Sodium Channel Selectivity Dependence on Internal Permeant Ion Concentration MICHAEL

CAHALAN

and T E D B E G E N I S I C H

From the Department of Physiology, University of Rochester School of Medicine, Rochester, New York 14642, the Department of Physiology and Biophysics, University of Washington School of Medicine, Seattle, Washington 98195, and the Marine Biological Laboratory, Woods Hole, Massachusetts 02543. Dr. Cahalan's present address is the Department of Physiology, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19174.

A B S T R A C X The selectivity of sodium channels in squid axon membranes was investigated with widely varying concentrations of internal ions. T h e selectivity ratio, PNa/PK, determined from reversal potentials decreases from 12.8 to 5.7 to 3.5 as the concentration of internal potassium is reduced from 530 to 180 to 50 mM, respectively. The internal KF perfusion medium can be diluted by tetramethylammonium (TMA), Tris, or sucrose solutions with the same decrease in PNa/PK. The changes in the selectivity ratio depend upon internal permeant ion concentration rather than ionic strength, membrane potential, or chloride permeability. Lowering the internal concentration of cesium, rubidium, guanidinium, or ammonium also reduces PNa/Plon. The selectivity sequence of the sodium channel is: Na > guanidinium > ammonium > K > Rb > Cs. INTRODUCTION

One approach toward a molecular understanding of transport through sodium c h a n n e l is to c o n s i d e r its selectivity. Hille (1971, 1972, 1975a) has p o s t u l a t e d that a 3 × 5-/~ selectivity filter c o u l d g o v e r n w h i c h ions a r e p e r m e a n t a n d has given p e r h a p s the m o s t detailed m o l e c u l a r i n t e r p r e t a t i o n f o r the selectivity o f the c h a n n e l . H o w e v e r , n o t h e o r y has successfully a c c o u n t e d f o r the d e g r e e to w h i c h s o d i u m is p r e f e r r e d o v e r p o t a s s i u m by a s o d i u m c h a n n e l . It has a p p e a r e d t h a t the selectivity o f s o d i u m c h a n n e l s m i g h t be a fixed p r o p e r t y o f the filter r e g i o n , b e i n g u n a l t e r e d by a variety o f p h a r m a c o l o g i c a l t r e a t m e n t s (Hille, 1968; N a r a hashi, 1974), by c h a n g e s in s o d i u m inactivation ( A r m s t r o n g et al., 1973), o r by a x o n d e t e r i o r a t i o n ( C h a n d l e r a n d Meves, 1965). H o w e v e r , C h a n d l e r a n d Meves (1965) also o b s e r v e d t h a t d i l u t i n g the i n t e r n a l p e r f u s i o n m e d i u m o f a squid a x o n with isotonic sucrose a p p e a r e d to r e d u c e the selectivity o f the c h a n n e l . T h e y s u g g e s t e d f o u r possible causes f o r this result: (a) a c h a n g e in ionic s t r e n g t h , (b) a c h a n g e in i n t e r n a l p o t a s s i u m activity, (c) a small c h l o r i d e p e r m e a b i l i t y , o r (d) an THE JOURNALOF GENERALPHYSIOLOGY"

VOLUME 68,

1976 • pages 111-125

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e f f e c t o f m e m b r a n e p o t e n t i a l u p o n selectivity. O u r r e s u l t s s h o w t h a t , o f t h e s e possibilities, t h e i n t e r n a l p o t a s s i u m c o n c e n t r a t i o n h a s t h e s t r o n g e s t e f f e c t u p o n t h e r a t i o o f p o t a s s i u m p e r m e a b i l i t y to s o d i u m p e r m e a b i l i t y . F u r t h e r m o r e , c h a n g i n g t h e i n t e r n a l activity o f a n y o f t h e five p e r m e a n t ions t e s t e d l e a d s to similar alterations of permeability ratios. A preliminary report of these results has b e e n p r e s e n t e d ( C a h a l a n a n d B e g e n i s i c h , 1975). T h e r e s u l t s i n d i c a t e t h a t selectivity is a v a r i a b l e p r o p e r t y o f t h e c h a n n e l r e s p o n d i n g to c h a n g e s in t h e ionic c o m p o s i t i o n o f t h e i n t e r n a l m e d i u m . METHODS

