Discrete B a 2+ Block as a Probe o f Ion Occupancy and Pore Structure in the High-Conductance CaZ+-activated K + Channel JACQUES NEYTON a n d CHRISTOPHER MILLER From the Graduate Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02254 ABSTRACT In this study, high-conductance Ca2+-activated K + channels from rat skeletal muscle were i n c o r p o r a t e d into planar phospholipid bilayers, and discrete blockade o f single channels by Ba ~+ was studied. With 150 mM K § held constant in the internal solution, increasing external K + over the range 100-1,000 mM raises the rate o f Ba 2+ dissociation. This " e n h a n c e m e n t effect," which operates at K § concentrations 3 - 4 o r d e r s o f magnitude higher than those r e q u i r e d for the "lockin" effect described previously, d e p e n d s on applied voltage, saturates with K § concentration, and is not observed with Na § The voltage d e p e n d e n c e o f the Ba ~+ off-rate varies with external K + in a way suggesting that K § entering the channel from the external side, forces Ba ~+ dissociation to the internal solution. With K § held fixed in the external solution, the Ba 2+ off-rate decreases as internal K + is raised over the range 0 - 5 0 mM. This "lock-in" effect is similar to that seen on the external side (Neyton a n d Miller, 1988), except that the internal lock-in site is o f lower affinity and shows only a fivefold preference for K § over Na § All the results taken together argue strongly that this channel's conduction pathway contains four sites o f very high affinity for K § all o f which may be simultaneously occupied u n d e r normal conducting conditions. According to this view, the mutual destabilization resulting from this high ionic occupancy leads to the unusually high conductance o f this K+-specific channel. INTRODUCTION Like m a n y K+-specific ion channels, the h i g h - c o n d u c t a n c e Ca~+-activated K + (BK) c h a n n e l o p e r a t e s by a m u l t i - i o n c o n d u c t i o n m e c h a n i s m , in which several K § ions s i m u l t a n e o u s l y o c c u p y the p e r m e a t i o n p a t h w a y in t h e i r j o u r n e y across the m e m b r a n e . I n the c o m p a n i o n study ( N e y t o n a n d Miller, 1988), we s h o w e d that K + a n d Ba ~+ s t r o n g l y i n t e r a c t within this c h a n n e l ' s c o n d u c t i o n p o r e . Specifically, a Ba 2+ ion e n t e r i n g the c h a n n e l f r o m the i n t e r n a l s o l u t i o n dissociates to the e x t e r n a l side, as l o n g as e x t e r n a l K + is absent; the a d d i t i o n o f K + to the e x t e r n a l s o l u t i o n p r e v e n t s Address reprint requests to Dr. Christopher Miller, Graduate Department of Biochemistry, Brandeis University, Waltham, MA 02254-9110. j. GEN.PHYSIOL.9 The Rockefeller UniversityPress 90022-1295/88/11/0569/18 $2.00 Volume 92 November1988 569-586 570 THE JOURNAL OF GENERALPHYSIOLOGY.VOLUME 9 2 . 1988 Ba 2§ dissociation to that side, a n d effectively " l o c k s " the Ba ~§ ion inside the channel. T h e s u p r i s i n g a s p e c t o f this result is t h e very high affinity with which K § acts as this e x t e r n a l " l o c k - i n " site; t h e c o n c e n t r a t i o n f o r half-inhibition is as low as 20 /~M. W e a r g u e d that the existence o f a single K + - b i n d i n g site o f such high affinity within the p e r m e a t i o n p a t h w a y is i n c o n s i s t e n t with the high c o n d u c t a n c e o f this channel, that at least two a d d i t i o n a l K § sites m u s t b e o c c u p i e d d u r i n g c h a n n e l cond u c t i o n . I n this study, we f u r t h e r e x p l o i t the p h e n o m e n o n o f discrete b l o c k by the Ba 2+ i o n to d e m o n s t r a t e the existence o f two a d d i t i o n a l K + - b i n d i n g sites within this channel. O n e o f these sites, w h e n o c c u p i e d by K § accelerates the dissociation o f Ba 2+ f r o m the c h a n n e l , a n d is l o c a t e d b e t w e e n the Ba ~+ b l o c k i n g site a n d the external lock-in site. T h e s e c o n d site is l o c a t e d t o w a r d s t h e i n t e r n a l face o f the channel, a n d p r o d u c e s a Ba ~+ lock-in effect f r o m this side. T a k e n t o g e t h e r , these e x p e r i - lOpA FIGURE 1. Effects of external K + on Ba ~+ block kinetics. Single BK channels were observed in planar bilayers in the presence of 150 mM internal KCI and 150 mM external NaCI media, with additional KCI added to the extemal medium. Blocks were i n d u c e d with internal Ba ~+, and the holding voltage was 40 mV. Top trace: no added K § in external solution; mean block time, 0.5 s. Middle trace: 10 mM K § added; mean block time, 4 s. Bottom trace: 500 mM K § added; mean block time, 1.7 s. Ba ~§ concentration was 1 #M in top trace, and 50 tiM in two other traces. m e n t s strongly suggest that the BK c h a n n e l c o n t a i n s at least f o u r K + - b i n d i n g sites within the c o n d u c t i o n pathway, at least t h r e e o f which a r e n e a r l y always o c c u p i e d u n d e r n o r m a l c o n d u c t i n g conditions. T h e results r e c o n c i l e this c h a n n e l ' s p u z z l i n g c o m b i n a t i o n o f high ionic selectivity a n d high c o n d u c t a n c e . M A T E R I A L S AND M E T H O D S Details of the experimental measurements were identical to those described in the companion paper (Neyton and Miller, 1988) except for the following point. In this study, because many experiments were carried out at negative potentials, we kept the channel highly activated by a combination of high Ca 2+ and Mg~+ in the internal solution. Mg~+ is known to act aUosterically to raise the affinity of this channel for activator Ca ~+ (Golowasch et al., 1986; Oberhauser et al., 1988). Therefore, many experiments reported here were performed with 10 mM Mg2+ along with 1-10 mM Ca ~§ in the internal solution. NEYTONAND MILLER K + Block of Ba 2+ Permecaion in C,a2+-activated K + Channels 571 RESULTS E x t e r n a l K § at H i g h Concentration Speeds Dissociation o f B a z + This study was i n i t i a t e d by t h e o b s e r v a t i o n illustrated in Fig. 1. I n this e x p e r i m e n t , the c h a n n e l was h e l d at + 4 0 m V a n d Ba g+ b l o c k kinetics w e r e a n a l y z e d as t h e e x t e r nal K + c o n c e n t r a t i o n was varied. A n i n c r e a s e in e x t e r n a l K + f r o m 0 to 10 m M p r o d