The β Subunit Increases the Ca²⁺ Sensitivity of Large Conductance Ca²⁺-activated Potassium Channels by Retaining the Gating in the Bursting States

Abstract

Coexpression of the β subunit (K_V,_Caβ) with the α subunit of mammalian large conductance Ca²⁺- activated K⁺ (BK) channels greatly increases the apparent Ca²⁺ sensitivity of the channel. Using single-channel analysis to investigate the mechanism for this increase, we found that the β subunit increased open probability (P _o) by increasing burst duration 20–100-fold, while having little effect on the durations of the gaps (closed intervals) between bursts or on the numbers of detected open and closed states entered during gating. The effect of the β subunit was not equivalent to raising intracellular Ca²⁺ in the absence of the beta subunit, suggesting that the β subunit does not act by increasing all the Ca²⁺ binding rates proportionally. The β subunit also inhibited transitions to subconductance levels. It is the retention of the BK channel in the bursting states by the β subunit that increases the apparent Ca²⁺ sensitivity of the channel. In the presence of the β subunit, each burst of openings is greatly amplified in duration through increases in both the numbers of openings per burst and in the mean open times. Native BK channels from cultured rat skeletal muscle were found to have bursting kinetics similar to channels expressed from alpha subunits alone.

introduction

Large conductance Ca²⁺-activated K⁺ channels (BK channels)¹ play an important role in regulating the excitability of nerve, muscle, and other cells by stabilizing the cell membrane at negative potentials (reviewed by Latorre et al., 1989; McManus, 1991; Kaczorowski et al., 1996). BK channels are activated by both intracellular calcium (Ca²⁺ _i) and membrane depolarization, and hence can serve as an important link to couple the effects of Ca²⁺ _i and membrane potential, two common forms of signaling in cells. To facilitate this linkage, the Ca²⁺ _i sensitivity of BK channels, defined as the Ca²⁺ _i required for half-maximal activation at a given voltage, is set to match the specific needs of the various cells. In some tissues, such as smooth muscle, BK channels are highly Ca²⁺ _i sensitive, while in other tissues, such as skeletal muscle, the channels are much less Ca²⁺ sensitive (Singer and Walsh, 1987; McManus and Magleby, 1991; Tanaka et al., 1997).

Recent studies have given some insight into the molecular basis for differences in Ca²⁺ sensitivity. BK channels can be formed of either α subunits alone or of α together with β subunits (Adelman et al., 1992; Garcia-Calvo et al., 1994; McManus et al., 1995; Dworetzky et al., 1996; Tseng-Crank et al., 1996). The larger pore-forming α subunits are encoded by the gene at the slo locus, mutations of which underlie the Drosophila slowpoke phenotype (Atkinson et al., 1991; Adelman et al., 1992; Butler et al., 1993; Pallanck and Ganetzky, 1994; Dworetzky et al., 1994; Tseng-Crank et al., 1994; Wallner et al., 1996). The α (slo) subunit shows homology with the pore-forming subunits of the voltage-dependent superfamily of K⁺ channels, which have at least six putative transmembrane domains, a pore-forming region between S5 and S6, and an S4 voltage-sensor region (Atkinson et al., 1991; Salkoff et al., 1992; Butler et al., 1993; Jan and Jan, 1997). However, the NH₂- and COOH-terminal ends of the α subunits differ from those of the superfamily. The NH₂ terminus of mammalian α subunits displays an additional transmembrane domain, S0, that places the amino terminal into the extracellular space and is required for the action of the β subunit (Wallner et al., 1996; Meera et al., 1997). The COOH-terminal tail is greatly extended, displays four hydrophobic domains, and appears to provide the Ca²⁺-sensing domain of the channel (Wei et al., 1994; Schreiber and Salkoff, 1997). The β subunit, with two putative transmembrane domains, shows no homology with other ion channel subunits (Knaus et al., 1994).