Axon segments averaging 420 ftm in diameter from the squid, Loligo pealii, were internally perfused and voltage clamped using the methods described in Begenisich and Lynch (1974). T h e m e m b r a n e potential, V, was measured using an internal 0.56 M KC1 pipette and an external 3 M KCI electrode. Membrane potentials have been corrected for the measured liquid junction potential at the 0.56 M KCl/internal solution interface. Reversal potentials were obtained in two experiments with a 3 M KCI internal pipette and were the same as the (corrected) values using the 0.56 M KC1 electrode. This is an indication of the accuracy o f the liquid junction potential corrections. T h e average resting potential of 65 axons bathed in K-free artificial seawater and perfused with 275 mM KF and 400 mM sucrose was - 6 8 . 4 mV (range - 5 7 . 3 to -75.3). Electronic compensation for series resistance was employed throughout; 2 - 3 flcm z were compensated for internal solutions o f normal ionic strength, while 4-7 l-lcm2 were compensated for solutions of lower ionic strength. Series resistance errors are expected to make little difference in d e t e r m i n i n g the sodium reversal potential (Vrev), since net ionic current at Vrev is small, consisting only o f leakage current. In four experiments varying the series resistance compensation from 2 to 7 l l c m 2 caused no detectable change in Vrev.

Solutions We designed solutions to distinguish between possible effects o f ionic strength versus potassium activity on the selectivity of sodium channels. For several different potassium activity levels we a d d e d varying amounts o f the i m p e r m e a n t cation, tetramethylammonium (TMA), to raise the ionic strength. T M A was recrystallized from ethanol to eliminate contamination by p e r m e a n t ions. Table I shows the solutions used for this series of experiments. Recrystallized tetraethylammonium (TEA) b r o m i d e was a d d e d to block most o f the delayed potassium conductance which could interfere with the sodium reversal potential measurement. Single ion activity coefficients (Kielland, 1937) were used to d e t e r m i n e the concentration o f KF needed to keep the potassium activity approximately constant as the ionic strength was increased by T M A . T h e buffer for all internal solutions was 1 mM HEPES (N-2-hydroxyethyl-piperazine-N'-2-ethanesulfonic acid), and the p H was 7.2-7.4 at 5°C. Enough sucrose was a d d e d to make the internal solution isosmotic within 3% with the artificial seawater, which was composed o f 440 mM NaCI, 10 mM CaCI2, 50 mM MgCI2, and 1 mM Tris buffer at p H 7.4. Additional Tris CI was used as a substitute for sodium in the low sodium artificial seawater. Solutions containing internal test cations other than potassium are given in Table II. T h e rubidium and guanidinium solutions were maintained at constant ionic strength by the addition of T M A , while ionic strength was allowed to vary for the cesium and a m m o n i u m solutions. All solutions contained at least 50 mM fluoride ion to enhance the survival of the axon. T E A was a d d e d to solutions containing rubidium or a m m o n i u m ions to block their passage t h r o u g h potassium channels. Stock solutions o f sucrose, KF, and

CAHALAN AND BEGENISICH

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113

TMACI were tested by flame photometry for contamination by sodium ions. These measurements were kindly made by Dr. Donald Geduldig. The solutions used contained less t h a n 0 . 5 m M N a r e p r e s e n t i n g a m a x i m a l e r r o r o f a b o u t 3 % in t h e c a l c u l a t e d p e r m e a b i l i t y r a t i o , PK/PNa. TABLE

COMPOSITION

I

OF INTERNAL

SOLUTIONS

WITH

K÷

KF concn (activity)

T M A C I conch

T E A B r concn

Sucrose concn

mM

raM

mM

raM

Total ionic s t r e n g t h

ram

530 297 189 97 63

(355) (199) (127) (65) (43)

230 346 443 482

20 20 15 10 5

-

550 550 550 550 550

275 175 90 59

(199) (127) (65) (43)

100 190 226

15 15 10 5

365 375 375 400

290 290 290 290

80 (65)

--

10

610

90

50 (43)

--

5

700

55

TABLE COMPOSITION Test ion

Test ion concn

OF INTERNAL

II

SOLUTIONS:

TMACL concn

T M A F concn

T E A Br concn

K + SUBSTITUTES Sucrose concn

Total ionic strength

mM

mM

mM

mM

ram

Rb CI

225 59

175

50 50

15 5

400 400

290 290

CsF

550 275

. --

--

--

400

550 275

NH4F

275 50

-

-

10 5

380 710

285 55

Guanidini u m CI

225 50

175

50 50

-

400 400

275 275

TMA

275

225

50

-

400

275

.

.

.

