Received 30 November 1977) SUMMARY

1. A three-electrode voltage clamp method was used to investigate the effects of Ba and Sr ions on the inwardly rectifying K conductance of resting frog sartorius muscle fibres. 2. When Ba2+ (0 01-5 mM) was added to the control (115 mM-K+) solution the inward currents recorded during hyperpolarizing voltage steps turned off exponentially with time as the blockade by Ba2+ developed. Outward currents showed no time-dependence. 3. Ba2+ ions reduced both the instantaneous and the steady-state values of currents recorded on hyperpolarization. The blockade was potential-dependent, steady-state currents being increasingly reduced with increasing hyperpolarization. 4. The concentration-effect relation for the blockade of instantaneous currents by Ba2+ could be fitted assuming 1 :1 binding of Ba2+ to a receptor, with the block being proportional to the number of Ba2+-filled receptors. The apparent dissociation constant at the holding potential (-5 mV) was 0-65 mm. Concentration-effect relations were shifted along the concentration axis to lower concentrations by hyperpolarization. The apparent dissociation constant was reduced e-fold for a 16-8 mV change in potential. 5. Increasing the [Ba]0 increased the rate of onset of the blockade at a given potential. 6. The rate of onset of the blockade had a high temperature dependence (Q10 =

3*15 + 0.08). 7. When [K]o was doubled to 230 mm, under conditions where [K]1 was also doubled, [Ba]0 had to be raised approximately fourfold to produce the same degree and rate of onset of blockade. Similarly, when [K]o was decreased, the degree and rate of onset of blockade were increased for a given [Ba]0. 8. The blockade could be readily removed by removal of Ba2+ from the bathing solution. In addition the blockade which develops on hyperpolarization is removed exponentially on return to the holding potential. 9. The blockade which exists at the holding potential may be removed by a depolarizing prepulse. 10. Sr causes a similar potential-dependent blockade to that by Ba2+, but is around 400 times less effective.

N. B. STANDEN AND P. R. STANFIELD 170 11. The results have been fitted with a model assuming that the permeability mechanism is an aqueous pore with a site which binds one Ba2+ ion or two K+ ions. The site must have a high affinity for Ba2+ and a low affinity for K+. INTRODUCTION

The resting K permeability of skeletal muscle displays inwardly rectifying properties (Katz, 1949; Adrian & Freygang, 1962b). Thus, the permeability to K+ is high when V -VK is negative and low when V - VE is positive (Hodgkin & Horowicz, 1959). Similar systems occur in other cells: examples are the starfish egg cell (Hagiwara, Miyazaki & Rosenthal, 1976), eel electroplaques (Nakamura, Nakajima & Grundfest, 1965), and certain nerve cell bodies of invertebrates (Kandel & Tauc, 1966) and vertebrates (Nelson & Frank, 1967). Two kinds of model have been proposed for the way in which the rectification might occur, based either on a carrier or on an aqueous pore. In the models which suppose that K+ crosses the membrane in combination with a carrier it had been argued that the rectifying properties occur either because a large surface potential at the inside of the membrane limits access of K to the internal surface of the membrane (Horowicz, Gage & Eisenberg, 1968) or because the carrier is buffered in concentration by some means at the inside of the membrane (Adrian, 1969). Armstrong (1975a) has suggested an aqueous pore having a blocking particle at the inside of the membrane, which is expelled from the pore by K+ moving in, but which strictly limits the efflux of K+. Recently, some insight into permeability mechanisms in excitable cells has been obtained by investigations of potential-dependent blockades of these mechanisms by various agents (for reviews, see Armstrong, 1975b; Hille, 1976). A potentialdependent blockade of the inwardly rectifying K+ permeability by caesium ions has been described both in skeletal muscle (Gay & Stanfield, 1977) and in starfish egg cells (Hagiwara et al. 1976). Sperelakis, Schneider & Harris (1967) have shown that Ba ions block this system, and in this paper we show that this blockade by Ba2+ is potential and concentration-dependent. We also describe a model made on the assumption that Ba2+ exerts this action by binding to a site, for which K+ competes with Ba2+, within an aqueous pore. METHODS A three-electrode voltage-clamp method was used to measure K currents in skeletal muscle fibres of the frog (Rana temporaria). The method has been described in detail elsewhere (Adrian, Chandler & Hodgkin, 1970; Stanfield, 1970a; Almers, 1972a) and only needs summarizing here. Three micro-electrodes were impaled in a muscle fibre of the frog sartorius near to its pelvic end. Two of the electrodes were filled with 3 M-KCl and were used to record membrane potential at distances 1 and 21 from the end of the fibre. These membrane potentials will be called V1 and VE respectively. A third micro-electrode, Sfiled with 2 M-K citrate was impaled in the fibre at a distance 21+ 50 #sm from the end of the fibre. This electrode was used to pass current, so that the membrane potential V1 could be controlled. It may be shown that, under the experimental conditions described, the current flowing across the membrane of the end 31/2 in length of the muscle fibre is approximately proportional to the potential difference (V2- V') between the two recording electrodes (Adrian et al. 1970). The membrane current is given by Im =

