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«THE RUBIDIUM AND POTASSIUM PERMEABILITY OF FROG MUSCLE MEMBRANE BY R. H. ADRIAN From the Physiological Laboratory, University of Cambridge (Received ...»

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-7 Fig. 8. The relation between AV and the membrane potential for three fibres from K-containing muscles in a sulphate solution with a potassium concentration of 100 m-equiv/l. (solution D). AV can be taken to be proportional to the membrane current; positive values of AV represent outward membrane currents. The photographic records show V and AV for outward current (a) and inward current (b).

current to membrane potential has a characteristic shape, with a region of negative slope conductance for internal potentials between zero or even 10 and 40 mV. Figure 8 shows three such curves from fibres containing potassium in a sulphate solution with a potassium concentration of 100 m-equiv/l. (solution D). Though the curves in Fig. 8 were obtained with constant current pulses, they are essentially the same as the curves obtained from isolated muscle fibres with a voltage clamp method (Adrian & Freygang, 1962b). If measurements of current and voltage are made on 149 Rb AND K IN MUSCLE a Rb-containing fibre in a sulphate solution with a rubidium concentration of 100 m-equiv/l. (solution E, Table 1), an entirely different curve is obtained (Fig. 9). Though the membrane potential for zero membrane current is the same in Figs. 8 and 9, the membrane current in Fig. 9 is related approximately linearly to the membrane potential and there is no region of zero or negative slope. The resistance of the membrane at all membrane potentials is comparable to the resistance of the membrane of a muscle in a 100 m-equiv/l. K+ sulphate solution with a large and positive internal potential.

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Fig. 9. The relation between AV and the membrane potential for two fibres from a Rb-containing muscle in a sulphate solution with a rubidium concentration of 100 m-equiv/l. (solution E). The internal cation concentrations of this muscle were: Rb, 122 m-mole/kg fibre water; K, 18 m-mole/kg fibre water; Na, 6 m-mole/ kg fibre water. Photographic records show V and AV for an inward current (a) and an outward current (b).

It is clear from Figs. 8 and 9 that the relation between current and voltage is quite different when rubidium replaces potassium on both sides of the membrane. The pathways which carry the large inward currents by means of potassium cannot carry much current when rubidium makes up the greater part of the cation on either side of the membrane. Figure 8 was obtained from a fresh muscle and Fig. 9 from a muscle which had been isolated from the frog for 5 days. It could be suggested that the ability to rectify disappeared because of the long period of isolation. Evidence to the contrary is provided by the experiment in Fig. 10. A set of measurements of the current and voltage was made on a fresh fibre in a sulphate solution containing 100 m-equiv/l. K+ (open circles, Fig. 10). Without removing the electrodes from the fibre the external solution was changed to an equivalent solution but containing 100 m-equiv/l. Rb+. A second R. H. ADRIAN 150 set of measurements was made after 3 min in the Rb-sol-ution (filled circles).

For inward current, now carried by rubidium, the resistance rises by a factor of nearly 20, even though the membrane potentials in the absence of current differed by only 7 mV in the two solutions (-7 mV, -14 mV).

For outward current, still presumably an outward potassium movement, the resistance becomes large and linear when the external cation is changed from potassium to rubidium. The difference between the current-voltage relation for outward current in the two solutions is clearly reflected in the shape of the voltage record in the two solutions. The inset photographic

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Fig. 10. The relation between AV and the membrane potential for one fibre in a K-containing muscle successively in sulphate solutions, with a K concentration of 100 m-equiv/l. (solution D), a Rb concentration of 100 m-equiv/l. (solution E), and a K concentration of 100 m-equiv/l. The set of measurenrents in the rubidium solution was taken within 3 min of the change of solutions. The last set of measurements (triangles) was taken 15 min after the change back to a potassiuim solution.

