Using Ba2+ as a probe, we performed a detailed characterization of an external K+ binding site located in the pore of a large conductance Ca2+-activated K+ (BKCa) channel from skeletal muscle incorporated into planar lipid bilayers. Internal Ba2+ blocks BKCa channels and decreasing external K+ using a K+ chelator, (+)-18-Crown-6-tetracarboxylic acid, dramatically reduces the duration of the Ba2+-blocked events. Average Ba2+ dwell time changes from 10 s at 10 mM external K+ to 100 ms in the limit of very low [K+]. Using a model where external K+ binds to a site hindering the exit of Ba2+ toward the external side (Neyton, J., and C. Miller. 1988. J. Gen. Physiol. 92:549–568), we calculated a dissociation constant of 2.7 μM for K+ at this lock-in site. We also found that BKCa channels enter into a long-lasting nonconductive state when the external [K+] is reduced below 4 μM using the crown ether. Channel activity can be recovered by adding K+, Rb+, Cs+, or NH4 + to the external solution. These results suggest that the BKCa channel stability in solutions of very low [K+] is due to K+ binding to a site having a very high affinity. Occupancy of this site by K+ avoids the channel conductance collapse and the exit of Ba2+ toward the external side. External tetraethylammonium also reduced the Ba2+ off rate and impeded the channel from entering into the long-lasting nonconductive state. This effect requires the presence of external K+. It is explained in terms of a model in which the conduction pore contains Ba2+, K+, and tetraethylammonium simultaneously, with the K+ binding site located internal to the tetraethylammonium site. Altogether, these results and the known potassium channel structure (Doyle, D.A., J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, and R. MacKinnon. 1998. Science. 280:69–77) imply that the lock-in site and the Ba2+ sites are the external and internal ion sites of the selectivity filter, respectively.

The large conductance Ca2+-activated K+ (BKCa) channel has a multi-ion pore (Yellen 1984b; Eisenmann et al. 1986; Cecchi et al. 1987; Neyton and Miller 1988a,Neyton and Miller 1988b), like many other potassium channels (Hodgkin and Keynes 1955; Stampe and Begenisich 1996; Doyle et al. 1998). Neyton and Miller 1988b reached the conclusion that the pore of BKCa channels can accommodate several K+ ions and that the K+ sites are of high affinity. In particular, they functionally characterized a high affinity K+ binding site facing the external solution; this site was revealed by the observation that increasing external [K+] slows down the rate of Ba2+ exit from the channel (Neyton and Miller 1988a). It is easy to interpret this observation by assuming that there is a K+ binding site located externally to the blocking site. When the channel is blocked by Ba2+, the outer K+ site is in equilibrium with the external [K+] so that, at very low external [K+], the site remains empty most of the time and Ba2+ can exit toward the external side more easily than to the internal side. This external K+ site was dubbed the “lock-in” site. In this study, we have determined the dissociation constant for K+ at the lock-in site with increased accuracy by lowering the external [K+] below the contamination level with a crown ether that binds K+ with high affinity. The value we obtained for the dissociation constant, 2.7 μM, indicates that K+ binding is approximately fivefold stronger than reported by Neyton and Miller 1988a. These results suggest that BKCa channels bind K+ as tightly as Ca2+ channels bind Ca2+ ions (Dang and McCleskey 1998). In this study, we also found that the mean Ba2+ blocked time is affected by tetraethylammonium (TEA+). The stabilizing effect of TEA+ on Ba2+ block is mainly due to a “trapping” of K+ in the lock-in site.

The large conductance Ca2+-activated K+ channel has a high degree of identity in the pore region with voltage-dependent K+ channels. The crystal structure of a K+ channel from bacteria was recently elucidated (Doyle et al. 1998). It revealed that the bacterial K+ channel could contain three K+ ions in its conduction pathway. One K+ ion was detected in a large water-filled cavity at the center of the pore near the cytoplasmic end of the selectivity filter. The other two were located at opposite ends of the selectivity filter, stabilized by backbone carbonyl groups. The TEA+ binding site, which is located outside the selectivity filter, is made by a ring of four tyrosines near the extracellular end of the pore. Our results imply that TEA, K+, and Ba2+ ions can coexist in the BKCa channel pore and set molecular constraints on the location of the lock-in and the Ba2+ sites. A picture that is consistent with our results and the potassium channel crystal structure (Doyle et al. 1998) is one in which the lock-in site corresponds to the K+ site located on the extracellular side of the selectivity filter, and Ba2+ binds to a site on the internal side of the selectivity filter.