-(I (V1A) V"A 2

Ba BLOCK OF INWARD RECTIFICATION

171

where a is the fibre radius and R. is the resistivity of the sarcoplasm. In the records illustrated in this paper, membrane current will be given as (V2 - V1). In most experiments I was set at 260 jsm, and the condition given by Adrian et al. (1970) for the approximation of eqn. (1), that (V2 - V1)/V1 should be less than 6, was kept throughout. The voltage clamp was used to hold the membrane potential of fibres at the resting potential during the experiments and to change the membrane potential from this level in a step-like manner. Soltdions. The composition of the solutions used is given in Table 1. Most of the experiments were carried out in the solution containing 115 mm-K+ (solution B), though in a number of experiments [K]0 was reduced to 58-75 mm (solution A) or increased to 230 mm (solution C). A few experiments used potassium at 10 mm (solution D). Acetate was used as an impermeant Na+

TABLE 1 Ca2+ K+

Acetate

Tris-HCl

119-85 118-6 233-6 118-6

5 5 10 5

(mm) Solution A Solution B Solution C Solution D

57-5 105

58-75 115 230 10

1-8 1-8 1-8

1-8

anion. Ba2+, Sr2+ or Ca2+ were added to these solutions as acetates. For most experiments the solutions were buffered with Tris-HCl, the pH being 7-5-7'7. In a few cases Tris-maleate buffer was used at 5 mM (pH 7 5). The results in solutions buffered with Tris-maleate, both without Bal+ and in the presence of 0 5 mm-Ba2+, did not differ from those in Tris-HlC buffered solutions. Each fibre was examined in one experimental solution. A t-test was used to compare results from groups of fibres. Most experiments were carried out at room temperature, 20-23 0C, but in some the temperature was reduced to 10-14 0C or 05-3 0C. RESULTS

The first results to be described are those in the 115 m -K+ solution (solution B, Table 1). In this solution the mean resting potential was - 4-87 + 0-15 mV (sixtyeight fibres). Under these conditions, both the delayed potassium conductance and the mechanical response are inactivated (Nakajima, Iwasaki & Obata, 1962; Adrian et al. 1970; Hodgkin & Horowicz, 1960). The K conductance which is examined in the experiments of this paper is that which normally exists at rest and which shows inwardly rectifying properties (Katz, 1949; Adrian & Freygang, 1962 b). Records of V2 - V1 (proportional to membrane current - see Methods) and membrane potential (V1), together with current-voltage relations are given in Fig. 1. The results are from two fibres, one immersed in solution B (115 mM-K+, Table 1) without Ba2+ and the other in solution B to which Ba2+ had been added at 0-5 mm. The Figure summarizes the main results, that Ba2+ produces a time- and potentialdependent blockade of the resting K+ permeability of skeletal muscle fibres. Fig. 1A shows records from the fibre in the control solution. Inward currents obtained upon hyperpolarizing the membrane are larger than outward currents obtained upon depolarization, because of the rectifying properties of the permeability mechanism. The inward currents show little decline with time when the membrane is hyperpolarized. Such decline as does occur may be attributed to depletion of K+ from the lumen of the T-system of the muscle, since much of the permeability lies in the walls of the T-system (Adrian & Freygang, 1962a; Almers, 1972a, b). The depletion process is very slow in high K+ solutions (Almers, 1972a). A current-

172

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-25 Fig. 1. A, records of membrane potential (VI, upper) and membrane current (V2-VL, lower) from a muscle fibre immersed in 115 mm-K+ solution (solution B). Holding potential -4 mV, temperature 23 0C. B, current-voltage relation for the same fibre as in 1A. The current (plotted as V. V1) is measured at the beginning of the pulse. The broken line shows the linear element (see text) obtained by extrapolating the current points above + 60 mV through the holding potential. C, records of membrane potential (V,, upper) and membrane current (V2 VF, lower) from a muscle fibre immersed in 115 mM-K+ solution containing 0 5 mm-Ba2+. Holding potential -4 mV, T 20*1 0C. Oscilloscope sweep 5 x faster than in A. D, current-voltage relation for the same fibre as in 10. 0O instantaneous currents (recorded at the beginning of the hyperpolarizing pulse). *, steady-state currents (recorded at the end of the hyperpolarizing pulse). The curves were drawn by eye. The inter-electrode distance, 1, was set at 250 jam in each case. Assuming a fibre diameter of 80 um, and a sarcoplasmic resistivity of 170 0. cm (Hodgkin & Nakajima, 1972), when V2- V is 10 mV, membrane current (Im) is 0-13 mA. cm-2. -

-

173 Ba BLOCK OF INWARD RECTIFICATION voltage relation, plotted from the currents at the beginning of the depolarizing and hyperpolarizing pulses, is given in Fig. 1B.