While α subunits assemble as tetramers to form functional channels by themselves (Shen et al., 1994), β subunits expressed alone do not (McManus et al., 1995). Rather, β subunits can associate with α subunits in a 1:1 stoichiometry (Garcia-Calvo et al., 1994), increasing the apparent Ca²⁺ sensitivity of the α subunits ∼10-fold (McManus et al., 1995). It is the presence of the β subunit that confers the greatly increased Ca²⁺ sensitivity to BK channels in smooth muscle (McManus et al., 1995; Tanaka et al., 1997). Although it is known that the β subunit slows activation and deactivation kinetics (Dworetzky et al., 1996; Meera et al., 1996; Tseng-Crank et al., 1996), while having little effect on channel open probability in the absence of Ca²⁺ _i (Meera et al., 1996), the mechanism by which the β subunit increases the apparent Ca²⁺ sensitivity of BK channels is not known. The β subunit could increase apparent Ca²⁺ sensitivity through fundamental changes in the gating mechanism, such as by generating additional conformational states or Ca²⁺-binding sites. Alternatively, the β subunit might act by modulating the gating of the α subunit to increase the rate of Ca²⁺ binding or to change the rates of selected transitions among the various conformational states.

We now use the resolving power of the single-channel recording technique to differentiate among these possible types of action by studying the kinetics of single BK channels comprised of α subunits alone, or of both α and β subunits. Our data suggest that the β subunit does not act by changing the fundamental gating mechanism, as neither the Hill coefficients for Ca²⁺ binding nor the numbers of detected kinetic states entered during gating were changed by the β subunit. The data also suggest that the β subunit had little effect on the initial Ca²⁺-binding steps involved in activation of the channel, as the durations of the gaps (the long closed intervals) between bursts of activity were little changed. Instead, the β subunit increased Ca²⁺ sensitivity through selected modulation of transition rates to retain the channel in the open and closed states that generate the bursts of activity (bursting states), increasing burst duration 20–100-fold. We also found that the β subunit inhibited transitions to subconductance states, and that the gating of native BK channels from cultured rat skeletal muscle was similar to the gating of BK channels expressed from α subunits alone.

methods

Heterologous Expression of BK Channels in Human Embryonic Kidney 293 Cells

Human embryonic kidney (HEK) 293 cells were transiently transfected with expression vectors (pcDNA3) encoding the α subunit (mslo from mouse, Genbank accession number MMU09383) and the β subunit (bovine β, Genbank accession number L26101) of BK channels, kindly provided by Merck Research Laboratories, and also with an expression vector encoding the green fluorescent protein (GFP, Plasmid pGreen Lantern-1; GIBCO BRL). Cells were transfected transiently using the Lipofectamine Reagent (Life Technologies, Inc.). The GFP was used to monitor successfully transfected cells. For transfection, cells at 30–40% confluency in 30 mm recording Falcon dishes were incubated with a mixture of the plasmids (total of 1 μg DNA), Lipofectamine Reagent (optimal results at 7 μl), and Opti-MEM I Reduced Serum Medium (GIBCO BRL). The mixture was left on the cells for 1 h, after which it was replaced with standard tissue culture media: DMEM with 5% fetal bovine serum (GIBCO BRL) and 1% penicillin-streptomycin solution (Sigma Chemical Co.). The cells were patch-clamped 2–3 d after transfection.

In the coexpression experiments, a fourfold molar excess of plasmid encoding the β subunit was used to drive coassembly with the α subunits in the expressed channels (McManus et al., 1995). Using the same promoter (cytomegalovirus) for the α and β subunits and the GFP increased the probability that if the GFP was expressed, the included subunits would also be expressed. While we did not prove directly that all BK channels studied from cells cotransfected with plasmids encoding for α and β subunits were indeed composed of both α and β subunits, the markedly different bursting kinetics of BK channels from such cells (see results) indicated that the coexpression of the β with the α subunit altered the gating of the channels.

Solutions

The intracellular solution contained 175 mM KCl, 5 mM TES [N-tris(hydroxymethyl)methyl-2-aminoethane sulfonic acid] pH buffer, and 10 mM EGTA and 10 mM HEDTA to buffer the Ca²⁺ (see below). The extracellular solution contained either 150 or 175 mM KCl and 5 mM TES and had no added Ca²⁺ or Ca²⁺ buffers. Both the intracellular and extracellular solutions were brought to pH 7. The amount of Ca²⁺ added to the intracellular solution to obtain approximate free Ca²⁺ concentrations of 0.1– 100 μM was calculated using stability constants for EGTA from Smith and Miller (1985) and for HEDTA from Martell and Smith (1993). These solutions were then calibrated using a Ca²⁺ electrode (Ionplus from Orion Research, Inc.) standardized against solutions with KCl and TES (as in the experimental solutions) in which a known amount of Ca²⁺ was added. Before adding Ca²⁺, any contaminating divalent cations were removed from the solution by treatment with Chelex 100 (Bio-Rad Laboratories). The solutions bathing the intracellular side of the patch were changed by means of a valve-controlled, gravity-fed perfusion system using a microchamber (Barrett et al., 1982).