u c e d the " l o c k - i n " effect d o c u m e n t e d in detail in the p r e c e d i n g p a p e r ( N e y t o n a n d Miller, 1988): a p r o f o u n d decrease in the r a t e o f Ba g+ dissociation. As e x t e r n a l K + was raised a b o v e 100 mM, h o w e v e r , the o p p o s i t e effect was o b s e r v e d : an increase in Ba g+ off-rate. A n a c c e l e r a t i o n o f a b l o c k e r ' s dissociation r a t e b y raising the conc e n t r a t i o n o f p e r m e a n t ions is n o t in the least surprising. This sort o f effect has b e e n o b s e r v e d in t h e case o f N a + b l o c k o f the d e l a y e d rectifier K + c h a n n e l o f squid a x o n (Bezanilla a n d A r m s t r o n g , 1972) a n d o f t h e BK c h a n n e l in b o v i n e c h r o m a f f i n cells (Yellen, 1984). I n d e e d , this is a n e x p e c t e d p r o p e r t y o f m u l t i - i o n channel. T h e 2 :o I I 400 t 800 [K+lout ,mM 1200 FIGURE 2. K + enhancement of Ba 2+ dissociation. The Ba ~+ dissociation rate (ko~) was measured at different concentrations of external K +. Conditions were as described in Fig. 1, except that the holding voltage was - 2 0 mV, and internal Ba 2§ was varied from 0.2 to 10 mM to obtain a high frequency o f blocking events. Experimental points were fitted with Eq. 1, where K D = 490 raM. b i n d i n g in a b l o c k e d c h a n n e l o f a n a d d i t i o n a l i o n destabilizes t h e b l o c k e r o n its b i n d i n g site d u e to e l e c t r o s t a t i c r e p u l s i o n b e t w e e n t h e two ions (Hille a n d Schwarz, 1978). N o t i c e that f o r the B K c h a n n e l , a n i n c r e a s e in Ba 2+ off-rate is o b s e r v e d a b o v e 100 m M e x t e r n a l K § i.e., u n d e r c o n d i t i o n s o f a l m o s t c o m p l e t e s a t u r a t i o n o f t h e e x t e r n a l lock-in site (Kt~ ffi 0.3 mM). This s t r o n g l y suggests that it is the e n t r y o f a s e c o n d K § ion into t h e e x t e r n a l p a r t o f t h e c o n d u c t i o n p a t h w a y that is r e s p o n s i b l e f o r this " e n h a n c e m e n t effect," which is the e n h a n c e d r a t e o f Ba g§ dissociation i n d u c e d by e x t e r n a l K § I f this p i c t u r e is c o r r e c t , t h e n t h e r a t e c o n s t a n t o f Ba g+ dissociation s h o u l d d e p e n d o n the o c c u p a n c y o f t h e e n h a n c e m e n t site, a n d h e n c e s h o u l d s a t u r a t e with e x t e r n a l K + c o n c e n t r a t i o n . W e u s e d e x t e r n a l K + c o n c e n t r a t i o n s a b o v e 10 mM, so t h a t t h e lock-in site c o u l d b e c o n s i d e r e d s a t u r a t e d , with Ba g+ dissociating to the i n t e r n a l s o l u t i o n exclusively ( N e y t o n a n d Miller, 1988). W e a s s u m e that Ba g+ dissociates at a l o w e r r a t e w h e n t h e e n h a n c e m e n t site is e m p t y , hi, t h a n it d o e s w h e n it is 572 THE JOURNAL OF GENERAL PHYSIOLOGY. VOLUME 9 2 . 1988 occupied, k~. Therefore, the observed dissociation rate, koer is the occupancyweighted average o f these two rates: koer = kl + (k2 - k l ) ( [ K + ] / K D + [K+]), (1) where [K +] represents the external K + concentration, and K o is the dissociation constant for K § Fig. 2 confirms that the e n h a n c e m e n t effect does follow this expected saturating behavior, and that it requires high K +, with K , in the range o f 3 0 0 - 6 0 0 mM. The m a x i m u m effect at very high K + is a 3 - 1 0 - f o l d increase in Ba ~+ dissociation rate. Voltage Dependence of B a 2 + Dissociation We showed in the preceding p a p e r that Ba 2+ can dissociate f r o m the channel to either the internal o r the external solution. With high internal K + and very low B A [K+]ou, : [K*]0ut 0 = JSo ~,M + 5 0 mV + 20 m V 4-2 0 m Y -IOmV -lOmV --40mV SpA ............ - 30 m V FIGURE3. Voltage dependence of Ba 2+ dissociation. Ba~+-blocking records were collected in two separate single-channel experiments, using different external K + concentrations, and at the indicated holding voltages. Ionic conditions were as described in Fig. 1. (A) No K + added to external solution, 1 tzM Ba 2+. (B) 150 mM K § added to external medium, 3 mM Ba~+ Arrows mark the zero-current levels. external K +, Ba ~+ nearly always dissociates to the external solution, and as e x t e m a l K § is raised, dissociation to the internal solution is progressively favored. We therefore expected that most o f the Ba 2+ dissociation events observed at high external K § would p r o c e e d to the internal solution. This expectation was confirmed by analysis o f the voltage d e p e n d e n c e o f the Ba ~+ off-rate, shown in Fig. 3. I n K+-free external solutions Ba ~+ block times b e c o m e shorter with depolarization (Fig. 3 A); in contrast, with 150 mM external K + present, the Ba ~+ blocks are lengthened by depolarization (Fig. 3 B). Fig. 4 A shows these effects o f voltage in m o r e detail. T h e Ba 2+ dissociation rate varies exponentially with applied voltage at b o t h high and low external K +, as expected for a reaction in which an effective charge, z, moves t h r o u g h a fraction o f NEYTONAND MILLER K + Block of Ba 2+ Permeation m Ca2+-activated K + Channels 573 the m e m b r a n e field, 6 (Woodhull, 1973): kon(V) = kofr(0)ex p ( - z r F V / R T ) . (2) T h e figure shows that as e x t e r n a l K + is raised, the effective valence o f the dissociation reaction, zr, changes sign. I n o t h e r words, high e x t e r n a l K + i n d u c e s a polarity reversal o f the voltage d e p e n d e n c e o f Ba 2+ dissociation, i n d i c a t i n g that Ba ~+ leaves mainly to the external s o l u t i o n at low K § (6 > 0) a n d to the i n t e r n a l solution at high K + (6 < 0). I n K+-free e x t e r n a l solutions, k ~ increased e-fold for 27 + 2 mV d e p o l a r i z a t i o n (z6 = 0.9). I n 150 m M e x t e r n a l K +, kofr decreased e-fold for 35 + 2 m V d e p o l a r i z a t i o n (z6 = - 0.71). A 10.0- [ K + ] ~ 0 S c... 1.0. .2 0 0,1 -5[ +]out=150mM I I I I -25 0 25 50 V, mV 1.0 0.00'5!~ OUTWARD z6 INWARD r 0 300 I 600 FIGURE 4. Influence of external K + on the voltage dependence of Ba2§ dissociation. (A) Ba2+ off-rate vs. holding voltage was measured as described in Fig. 3 at two different external K§ concentrations. Solid lines are drawn according to Eq. 2, with effective valence measured from the slopes of the lines. Open circles: no added K +, zfi = 0.81. Filled circles: 150 mM external K +, z~$= - 0 . 