The blockade of inward currents by Ba2+ Fig. 1C shows records obtained in a fibre in the 115 mM-K+ solution, containing Ba2+ at 0 5 mm. Note that the sweep speed is five times faster in Fig. 1 C than Fig. .IA. As in Fig. 1A, the inward currents obtained on hyperpolarizing are larger than the outward currents obtained when the membrane is depolarized. However, the inward currents now turn off with time, since the blockade of these currents by Baa+ is enhanced by hyperpolarization of the membrane (see p. 6). Outward currents show no detectable time dependence. Current-voltage relations for this fibre are plotted in Fig. 1D. That plotted for the currents at the beginning of the hyperpolarizing pulse (0) shows inward rectification, though the size of these currents is smaller in the presence of Ba2+ than in its absence, (see below p. 6). The steady-state currents (@), plotted from currents at the end of the pulse, show that the inward currents are shut off upon hyperpolarization. --10

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179 Ba BLOCK OF INWARD RECTIFICATION 230 mM-K+ solutions was approximately twice that of the 115 mM-K+ solutions. That [K]1 increased with the increase in osmolarity indicates the impermeance of acetate. In the 58-75 mM-K+ solution, the mean resting potential was -19-46 + 0-42 mV (thirteen fibres). Blockade of in8tantaneou8 currents by Ba2+ in 58-75 mM-K+ and 230 mM-K+. The general result from these experiments is that Ba2+ is much more effective at blocking K currents when the K+ concentration is reduced, and less effective when it is increased. A -120

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Fig. 7. Current-voltage relations in 58-75 mM-K+ and 230 mM-K+ solutions. A, 58-75 mi-K+ (solution A). O. currents in control solution (five fibres). A, instantaneous currents in 58-75 mu-K++0.5 mM-Ba2+ solution. *, steady-state currents in 58-75 mi-K+ + 0 5 mM-Ba2+ solution (eight fibres). Bars give 2 x s.E. of mean. B, 230 mm-K+ (solution C). 0O currents in control solution (nine fibres). A, instantaneous currents in 230 mm-K+, 5 m -Ba2+. A, steady-state currents in 230 mm-K+, 5 mM-Ba2+ (seven fibres). Bars give 2 x s.z. of mean. Note smaller scale on ordinate compared with A. The curves were drawn by eye.

Fig. 7A shows mean instantaneous current-voltage relations (open symbols) from fibres in the 58-75 mM-K+ solution without Ba2+ and with Ba2+ at 0.5 mM. The instantaneous currents are reduced to 35-9 + 22 0% by 0 5 mM-Ba2+ when [K]o is 58-75 mm, compared with a reduction to 49-6 + 8.5% in 115 mM-K+. In 230 mM-K+, 0 5 mM-Ba2+ did not significantly reduce instaneous currents from their value in the control solution (P > 0.25). Fig. 7B shows mean instantaneous current-voltage relations (open symbols) from fibres in 230 mM-K+ solution without Ba2+ and with Ba2+ at 5 mm. The instantaneous currents are reduced to 32-4 _ 3.7 % of their control values by 5 mM-Ba2+. That instantaneous currents are reduced to approximately the same amount by 0 5 mm-Ba2+ in the 58-75 mM-K+ solution and by 5 mM-Ba2+ in the 230 mM.K+ solution might suggest that a fourfold increase in K+ concentration requires a tenfold increase in [Ba]0 to produce the same

N. B. STANDEN AND P. R. STANFIE1LD

180

effect. However, we believe that the K concentration at the level of a binding site will not necessarily change fourfold when external [K] is changed fourfold. In the model described in the Discussion (pp. 185-189), we assume that the K+ concentration at the binding site is proportional to [K]0 only when [K]0 and [K]1 are changed together, as in our experiments in solutions containing 115 and 230 mM-K+. A

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Fig. 8. A, concentration-effect relation for the action of Ba2+ on the resting K+ permeability mechanism in 230 mM-K+ solutions. Ordinate: mean currents as fraction of mean control values. O, instantaneous currents. *, steady-state currents at a membrane potential of -25 mV. A, steady-state currents at -45 mV. Means from five to seven fibres. Bars give 2 x s.E. of mean. The continuous lines are drawn assuming reversible binding of one Ba ion to one receptor with dissociation constants of 3 0, 0-68 and 0-26 mm respectively. B, dependence of the apparent dissociation constant for Ba2+ on membrane potential in 230 mM-K+ solutions. The KYpp changes e-fold for a 19-5 mV change in potential. The straight line was fitted by eye.