Analysis The membrane potential was normally held between -65 and -75 inV. Depolarizing test p u l s e s w e r e p r e c e d e d b y a 6 0 - m s h y p e r p o l a r i z a t i o n o f 30 m V to r e m o v e s o d i u m i n a c t i v a tion. Peak sodium currents were measured for each test pulse. Usually a linear leakage correction was applied from the leakage current measured during a 60-mV hyperpolarizing pulse, but in some experiments tetrodotoxin was added and the voltage clamp series r e p e a t e d to p r o v i d e a m o r e a c c u r a t e s u b t r a c t i o n o f t h e l e a k a g e c u r r e n t a n d a n y r e s i d u a l

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potassium current not blocked by the internal TEA ions. The reversal potentials agreed within 2 mV for either leakage subtraction method. Reversal potentials, Vrev, were determined by interpolation of leak-corrected sodium current to the zero current axis of the current-voltage relation. This method agrees well in practice with the method of simply observing the characteristic change or turnover of the current trace as the potential is increased in small increments from just below to just above the reversal potential. External sodium and internal potassium or the ions of Table II were the only measurably permeant ions present excepting calcium present at 10 mM concentration and having a PNa/Pcaof perhaps 100, (Baker et al., 1971). Consequently we have ignored the small degree of calcium permeability, and permeability ratios PK/PNaor Plon/eNawere calculated from the reversal potentials by Vre v

= RT/F.ln(PNa[Na]o/Plon[ion],)

(1)

(Goldman, 1943; Hodgkin and Katz, 1949), where R, T, and F have their conventional meanings with RT/F = 24.0 mV at 5°C. Single-ion activities (Kielland, 1937) rather than concentrations were used in the permeability ratio computations. The calculations were repeated using salt activity coefficients with no significant changes in the results. RESULTS

Dilution of the Internal Medium Increases PK/PNa Fig. 1 A shows sample voltage clamp records o f sodium currents before and after dilution o f the internal KF m e d i u m by isotonic sucrose. T h e KF concentration in this case was r e d u c e d from 275 to 50 mM as the ionic strength went from 290 to 55 mM. T e t r a e t h y l a m m o n i u m ions were present to block the delayed t u r n - o n o f potassium c o n d u c t a n c e . For the h i g h e r concentration o f KF (Fig. 1 A, top) currents are just inward for a depolarization to +60 mV and o u t w a r d for the next h i g h e r clamp step to +70 mV. W h e n the internal solution was diluted with additional sucrose, the reversal potential increased to between 70 and 80 mV. Fig. 1 B shows the relationship between peak sodium currents and the potential for these two voltage clamp series. T h e reversal potential increased f r o m 61 to 75 m V with dilution. T h e predicted increase in reversal potential AVrev, assuming no change in the permeability ratio PK/PNa, can be c o m p u t e d f r o m : AVrev- RTIn [K]J[K]~'. F

(2)

Substituting [K]~ = 199 mM and [K]i' = 43 mM gives an increase o f 36 mV for the predicted c h a n g e in reversal potential r a t h e r than the m e a s u r e d 14-mV increase. This discrepancy can be resolved if the permeability o f potassium relative to sodium increases with dilution. T h e n , from Eq. 1, PK/PNa must increase from 0.12 to 0.31 when the potassium concentration is decreased f r o m 275 to 50 mM. In seven axonsPK/PNa increased to 0.276 - 0.03 (mean + SEM) when the internal potassium was diluted to 50 mM by isotonic sucrose. T h e s e results are in a g r e e m e n t with the findings o f C h a n d l e r and Meves (1965) for dilutions o f the internal perfusion m e d i u m . F r o m o u r results PK/Psa decreased from 0.124 0.003 (mean +- SEM, n = 37) to 0.078 - 0.004 (n = 9) on replacing 275 mM KF

CAHALANAND BI~C.ENISICH ConcentrationDependenceof Sodium ChannelSelectivity

115

a n d sucrose by a solution containing 530 m M KF. T h e r a n g e o f PK/PNa with a variety o f internal solutions is indicated in T a b l e I I I .

Chloride and Tetramethylammonium Are Not Measurably Permeant O n e alternative e x p l a n a t i o n to a c h a n g e in the selectivity ratio for the experim e n t s just described would be a small permeability to chloride ions. I f chloride were p e r m e a n t the reversal potential would be given by:

RT In { V,.~,, = ~

Psa [Na]o Px [K], + Pc] [Cl]oJ "

(3)

T h e n , in o r d e r to duplicate the 14-mV increase in reversal potential o b s e r v e d in

A V= I I0 , . ~ . . . . . . .

275KF

B

I(mA/cm2) I

//o/ /',,~ ~' 4 0 / / o 8o V(mV)

t ImA/cm 2~ V = 120 . . . . .