Despite the similarity with voltage-dependent K+ channels, BKCa channels do not show external K+-dependent phenomena such as C-type inactivation (López-Barneo et al. 1993) or the loss of functional channels after removal of K+ ions from both sides of the membrane (e.g., Almers and Armstrong 1980). Actually, it is possible to record BKCa channel activity for periods of hours without a hint of inactivation (e.g., Candia et al. 1992). A possible explanation for the stability of channels in the virtual absence of K+ is their avidity for K+ ions. In other words, the affinity of the channel for K+ is so high that the low [K+] present in nominally “K+-free” solutions (≈4 μM) is sufficient to saturate the relevant K+ binding site(s) in the pore. To test this hypothesis, we have lowered the external [K+] below the K+-contamination level using a crown ether that chelates K+ with high affinity. Our results show that when channels are exposed to external solutions containing less than 4 μM, K+ channel electrical activity suddenly ceases, a result that is consistent with our hypothesis.

Lipid Bilayers and Channel Incorporation

All measurements were performed on planar bilayers with a single BKCa channel inserted. Since depolarizing voltages and cytoplasmic Ca2+ activates BKCa channels, the “internal” side of the membrane was defined according to the voltage and Ca2+ dependence of the channel. Accordingly, the physiological voltage convention is used throughout, with the external side of the channel defined as zero voltage. Bilayers were cast from an 8:2 mixture of 1-palmitoyl, 2-oleoyl phosphatidylethanolamine (POPE) and 1-palmitoyl, 2-oleoyl phosphatidylcholine (POPC) in decane. Lipids were obtained from Avanti Polar Lipids. Bilayers were formed in 0.01 M 3-[N-morpholino]propane-sulfonic acid-N-methyl d-glucamine (MOPS-NMDG), pH 7. Concentrated KCl and CaCl2 were added to the internal solution to a final concentration of 0.1 M and 125 μM, respectively. The internal [Ca2+] used fully activates the BKCa channel from skeletal muscle (e.g., Moczydlowski and Latorre 1983). In some experiments Ba2+ (75–200 nM) was added to the internal solution to increase the probability of Ba2+ blockade events.

Rat skeletal muscle was used to prepare membrane vesicles containing BKCa channels as previously described (Latorre et al. 1982). Membrane vesicles were added very close to the bilayer and, once a channel incorporated, concentrated MOPS-NMDG, pH 7, and EGTA-NMDG were added to the extracellular side to a final concentration of 0.11 M and 400 μM, respectively. Single channel currents were recorded at 0 mV.

Data Acquisition and Analysis

Single-channel recordings were acquired using a custom-made current-to-voltage converter amplifier (Cecchi et al. 1987) connected to the solution through agar bridges made with ultrapure NaCl (Alfa Aesar). Continuous single-channel current records (3–30 min) were filtered at 400 Hz and digitized at 500 μs/point. Open and closed events were identified using a discriminator located at 50% of the open-channel current. Dwell-time histograms were logarithmically binned and fitted to a sum of exponential probability functions with Pclamp 6 software (Axon Instrument, Inc.). Closed dwell-time histograms were fitted to the sum of two exponential functions. The slow component is a Ba2+ block previously described in detail (Vergara and Latorre 1983; Miller et al. 1987; Neyton and Miller 1988a). The mean Ba2+ blocked times were measured in the range of 2 × 10−8 to 10−2 M K+. Data were grouped in decades of K+ concentration and the average of the logarithms of mean blocked time and the average of the logarithm of the K+ concentrations ± SD were used in Fig. 2. The mean Ba2+-blocked data obtained at various external [K+] were described using the equation (Neyton and Miller 1988a):

\begin{equation*}{\mathrm{{\tau}}}_{{\mathrm{0}}-{\mathrm{Ba}}}= \left \left({1}/{ \left \left[{k_{{\mathrm{in}}}+k_{{\mathrm{ext}}}}/{ \left \left(1+{ \left \left[K\right] \right }/{K_{{\mathrm{d}}}^{K}}\right) \right }\right] \right }\right) \right {\mathrm{,}}\end{equation*}
1

where kin is the dissociation rate constant toward the internal side and kext is the dissociation rate constant toward the external side of the channel when the lock-in site is empty, and KdK is the dissociation constant for K+ from the channel containing a K+ and a Ba2+ simultaneously. We used a nonlinear least-square fit procedure to find the values of kin, kext, and KdK, where the statistical weight of each point was the number of observations on each decade (Alvarez et al. 1992).