-181 Ba BLOCK OF IN WARD RECTIFICATION Fig. 8A gives the concentration-effect relation for the effect of Ba2+ on the instantaneous currents in 230 mm-K+. As with the relations of Fig. 4A, we have attempted to fit the points with a line drawn on the assumption that one Ba ion binds reversibly to one receptor. In this case, the dissociation constant is increased to 3 mm, an increase to 4-6 times its value in 115 mM-K+. Although the fit in the case of the results in 230 mM-K is not as good as in the case of those in 115 mm-K+, the increase in dissociation constant strongly suggests competition between Ba2+ and K+ for a site in the permeability mechanism. The shift of over 4 times for a twofold change in [K]o suggests that two K+ ions or one Ba2+ ion may bind to one receptor (see Discussion). 400 B

A

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0 -40 -80 Membrane potential (mV) Fig. 9. A, dependence of the time constant, r, for the onset of the blockade by Ba2+ on membrane potential in 58.75 mM-K+, 0-5 mm-Ba2+ solution. Means from eight fibres. Bars 2 x s.E. of mean. B, dependence of rTon membrane potential in 230 mm.K+ solutions. O, 0-5 mII.Ba2+ (seven fibres). *0, 2 mm-Ba2+ (five fibres). A. 5 mm-Ba2+ (seven fibres). Bars 2 x S.E. of mean. The curves were drawn by eye. 0

-120

Blockade of 8teady-8tate current by Ba2+ in 58Z75 mM-K+ and 230 mM-K+. The effect of Ba2+ on the steady-state currents, and therefore on the degree of blockade which develops on hyperpolarizing the membrane, is also enhanced by reducing [K]o to 58-75 mm and reduced by increasing [K]o to 230 mm, as may be seen by comparing the steady-state current-voltage relations of Fig. 7 with those of Fig. 3 B and C. Fig. 8A gives concentration-effect relations between [Ba]o and the amplitude of the steady-state currents expressed as a fraction of the amplitude of the currents in the 230 mM-K+ control solution. These relations are at membrane potentials of -25 and -45 mV. The apparent dissociation constants are 0-68 and 0*26 mm respectively. The relationship between the apparent dissociation constant and

N. B. STANDEN AND P. R. STANFIELD potential, given in Fig. 8B, suggests that the dissociation constant changed e-fold for a 19 5 mV change in membrane potential. We investigated the effect of only one Ba2+ concentration in the 58-75 mM-K+ solution. Effects of Ba2+ on rate of onset of blockade in 58 75 mM-K+ and 230 mM-K+. Fig. 9A shows the potential-dependence of the time constant for the onset of the blockade by 0 5 mM-Ba2+ in 58-75 mM-K+, while Fig. 9B shows time constants for 0 5, 2 and 5 mM-Ba2+ in the 230 mM-K+ solution. Again, the onset of the blockade is faster for a given potential and a given [Ba]o when [K]o is low and slower when [K]0 is high. In 0 5 mM-Ba2+, for example, when [K]0 is increased from 115 to 230 mm, the time constants are increased from 143 + 7 msec (nine fibres) to 328 + 11 msec (six fibres) at a membrane potential of -25 mV, and from 43 + 3 msec (nine fibres) to 128 + 8 msec (six fibres) at a membrane potential of -65 mV. The average increase for membrane potentials between -25 and -85 mV was 2-80 times. In 2 mM-Ba2+, the average increase in time constant is 4 40 times when [K]o is increased from 115 to 230 mM. 182

Recovery from Ba2+ blockade Reversibility of blockade on removal of Ba2+. In order to test whether the blockade by Ba could be reversed when Ba2+ was removed from the bathing solution, six fibres which had previously been exposed to Ba-containing solutions (at Ba2+ concentrations from 0 01 to 2-0 mM) were voltage-clamped in control solution (Table 1 B). The currents recorded from these six fibres were not significantly different (P > 0.33) from those recorded in control solution from fibres which had not been previously exposed to Ba2+. Thus the blockade can be completely reversed by washing in Ba2+-free solution. Recovery from blockade on return to the holding potential. Since the blockade by Ba2+ is potential-dependent that part of the blockade which develops upon hyperpolarization will be removed when the membrane is returned to the holding potential. The rate of this recovery from blockade was examined in two-pulse experiments in which the time interval between two identical hyperpolarizing pulses was varied between 5 and 3000 msec. Records from such an experiment are shown in Fig. 10A. The time course of the recovery is shown in Fig. lOB. The fractional recovery is expressed as '2/Il where '2 is the current measured 20 msec after the start of the second hyperpolarizing test pulse minus the current at the end of the pulse and I, is the current measured 20 msec after the start of the first test pulse minus the current at the end of the pulse. The recovery followed an exponential time course with a time constant of 560 msec. Since the degree of steady-state blockade increases with increasing hyperpolarization, partial recovery from blockade also occurs at potentials more negative than the holding potential, but less negative than the initial hyperpolarizing pulse. Fig. 11A shows records from such an experiment. The fibre was first hyperpolarized to - 105 mV for 100 msec and then repolarized to -35 mV (the holding potential was -5 mV). It can be seen that during the first pulse the current decreased exponentially as the blockade developed, but that on repolarization to -35 mV the current increased exponentially, showing the removal of the blockade at that potential. The time constant for recovery was 55 msec in this case.