./e/° /o o/o

,

50KF

/o///

\ \

_~ // %-

~e°/ ~..~o

aK VrevP/P ol99 64 0.10 o 43 7,5 031

O5 ms

FIGURE 1. Dilution of the internal perfusion medium by isotonic sucrose. Traces on left show sodium currents during step depolarizations separated by 10 inV. The range is from - 7 0 to 110 mV for 275 KF inside (top), and from - 7 0 to 120 mV for 50 KF inside (bottom). The peak sodium current-voltage relations for these traces are plotted in part B. The arrow at +97 mV indicates the predicted reversal potential for 50 KF on the assumption that there was no change in selectivity upon diluting. The potassium activities, reversal potentials, and permeability ratios Px/ Psa (abbreviated by P/P) calculated from Eq. 1 are shown in the inset. Fig. 1 B, t h e r e would have to h a v e b e e n a PNa]Pct ratio o f 31.5, while all permeability ratios r e m a i n e d constant in both solutions. Several e x p e r i m e n t a l observations rule o u t the possibility o f a chloride permeability o f this m a g n i t u d e . In one e x p e r i m e n t the external chloride ions were replaced by larger isethionate ions with no m e a s u r e d c h a n g e in the reversal potential. IfPNa/Pcl = 150 a n d if isethionate ions are i m p e r m e a n t , replacing the e x t e r n a l chloride by isethionate would lead to a just-detectable 2-mV c h a n g e in the reversal potential. H e n c e Psa/ Pc] m u s t be g r e a t e r t h a n 150 f r o m this e x p e r i m e n t . A n o t h e r e x p e r i m e n t indicates that chloride must be even less p e r m e a n t t h a n this. All o f the internal potassium ions were replaced by T M A ions, while the external solution c o n t a i n e d 440 m M Tris C1 a n d no s o d i u m . C u r r e n t s were

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m e a s u r e d in response to depolarizing pulses as shown in Fig. 2 A. T h e small transient c u r r e n t just after the voltage step may be c h a r g e m o v e m e n t in association with the gating process o f sodium channels ( A r m s t r o n g and Bezanilla, 1974; Keynes and Rojas, 1974). T h e n the same T M A solution with 1 mM sodium was TABLE

III

REVERSAL POTENTIALS AND P~/Psa K activity

Ionic strength

V~v

raM

raM

m V'*'SEM

Pa/Ps.

No. o f

355

550

57.3+- 1.2

0.078

9

199 199

550 290

58.7+-0.9 60.1+- 1.0

0.132 0.124

6 37

127 127

550 290

62.0 + - 1.1 63.4+- 1.0

0.180 0.170

3 3

65 65

550 290

73.3+-5.4 70.1 +-3.8

0.217 0.249

2 3

43 43 43

550 290 55

76.2 +-2.8 76.9+-2.0 77.6+-2.7

0.293 0.285 0.276

8 8 7

A

axons

B 275TMA

0 1 mA/cm

2

275TMA ÷lNa 0.1 m ,0Jcm 2

/__

I' 0.5rns

0.Sms

FIGUR~ 2. (A) Currents with no known permeant ions. With Tris seawater outside and 225 TMACI + 50 TMAF inside only leakage and possibly gating currents are observed. Depolarizations are separated by 20 mV from -60 to + 120 mV. (B) IL, Isate, + Isa with 1 mM sodium inside. Depolarizing pulses range from +40 to + 120 mV in 20-mV increments. Note the difference in current scales for parts A and B. i n t r o d u c e d inside the axon. A d d i n g 1 mM internal Na caused an o u t w a r d b u m p o f c u r r e n t for voltage pulses to +80 mV and above as shown in Fig. 2 B. Since there were 275 T M A ions, 440 Tris ions, and 440 CI ions for every sodium ion, the combined permeability o f T M A , Tris, and CI relative to sodium must have been less than 1/500 because c u r r e n t f r o m 1 mM sodium was clearly visible for a depolarization to +80 mV, whereas no c u r r e n t in Na channels was recognized in the absence o f internal sodium. In any event, a chloride permeability could not

CAHALANAND BEGENISXCH ConcentrationDependenceof Sodium ChannelSelectivity

117

account for the small change in reversal potential when the internal solution was diluted with sucrose. This e x p e r i m e n t also shows that T M A ions are acceptably i m p e r m e a n t to serve as a means o f increasing ionic strength without a d d i n g p e r m e a n t ions.