Solutions

Determination of the free K+ concentration in solutions containing low K+ and crown ether requires knowledge of the [K+] of “K+-free” solutions and the dissociation constant of the K+-crown ether in the presence of 0.11 M MOPS-NMDG. The [K+] was determined using an ion-specific electrode (Orion 9319BN; Orion Research, Inc.) that is linear in the [K+] range between 1 μM and 1 M. The average K+ contamination of the MOPS-NMDG solutions used in the present study was 4.4 μM. The contaminating [K+] of the stock of MOPS-NMDG and EGTA-NMDG solutions was also determined by atomic absorption spectrophotometry. A crown ether (a gift from Dr. Jacques Neyton, Laboratoire de Neurobiologie, Ecole Normale Supérieure, Paris, France), (+)-18-Crown-6-tetracarboxylic acid (18C6TA) from Merck, was used to chelate the contaminating external K+ and contaminating Ba2+ in the internal solution. The 18C6TA:cation stoichiometry is 1:1 (e.g., Díaz et al. 1996). The crown ether binds K+, Ca2+, and Ba2+ with dissociation constants of 3.3 × 10−6, 10−8, and 1.6 × 10−10 M, respectively (Dietrich 1985; Díaz et al. 1996; Neyton 1996). The dissociation constant of the K-crown ether complex in the presence of 0.11 M MOPS-NMDG was 6.3 × 10−6 M. This value was obtained using an ion-specific electrode to measure the free [K+] in solutions of known concentrations of total K+ and crown ether. The dissociation constant of the Ba-crown ether complex in the presence of 150 mM KCl was considered to be 1.6 × 10-10 M (Díaz et al. 1996; Neyton 1996).

Lowering External [K+] Modifies Slow Ba2+ Block, Induces the Appearance of a Flickering Ba2+ Block, and Alters the Channel-gating Kinetics

Fig. 1 shows K+ currents from single BKCa channel recordings with 70 nM internal [Ba2+] and different external K+ concentrations along with the corresponding closed dwell time histograms. Three different features are evident from the figure. (a) There is a slow internal Ba2+ block described previously (Vergara and Latorre 1983; Miller et al. 1987; Neyton and Miller 1988a,Neyton and Miller 1988b). Low concentrations (∼70 nM) of internal Ba2+ induce long-lived nonconducting intervals separated by “bursts” of channel activity (clearly seen in Fig. 1, top). At the largest external [K+] used, the open probability inside a burst is close to 1. Vergara and Latorre 1983 showed that each of these long-lived blocked events represents the binding of a single Ba2+ ion to the channel, and they presented strong evidence that the site of Ba2+ binding is located within the conduction pore. (b) There is an increase in the number of fast closing events with decreasing external [K+], clearly revealed by an increase in the size of the fast component of the closed dwell-time distributions (Fig. 1, right). This increase in the number of fast closing events has not been described before and, as discussed below, may be due to a change in channel kinetics or to a fast Ba2+ blockade. (c) A long-lasting closed state appears at very low external [K+] (Fig. 1, bottom, and see also Fig. 3).

Slow Ba2+ block.

Fig. 1, right, shows that the distribution of dwell times in the closed state is multiexponential. Note that mean block times of the slow component became shorter and the number of events increased as the external [K+] was decreased. Upon decreasing the external [K+] from 24 to 0.09 μM, the mean Ba2+ blocked time decreased from 660 to 50 ms. Fig. 2 shows a fit to the τo-Ba-[K+]ext data using . The best fit was obtained with kext = 7.6 ± 1.7 s−1, kin = 0.11 ± 0.02 s−1, and KdK = 2.7 ± 0.4 μM. The value of KdK found indicates that BKCa channels bind K+ fivefold tighter than previously thought (Neyton and Miller 1988a).

Our value of kext was determined at 0 mV applied voltage. Neyton and Miller 1988a found that in a solution containing “0” external K+ (<5 μM) and 150 mM Na+, kext increased e-fold with every 27-mV depolarization. At 50 mV, in the presence of external 150 mM NMDG and contaminating K+, they measured a kext = 20 s−1. Using the expression kext(V) = kext(0)exp(V/27), we find that if kext (0) is 7.6, then kext(50) is 48 s−1, which is 2.4× larger than the value found by Neyton and Miller 1988a. The larger value we predict is due to the reduction in the background contaminating [K+] by the addition of the crown ether to the external solution.

KdK is also voltage dependent and Neyton and Miller 1988b showed that the external lock-in site senses 18% of the voltage drop measured from the outside. Using the expression KdK (V) = Kd K (0)exp(−zδeV/kT) with zδ = 0.18 and a KdK (0) = 2.7 μM, we find that KdK (50) = 3.9, a value fivefold lower than the KdK of 19 μM determined by Neyton and Miller 1988a. Hence, by examining a wider range of external [K+]s and using 18C6TA, we have been able to determine kext and KdK with more precision.