Ba BLOCK OF IN WARD RECTIFICATION 183 This recovery was also examined using three-pulse experiments. Two identical 100 mV hyperpolarizing pulses were separated by a 20, 40 or 60 mV hyperpolarizing pulse, the duration of which was varied. The time course of recovery for a 20 mV intermediate pulse is shown in Fig. lOB. With 40 or 60 mV intermediate pulses recovery was very slight and it was difficult to determine the time course. A

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Fig. 10. Recovery from Ba2+ blockade on return to the resting potential. A, records of membrane potential, V1 (above) and current V2 - V1 (below) from a fibre immersed in 115 mM-K+, 05 mM-Ba2+ solution. Holding potential -5 mV, 20-1 'C. The interelectrode distance, 1, was set at 250 jum. Assuming a fibre diameter of 80 /sm, and a sarcoplasmic resistivity of 170 0. cm, when V2 - V1 is 10 mV, membrane current (Im) is 0-13 mA.cm-2. B, recovery from blockade as a function of interval between two test pulses. Ordinate: '2/I1 where I2 = current measured 20 msec after the start of the second test pulse minus the current at the end of the second test pulse. I = current measured 20 msec after the start of the first test pulse minus the current at the end of the first test pulse. Abscissa: interval between the two test pulses. Same fibre as in part A. 0O membrane potential during interval between test pulses = -5 mV. *, membrane potential during interval = -25 mV.

In the three-pulse experiments, the time constants for recovery in two fibres were 132 and 70 msec during a 20 mV hyperpolarization, and 20 msec (in the second fibre) during a 40 mV hyperpolarization. Release by depolarization of the blockade at the holding potential. The blockade of the instantaneous currents seen on hyperpolarization could be that component of the potential-dependent blockade which is already present at the holding potential or, alternatively, might be a different type of blockade from that which develops upon hyperpolarization. If the former is the case than it should be possible to relieve the blockade of instantaneous currents by depolarization of the membrane. Fig. 1 B shows records from an experiment designed to test this idea. First, a hyperpolarizing test pulse (to - 105 mV) was presented alone and then the same test pulse was preceded by a 1 sec depolarizing prepulse to +95 mV. It can be seen that the current during the hyperpolarizing pulse was substantially larger (by 90 % for the

N. B. STANDEN AND P. R. STANFIELD 184 instantaneous currents minus the current at the end of the pulse) in the second case. This suggests that the blockade which exists at the holding potential is the same potential-dependent blockade as that which develops when the membrane is hyperpolarized. The results of an experiment showing the steady-state distribution of the blockade with voltage are given in Fig. 13D, which is further described in the Discussion (p. 189). A

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Fig. 11. A, recovery from blockade at a potential negative to the holding potential. 115 mm-K+, 05 mM-Ba2+. Holding potential -5 mV. 20.0 'C. B, C, records showing removal of blockade at the holding potential by a depolarizing prepulse. Upper traces, membrane potential; middle traces, membrane current (V-V1). Lower traces, membrane current during the hyperpolarizing test pulse displayed at a higher sweep speed. B, hyperpolarizing test pulse alone. C, hyperpolarizing test pulse preceded by a depolarizing prepulse. Fibre immersed in 115 mM-K+, 0.5 mM-Ba2+. Holding potential -5 mV. Temp. 20-3 'C. The inter-electrode distance, 1, was set at 250 /sm. Assuming a fibre diameter of 80 #m and a sarcoplasmic resistivity of 170 Ql.cm, when V2 - V1L is 10 mV, membrane current (I.) is 0-13 mA.cm-2.