Single-Channel Recording and Analysis

Currents flowing through single BK channels in patches of surface membrane excised from HEK 293 cells transfected with clones for either α or α and β subunits were recorded using the patch-clamp technique (Hamill et al., 1981). All recordings were made using the excised inside-out configuration in which the intracellular surface of the patch was exposed to the bathing solution. BK channels were identified by their large conductance and characteristic voltage and Ca²⁺ dependence (Barrett et al., 1982). Endogenous BK channels in nontransfected HEK 293 cells were not seen, but we cannot exclude that they might exist at a low density. Currents were recorded with an Axopatch 200A amplifier (Axon Instruments) and stored on VCR tapes using a VR-10B digital data recorder. The currents were then analyzed using custom programs written in the laboratory. Single-channel patches were identified by observing openings to only a single open-channel conductance level during several minutes of recording in which the open probability was >0.4. Except for two experiments in which patches containing two BK channels were used to measure the effect of Ca²⁺ on open probability (P _o), all data were from patches containing a single BK channel. Experiments were performed at room temperature (20–25°C).

Single-channel current records were low-pass filtered with a four-pole Bessel filter to give a final effective filtering of typically 4.5–10 kHz (−3 dB) and were sampled by computer at a rate of 125–250 kHz. The methods used to select the level of filtering to exclude false events that could arise from noise, measure interval durations with half-amplitude threshold analysis, and use stability plots to test for stability and identify activity in different modes have been described previously, including the precautions taken to prevent artifacts in the analysis (McManus et al., 1987; McManus and Magleby, 1988, 1989; Magleby, 1992). The kinetic analysis in this study was restricted to channel activity in the normal mode, which typically involves ∼96% of the detected intervals (McManus and Magleby, 1988). Activity in modes other than normal, including the low activity mode (Rothberg et al., 1996), was removed before analysis, as were transitions to subconductance levels, except when the subconductance levels were being studied specifically. The numbers of intervals during normal activity analyzed for each experimental condition ranged from ∼1,500 to ∼200,000, with the greater numbers of intervals being obtained for higher Ca²⁺ _i where the channel activity was higher.

The methods used to log-bin the intervals into dwell-time distributions, fit the distributions with sums of exponentials using maximum likelihood fitting techniques (intervals less than two dead times were excluded from the fitting), and determine the number of significant exponential components with the likelihood ratio test have been described previously (McManus and Magleby, 1988, 1991; Colquhoun and Sigworth, 1995). Dwell-time distributions are plotted with the Sigworth and Sine (1987) transformation, which plots the square root of the number of intervals per bin without correcting for the logarithmic increase in bin width with time. With this transform, the peaks in the plots fall at the time constants of the major exponential components.

The method of defining a critical gap (closed interval) in order to identify bursts is detailed in Magleby and Pallotta (1983). In brief, the distributions of closed-interval durations were first fitted with, typically, the sum of five exponential components. The closed intervals from the one to two exponential components with the longest time constants were then defined as gaps between bursts, as there was typically a difference of one to three orders of magnitude in the time constants separating the components generating gaps between bursts from those generating closed intervals within bursts. A critical time was then defined to separate closed intervals that were gaps between bursts from those that were gaps within bursts, so that the numbers of misclassified closed intervals would cancel out. The critical time was found to be relatively insensitive to the numbers of exponentials used to fit the dwell-time distribution. Burst analysis was performed on data sets from single channels in which P _o was typically less than ∼0.8, since it became increasingly difficult to define gaps between bursts as the P _o approached its maximum value of ∼0.96 during activity in the normal mode.