Fast component of the closed dwell-time distribution.

The fast component of the closed dwell-time distribution was also modified by external [K+]. As in the case of the slow Ba2+ block, the number of events increased as the external [K+] concentration was reduced (see dwell time histograms in Fig. 1). However, in contrast to the slow component, the mean fast blocked time of the fast component of the closed time histogram is almost unchanged by a 10-fold reduction in the external [K+]. Is the difference in slow and fast dwell-time dependence on [K+] due to a modification of channel gating proper or is it the manifestation of a Ba2+ flickering block? (e.g., Sohma et al. 1996). To answer this question, we added crown ether to the internal side of the channel to a final concentration of 225 μM. This experimental maneuver decreases the internal [Ba2+] from 70 to 5 nM, decreases the number of fast closed events by 30%, and increases Po by 18% (from 0.6 to 0.73). The number of fast block events per unit open time, NB, is predicted to be

\begin{equation*}N_{{\mathrm{B}}}=k_{{\mathrm{on}}} \left \left[{\mathrm{Ba}}^{2+}\right] \right {\mathrm{P}}_{o}{\mathrm{,}}\end{equation*}
2

where kon is the association rate constant for Ba2+ binding, and Po the probability of opening. Therefore, a 14-fold decrease in [Ba2+], considering the Pos before and after the addition of Ba2+, should induce a 90% decrease in NB. The theoretically expected decrease in NB after lowering [Ba2+]int is much more pronounced than the one found experimentally. This analysis suggests that upon diminishing [K+]ext, the increase in NB is only partly due to a Ba2+ flickering block and that the reduction in external K+ also induces the appearance of fast closed events.

The long-lasting closed state.

Occupancy of the outer mouth of the pore of Shaker K+ channels by K+ slows the rate of C-type inactivation (López-Barneo et al. 1993). The site at which K+ directly slows down inactivation appears to be a high-affinity binding site involved in the ionic selectivity mechanism (Kiss and Korn 1998). In fact, this site appears to be located in the neighborhood or in the channel selectivity filter, and Kiss et al. 1999 have argued that the selectivity filter itself is the inactivation gate. Since the selectivity filter is highly conserved among different K+ channels, it is pertinent to ask why an inactivated state has not been previously observed in the BKCa channel even at very low [K+].

The single-channel current recorded at 0.09 μM K+ in Fig. 1 shows a closed state of very long duration. Fig. 3 A shows that the channel enters this nonconducting state of very long duration when the [K+]ext is reduced from the contaminating level (4.4 μM; Fig. 3 A, top) to 0.01 μM by the addition of crown ether to the external solution (Fig. 3 A, middle). After spending several minutes in the quiescent state, normal channel activity was recovered by adding K+ to the external side to a final concentration of 10 μM (Fig. 3 A, bottom). The recovery of channel activity after a drastic reduction in external [K+] occurred in 15 of 22 trials. It appears then that the BKCa channel conductance collapses at external [K+]s much lower than those necessary to arrest other K+ channels.

Lithium, Na+, Rb+, Cs+, and NH4+ were also tested for their abilities to recover the BKCa channel from its long-lasting nonconductive state. Rubidium (20 mM), Cs+ (20 mM), and NH4+ (3.5–50 mM) were able to recover the channel from the nonconducting state. Fig. 3 B shows an example of recovery from the quiescent state when NH4 + is added to the external solution to a final concentration of 10 mM. Sodium (20–40 mM) and Li+ (20–100 mM) were not able to recover channel activity, suggesting that only permeant cations are able to recover the channel from the conformation it adopts at very low [K+].

External TEA+ Traps K+ Inside BKCa Channels

In Shaker K+ channels, one specific amino acid location in the pore-forming region (position 449) is crucial in determining sensitivity to external TEA+ (MacKinnon and Yellen 1990; Kavanaugh et al. 1991). An aromatic residue at the 449 position is a requirement for high affinity TEA+ blockade and Heginbotham and MacKinnon 1992 showed that a bracelet of pore-lining tyrosines forms the high affinity TEA+ receptor. BKCa channels are also blocked by TEA+ and they show a high affinity for this quaternary ammonium ion (Blatz and Magleby 1984; Vergara et al. 1984; Yellen 1984a). In BKCa channels, there is a tyrosine residue at a position corresponding to the TEA+-sensitive position in Shaker K+ channels (Adelman et al. 1992). We reasoned that since a TEA+ binding site in BKCa channels is structurally well defined (Shen et al. 1994), it would be of interest to see whether or not TEA+ behaves as a lock-in ion like external K+.