Effects of Sr on K currents We also investigated the possibility that Sr2+ and Ca2+ might have an effect similar to that of Ba2+ in blocking potassium currents. Sperelakis et al. (1967) found Sr2+ to be without effect at similar concentrations to Ba2+, but our results show that Sr2+ does produce a blockade at higher concentrations. We were unable to detect any blockade by 10 mM-Ca2+ even in solutions containing only 10 mM-K+. Experiments with Sr2+ in 115 mM-K+ solutions. Experiments were carried out in 115 mM-K+ solutions (solution B, Table 1) to which strontium acetate was added at 5 or 10 mM. Fig 12. summarizes the results obtained with 10 mM-Sr2+. As with Ba2+

Ba BLOCK OF INWARD RECTIFICATION 185 the currents shut down substantially along an exponential time course on hyperpolarization (Fig. 12 A) and the degree of steady-state blockade increases with increasing hyperpolarization (Fig. 12 B). Fig. 12C shows a plot of the time constants for the onset of blockade by Sr2+ against membrane potential. The value of these time constants lies between those obtained in 0-01 and 0-05 mM-Ba2+. Comparison with Fig. 5B suggests that Sr2+ is around 400 times less effective than BaO+ at blocking the K currents. A

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-180 -140 -100 -60 -20 Membrane potential (mV) Fig. 12. The blockade by 10 mM-Sr2+ in 115 mM-K+ solution. A, records of membrane potential, above, and membrane current (as V. - VT'), below, from a fibre immersed in 115 mM-K+, 10 mM-Sr2+ solution. Holding potential -7 mV. 23-8 'C. The inter-electrode distance, 1, was set at 250 ,um. Assuming a fibre diameter of 80 /zm and a sarcoplasmic resistivity of 170 0 . cm, when V2- V1 is 10 mV, membrane current (Im) is 0-13 mA. cm-2. B, current-voltage relation for fibres in 115 mM-K+, 10 mM-Sr2+ solution. 0O instantaneous currents. 0, steady-state currents. Means from three fibres. Bars 2 x s.E. of mean. C, dependence of time constants for onset of blockade by 10 mM-Sr2+ on membrane potential. Mean from three fibres. Bars 2 x s.E. of mean. The curves were drawn by eye. DISCUSSION

Our results show that the alkaline earth metals Ba2+ and Sr2+ cause a potentialdependent blockade of the inwardly rectifying K+ permeability of frog skeletal muscle, much as Ca+ does (Gay & Stanfield, 1977). Unlike the blockade by Cs+, which is virtually instantaneous, that by Ba2+ develops slowly on hyperpolarization of the membrane. Several authors have described potential-dependent blockades of conductance mechanisms in excitable cells. Armstrong (1975b) has reviewed a number of these experiments. The tetraethylammonium (TEA) and nonyltriethylammonium (C9) ions produce such a blockade in the delayed K+ conductance of squid axon (Armstrong, 1971) and frog node of Ranvier (Armstrong & Hille, 1972) when applied from the inside. Similarly, Strichartz (1973) has described a blockade of the Na conductance of frog node by a quaternary ammonium derivative of lidocaine. These findings are usually explained by suggesting that the gating mechanisms of these

N. B. STANDEN AND P. R. STANFIELD 186 conductances restrict access of the blocking agents to an aqueous channel: blockade occurs when the channels are opened by depolarization. Woodhull (1973) has described a blockade by H+ of Na currents in frog node and has suggested that these ions are attracted into a channel, where they bind, by the electrical field of the membrane. The potential dependent blockade by Cs+ of the inwardly rectifying K+ permeability of skeletal muscle (Gay & Stanfield, 1977) and of starfish egg (Hagiwara, Miyazaki & Rosenthal, 1976) may be explained in a similar way (Hagiwara et al. 1976; L. A. Gay, personal communication). The blockade by Ba+ reported here appears to depend on membrane potential, while the direction in which K+ moves, and the rectifying properties of the conductance (Hodgkin & Horowicz, 1959; Adrian & Freygang, 1962 b), depend upon the driving force on K (V-VK). A substantial degree of blockade exists at the resting potential (and holding potential) which cannot depend on a net inward movement of K+. This block is potential-dependent and is removed by depolarization. Further (Fig. 11 A) the blockade produced by hyperpolarizing the membrane by 100 mV can be partly removed by reducing the hyperpolarization to only 30 mV, under conditions where K+ is still moving in. In addition, the onset of the blockade clearly does not depend on a transport number effect, with every nth ion moving into an aqueous channel being a Ba ion. Doubling [K]0 produces an approximately fourfold shift in the dependence of both the speed of onset and equilibrium position of the blockade on [Ba]0. The implications of this for the blockade and for the effect of [K]0 will be discussed further below. The blockade by BaO+ appears to be produced by the binding of Ba2+ to some site in the membrane. First, our results give a reasonable fit to concentration-effect curves predicted by assuming one-to-one binding of barium to a receptor. Secondly, the blockade has a high temperature-dependence, whereas Almers (1972b) has shown that the currents flowing through this permeability mechanism have a low temperature-dependence (Q10 value of 1.57). The rate of onset of the blockade at a given membrane potential has a Q10 of 3-15 + 0-08 (Fig. 6). This value shows that the blockade is dependent on a reaction between Ba2+ and a site in the membrane rather than on Ba2+ simply moving partway into an aqueous pore. We have attempted to fit our results with a model proposing that the permeability mechanism is composed of aqueous pores each containing a binding site which will bind one Ba2+ ion or two K+ ions. Ba2+ has access to the site from the outside of the membrane, but does not pass through the permeability mechanism. We have assumed that the site will bind two K ions since, comparing our experiments in 115 and 230 mM-K+ solutions (where the resting potential is virtually unaltered because of shrinkage of the muscle fibres in the 230 mM-K+ solution), the concentration effect relation is shifted to approximately four-fold higher Ba2+ concentrations (Figs. 4A and 8A). A similar shift is also suggested by comparing rates of onset of the blockade in 115 and 230 mM-K+ solutions. If Figs. 5B and 9B are compared, the predicted [Ba]o which would have the same effect in 115 mM-K+ as 0-5 mM-Ba2+ has in 230 mM-K+ is 0*17 mm. Similarly, the predicted concentrations which would have the same effect in 115 mM-K+ as 2 mM and 5 mM-Ba2+ do in 230 mM-K+ are