Potassium Concentration not Ionic Strength Affects Px/PNa Eighteen e x p e r i m e n t s were d o n e to d e t e r m i n e w h e t h e r dilution o f the internal KF solution reduces sodium channel selectivity by a decrease in potassium concentration or by a decrease in ionic strength. Using solutions in Table I potassium activity was varied at constant ionic strength, or ionic strength was varied at constant potassium activity. Ionic strength was varied i n d e p e n d e n t l y by changing the concentration o f i m p e r m e a n t T M A ions. In some e x p e r i m e n t s Tris was used to vary the ionic strength with the same basic conclusions as for internal T M A . Tris, however, also a p p e a r e d to change the rectification o f sodium channels by blocking outward c u r r e n t more than inward c u r r e n t . Fig. 3 A illustrates voltage clamp sodium currents for an e x p e r i m e n t in which potassium activity was varied f r o m 355 to 43 mM while ionic strength was held constant at 550 raM. In the top trace with a potassium activity o f 355 mM sodium currents turn o v e r f r o m inward to outward for a depolarization to between 50 and 60 mV. W h e n the internal potassium activity was lowered to 199 mM the reversal potential increased to between 55 and 65 mV and increased f u r t h e r to between 70 and 80 mV for a potassium activity o f 43 mM. Fig. 3 B shows the current-voltage relations for this e x p e r i m e n t . As in the dilution e x p e r i m e n t s described previously PK/PNa calculated f r o m Eq. 1 varied f r o m about 0.08 for high K activity to 0.3 for low K activity even t h o u g h ionic strength was held constant in this case. T h e reversal potential for this axon in 275 KF and sucrose (ionic strength, ~, = 290 raM) was the same value (62.5 mV) before and after the solution changes at h i g h e r ionic strength, providing a good check on the stability and reversibility o f the m e a s u r e m e n t s . Fig. 4 illustrates an e x p e r i m e n t in which two d i f f e r e n t potassium activity levels and two d i f f e r e n t ionic strengths were directly c o m p a r e d . Changing the ionic strength by itself had little effect on the m e a s u r e d reversal potentials. T h e permeability ratios are shown again to d e p e n d on potassium activity and not on ionic strength. Table III summarizes the results o f all e x p e r i m e n t s in which potassium activity and ionic strength were varied i n d e p e n d e n t l y inside the axon. T h e r e is little effect o f ionic strength on selectivity, but PK/PNa increases as the potassium activity is r e d u c e d .

Other Permeant Ions Exhibit Concentration-Dependent Permeability Alterations in sodium channel permeability ratios with changes in the internal concentration are not limited to the potassium ion, as revealed in e x p e r i m e n t s with internal p e r m e a n t ions o t h e r than potassium. Reducing the concentration o f cesium, r u b i d i u m , a m m o n i u m , or guanidinium inside the axon causes the selectivity ratio Pion/PNa to increase as shown in T a b l e IV. For instance, guanidinium at an internal concentration o r S 0 mM is as p e r m e a n t as sodium, while at 225

118

THE

JOURNAL

v=8o7"~ 530KF '~-._______

OF

GENERAL

/ ; , . j. ....

B

~'~

I2C~__..~,__ 63KF

" 555

~_~/Y-2

54

199 59

0 09 0,3

=127

6~

0~9

- 43

73

033

--

\ ~

6 8 • 1976

//~.

[(mA/cmZ)

A

" VOLUME

constont ionic strength

,

V=

PHYSIOLOGY

O~m~

FIGURE 3. (A) Sodium currents with varying internal K at constant ionic strength. TMACI was a d d e d to keep the ionic strength at 550 mM. Voltage clamp steps are separated by 10 mV, with the largest depolarizing pulse indicated to the left o f each current family. (B) Current-voltage relations with constant ionic strength and varying internal potassium. Reversal potentials and permeability ratios PK/PNaa r e shown in the table for each potassium activity.

I(mA/cm 2) o

/ -4O

. b,/~;/ / . ; ~ z ao

v(mv)

/Z/

'/;)Y /'/~/ H

~

,;.~/~, 0

oK

J4, Vrev PiP

0,99 290 eo

0.,26

o

• 65

550

70

0249

3

el99

550

56

0147

FIGURE 4. Current-voltage relations for two different potassium activities and two ionic strengths in the same axon. m M g u a n i d i n i u m is a b o u t o n e - h a l f as p e r m e a n t . T h e s e q u e n c e o f i o n selectivity r e m a i n s t h e s a m e at h i g h o r low c o n c e n t r a t i o n s : Na. > g u a n i d i n i u m > N H 4 > K > R b > Cs. T h e o r d e r o f g u a n i d i n i u m a n d a m m o n i u m in this s e q u e n c e is r e v e r s e d c o m p a r e d to t h e n o d e o f R a n v i e r ( H i l l e , 1072).

CAHALANAND BEGENISICH ConcentrationDependenceof Sodium Channel Selectivity

119

P~/PNa Is Unaffected by External Na or Membrane Potential In seven e x p e r i m e n t s we m e a s u r e d the c h a n g e in reversal potential p r o d u c e d by diluting the e x t e r n a l Na to 1/4 n o r m a l . In five e x p e r i m e n t s the internal solution was 275 KF a n d sucrose, while in two o t h e r e x p e r i m e n t s the internal solution was 59 KF a n d 225 T M A C I a n d sucrose. Tris was used as the external s o d i u m substitute. T h e f o u r f o l d reduction in external sodium shifted the reversal potential by - 3 0 --- 1.1 m V ( m e a n +-- SEM). Since the e x p e c t e d c h a n g e in reversal potential is - 3 2 . 6 m V a s s u m i n g no c h a n g e in PK/PNa, lowering the s o d i u m concentration or c h a n g i n g potential by 30 m V had little effect on the p e r m e a b i l ity ratio. DISCUSSION