Since we expected TEA+ to increase Ba2+ mean blocked time, we reduced [K+]ext to begin the experiment with short mean Ba2+ block time. The crown ether concentration was adjusted to decrease the potassium concentration from the basal level down to values where the channels would not enter into the long lasting nonconducting state. Furthermore, TEA+ seems to protect the channel from falling into the long lasting closed state since we observed stable channel activity with [K+]ext as low as 0.007 μM. In the experiment shown in Fig. 4, we reduced the external [K+] concentration from 6 to 0.03 μM by adding 0.9 mM crown ether to the external solution. The figure shows the effect of external TEA+ on the nonconducting dwell times induced by the presence of internal Ba2+. TEA+ reduces the open channel current and also increases the duration of the closed dwell times. In the absence of TEA+, the measured mean block time was 160 ms; after increasing the external TEA+ to 900 μM, the mean block time increased to 1,700 ms.

Surprisingly, if external [K+] is reduced from 0.06 to 0.007 μM by the addition of crown ether, in the presence of external TEA+, the mean block time is decreased (Fig. 5). Fig. 5, middle and bottom, shows that channel conductance is not affected by the addition of crown ether. Therefore, the complexing agent does not affect TEA+ concentration.

Fig. 6 shows that the effect of TEA+ on Ba2+ block strongly depends on external K+ concentration. In the presence of 130 μM external K+, 2 mM TEA+ brings the mean Ba2+ blocked time to ∼20 s. Therefore, the blocked time is even longer than the maximum value expected for Ba2+ leaving toward the internal side of the channel in the presence of high external [K+](compare Fig. 2). However, in the presence of 0.04 μM K+, the same TEA+ concentration induces a mean Ba2+ blocked time of only 2 s.

A Possible Model

The ability of external TEA+ to slow down Ba2+ dissociation cannot be reconciled with the idea that TEA+ and K+ compete for the same binding site in the channel or with the simple picture of ion–ion repulsion within the pore. In both cases, it is expected that TEA+ should behave less effective as a lock-in ion in the presence of K+.

To interpret our results quantitatively, we propose the model illustrated in Fig. 7. The channel is viewed as having three sites: a Ba2+-blocking site, a K+-binding site located externally to the blocking site, and the external TEA+ site. As shown by Neyton and Miller 1988a and documented in Fig. 2, at very low [K+] and in the absence of external TEA, Ba2+ can dissociate and exit to the external solution with a rate (kext) much greater than the exit rate toward the internal side (kin) (Fig. 7). The results shown in Fig. 2 were interpreted in terms of an increase in the occupancy of an external K+ site as the external [K+] was increased (S2 in Fig. 7). The model proposes that TEA+ can bind to the singly or doubly occupied channel. Therefore, TEA+ can trap K+ inside the pore and the blocking Ba2+ ion must then either dissociate to the internal solution, or wait for the TEA+ and K+ sites to become empty. Assuming that the unblock–block reactions are slow compared with the K+ and TEA+ binding reactions, the model presented in Fig. 7 predicts the following relation for the mean Ba2+ blocked time, το-Βα:

\begin{equation*} \left {\mathrm{{\tau}}}_{0-B{\mathrm{{\alpha}}}}= \left \left[k_{{\mathrm{in}}}P_{{\mathrm{Ba}}-{\mathrm{K}}-{\mathrm{S3}}}+k_{{\mathrm{in}} \left \left(K,{\mathrm{TEA}}\right) \right }P_{{\mathrm{Ba}}-{\mathrm{K}}-{\mathrm{TEA}}} \right +k_{{\mathrm{in}} \left \left({\mathrm{TEA}}\right) \right }P_{{\mathrm{Ba}}-{\mathrm{S}}2-{\mathrm{TEA}}}+ \left \left(k_{{\mathrm{ext}}}+k_{{\mathrm{in}}}\right) \right P_{{\mathrm{Ba}}-{\mathrm{S}}2-{\mathrm{S3}}}\right] \right ^{-1}{\mathrm{,}}\end{equation*}
3

where PBa, PBa-K, PBa-TEA, and PBa-K-TEA are the probabilities of finding the channel occupied by Ba2+ only, by Ba2+ and K+, by Ba2+ and TEA+, or by Ba2+, K+, and TEA+, respectively. These probabilities are given by the following relationships:

\begin{equation*}\begin{matrix}P_{{\mathrm{Ba}}-{\mathrm{S}}2-{\mathrm{S3}}}= \left 1+ \left \left({ \left \left[{\mathrm{K}}^{+}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}}}^{{\mathrm{K}}}\right) \right \right \\ \left \left \left(1+{ \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}1}}^{{\mathrm{TEA}}}\right) \right +{ \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}2}}^{{\mathrm{TEA}}} \right ^{-1}\end{matrix}\end{equation*}
4a
\begin{equation*}P_{{\mathrm{Ba}}-{\mathrm{K}}-{\mathrm{S3}}}={ \left \left[{\mathrm{K}}^{+}\right] \right }/{ \left \left \left[{\mathrm{K}}^{+}\right] \right +{\mathit{K}}_{{\mathrm{d}}}^{{\mathrm{K}}} \left \left(1+{ \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}2}}^{{\mathrm{TEA}}}\right) \right + \left \left[{\mathrm{K}}^{+}\right] \right { \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}2}}^{{\mathrm{TEA}}} \right }\end{equation*}
4b
\begin{equation*}P_{{\mathrm{Ba}}-{\mathrm{S}}2-{\mathrm{TEA}}}={ \left \left[{\mathrm{TEA}}\right] \right }/{ \left \left \left[{\mathrm{TEA}}\right] \right +{\mathit{K}}_{{\mathrm{d}}2}^{{\mathrm{TEA}}} \left \left(1+{ \left \left[{\mathrm{K}}^{+}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}}}^{{\mathrm{K}}}\right) \right \left \left(1+{ \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}1}^{{\mathrm{TEA}}}}\right) \right \right }\end{equation*}
4c
\begin{equation*}P_{{\mathrm{Ba}}-{\mathrm{K}}-{\mathrm{TEA}}}={ \left \left[{\mathrm{TEA}}\right] \right }/{ \left \left \left[{\mathrm{TEA}}\right] \right +K_{{\mathrm{d}}1}^{{\mathrm{TEA}}} \left \left(1+{ \left \left[{\mathrm{K}}^{+}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}}}^{{\mathrm{K}}}\right) \right \left \left(1+{ \left \left[{\mathrm{TEA}}\right] \right }/{{\mathit{K}}_{{\mathrm{d}}2}^{{\mathrm{TEA}}}}\right) \right \right }{\mathrm{,}}\end{equation*}
4d

where KdK is the dissociation constant for K+, Kd1TEA is the dissociation constant for TEA+ from the triply occupied state, and Kd2TEA is the dissociation constant for TEA+ from the doubly occupied state. There are five different rate constants for Ba2+ exit: kext is the rate of exit to the extracellular side when the channel is occupied only by a Ba2+ ion, kin is the rate constant of exit to the intracellular side when the channel is occupied only by a Ba2+ ion, and kin(K), kin(TEA), kin(K, TEA) are the rate constants of exit toward the extracellular side when the channel is occupied by Ba2+ and K+, by Ba2+ and TEA+, or by Ba2+, K+, and TEA+, respectively.

The model accommodates rate constants for Ba2+ exit toward the internal side that are different (compare Fig. 2 and Fig. 6) in the absence and presence of TEA+. Experimentally, we found that when the quaternary ammonium ion and K+ are present in the external solution, kin(K,TEA) is approximately twofold slower than in the absence of TEA. On the other hand, the fit to the data with the model shown in Fig. 7 indicates that in the absence of K+, the rate constant for Ba2+ exit, kin(TEA), is approximately four times larger than kin(K,TEA) (see Fig. 6). We have tested our model by comparing the measured mean Ba2+ blocked times at different [K+] and [TEA+] from 26 different single-channel membranes with the calculated mean blocked times obtained using . The model proposed in Fig. 7 describes the data rather well (Fig. 8 A). The model is unable to predict the experimental results if triple occupancy is not allowed (Kd1TEA = ∞) (Fig. 8 B) or if TEA+ is unable to bind the channel unless it is occupied by K+ (Kd2TEA = ∞) (Fig. 8 C). Fig. 8 B shows that if triple occupancy is not allowed, the model predicts an attenuated effect of TEA+ on the mean Ba2+ blocked time relative to that found experimentally. On the other hand, Fig. 8 C illustrates that if TEA+ can only bind to the Ba2+-occupied channel in a triple occupancy configuration (when the lock-in site for K+ is full), then the model fails to account for the data obtained at very low [K+]. The best correlation between model generated and experimental values of the mean Ba2+ block time was obtained when TEA+ binding was allowed in any configuration of the model with rate constants of Kd1TEA = 180 μM and Kd2TEA = 67 μM. It is very interesting that the ratio between these two dissociation constants (2.5) reveals a K+–TEA+ repulsion of ∼0.6 kcal/mol. This very low repulsion energy implies that the bound TEA+ ion is essentially shielded from the K+ ion occupying the external lock-in site.