The photographic records show V and AV for outward currents. They are from another similarly.treated fibre. The upper record is from the fibre in the rubidium solution, the lower record is from a fibre in the potassium solution. Note the difference in the fall of V at the end of the current pulse.

records in Fig. 10 show that the asymmetry of the charging and discharging of the membrane capacity is abolished in the Rb-solution, which would be expected from the changed shape of the current-voltage curves for outward current.

The ability of the fibre to pass large inward currents is lost when the external cation is rubidium but it returns when the rubidium is replaced by potassium (open triangles, Fig. 10). Though the effect of rubidium is reversible, the high resistance in the rubidium solution is established much Rb AND K IN MUSCLE 151 sooner after the change from potassium to rubidium, than the low resistance is restored when the rubidium is changed back to potassium. In Fig. 10 the curve in the rubidium solution (filled circles) was measured 3 min from the solution change, but the curve after the return to potassium (triangles) took about 15 min to approximate to the initial curve in potassium (open circles). The rise and fall of the potassium concentration at the surface fibres of the muscle should be reasonably symmetrical, and so the high resistance in the Rb-solution should develop with about the same time course as the return to a low resistance in the K-solution.

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Fig. 11. The relation between AV and the membrane potential for one fibre in a K-containing muscle. The muscle was in solution D, then in solution J, and finally in solution D (triangles). The addition of Rb 10 m-equiv/l. approximately doubles the change in membrane potential for large values of inward current.

However, if the presence of rubidium interfered with the movement of potassium across the membrane, an asymmetric time course might be expected. To test this possibility 5 m-mole/l. of the Na2SO4 in solution D were replaced by the same quantity of Rb2SO4. The relations between inward current and membrane potential were compared in the two solutions, both with 100 m-equiv/l. K+ and one with 10 m-equiv/l. Rb +. The presence of 10 m-equiv/l. Rb+ somewhat more than doubles the membrane resistance (Fig. 11). The effect is reversible and is not accompanied by any measurable change of the membrane potential in the absence of current.

If a muscle whose fibres contain a substantial proportion of rubidium is put into a sulphate solution with 100 m-equiv/l. K+, in the absence of current the internal potential is between + 8 and + 10 mV. This membrane R. H. ADRIAN 152 potential is consistent with an effective value of 0 5 for the ratio of the permeabilities for rubidium and potassium. The open circles and triangles in Fig. 12 show how the membrane current varies with the membrane potential for a Rb-containing fibre in a sulphate solution with a potassium concentration of 100 m-equiv/l. The filled circles show, for comparison, the behaviour of a K-containing fibre in the same solution. The resistance of the Rb-containing fibre is high and linear for outward current; large inward potassium currents are possible in both muscles, and for internal potentials more negative than -10 mV the inward currents in each muscle become

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--~~4. -5 Fig. 12. The open circles and triangles show the relation between AV and the membrane potential for two fibres from a Rb-containing muscle in a sulphate solution with a K concentration of 100 m-equiv/l. (solution D). The filled circles show the current potential relation for a K-containing fibre in the same solution.

The internal cation concentrations of the Rb-containing muscle were: Rb, 124 m-mole/kg fibre water; K, 28 m-mole/kg fibre water; Na, 1 im-mole/kg fibre water.

nearly equal. The similarity of the two curves for inward current is to some extent a coincidence and therefore difficult to interpret. The two curves are from fibres of different muscles. If it is assumed that the inward current at a particular membrane potential is independent.of the internal potassium concentration, one must conclude that rubidium inside the fibre cannot interfere with the movement of potassium into the cell.

Alternatively, if the potassium permeability is some function of the difference between the membrane potential and the potassium equilibrium potential, then one may conclude that internal rubidium as well as external rubidium can interfere with the inward movement of potassium. That internal rubidium does have some effect is suggested by the experiment shown in Fig. 7. The increase in conductance with hyperpolarization in a 153 Rb AND K IN- MUSCLE K-Ringer's solution is much less marked when rubidium, rather than potassium, is the major internal cation.

Membrane potential and external concentration of rubidium and potassium.