PK/PNa as a Variable A c o r n e r s t o n e o f the ionic hypothesis is the finding that changes in the e x t e r n a l sodium concentration p r o d u c e changes in the sodium equilibrium potential in TABLE

IV

REVERSAL POTENTIALS AND Plon/PNa FOR O T H E R IONS Ion

alon

V~.

mM

mV

Pton/PsJ

No. of

Cs

350 275

93.6-+ 1.2 99.5-+2.7

0.017 0.023

3 3

Rb

162 43

88.7 94.3-+5.2

0.045 0.136

1 3

NH4

199 43

39.4-+0.7 59.7-+4.6

0.301 0.592

4 3

Guanidinium

163 43

33.0-+0.3 51.5---3.0

0.482 0.99

2 2

axons

accord with the N e r n s t equation for a sodium electrode ( H o d g k i n a n d H u x l e y , 1952). In a n a l o g o u s e x p e r i m e n t s we find that c h a n g i n g the p e r m e a n t ion concentration on the inside o f the m e m b r a n e changes the reversal potential less than would be e x p e c t e d f r o m the G o l d m a n - H o d g k i n - K a t z equation. I f the selectivity ratio PNa/Plon r e m a i n s constant as the concentration o f the ion is varied on the inside o f the a x o n , t h e r e should be a shift in the reversal potential o f 2.3 R T / F , or 55 m V at 5°C, for a 10-fold c h a n g e in concentration. H o w e v e r , we find that the shift is substantially less t h a n 55 m V p e r 10-fold concentration c h a n g e for any o f the five p e r m e a n t ions tested on the inside. Fig. 5 A illustrates this effect for changes in the internal potassium activity at two ionic strengths. Reversal potentials do not c h a n g e as m u c h as predicted for a potassium electrode, w h e n the internal potassium activity is varied. T h e line in Fig. 5 A r e p r e s e n t s a slope o f 55 m V p e r 10-fold K activity change. T h e variable selectivity o f the s o d i u m channel, as e x p r e s s e d by PNa/PK (regardless o f ionic

120

THE JOURNAL OF GENERAL PHYSIOLOGY ' VOLUME 68 • 1976

strength), is plotted against the internal potassium activity in Fig. 5 B. T h e linear regression line provides the following empirical description o f o u r results:

PNa/PK = 0.029[K]~ + 2.21.

(4)

For high levels o f internal potassium we find good a g r e e m e n t with previous IOOr9 0 l ~ Vr, v (mV) I 80

• p = 5 5 0 rnM = }J=290mM

~

I

0 '0 2

0'~

O lI

0.5

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F I G U R E 5. (A) Reversal potentials at different internal potassium activities. The reversal potentials, Vrev, and SEM limits are plotted against the logarithm of the potassium activity ([K]l), for two different ionic strengths (I-~= 550 raM, • and ~ = 290 mM, [2). The solid line has a 55 mV/decade (Nernstian) slope. (B) PNa/PKat different internal potassium activities. Filled circles are averages of all data, regardless of ionic strength. The solid line is the linear regression line for the data.

m e a s u r e o f the selectivity ratio, PNa/PKo f about 12 ( C h a n d l e r a n d Meves, 1965; M o o r e et al., 1966; Binstock a n d Lecar, 1969; Atwater et al., 1969; Hille, 1972), whereas for m u c h lower potassium levels the selectivity ratio is r e d u c e d to a b o u t 3.5. C o n c e n t r a t i o n - d e p e n d e n t p e r m e a b i l i t y ratios have b e e n f o u n d for PNa/PK

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(Meyers and H a y d o n , 1972) and PTI/PK (Eisenman et al., 1976) in the ionic channel f o r m e d by the antibiotic gramicidin A. 1

Concentration Dependencefor Selectivity T h e r e are several control e x p e r i m e n t s which point to the activity o f the internal p e r m e a n t ion as the i m p o r t a n t variable for selectivity. First, as a check on the completeness o f the internal solution change, we varied the concentration o f sodium in the internal perfusion m e d i u m with no o t h e r p e r m e a n t ions present. With sodium as the only p e r m e a n t ion the reversal potential should be determined by Vrev = RT/F" In ([Na]o/[Na]0. T h e m e a s u r e d reversal potentials a g r e e d within 3 mV o f the expected values, indicating that there was a complete exchange o f the internal solution. O t h e r consequences o f this result are discussed below. Second, a small a m o u n t o f chloride o r fluoride permeability cannot be responsible for the a p p a r e n t change in the selectivity ratio. Changing the anion f r o m chloride to isethionate on the outside did not alter the reversal potential. F u r t h e r m o r e , the presence o f 1 mM Na in the internal solution (Fig. 2) was easily detectable when only Tris, T M A , C1, and F were present in the internal and external solutions. T h u s , the c o m b i n e d permeability o f these f o u r ions must be less than about 1/500 that o f sodium. This very low d e g r e e o f chloride p e r m e a bility would not contribute significantly to the m e a s u r e d reversal potential. Finally, as described in Results, neither ionic strength, external Na concentration, or m e m b r a n e potential p r o d u c e d changes in permeability ratios. T h e r e fore, the major part o f the PNa/Plon change can be attributed to changes in internal ion activity. T h e concentration d e p e n d e n c e for selectivity may be asymmetrical with respect to the m e m b r a n e . Changes in the external sodium concentration did not alter the selectivity ratio, in contrast to the effect o f the internal p e r m e a n t ion concentration. It would be o f interest in this connection to d e t e r m i n e if external potassium or o t h e r ions in the absence o f external sodium, have effects on the selectivity ratio.