The kinetics of block by TEA+ are rapid, operating in the time scale of microseconds (Blatz and Magleby 1984; Vergara et al. 1984; Yellen 1984a; Villarroel et al. 1988); therefore, the TEA+ blocking events are too fast to be directly observed since they are filtered by the measuring electronics. Therefore, TEA+ appears to reduce the observed channel current (Fig. 4 and Fig. 5). Because of this effect, the ratio between the average single-channel current value in the absence of TEA+, io, and its value in the presence of the quaternary ammonium ion, 〈i 〉, is a measure of the channel occupancy by TEA+ at its blocking site:

\begin{equation*}{i_{0}}/{{\ll}i{\gg}}= \left \left(1+{ \left \left[{\mathrm{TEA}}^{+}\right] \right }/{K_{{\mathrm{d}}}^{{\mathrm{TEA}}}}\right) \right {\mathrm{.}}\end{equation*}
5

Since in this case TEA+ blocks a channel containing only K+ ions in its conduction machinery, it is pertinent to ask whether the dissociation constant for TEA+, KdTEA, is similar to that obtained from its effect on the mean Ba2+ block time.

Fig. 9 illustrates the dependence of the channel current on TEA+ concentration at 0 mV and in different [K+] (each symbol represents a different [K+]). There is a linear relationship that is well described by with a KdTEA = 106 μM (Fig. 9, solid line). Notice that the fit to is reasonably good for all the [K+] tested, indicating that there is not a single hint of competition between K+ and TEA+ for a site(s). Moreover, the value of KdTEA+οβταιν∈δ ισ ω∈ρυ σιμιλαρ το τηατ οβταιν∈δ βυ Ωιλλαρρο∈λ ∈τ αλ> ≲+′°°≳ ≲+−″ μM) under symmetrical 100-mM KCl conditions.

The crystal structure of the K+ channel pore from Streptomyces lividans revealed two binding sites for potassium in the selectivity filter that are ∼0.75-nm apart (Doyle et al. 1998). In this channel, like in the BKCa channel, the TEA+ binding site is comprised of four tyrosines located externally to the outer K+ binding site (Heginbotham and MacKinnon 1992). Since TEA+ can trap K+ ions inside BKCa channels, we assigned lock-in site to the outer K+ binding site described by Doyle et al. 1998. Since the crystal radius of Ba2+ is similar to the crystal radius of K+, Ba2+ probably occupies the inner site. A third site was identified at the pore center in a large cavity (Doyle et al. 1998). An ion is stabilized in this central position by the aqueous environment and by α helical structures pointing their partial negative charge toward the cavity where the ion is located. We hypothesize that the Ba2+ flickering block originates from Ba2+ entering and leaving the pore from the pore cavity.

In the case of potassium channels, it is clear that permeating ions within the conduction pathway affect some of the structural changes associated with gating (Almers and Armstrong 1980; Pardo et al. 1992; Gómez-Lagunas 1997; Jåger et al. 1998; Melishchuck et al. 1998) and C-type inactivation (López-Barneo et al. 1993; Levy and Deutsch 1996; Kiss and Korn 1998). Squid axon K+ channels become nonfunctional when K+ is removed from the internal and external solutions, but these channels can survive in an internal K+-free solution if external K+, Cs+, NH4+, or Rb+ ions are present (Almers and Armstrong 1980). Shaker K+ channels in K+-free solutions become irreversibly nonconducting, but only after opening. This long-lasting state can be entered only if there is inward gating charge movement (Melishchuck et al. 1998). Shaker K+ channels can be protected against the deleterious effects of the absence of K+ by mutations that remove C-type inactivation. On the other hand, some mammalian delayed rectifier K+ channels remain stable after removal of internal and external K+ and become permeable to Na+ ions (e.g., Kiss et al. 1998).