6 4 . (B) Variation of effective valence (z~) with external K +. Ba 2+ off-rate as a function of voltage was measured as in A, at the indicated external K + concentrations. For each set of conditions, the effective valence was measured from three to six voltage values. Each point represents the mean _+ SE of three separate experiments. [K+]out , mM T h e reversal o f the voltage d e p e n d e n c e o f kofr by external K + is a progressive effect. Fig. 4 B shows the effective valence for Ba ~+ dissociation as a f u n c t i o n o f external K § This effective valence, initially positive at zero K +, rapidly a p p r o a c h e s zero over the r a n g e 0 - 1 0 m M e x t e r n a l K § as the i n t e m a l lock-in site b e c o m e s filled, a n d dissociation p r o c e e d s to b o t h sides at r o u g h l y equal rates (Neyton a n d Miller, 1988). O n l y as K + is raised above 50 m M does the effective valence b e c o m e increasingly negative, r e a c h i n g a s a t u r a t i o n value at very high K § It is precisely over this r a n g e o f high K + c o n c e n t r a t i o n s that the e n h a n c e m e n t o f kofr by K § is observed. Thus, the effects o f K § o n the effective valence o f the Ba 2+ off-rate are fully consistent with the p i c t u r e that external K + retards inward dissociation at low c o n c e n t r a - 574 THE JOURNAL OF GENERAL PHYSIOLOGY 9 VOLUME 9 2 9 1 9 8 8 tions ( 0 - 1 0 raM) a n d e n h a n c e s o u t w a r d dissociation at h i g h e r c o n c e n t r a t i o n s ( > 5 0 raM). Voltage Dependence of the K+-enhancement Effect T h e p r e c e d i n g section d e m o n s t r a t e d t h a t Ba 2+ dissociation is voltage d e p e n d e n t . T h e efficacy o f e x t e r n a l K § in e n h a n c i n g Ba ~+ dissociation is also voltage d e p e n d e n t , as Fig. 5 d e m o n s t r a t e s . H e r e , we show K + - e n h a n c e m e n t curves at two values o f a p p l i e d voltage. It is clear that b o t h the K D a n d t h e m a x i m u m effect a r e voltage d e p e n d e n t . M o r e negative voltages, which t e n d to d r a w K + into the c h a n n e l f r o m the e x t e r n a l solution, a n d Ba ~+ o u t o f it into the i n t e r n a l solution, t e n d to favor K + b i n d i n g at the e n h a n c e m e n t site a n d to p r o d u c e a l a r g e r m a x i m u m increase in Ba 2+ off-rate. F r o m a series o f t h r e e e x p e r i m e n t s , KD was f o u n d to i n c r e a s e with d e p o l a r ization, with values o f 300 _+ 20 m M at - 30 mV, a n d 550 -+ 120 m M at 0 mV. T h e fact that the K + dissociation c o n s t a n t at the e n h a n c e m e n t site is voltage d e p e n d e n t a r g u e s that this site lies within the t r a n s m e m b r a n e voltage d r o p , as will b e discussed later. T= ,,= Jro i i i 400 800 1200 [ K + ] o u t ,raM FIGURE 5. Voltage dependence o f K + - e n h a n c e m e n t effect. Ba 2+ off-rate was measured, as in Fig. 2, as a function of external K § concentration, at two different holding potentials. Both curves shown were taken on the same channel. Triangles, - 3 0 mV. Solid curve is drawn according to Eq. 2, with k] = 0.1 s -j, k2 = 2.3 s -1, and K D = 580 mM. Squares, zero voltage. Solid curve is drawn with k] = 0.1 s -1, ks = 1.3 s -j, andKD = 580 mM. Selectivity of the External Enhancement Site Fig. 6 c o m p a r e s off-rate variations o b s e r v e d w h e n raising e x t e r n a l K +, R b +, a n d N a +. As with K +, an e x t e r n a l Rb + c o n c e n t r a t i o n a b o v e 50 m M increases ko~. T h e maximal a m p l i t u d e o f the R b + e n h a n c e m e n t effect, a n d also the value o f KD a r e smaller t h a n f o r K § (for R b +, KD = 205 + 45 m M at z e r o voltage, less t h a n h a l f the value f o r K+). Thus, R b + a p p e a r s to b i n d with a h i g h e r affinity to the e n h a n c e m e n t site, b u t o n c e b o u n d it e x e r t s less o f a destabilizing f o r c e o v e r Ba 2+ t h a n d o e s K § I n c o n t r a s t with the p e r m e a n t ions, e x t e r n a l N a + is u n a b l e to s p e e d Ba ~+ dissociation, even at c o n c e n t r a t i o n s as high as 1.2 M. T h e d e c r e a s e in off-rate seen at high N a § in Fig. 6 is the tail o f the Ba 2+ lock-in effect by e x t e r n a l N a + (Neyton a n d Miller, 1988). It is thus a p p a r e n t that only p e r m e a n t ions a r e able to e x e r t an e n h a n c e m e n t effect. NEYTONAND MILLER K + Block of Ba 2§ Permeation in Ca2+-activated K + Channels 575 Internal K + Locks B a 2§ into the Channel T h e e x p e r i m e n t s a b o v e a n d in t h e p r e c e d i n g s t u d y f o c u s e d o n t h e i n t e r a c t i o n s o f Ba 9+ with e x t e r n a l K +. W e n o w r e v e r s e the system's p o l a r i t y a n d investigate interactions o f i n t e r n a l K + with Ba 2+ (which is still a d d e d to the i n t e r n a l s o l u t i o n in all e x p e r i m e n t s ) . W e m a i n t a i n e d e x t e r n a l K + c o n s t a n t at 150 mM, a n d v a r i e d i n t e r n a l K +. Fig. 7 shows t h a t the d u r a t i o n o f Ba 2+ blocks is strongly i n c r e a s e d by i n t e r n a l K +. A t 300 m M i n t e r n a l K § t h e m e a n b l o c k time is o v e r 10 times l o n g e r t h a n K § free c o n d i t i o n s . Raising K § also increases t h e d u r a t i o n o f t h e bursts, b u t the effect is m u c h weaker: a t h r e e f o l d i n c r e a s e in t h e m e a n b u r s t time is o b s e r v e d w h e n the i n t e r n a l c o n c e n t r a t i o n o f K § is c h a n g e d f r o m 0 to 300 mM. Thus, in analogy to the effect o f e x t e r n a l K +, i n t e r n a l K + also i n d u c e s a Ba ~+ lock-in effect. Fig. 8 illustrates quantitatively t h e effects o f i n t e r n a l K + o n the Ba~+-blocking kinetics. I n the c o m p l e t e a b s e n c e o f i n t e r n a l K § the off-rate is r a p i d , a n d the addi- ,), 0 Rb+ . I I 400 800 [X§ t ,mM FIGURE 6. Ion selectivity of enhancement effect. Ba ~§ offrate was measured between - 10 and 0 mV as a function of the concentration of the indicated cation a d d e d to the external medium. 