Native BK Channels from Cultured Rat Skeletal Muscle

The parameters describing bursting kinetics for native BK channels from cultured rat skeletal muscle were obtained by analyzing data from previous experiments by McManus and Magleby (1991) and Rothberg and Magleby (1998), which can be consulted for the experimental details.

results

The β Subunit Alters the Gating of mslo as Revealed by Single-Channel Kinetics

The patch-clamp technique was used to record currents from single BK channels in patches of membrane excised from HEK 293 cells after transfection with either the α subunit (referred to as α channels) or with both α and β subunits (referred to as α + β channels). The effects of the β subunit on the gating are illustrated in Fig. 1, which shows representative single-channel currents recorded with 1.8, 3.6, or 5.4 μM calcium at the inner membrane surface (Ca²⁺ _i). The activity of both α and α + β channels increased with increasing Ca²⁺ _i, and for each Ca²⁺ _i, the presence of the β subunit further increased the activity. These observations are fully consistent with earlier studies, using mainly currents through multiple channels, that established that the β subunit increases the open probability (P _o) (McManus et al., 1995; Dworetzky et al., 1996; Meera et al., 1996; Tseng-Crank et al., 1996).

Figure 1.

Single-channel current traces recorded from BK channels expressed from α or α + β subunits. Representative currents recorded with the patch-clamp technique from inside-out patches of membrane excised from HEK 293 cells transfected with only α subunits (α) or with both α and β subunits (α + β) with 1.8, 3.6, or 5.4 μM Ca²⁺ _i and with a membrane potential of +30 mV. Data are presented on slow (A) and fast (B) time bases. The average P _o for the entire record from which each excerpt was obtained were: 0.0041, 0.087, and 0.16 for the α channel (top to bottom), and 0.15, 0.86, and 0.95 for the α + β channel. The β subunit increased burst duration and P _o. Current traces were low-pass filtered at 2 kHz for display. Effective filtering was 9 kHz for analysis. Symmetrical 175 mM KCl (see methods). α Channel, C62; α + β channel, C64.

The first clues towards the mechanism by which the β subunit increases P _o are readily apparent in Fig. 1. The β subunit had marked effects on the single-channel gating kinetics: at a fixed Ca²⁺ _i, the β subunit greatly increased the durations of the bursts of activity while appearing to have little effect on the durations of the gaps (closed intervals) between bursts. This characteristic effect of the β subunit on the bursting kinetics of the single-channel current records was consistently observed in comparisons of data from 19 α channels and 10 α + β channels. 10 of these channels (5 α and 5 α + β) were then analyzed in detail to obtain the results in the rest of the paper.

The β Subunit Increases P_o while Having Little Effect on the Hill Coefficient

As evident in Fig. 1, α + β channels are open a greater fraction of the time at a given Ca²⁺ _i than are α channels. To further examine this difference in Ca²⁺ sensitivity, we plotted P _o vs. Ca²⁺ _i for α and for α + β channels. Typical results are shown in Fig. 2 A, where the Ca²⁺ _i for a P _o of 0.5 (K _d) was 9.2 ± 2.3 μM (mean ± SD) for the α channels, shifting to 2.6 ± 0.52 μM for the α + β channels (+30 mV). In a series of similar experiments, the K _d was 14.2 ± 7.2 μM (range: 6.9–22.86 μM, n = 5) for a channels and 3.5 ± 1.3 μM (range: 2.2–4.9 μM, n = 5) for α + β channels. Thus, the effect of the β subunit on P _o was equivalent to increasing Ca²⁺ _i approximately fourfold.

Figure 2.

The β subunit increases P _o by increasing mean open times and decreasing mean closed times over a range of Ca²⁺ _i. (A) Plots of P _o vs. Ca²⁺ _i for α channels (open symbols) and α + β channels (filled symbols). Four of the six examined patches contained a single BK channel and two contained two BK channels. Each symbol type plots data from a different patch. The lines are fits of each symbol to the Hill equation, with the mean values of the parameters given in the text. Membrane potential, +30 mV. (B and C) Plots of mean open and closed times vs. Ca²⁺ _i for one representative α channel (open symbols) and one representative α + β channel (filled symbols). The straight lines (linear least square fits to the logs of the values) and curved lines (B-spline) are used to group the points for viewing in this and the following figures, unless indicated otherwise. (B and C) Same experimental conditions and channels as used for Fig. 1

The Hill coefficients derived from the P _o vs. Ca²⁺ _i plots like those in Fig. 2 A were 4.6 ± 1.8 for α channels and 4.5 ± 1.6 (mean ± SD) for α + β channels (the slopes were not significantly different: P > 0.9), suggesting that four to five Ca²⁺ ions (range: 2–6) typically bound to activate the BK channels in our experiments. These values are within the ranges of 2–5 typically observed for both native and cloned BK channels (McManus, 1991; Cox et al., 1997, and references therein).