Models for the Selectivity Change T h e following sections consider several models for the observed behavior o f the sodium reversal potential as the internal p e r m e a n t ion concentration is varied. We have described o u r results in terms o f changes in a permeability ratio calculated f r o m the G o l d m a n (1943), H o d g k i n and Katz (1949) voltage equation, and will consider several models within this f r a m e w o r k that might account for the data. One should bear in mind, however, that o t h e r formulations o f the concept o f permeability are possible d e p e n d i n g u p o n the transport model for sodium t h r o u g h the m e m b r a n e . For example, H e c k m a n n (1972) has shown that for pores in which there is single-filing o f ions past several sites in the channel, permeability can be concentration d e p e n d e n t and have asymmetrical properties. Likewise, Lafiger (1973) and Hille (1975a,b) have shown that for one-ion p o r e I Dr. L. Goldman and Dr. G. Ebert have recently performed similar experiments with changes of the internal potassium concentration in perfused Myxicolaaxon and find similar changes in the sodium channel selectivityratio. We thank Drs. Goldman and Ebert for this communication.

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models f e a t u r i n g saturable b i n d i n g to sites in the channel, permeability is concentration d e p e n d e n t , t h o u g h permeability ratios may r e m a i n constant for varying d e g r e e s o f saturation. T h e failure o f o u r observations to be described by a constant PK/PNa may m e a n that t h e r e are structural changes in the m e m b r a n e when the internal potassium is varied that alter the m o l e c u l a r p r o p e r t i e s o f the filter region, or it m a y be that o u r concept o f permeability needs to be m o d i f i e d because o f n o n i n d e p e n d e n t ion m o v e m e n t in ionic channels. A RESTRICTED S P A C E W I T H L O W [ K ] O R H I G H [Na] O n e possible e x p l a n a t i o n for o u r results would be that the concentration o f potassium at the i n n e r surface o f the m e m b r a n e is lower than in bulk solution. O n e m i g h t imagine a special reservoir f o r m i n g p a r t o f the i n n e r m o u t h o f the channel, access to which m i g h t involve binding or some process to limit the concentration. T h i s type o f mechanism could lead to reversal potentials which shift less t h a n e x p e c t e d w h e n the potassium concentration in the p e r f u s i o n m e d i u m is altered. Such a space, however, would have to have r a t h e r special p r o p e r t i e s , since, as described above, changes in internal sodium shift the reversal potential in accord with the N e r n s t equation. A n o t h e r possible e x p l a n a t i o n involving a restricted v o l u m e n e a r the i n n e r .mouth o f the p o r e is a c c u m u l a t i o n o f sodium ions. H o w e v e r , again the a c c u m u lation m e c h a n i s m would have to have very unusual p r o p e r t i e s , as d i f f e r e n t a m o u n t s of accumulation for d i f f e r e n t internal ions would have to be postulated. Also, we find g o o d a g r e e m e n t between the reversal potentials for instantaneous sodium c u r r e n t s and p e a k s o d i u m currents. Finally, as described above, o u r e x p e r i m e n t s with c h a n g i n g the internal sodium concentration are in accord with the N e r n s t equation without postulating internal s o d i u m accumulation. For these reasons it seems unlikely that a simple m e c h a n i s m involving internal sodium accumulation can explain o u r results. BARRIER MODELS We have investigated the possibility that an Eyring rate m o d e l for t r a n s p o r t t h r o u g h the c h a n n e l ( W o o d b u r y , 1971; L a r g e r , 1973; Hille, 1975b) might a f f o r d one a p p r o a c h to explain c o n c e n t r a t i o n - d e p e n d e n t p e r m e a bility ratios. Hille has pointed out several features o f the f o u r - b a r r i e r , one-ion p o r e with r e g a r d to selectivity, including the fact that the m o d e l has selectivity ratios that d e p e n d on m e m b r a n e potential. T h e lack o f effect o f m e m b r a n e potential in the e x p e r i m e n t s with external sodium concentration changes puts o n e restriction on the types o f e n e r g y profile we can consider. With this restriction it is necessary to conclude that no single set o f e n e r g y barriers a n d wells, o n e for sodium a n d o n e for potassium, can account for concentrationd e p e n d e n t permeability ratios. Within the m o d e l it would be necessary to alter the height o f barriers arbitrarily either by raising sodium barriers or by lowering potassium barriers w h e n the internal potassium concentration is r e d u c e d . T h u s the a p p r o a c h does not lend itself toward a clarification o f the basic m e c h a n i s m u n d e r l y i n g c o n c e n t r a t i o n - d e p e n d e n t permeability ratios.