150 mM NMDG § was present in all external solutions. Curves for K + and Rb + are drawn according to Eq. 1, with a KD of 330 mM for K § and 160 mM for Rb § Maximum values of offrates are 1.7 and 0.2 s-i for K + and Rb § respectively. The decrease in off-rate with added Na + is due to the very lowaffinity "lock-in" effect seen for this cation. tion o f K + r e d u c e s this rate. I t is i m p o r t a n t to r e m e m b e r that these e x p e r i m e n t s were c a r r i e d o u t in h i g h e x t e r n a l K +, w h e r e the e x t e r n a l lock-in site is always occupied; t h e r e f o r e , n e a r l y all the Ba 2+ dissociation events p r o c e e d to t h e i n t e r n a l solution, as i n d i c a t e d by the voltage d e p e n d e n c e above. As with the e x t e r n a l lock-in effect, t h e i n h i b i t i o n o f Ba ~+ off-rate by i n t e r n a l K + follows a r e c t a n g u l a r h y p e r b o l i c f u n c t i o n o f the i n t e r n a l c o n c e n t r a t i o n o f K § (Fig. 8 A). T h e K § c o n c e n t r a t i o n o f half-inhibition (Ki) is in this case 8 mM. T h e Ba 2+ association r a t e also d e c r e a s e s w h e n the i n t e r n a l c o n c e n t r a t i o n o f K + is r a i s e d (Fig. 8 B). H o w e v e r , m u c h h i g h e r i n t e r n a l K § c o n c e n t r a t i o n s a r e r e q u i r e d to o b t a i n a significant r e d u c t i o n o f the onrate: K i was ~ 2 0 0 mM. T h e similarity b e t w e e n the Ba ~+ lock-in effects i n d u c e d by e x t e r n a l a n d i n t e r n a l K + a r g u e s f o r a similar u n d e r l y i n g m e c h a n i s m . I n strict a n a l o g y to t h e effects o f e x t e r n a l K § ( N e y t o n a n d Miller, 1988), we p r o p o s e that the c o n d u c t i o n p a t h w a y 576 THE JOURNALOF GENERALPHYSIOLOGY.VOLUME 9 2 . 1988 contains a K§ site l o c a t e d o n the i n t e r n a l side o f the Ba~+-blocking site. This internal lock-in site m u s t b e u n o c c u p i e d f o r a Ba 2+ ion to e n t e r the p o r e , o r f o r a Ba ~+ ion inside the p o r e to leave it to t h e i n t e r n a l solution. AjOlnity and Selectivity of the Internal Lock-In Site T h e e x t e r n a l lock-in site was shown to b e highly selective f o r p e r m e a n t ions (Neyton a n d Miller, 1988). This is n o t the case f o r the i n t e r n a l lock-in site. Fig. 9 shows that b o t h K + a n d N a + in the i n t e r n a l s o l u t i o n a r e able to lock Ba 2+ in the channel. T h e affinity o f the i n t e r n a l lock-in site is a b o u t fivefold l o w e r f o r N a + t h a n f o r K +. F r o m a series o f eight e x p e r i m e n t s c a r r i e d o u t with 1 - 5 m M i n t e r n a l Ca + p r e s e n t , K i values were f o u n d to b e 7 + 1 m M f o r K + a n d 36 + 3 m M f o r N a +. I n t e r n a l R b § p r o d u c e d a lock-in effect as well (Ki = 9 mM), as d i d Ca 2+ (Ki = 27 raM). Thus, the i n t e r n a l lock-in site a p p e a r s p o o r l y selective a m o n g cations, b u t definitely favors c o n d u c t i n g cations. 12# ,6 .L, .... FIGURE 7. Effect of internal K + on Ba 2+ dissociation. Single-channel recordings were collected with 150 mM external K + and 150 mM internal NMDG + held fixed, while internal K + was added to the indicated concentrations. Ba 2+ was 100 #M and the voltage was 20 inV. Mean block times were 0.3, 1.2, and 3.0 s at 0, 10, and 300 mM internal K +, respectively. DISCUSSION I n the p r e c e d i n g investigation ( N e y t o n a n d Miller, 1988) we s h o w e d that two ions, Ba ~+ a n d K +, can s i m u l t a n e o u s l y b i n d with high affinity inside the p o r e o f the large BK channel. By e x p l o i t i n g the i n t e r a c t i o n o f Ba ~+ with the c h a n n e l as a p r o b e , we have now i d e n t i f i e d two a d d i t i o n a l effects o f K + o n Ba ~+ dissociation: an e x t e r n a l e n h a n c e m e n t effect a n d an i n t e r n a l lock-in effect. W e t h e r e f o r e p r o p o s e that the ion c o n d u c t i o n p a t h w a y o f the BK c h a n n e l c o n t a i n s f o u r i o n - b i n d i n g sites lined u p in single file: two lock-in sites, an e n h a n c e m e n t site, a n d the Ba~+-blocking site. Several questions i m m e d i a t e l y arise. First, d o the t h r e e distinct effects o f K + o n Ba 2§ dissociation m e a n that t h e r e a r e t h r e e physically distinct K + - b i n d i n g sites involved? H o w m a n y o f these sites m a y b e s i m u l t a n e o u s l y o c c u p i e d ? H o w a r e the o b s e r v e d affinities o f these sites r e l a t e d to ionic c o n d u c t i o n a n d selectivity o f this channel? By e x a m i n i n g these questions in light o f o u r e x p e r i m e n t a l results, we will see that a minimal m o d e l f o r the c o n d u c t i o n p a t h w a y o f this c h a n n e l m u s t c o n t a i n f o u r phys- NEe-CONANO MtLLEI~ K § Block e l b a z§ Permeation in Ca2 *-aairmted K § Channels 577 ically distinct K§ sites, all o f which are simultaneously o c c u p i e d most o f the time d u r i n g normal K + conduction. Are There Separate Sites? Previous work has shown that the BK channel's c o n d u c t i o n pathway contains a site that binds a single Ba ~+ ion with high affinity (Vergara and Latorre, 1983; Miller, 1987; Miller et al., 1987). It is very likely, t h o u g h n o t rigorously proven, that this site is designed for K § conduction, a n d that Ba ~+ binds as a "substrate analogue" because o f its similarity in size to K § (Latorre and Miller, 1983; Miller et al., 1987). We know that as long as Ba 2+ ion resides o n this blocking site, the channel c a n n o t A 4 0 200 o ~ 400 600 =170m ~ I 200 [Kr ! 400 FIGURE 8. Lock-in effect induced by internal K +. Ba ~+ off-rate (A) and on-rate (B) were measured as a function of internal K +, under conditions similar to those found of Fig. 7. Solid curves were fit by rectangular hyperbolas, with half-inhibition concentrations of 8 mM for the off-rate and 160 mM for the on-rate. ! 