Figure 13 shows the values of the internal potential in the absence of any externally applied current, for three concentrations (25, 50 and 100 mequiv/l.) of both potassium and rubidium for muscles which contain either potassium or rubidium. The solutions contain no chloride (solutions D-I, Table 1). When the external cation concentration is 100 m-equiv/l., and the same cation is on both sides of the membrane, the potential is

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-50 Fig. 13. The relation between the membrane potential in the absence ofany applied current and the external cation concentration. The muscles contained either K or Rb (the external and internal cation are indicated; e.g. K./K, or K./Rbi) and all the measurements were made in sulphate solutions (solutions D-I). The internal cation concentrations of the Rb-containing muscle were: Rb, 126 m-mole/ kg fibre water; K, 21 m-mole/kg fibre water; Na, 3 m-mole/kg fibre water.

within a very few mV of the Nernst potential for that ion. When the external concentration is 100 m-equiv/l., with rubidium on one side and potassium on the other side of the membrane, the potential can be predicted by assuming a value of 0 5 for the ratio of the permeabilities to rubidium and potassium. If no ion other than rubidium and potassium can carry any substantial amount of current across the membrane, and if the permeability ratio is constant for the range of potentials and concentrations in Fig. 13, then the measured potentials should lie on three parallel straight lines with a 58 mV change in potential for a tenfold change in external concentration. The potentials for the two cases where the same R. H. ADRIAN 154 ion is on both sides of the membrane should be the same at any particular external concentration. Experimentally the potential change only approximates to the theoretical 58 mV when the external ion is potassium, and it does so whether the internal ion is rubidium or potassium. When the external ion is rubidium the potentials for the lower external concentrations are less negative than would be expected, and the potential change for a tenfold change in external concentration is substantially less than 58 mV. The reduction in slope is explicable if the membrane has a permeability to sodium, and if the presence of external rubidium reduces the potassium permeability so that it is only about twice as large as the rubidium permeability. No doubt other arbitrary combinations of constants would be equally explanatory. However, Fig. 13 does throw light on the question of whether internal rubidium restricts potassium movement as effectively as external rubidium. When potassium is outside and rubidium is inside a fibre, the potential changes by very nearly the theoretical 58 mV for a tenfold change in external concentration. In this case the sodium conductance of the membrane can only be a very small part of the total conductance of the membrane, and one must conclude (provided PNa is constant) that the permeabilities to potassium and rubidium are both greater when potassium is outside and rubidium is inside than when rubidium is outside and potassium inside the muscle fibre. That this is the case is already strongly suggested by the results of Fig. 2. In that figure the net loss of rubidium into a potassium solution takes place at a rate that is about four times the rate of loss of potassium into a rubidium solution.

DISCUSSION The conclusions from this work are: (1) rubidium substitutes well for potassium in the mechanisms of the action potential. (2) Muscular contraction, crudely observed, and its initiation by an action potential are not affected by rubidium, though these points deserve fuller investigation.

(3) The pathways that allow large inward potassium currents allow only small rubidium currents in either direction. (4) Rubidium in the external solution interferes with the inward movement of potassium ions. It seems likely, but it is by no means established, that the effect of rubidium on the movement of potassium depends upon whether rubidium is inside or outside the cell, being greater when rubidium is outside.

The replacement of internal potassium by rubidium takes place at a remarkably slow rate when the soaking solutions are made with sulphate and the external rubidium concentration is 100 m-equiv/l. If the efflux of potassium into this solution is only 2x3 p-mole/cm2/sec (see p. 139), then the constant field permeability for potassium in these conditions is 0x027 x 10-6 cm/sec. The sodium permeability for depolarized muscles is not Rb AND K IN MUSCLE 155 known, but it is approximately 0x01 x 10-6 cm/sec at the resting potential.

Obviously it is unwise to ignore the sodium currents (as was done on p. 139) when attempting to assess the relative permeabilities of the membrane to rubidium and potassium. The potassium permeability is so variable that a permeability ratio only has meaning when it is related to a particular set of circumstances.

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