A SITE-CONTROLLING SELECTIVITY A n o t h e r m e c h a n i s m for explaining o u r results m i g h t be a m o d e l in which a site at the i n n e r m e m b r a n e surface or a site within the m e m b r a n e accessible f r o m the inside, controls the c o n f o r m a t i o n o f

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the sodium c h a n n e l filter region. I f the sites were completely occupied by potassium, PNa/PK would be s o m e m a x i m u m value. T h e actual selectivity ratio for an e n s e m b l e o f channels at a given potassium activity would be d e t e r m i n e d by the fractional occupancy o f the site by potassium. T h e higher the internal potassium c o n c e n t r a t i o n , the g r e a t e r the occupancy o f the site, a n d hence, the l a r g e r the value o f PNa/PK. It is p e r h a p s not u n r e a s o n a b l e to expect s o m e r e a r r a n g e m e n t o f the local molecular e n v i r o n m e n t o f the filter region in r e s p o n s e to the p r e s e n c e o f an ion in the channel. T h e site m o d e l j u s t d e v e l o p e d m i g h t reflect just this sort o f interaction. Let us s u p p o s e that potassium ions interact with the filter region o f the c h a n n e l as they p e r m e a t e and leave the filter in an altered c o n f o r m a t i o n with a relatively high PNa/PK. A f t e r the d e p a r t u r e o f a potassium ion the filter t h e n relaxes back to its original state with a lower PNa/PK. O n e n e e d only s u p p o s e that this relaxation time o f the molecules c o m p r i s i n g the filter region is l o n g e r t h a n the interval b e t w e e n e n t r y o f potassium ions, p e r h a p s on the o r d e r o f a microsecond. T h e n , on the a v e r a g e , the selectivity ratio would reflect the " m e m o r y " o f the filter having b e e n altered by a potassium ion t h r o u g h a redistribution o f channels between the altered a n d original (unoccupied) states. F u r t h e r e x p e r i m e n t s are n e e d e d to test these ideas m o r e completely. A c o m p l e t e series o f selectivity ratios at several concentrations (instead o f only two in the p r e s e n t study) o f a n o t h e r p e r m e a n t ion such as g u a n i d i n i u m , a m m o n i u m , or r u b i d i u m , would be o n e a p p r o a c h . E x p e r i m e n t s n e e d to be d o n e to determine if permeability ratios can be altered by ions on the outside o f the m e m b r a n e . E x p e r i m e n t s testing the ability o f one ion to alter a n o t h e r ' s selectivity ratio could also be d o n e . Conclusions

O u r basic e x p e r i m e n t a l finding is that reversal potentials d o not shift in accord with the G o l d m a n (1943), H o d g k i n a n d Katz (1949) voltage equation (see Fig. 5 A), when the internal p o t a s s i u m c o n c e n t r a t i o n is varied. T w o f u n d a m e n t a l l y d i f f e r e n t possibilities exist to explain this finding. First, t h e r e may be a structural change in m a c r o m o l e c u l e s c o m p r i s i n g a selectivity filter of the s o d i u m c h a n n e l resulting in a less selective filter w h e n internal potassium is lowered. Second, t h e r e is no structural or chemical c h a n g e within the m e m b r a n e , but o u r conception o f permeabilities m u s t be m o d i f i e d d u e to limitations in the G o l d m a n , H o d g k i n , a n d Katz equation, possibly because o f difficulties in the a s s u m p t i o n o f i n d e p e n d e n t ion m o v e m e n t s . F u t u r e e x p e r i m e n t s in this a r e a must be accompanied by the d e v e l o p m e n t o f new ways to consider permeability in systems violating the a s s u m p t i o n s that are implicit in the constant field equation. We thank Drs. C. M. Armstrong and F. Bezanilla for providing laboratory space and advice, Dr. L. J. Mullins for much of the equipment, Dr. B. Hille for suggesting and providing computer programs for the four-barrier model, and Diana A. Forwalter for valuable secretarial help. This work was supported by grants HS08951, NS08174, and RR0374 all from the National Institutes of Health. Receivedfor publication 22 December1975.

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