The β Subunit Increases Mean Open Time and Decreases Mean Closed Time

To investigate the basis for the β subunit–induced increase in P _o, we measured the observed durations of the open and closed intervals for data obtained from patches containing either a single α or an α + β channel over a range of Ca²⁺ _i. Since determinations of observed mean open- and closed-interval duration are highly dependent on the time resolution, comparisons between specific α and α + β channels were made only for data obtained at the same level of filtering. Results are shown in Fig. 2, B and C, for a representative comparison, where the β subunit increased mean open times 3–7-fold and decreased mean closed times ∼10-fold over the examined ranges of Ca²⁺ _i. Similar results were found for comparisons between four additional α and four additional α + β channels, each channel from a different experiment, paired for the same level of filtering, over a range of filtering (4.5–10 KHz).

Thus, the β subunit increases P _o through a dual effect of increasing observed mean open times and decreasing observed mean closed times. (It will be shown in a later section that the decrease in mean closed times with the β subunit results in large part from a decrease in the frequency, rather than the duration, of the longer closed intervals.) At high levels of Ca²⁺ _i, and consequently high P _o, the mean durations of the closed intervals were brief, and the β subunit had less of an effect on the durations of these already brief closed intervals. We did not explore the effects of nominally zero Ca²⁺ _i, where the β subunit has been reported to have little effect on P _o (Meera et al., 1996).

The β Subunit Does Not Change the Number of Detected Kinetic States Entered during Gating

The gating of BK channels has been described by kinetic schemes in which the channel makes transformations among a number of different kinetic states (e.g., McManus and Magleby, 1991; Wu et al., 1995; Cox et al., 1997). To examine whether the β subunit changes the number of kinetic states entered during gating, we fitted sums of exponential components to dwell-time distributions (frequency histograms) of open and closed interval durations for four single α and three single α + β channels. The numbers of significant exponential components required to fit the distributions gives an estimate of the minimum number of states entered during gating (Colquhoun and Hawkes, 1981, 1995). (Examples of dwell-time distributions will be presented in a later section.)

Fig. 3 plots the number of significant exponential components required to describe the open (A) and closed (B) dwell-time distributions for α channels and α + β channels. The estimates are plotted against the numbers of analyzed intervals, as the ability to detect exponential components is dependent on the numbers of intervals analyzed (McManus and Magleby, 1988). Estimates of the minimal numbers of open states (the number of significant exponential components) ranged from two to four for both types of channels, with the lower estimates of two open states associated with the smaller data sets. The mean number of detected open states for α channels (3.0 ± 0.5; mean ± SD) was not significantly different (P > 0.38, Mann-Whitney test, from Snedecor and Cochran, 1989) from the mean number of detected open states for α + β channels (3.1 ± 0.6). Estimates of the numbers of detected closed states ranged from three to seven for α channels and from four to seven for α + β channels, with the estimate of three associated with a small data set. The mean number of detected closed states for α channels (5.4 ± 0.9) was not significantly different (P > 0.37, Mann-Whitney test) from the mean number of detected closed states for α + β channels (5.6 ± 1.0).

Figure 3.

The β subunit does not change the number of detected open and closed states entered during gating. Estimates of the minimum number of detected open (A) and closed (B) states entered during gating are plotted against the number of intervals analyzed. The β subunit had no significant effect on the number of open (P > 0.58) or closed (P > 0.53) states. Estimates for α channels are from fitting 21 sets of data from four channels, and those for α + β channels are from 15 sets of data from three channels. The numbers of fitted intervals ranged from ∼600 to ∼85,000. Data were obtained over a range of Ca²⁺ _i for both types of channels. There was no obvious effect of Ca²⁺ _i on the estimated numbers of states, so the estimates obtained at different Ca²⁺ _i are plotted on the same graph.