Ba BLOCK OF INWARD RECTIFICATION 187 0-52 and 1*25 mM respectively. On average, Ba2+ is 3*6 x less effective in 230 mM than in 115 mM-K+ from the evidence of rates of onset of block. Thus we propose that the reactions between Ba2+ and K+ and the binding site (R) are of the following kind: Ba+R = BaR 2K+R = K2R and the dissociation constants KBa and KK are given by

= [Ba]R {[R]TOtal -[BaR] - [K2R]} KBa a ~~~[BaR] KK= [K]P {[R]Tot&l-[BaR] - [K2R]}

[K2R]

where [R]TOW1 is the total concentration of sites and [Ba]R and [K]R are the concentrations of Ba2+ and K+ at the binding site. The concentration of sites filled by Ba2+ will then be given by [BaR]

[R]Total

(2)

In attempting to fit our results we have supposed that the concentration of Ba2+ at this site is related to [Ba]o by a Boltzmann relation in the form [Ba]R = [Ba]o exp (- z4VF/RT) (3) where 4 is the fraction of the potential difference (V) across the membrane experienced at the level of the binding site, z is the valency of Ba2+ and RT/F = 25 mV. This expression is identical in form to that used by Frankenhaeuser & Hodgkin (1957) in discussing the effects of external Ca on excitability of squid axon. From Figs. 4B and 8B, the apparent dissociation constant for Ba2+ changes e-fold for a 16*8 mV change in potential in 115 mM-K+ and for a 19-5 mV change in 230 mM-K+. The theoretical change would be e-fold for a RT/zF4 (= 12-5 mV/4) change in potential, giving values for 6 of 0 74 and 0'64 respectively. We have used the value 6 = 0 7 in our calculations. While it is likely that [K]R varies in a complex way with membrane potential, we have used a simplifying assumption that the concentration is independent of membrane potential. Under conditions where [K]O and [K]1 are changed together, as in our 115 m and 230 mM-K+ experiments, we have supposed that [K]K is proportional to [K]o, and have incorporated the proportionality constant into KK. It seems incorrect to assume that [K],R depends upon potential in the same way as [Ba]R, that

[K]B = [K]O exp (- &VF/RT)

(4)

since K+ must have access to the proposed binding site from both sides of the membrane. Thus, hyperpolarization of the membrane might be expected to lead to a build up of K+ on the outside of the blocked region of a pore but would reduce it on the inside. In the absence of blockade, where K is able to cross the membrane, [K], would not build up in the way given by eqn. (4). One further consideration is that eqn. (4) leads to unrealistic values for [K]B. For example, where [K]0 is 230 mm, eqn. (4) predicts that [K]1 would rise to 4-3 M during a hyperpolarization of 100 mV.

N. B. STANDEN AND P. R. STANFIELD 188 Eqns. (2) and (3) may be combined to give

[BaR]