600 c o n d u c t K + ions, since, as with m a n y K + channels (Hille and Schwarz, 1978), the p o r e is so n a r r o w that ions c a n n o t pass o n e another. The evidence for three additional ion-binding sites comes f r o m the present studies on K + interactions in the Ba*+-blocked channel. We f o u n d that low concentrations o f external K + greatly r e d u c e the rate o f Ba ~+ dissociation. The very high affinity o f K* in p r o d u c i n g this lock-in effect, and the high ion selectivity for c o n d u c t i n g ions d e m o n s t r a t e that a specific site exists at which K + "blocks" the dissociation o f Ba 2+ (Neyton a n d Miller, 1988). A n identical a r g u m e n t can be m a d e f o r the internal lock-in site d o c u m e n t e d in this work; here, neither the affinity n o r the selectivity o f the binding is as high as with the external site, but still they are high e n o u g h to rule 578 T H E J O U RN A L O F GENERAL PHYSIOLOGY 9 VOLUME 92 - 1988 out nonspecific effects, such as the screening o f local surface potentials. It is also clear f r o m these results that the two lock-in sites are physically distinct, since they are located o n different sides o f the blocking Ba 2+ ion. O u r results f u r t h e r d e m o n s t r a t e the existence o f a third K+-binding site located o n the external side o f the blocking Ba 2+ ion, the e n h a n c e m e n t site. This site, when o c c u p i e d by a K + ion, destabilizes Ba 2+ o n its binding site, and thus speeds its dissociation to the internal solution; this is analogous to the conventional "knock-off'' effects o f p e r m e a n t ions o n blockers, long known in a variety o f K § channels (Bezanilla and A r m s t r o n g , 1972; A d e l m a n and French, 1978; Yellen, 1984; Cecchi et al., 1987). This e n h a n c e m e n t site, requiring K + at concentrations > 5 0 mM, is o f very low affinity, but it maintains high selectivity; only c h a n n e l - p e r m e a n t ions produce the effect. This selectivity allows us to conclude that the e n h a n c e m e n t effect is the result o f specific o c c u p a n c y o f a site, and, t o g e t h e r with the voltage d e p e n d e n c e o f the e n h a n c e m e n t site affinity, that this site is most likely located within the chan- z 2 ~ ~ I I I tO0 200 300 FIGURE 9. Ion selectivity of internal lock-in effect. The Ba '2+ off-rate was measured against internal concentrations of either K § or Na +, under conditions similar to those found in Fig. 7. Half-inhibition constants of solid curves under 8 mM for K + (triangles) and 41 mM for Na + (squares). Ix+]in,raM nel's c o n d u c t i o n pathway. Moreover, it is clear that the e n h a n c e m e n t site is distinct f r o m either o f the lock-in sites. Concentrations o f K + p r o d u c i n g the e n h a n c e m e n t effect are orders o f m a g n i t u d e higher than those required to saturate the lock-in sites. In studying ion channels, or any o t h e r types o f enzymes, it is usually i m p r o p e r to identify a saturating process with o c c u p a n c y o f a binding site. T h e reason that we can make this identification here without apology is that all o u r experiments are designed so that the K + interactions u n d e r scrutiny are at true t h e r m o d y n a m i c equilibrium. T h e reason for this is that these experiments focus on the dissociation o f Ba 2+ f r o m a blocked, n o n c o n d u c t i n g channel, i.e., a channel which K § c a n n o t permeate. Because the Ba ~+ ion prevents K + m o v e m e n t across the pore, any K + ion inside the channel must leave it to the same solution f r o m which it had entered. This means that as long as Ba 2+ remains b o u n d , K + o c c u p y i n g a site within the channel is in equilibrium with the bulk solution o n the same side o f the Ba 2+. By focusing o n the Ba 2+ dissociation process, we are necessarily studying the channel while it is NEYrONANDMILLER K § Block of Ba2§ Permeation in CaZ§ K § Channels 579 blocked in this way. We assume, o f course, that K + enters and leaves the channel on the conduction time-scale (nanoseconds to microseconds) many orders o f magnitude m o r e rapidly than Ba 2+ dissociates f r o m its blocking site. It is for these reasons that we can validly identify the saturating effects of K + on Ba ~+ dissociation kinetics with occupancy o f sites within the conduction pathway. How Many Sites Can Be Simultaneously Occupied? The arguments above identify the three K+-binding sites as distinct, but they do not tell us whether these sites can be occupied simultaneously. The apparent dissociation constants of both the external and internal lock-in sites are low: ~20 #M and 8 raM, respectively, when measured in 150 mM N-methyl-~glucamine (NMDG+)-con taining solutions, Each o f these dissociation constants was measured in the presence of 150 mM K + in the opposite compartment, i.e., with the opposite lock-in site almost saturated. Thus, in 150 mM K + on both sides, both lock-in sites are nearly always occupied simultaneously, with Ba ~+ on its blocking site between them. Is the enhancement site occupied simultaneously with the lock-in sites? The enhancement site, located on the external side o f the blocking Ba ~+, starts to be significantly occupied only above 50 mM K +, many orders o f magnitude above the dissociation constant o f the external lock-in site. The externally located lock-in and enhancement sites can therefore be occupied at the same time. Moreover, enhancement of Ba ~+ dissociation by external K + was analyzed in 150 mM internal K +, i.e., with the internal lock-in site highly occupied. It might be argued that u n d e r the very high external concentration o f K + required to fill the enhancement site, the affinity o f the internal lock-in site for K + might be lower. This is not the case, however, since identical lock-in effects are seen at all external K + concentrations tested; at 150, 300, and 500 mM external K +, KD values for the lock-in effect were 10, 11, and 8 raM, respectively. In conclusion, in a Ba2+-blocked channel, the external lock-in and enhancement sites as well as the internal lock-in site can be occupied at the same time. Moreover, the simultaneous occupancy o f these three K+-binding sites occurs along with a Ba r+ ion residing inside the conduction pathway in addition. These four cation-binding sites u n d e r study must therefore be separate entities. A Physical Picture o f K+-Ba 2+ Interactions Inside the Pore The lock-in effects observed at low K + concentrations are easily rationalized in terms of the single-filing behavior of this K § channel (Neyton and Miller, 1988). H o w can we understand the ability o f external K + at high concentrations to speed Ba 2+ dissociation? O u r results show that this effect is due to the low-affinity binding, in the external part o f the channel's p o r e already occupied by the lock-in K +, of a second K + ion. Given that this is a single-filing channel, we would like to know which o f these sites is located m o r e externally, and which is deeper inside, closer to the Ba 2+ ion. We can distinguish the two possible arrangements o f sites by taking advantage o f the fact that K + binds to these sites at true thermodynamic equilibrium, as discussed above. Because o f this, the observed "half-saturation concentration" for each effect rigorously represents the dissociation constant of the K + ion on the relevant site. In such a case, the voltage dependence of the K D provides an unequivocal indicator o f 580 THE JOURNAL OF GENERAL PHYSIOLOGY 9 VOLUME 92 9 1988 the position of the site in the applied voltage drop within the channel, fi (Eq. 2). We therefore measured the voltage dependence o f KD for all three K+-binding sites (Fig. 10). The binding o f external K § to the external lock-in and enhancement sites weakens with depolarization, while binding of internal K + to the corresponding lock-in site strengthens. From a series of five experiments, the values of fi for the externally facing site were 0.18 _ 0.02 for the external lock-in site, and 0.57 _+ 0.13 for the enhancement site. The external lock-in site is therefore located in the most external part of the channel's conduction pathway. The enhancement of Ba l+ dissociation by external K + arises f r o m the occupancy o f a site located more deeply in the pore, closer to the Ba~+-blocking site. The most natural explanation o f this effect is simple electrostatic destabilization of Ba 2+ on its site by the K § ion nearby. Fig. 10 further shows that the internal lock-in site experiences about one-third of the voltage drop, as measured f r o m the inside (~, - 0 . 3 6 _+ 0.04). An immediate objection may arise to the picture of the enhancement effect just offered. The very high affinity of the lock-in site ensures that this externally located site is virtually always occupied at the high K § concentrations required to load the Ext lock 0 v Y 0.5 0.2 ' , -40 I 0 ~ ' ~ ~ V, m V Int lock I 40 , f 80 FIGURE 10. Voltage dependence of the three K § binding effects. Variation of the apparent dissociation constants for the three effects of K + on Ba2+ off-rate, measured in three separate experiments. Open circles: external lock-in site, zfi = 0.18. Filled circles: enhancement site, z~ = 0.42. Open triangles: internal lock-in site, z~ = -0.45. enhancement site. How, then, can K + ions ever gain access to the more internally located site if the single-filing rule applies? There are two answers to this objection. First, we may remind ourselves that in a true binding equilibrium, the kinetic path for going from an initial state to a final state need not be specified. The enhancement effect simply represents a change f r o m the initial state with only the externally facing lock-in site occupied, to a final state with both K+-binding sites occupied. The voltage dependence of the K D tells us that regardless o f how this reaction occurs, a net charge moves about half-way down the voltage gradient. Despite the thermodynamic purity of this argument, it might be worthwhile to suggest a concrete way for the enhancement site to become occupied even though the m o r e externally located lock-in site is of much higher apparent affinity. When only one of these K+-binding sites is occupied, there will be a dynamic equilibrium of the single K § ion between the two sites. Since the external site is of much higher affinity, the K § ion resides on this site nearly all the time. Very rarely but inevitably, however, the K + ion will occupy the lower affinity enhancement site, and during such moments the externally located site will become available for attack by a K § ion NEYTONANDMILLER K § Block of Ba z+ Pen,neation in Ca2 +-activated K + Channels 581 in bulk solution. The net result o f this reaction will be to fill the e n h a n c e m e n t site by a conventional vacancy mechanism. T h e r e is really n o theoretical p r o b l e m at all, as long as the rates o f ion m o v e m e n t a m o n g the K+-binding sites are fast c o m p a r e d with the Ba ~+ dissociation rate. Ironically, the site a b o u t which we have the least information is the Ba~+-blocking site itself. We know neither its affinity for K + n o r its ion selectivity. Since we rely u p o n the Ba~+-blocked channel as the object o f all o u r m e a s u r m e n t s here, we cannot manipulate the blocking site. We should ask if this even is a single, well-defined site, o r w h e t h e r the Ba ~+ ion can exchange a m o n g the o t h e r K+-binding sites, as apparently occurs in the squid a x o n delayed rectifier (Armstrong et al., 1982). The present model asserts that when either lock-in site is empty, the Ba ~+ moves into this site just before dissociation; the high Ba 2+ off-rate at zero K + o n either side (>4 s -1) would represent the rate o f m o v e m e n t f r o m the high-affinity blocking site into the lock-in site f r o m which Ba ~+ rapidly exits. This would be possible with b o t h lock-in sites filled (K + > l m M external and 100 mM internal), but when the e n h a n c e m e n t site is empty, Ba ~+ would be able to exchange between the blocking site and the e n h a n c e m e n t site. Thus while Ba ~+ may not be physically confined to a single site, it must remain in the region between the two lock-in sites for times on the o r d e r o f h u n d r e d s o f milliseconds. O n e puzzle f o r which we d o n o t have a satisfactory explanation is the fact that as K + o n b o t h sides raised, the Ba ~+ off-rate a p p r o a c h e s a n o n z e r o value o f ~0.2 s -1. A model with only a lock-in site o n the internal side would predict that at fixed high external K +, as internal K + is increased without limit, the Ba 2+ off-rate should a p p r o a c h zero. A possible explanation for this is that an additional e n h a n c e m e n t site exists on the inner side o f the Ba2+-blocking site, and that as this site becomes filled at very high internal K +, Ba ~+ is p u s h e d o u t to the external solution. We have no direct evidence for such a fifth binding site, and are presently searching for experimental conditions suitable for observing internal e n h a n c e m e n t effects. An a p p a r e n t oddity a b o u t the p h e n o m e n a r e p o r t e d here is the different effects o f K + o n the association and dissociation rates for Ba ~+. K + decreases b o t h these rates, but over different c o n c e n t r a t i o n ranges. H o w can this be, if K § exerts its effect at the same site in b o t h