The data presented here shows that occupancy of a very high affinity site for K+, most likely the lock-in site, controls ion permeation in the BKCa channel. Emptying the channel of K+ ions could lead to the equivalent of the C-type inactivation or to the K+ conductance collapse phenomena described for other K+ channels. When the lock-in site is empty, the channel clearly undergoes structural changes that lead finally to the long-lasting inactivated state. These changes are probably triggered by electrostatic repulsion of the carbonyl groups, which makes the selectivity filter atoms move apart. Fig. 2 shows that the KdK for the lock-in site is 2.7 μM, which corresponds to an energy well of −13 kT. Considering that this value of KdK is for the double occupied [K+–Ba2+] channel, this energy is an upper limit that indicates that the binding of K+ to BKCa channels as tight as the binding of Ca2+ to Ca2+ channels (e.g., Dang and McCleskey 1998). On the other hand, the ratio of the rate constants kext/kin is 100 and this implies that Ba2+ must jump an energy barrier 2.8 kcal/mol larger when leaving the channel toward the internal side.

Although we do not know the details of the molecular mechanism that governs C-type inactivation, it is known that external TEA+, K+, and other monovalent cations inhibit it. Point mutations in Shaker K+ channels have also shown that the rate of C-type inactivation and the K+ permeability properties can be altered simultaneously (López-Barneo et al. 1993). The general explanation of this phenomenon is that occupancy of a site by K+ or other permeant cations hinders the C-type inactivation conformational change, probably a collapse of the selectivity filter (Kiss and Korn 1998). We have demonstrated here that TEA+ binds to the Ba2+-blocked channel when the lock-in site is occupied by K+, and prevents K+ from leaving this site. This turns TEA+ into an ion that can protect the channel from C-type inactivation, by binding to a site different from the typical lock-in site. Considering that K+ protects BKCa channels from entering into a very stable nonconducting state, how is it that the BKCa channel is not protected by the internal K+ ions flowing through it? Our results suggest that Ba2+ cuts off potassium flow to the external K+ site. During a Ba2+ block at very low [K+]ext, the channel has two possibilities when the lock-in site is empty: (a) it can enter a long lasting nonconducting state leaving the Ba2+ trapped inside or (b) Ba2+ can occupy the lock-in site and exit the channel toward the external side, making the channel enter into a burst of activity. A similar effect of extracellular K+ and internal blockade has been shown in Shaker K+ channels (Baukrowitz and Yellen 1996). In this case, a hydrophobic TEA+ analogue applied internally hindered the potassium flow to a site in the pore and thereby greatly increased the rate of C-type inactivation. Internal TEA+ also prevents the refilling of the pore by K+ in the case of the potassium channel of the squid axon (Khodakhah et al. 1997). In the absence of external K+, this produces an irreversible decrease of the K+ current.

The effect of external K+ on the ability of TEA+ to lock Ba2+ into the channel was explained using a model in which Ba2+, K+, and TEA+ can simultaneously occupy the channel. The analysis of our results demonstrated that TEA+ binding to the Ba2+-blocked channel is essentially the same whether or not a K+ ion is bound and that the binding constant is not very different from the one obtained measuring the current amplitude in the presence of different [TEA+] and [K+]. This result implies that there is little electrostatic repulsion between the K+ in the external lock-in site and the TEA+ bound to its external receptor. The crystal structure of the K+ channel from Streptomyces lividans showed that the distance separating the K+ ion located in the external site of the selectivity filter and the TEA+ ion is 0.8 nm (Doyle et al. 1998). Given this distance, the expected electrostatic repulsion is 41 kcal/mol if a nonpolarizable medium separates the two ions, or 2 kcal/mol if a medium with a dielectric constant of 20 separated the ions. The fact that the expected repulsion between these two ions is not detected by our experiments can only be explained if the K+ ion in the lock-in site is shielded from the TEA+. It is possible that the ring of aspartates located in position 295 in mSlo (Shen et al. 1994) supplies this shielding.

We thank Joan Haab and Dorine Starace for helpful comments on the manuscript.

This work was supported by Chilean grants FONDECYT 197-0739 (R. Latorre), 198-1053 (C. Vergara), and Cátedra Presidencial and a group of Chilean companies (AFP Protection, CODELCO, Empresas CMPC, CGE, Gener S.A., Minera Escondida, Minera Collahuasi, NOVAGAS, Business Design Association, and XEROX Chile) and a grant from Human Frontiers in Science Program (to R. Latorre).

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Abbreviations used in this paper: BKCa, large conductance Ca2+-activated K+; MOPS, 3-[N-morpholino]propane-sulfonic acid; NMDG, N-methyl d-glucamine; TEA+, tetraethylammonium.

Barium is effective from either side of the membrane, but is much more potent when applied to the internal solution. At zero applied voltage, the association rate constant for internally applied Ba2+ is ∼50× higher than that for external Ba2+, while the dissociation rate does not depend on the side of application (Vergara and Latorre 1983).