[=Tot

~~~~+ [Ba]0 + KK exp (- z5VF/RT) If the fraction of channels blocked is equal to [BaR]/[R]TOtal, the fraction of channels open (y) will be given by (5) + [K]V + [Ba]0 exp (-K Fig. 13 summarizes our attempts to fit our experimental results by eqn. (5) using the values a = 0 7 and KB8 = 0-02 mm. We have chosen values for [K]R/KK of 44-1 (= (115)2/300) in 115 mM-K+ and 176-3 in 230 mM-K+. It should be stressed that the values taken for the dissociation constants KB8 and KK are in no sense absolute, since similar results can be predicted by changing these values over a large range, but keeping the ratio between them about the same. Where [K]R/KK > 1, eqn. (5) reduces to the following form

1-Y = (1+[Ba]

VFKR)

exp (-z8 Our results may then be fitted with 6 = 0-7 and KB./KK = 0.02/300, using eqn. (6).

(6)

Fig. 13A shows concentration-effect curves predicted by the model. Comparison with the experimental results (Figs. 4A, 8 A) shows that in 115 mM-K+ at -5 mV the predicted apparent dissociation constant (Kapp) for Ba2+ was 0-68 mm, compared with an experimental value of 0 65 mm. In 115 mM-K+ at -25 mV and -45 mV the predicted Kapp values are 0-22 mm and 0 07 mm respectively, compared with experimental values of 0-12 and 0 03 mm. When [K]0 was increased to 230 mM, the predicted Kapp was 2-6 mm and the experimental value 3 0 mM. Fig. 13B shows current-voltage relations predicted in 115 mM-K+ solutions with [Ba]o at 0.05 and 0 5 mm. It can be seen by comparison with Fig. 3 that both the predicted instantaneous and steady-state curves are similar to those observed experimentally. The control current-voltage relation in 230 mM-K+, together with the instantaneous (dashed) and steady-state (dotted) relations in 5 mM-Ba2+ predicted by the model are shown in Fig. 13C. Again, comparison with Fig. 7B shows the similarity to the results observed experimentally. The relation between the steady-state blockade and membrane potential which the model predicts is shown in Fig. 1 3D by the continuous line. The filled circles show the experimental points obtained from one fibre. An alternative explanation is that Ba2+ and K+ compete for a carrier in the membrane, and that the potential-dependence of the blockade is due to hyperpolarization bringing more carrier to the outside surface of the membrane. We regard this explanation as less likely because such a carrier would have to have a lower affinity for K+ than for Ba2+ and Sr2+. Also, with such a carrier, the access of Ba2+ and K+ to the binding site would be expected to vary in the same way with potential. It seems unlikely from our model, which assumes an aqueous pore, that this is so.

189 Ba BLOCK OF INWARD RECTIFICATION Thus the model described here predicts the experimental results which we have obtained rather well. We suggest, therefore, that Ba2+ exerts its blockade of the inward rectifier by binding to a site in an aqueous pore. This site will also bind two K+ ions and so K+ competitively inhibits the Ba2+ blockade. It is clear from the KB,3 and KK values which are needed to fit the experimental results that the proposed A

10 r

C -120 -80 -40 + L. .....!.I .. I I

I

0-8 -F y

04 0.2

-

I

0-0010-0050 01 0 05 0-1 B rBal (m

I

0-5 1

I

I

5 10

0-*

_11-

D

N

t05

L1

-120

1

I

I

I

I

I

-80 -40 +40 +80 Membrane potential (mV)

l

Fig. 13. Results predicted by the model described in the test. A, concentration-effect curves. Continuous line, predicted curve in 115 mM-K+ at the holding potential, -5 mV; dotted line, 115 mm-K+ at -25 mV; dashed line, 115 mM-K+ at -45 mV; dashed and dotted line, 230 mM-K+ at -5 mV. B, predicted current-voltage relations in 115 mM-K+ solutions. Continuous line, instantaneous relation in 0 05 mm-Ba2+. Dashed and dotted line, steady-state relation in 0-05 mM-Ba2+. Dashed line, instantaneous relation in 0 5 mM-Ba2+. Dotted line, steady-state relation in 0 5 mM-Ba2+. C, current-voltage relations in 230 mM-K solutions. Continuous line, mean experimental control relation. Dashed line, predicted instantaneous relation in the presence of 5 mM-Ba2+. Dotted line, steady-state relation in 5 mm-Ba2+. D, continuous line, predicted relation between steady-state blockade and membrane potential for 115 mmK+, 0-5 mM-Ba2+. Filled circles, experimentally determined points from one fibre in this solution.

site has a rather high affinity for Ba2+, but a comparatively low affinity for K+. The voltage-dependence of the blockade gives a value for a of 0-7, corresponding to a distance of 0-7 x the thickness of the membrane from the outside if the potential gradient across the membrane were constant. We thank Louise A. Gay for helpful discussion during the course of this work, Dr S. A. Petersen for help with computing and the Royal Society for an equipment grant to P.R.S.

190

N. B. STANDEN AND P. R. STANFIELD

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STANrIELD, P. R. (1970 b). The differential effects of tetraethylammonium and zinc ions on the resting conductance of frog skeletal muscle. J. Phygiol. 209, 231-256. STRICHARTZ, G. R. (1973). The inhibition of sodium currents in myelinated nerve by quaternary derivatives of lidocaine. J. gen. Phy8iol. 62, 37-57. WOODHULL, A. M. (1973). Ionic blockage of sodium channels in nerve. J. gen. Physiol. 61, 687-708.