places? The resolution o f this p a r a d o x lies in the fundamental difference in K + interaction with the channel in its c o n d u c t i n g and blocked states. As pointed o u t above, in the blocked channel, K + binds to its site in a true equilibrium reaction; the blocking Ba ~+ ion effectively isolates o n e side o f the channel f r o m K + ions on the o t h e r side. I n contrast, the c o n d u c t i n g channel, which allows K + to enter f r o m b o t h sides, is a m u c h m o r e complicated system. Here, the effect o f external K +, for instance, o f r e d u c i n g the Ba 2+ on-rate does not measure the o c c u p a n c y o f the lock-in site, but is the c o n s e q u e n c e o f a large n u m b e r o f rate processes in this multi-ion pore. We have n o inclination to model such a complicated process with so m a n y free parameters. M u l t i - I o n Conduction by the B K C h a n n e l O u r picture o f K+-binding sites within this channel's c o n d u c t i o n pathway has e m e r g e d f r o m experiments carried o u t o n the n o n c o n d u c t i n g , Ba~+-blocked channel. Nonetheless, these results i n f o r m us a b o u t the mechanism o f K + p e r m e a t i o n 582 THE JOURNAL OF GENERAL PHYSIOLOGY 9 VOLUME 92 9 1 9 8 8 through the conducting channel. Assuming that the Ba2+-blocking site is designed to interact with K + u n d e r normal conducting conditions, we conclude that this channel contains at least four sites that may all be simultaneously occupied during K + conduction. We further propose that these four K§ sites are of inherently very high affinity for K § and selective for K + over Na +, although with different degrees of selectivity. We will argue that this proposal leads to a plausible picture of ion conduction through this channel. How can we reasonably argue that all the sites are of inherently high affinity for K +, when we observe an enormous range o f affinities for these sites? The external lock-in site shows a K D of 20 tzM, while the KDs of the internal lock-in and enhancement sites are on the o r d e r of 10 and 300 mM, respectively. To answer this objection, we must distinguish between the inherent affinity of a site and its observed affinity. By the inherent affinity o f a site in this channel, we mean the affinity of the site _C 13kcollrnoI Empty Chonnel :)-Occupied SiteAffinity Chonges with Occuponcy 4-Occupied ] F]GURE 11. Destabilization of ion binding by multiple occupancy. This cartoon qualitatively represents the effect of ion occupancy on the free energy profile of a multiply occupied channel. The channel has four identical sites of high affinity. The free energy profile for the unoccupied channel is drawn ~8 kcal/mol below the level of the external solution (1 molal standard state), which is equivalent to KD = 1 uM for the first K+-binding step. Also drawn are the doubly occupied channel (free energy profile seen by the third ion binding step) and the fully occupied channel. Free energy scale is drawn for heuristic purposes only, and to correspond roughly to the range of K, values seen in this study. for a K + ion, given that all the other sites are unoccupied. In other words, the inherent affinity refers to the binding o f an ion to the empty channel. In general, the observed affinity of sites in a multi-ion channel will be lower than the inherent affinity because of electrostatic repulsion between ions (Levitt, 1978). The point is illustrated in Fig. 11, which shows the free energy profiles we propose for this channel at various degrees of occupancy by K +. The empty channel contains four identical sites of very high affinity, equivalent to a KD in the submicromolar range. A K + ion alone inside this channel would be stuck in a very deep energy well; it would be able to move rapidly a m o n g the four sites, but not to leave the channel easily. As K + concentration is raised, additional sites begin to become significantly occupied. A K + ion about to enter the doubly occupied channel would see a much higher energy profile, equivalent to an observed K D of 1 mM, for exam- NZYTONANDMILLER K + Block of Baz+ Permeation in Ca2+-aaivated K + Channels 583 pie. The last K + ion would bind with an even lower affinity to the triply occupied channel. In this way, all the ions in the fully occupied channel would mutually destabilize each other, so that the rates o f escape f r o m the pore would be high enough to account for the high conductance actually observed in this channel. This argument must remain qualitative, however, since we do not know the physical separation between the sites, and thus cannot calculate the energies o f mutual destabilization. Experimental and theoretical studies o n gramicidin A, (Levitt, 1978), however, show that identical sites separated by 1 n m can easily produce KD values differing by factors of 100-1,000. Since these are the sorts of destabilization factors we observe here, it is reasonable to propose that these four sites span a distance of ~3 nm. This estimate is in harmony with the length o f the channel measured by bis-quaternary a m m o n i u m blockers, 3.5 nm (Villarroel et al., 1988). We find a very low K D of 20 #M for K + binding to the external lock-in site. This is the highest affinity yet reported for any K+-specific protein binding site. Since this m e a s u r e m e n t was made with a divalent Ba 2+ ion in the blocking site and a K + in the O --K -- Bo2+ Bo-Block OUT g / / / / / / I / / / / / I / I / / / / / / / l 0 IIlIIIIIIIIIIIIIIIIIIIIA 8 = 0 I 0.15 t 0.5 I 0.7 I Lock-in Enhoncement Lock-in 1.0 I FIGURE 12. A model of the pore of the BK channel. This cartoon summarizes our conclusions from this and the companion study. The channel is pictured as containing four IN K*-binding sites located at the indicated electrical distances, measured from a series of 12 experiments as in Fig. 10. The Bae+-blocking site is constrained to be located between the internal lock-in and enhancement sites. internal lock-in site, the inherent affinity of this site must be even higher than this. Likewise, the observed KD (8 mM) of the internal lock-in site was measured in the presence of Ba ~+ and a single K § already in the channel. The enhancement site begins to fill only above 50 mM K +, but this occurs in a channel already occupied by a Ba l+ and two K+ions. Moreover, the enhancement site is located closer to the Ba ~+ site, as j u d g e d by the voltage dependence o f its binding (Fig. 10), so ionic repulsion here is expected to be particularly strong. For these reasons, we consider it plausible to propose the simple picture here of four structurally similar, high-affinity K+-binding sites. According to this view, significant K + conduction occurs only when the channel is occupied by at least three K + ions. For lower occupancies, K § conduction is retarded because the resident ions bind too tightly to the pore. Only at higher ion occupancies do the K § ions mutually destabilize each other and rapidly permeate the channel; this mutual destabilization raises the K § dissociation constants by factors on the order of 10 s, thus lifting the free energy profile up by ~7 kcal/mol (Fig. 584 T H E J O U RN A L OF GENERAL PHYSIOLOGY 9 VOLUME 92 9 1988 1 |). Since this channel allows K + conduction at rates approaching diffusion limitation (Latorre and Miller, 1983), there cannot be significant barriers to K + movement within the pore itself. Instead, we picture the p o r e as a structure that allows thermodynamically favorable specific liganding o f K + over an extended region of ~3 nm, as pictured in Fig. 12. As a speculative interpretation o f o u r results, this cartoon cannot be taken seriously in detail; but the essential point expressed in this proposed structure, the existence o f a long pore containing numerous sites suited to interact strongly with the K § ion, follows inescapably from o u r results. This model is consistent with this channel's unusual relation between single-channel conductance and symmetrical K + concentration (Moczydlowski et al., 1985), which can be fit in the high concentration range (where local surface potentials are largely screened) by a rectangular hyperbola of Km = 130 mM. While this relation cannot be expected to correspond precisely to the binding steps described here, the increase in conductance in the range o f 100-1,000 mM probably represents the filling o f the fourth site identified in this study. The kind of picture offered here is a wholly conventional view of K + channel structure. Hodgkin and Keynes (1955) originally proposed a "long p o r e " model for the squid axon delayed rectifier, and Hille and Schwarz (1978) pointed out that multi-ion, single-file conduction applies in many K + channels. Estimates of pore occupancies of two or three K + ions have been made from flux ratio measurements on squid axon-delayed rectifier K + channel (Hodgkin and Keynes, 1955; Begenisich and deWeer, 1980), the inward rectifier o f skeletal muscle (Spalding et al., 1981), and a Ca2+-activated K + channel from h u m a n erythrocytes (Vestergaard-Bogind et al., 1985). The only novel aspect o f o u r structure is the enhanced detail that we can plausibly propose. O u r data force us to two unexpected conclusions: (a) that a large n u m b e r of ion-binding sites, at least four, can be simultaneously occupied inside the confines of this highly selective pore, and (b) that the inherent affinity o f this pore for K + is extremely high, many orders o f magnitude higher than the affinity deduced by conduction properties alone. O f course, the high inherent binding affinity is required for multiple occupancy here; it is the large favorable free energy of binding that allows several ions to overcome their mutual repulsion and cohabit the pore. These results lead us to a less conventional view of the mechanism o f K + selectivity. Traditionally, K+-selective channels have been considered to select against Na +, not by favoring the binding of K +, but by placing large barriers to Na § movement at the channel's "selectivity filter" (Armstrong, 1975; Coronado et al., 1980), although Hille and Schwarz (1978) have pointed out that multi-ion channels are so complicated that their ionic conduction properties tell us almost nothing about the underlying energy profile experienced by a permeating ion. O u r results show that the channel contains binding sites that interact strongly with K + and much less strongly with Na § For example, the K + / N a + binding affinity ratio is > 1,000 for the external lock-in site, and at least 10 for the enhancement site. (The internal lock-in site is less selective, with K + favored over Na + only by a factor o f 5.) We imagine that Na + fails to permeate the channel simply because most of the cation-liganding region has a low inherent affinity for this ion. The presence of even a minute concentration o f K + will effectively exclude Na + from the channel, exactly as Ca ~+ NEYTONAND MILLER K + Block of Baz+ Permeation in Ca2+-activated K + Channels 585 blocks m o n o v a l e n t cation c o n d u c t i o n t h r o u g h the "L-type" Ca ~+ c h a n n e l (Almers a n d McCleskey, 1984; Hess a n d Tsien, 1984). T h e fact that the i n t e r n a l lock-in site can a c c o m m o d a t e a Na + ion with a Ba 2+ a n d a K + in the c h a n n e l may m e a n that the i n h e r e n t affinity o f this p a r t i c u l a r site is actually quite high for N a +. I n d e e d , this may be the site o f i n t e r n a l N a + block o f this c h a n n e l (Marty, 1983; Yellen, 1984). A c o m b i n a t i o n o f a single high-affinity N a + site in series with several o t h e r low-affinity N a + sites w o u l d explain this c h a n n e l ' s failure to c o n d u c t N a § appreciably in the total a b s e n c e o f K +. We are grateful for Dr. Rod MacKinnon's suggestions and provocations throughout the course of this investigation. Support was provided by a National Institutes of Health grant GM-31768. Dr. Neyton was supported by a Fogarty International Fellowship TWO 3898, a European Molecular Biology Organization Fellowship ALTF90-1986, and by the Centre National de la Research Scientifique. Original version received 1 April 1988 and accepted version received 27 June 1988. REFERENCES Adelman, W., and R.J. French. 1978. Blocking of squid axon potassium channel by external caesium ions. Journal of Physiology. 276:13-25. Aimers, W., and E. McCieskey. 1984. Nonselective conductance in calcium channels of frog muscle: calcium selectivity in a single-file pore.Journal of Physiology. 353:585-608. Armstrong, C. M. 1975. Potassium pores of nerve and muscle membranes. In Membranes, A Series of Advances. vol. 3. G. Eisenman, editor. Marcel Dekker, New York. 325-358. Armstrong, C. M., R. P. Swenson, and S. 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