While it cannot be ruled out that changes in the numbers of kinetic states did occur with the β subunit but were not detected due to overlapping time constants and/or small areas of some of the exponential components, the data in Fig. 3 do indicate that the pronounced effect of the β subunit on channel activity did not arise from an obvious change in the numbers of detected kinetic states entered during gating. This observation, that the β subunit did not change the numbers of detected kinetic states, and the observation in a previous section that the β subunit did not change the Hill coefficients, suggests that the β subunit may exert its effects by changing transition rates among states rather than through fundamental changes in the gating mechanism, such as changes in the numbers of states or in the number of Ca²⁺-binding sites.

The β Subunit Greatly Increases Burst Duration

As a first step towards determining which transition rates may be affected, we examined the effect of the β subunit on bursting kinetics, since the single-channel records in Fig. 1 suggest that the β subunit greatly increases the durations of the bursts. A critical gap (closed interval between bursts of openings) was used to identify bursts (see methods). Over the examined range of Ca²⁺ _i, the β subunit increased mean burst duration 20–100-fold (Fig. 4 A), while having little effect on the mean durations of the gaps (closed intervals) between or within bursts (Fig. 4 B).

Figure 4.

Differences in bursting kinetics between α and α + β channels. Bursts of intervals were identified with a critical gap (closed interval duration), as defined in methods. Each burst included all open and closed intervals between two closed intervals with durations greater than the critical gap. Over the examined range of Ca²⁺ _i, the β subunit greatly increased mean burst duration (A) and the mean number of openings per burst (C), while having little effect on the mean durations of the gaps (closed interval durations) between or within bursts (B), and decreasing the fraction of total closed intervals that represent gaps between bursts (D). Data are plotted for a single representative α channel and a single representative α + β channel. Same experimental conditions and channels as used for Fig. 1. (E and F) The mean burst duration and mean duration of gaps between bursts are plotted for five patches, each containing a single α channel (open symbols), and another five patches, each containing a single α + β channel (filled symbols). Each symbol type plots data from a different channel. The continuous lines in F are B-spline lines passing through the means of the logs of mean gap duration at each Ca²⁺ _i for the α (top line) and α + β (bottom line) channels.

This marked increase in mean burst duration by the β subunit was associated with pronounced increases in both the mean open times (Fig. 2 B) and in the mean number of openings per burst (Fig. 4 C). Since the addition of each opening to a burst requires an intervening (brief) closed interval, the numbers of closings per burst (given by one less than the number of openings in Fig. 4 C) also increased dramatically. The β subunit– induced lengthening of bursts decreased the fraction of the total closed intervals that were gaps between bursts (Fig. 4 D). For example, with 3.6 μM Ca²⁺ _i, 21.7% of the observed closed intervals were gaps between bursts for α channels, and this decreased to 1.8% for α + β channels. Since the gaps between bursts are the longer closed intervals, this fractional reduction in the numbers of such intervals by the β subunit contributes greatly towards the increase in P _o by the β subunit.

Since estimates of both mean burst duration and the mean duration of gaps between bursts were relatively insensitive to the level of filtering, these parameters were compared directly for five α channels and five α + β channels, each obtained from a patch containing a single channel, in Fig. 4, E and F. The data from the 10 channels support the representative data shown in Fig. 4, A and B, for one channel of each type: the β subunit greatly increased mean burst duration while having little effect on the duration of gaps between bursts. While there was considerable variability in estimates of mean burst duration among channels of the same type, all of the individual estimates of mean burst duration for α channels when compared with α + β channels were clearly separated at each examined Ca²⁺ _i, differing by at least an order of magnitude (Fig. 4 E). Hence, the magnitude of the effect of the β subunit on mean burst duration was greater than the variability among channels of the same type.

Since the mean open time, the mean number of openings per burst, and the mean duration of the gaps within bursts were all highly sensitive to differences in filtering, we only compared estimates of these parameters for channels that were filtered the same. Results similar to those in Figs. 2, B and C, and 4, A–D, were found for four such additional detailed comparisons between α and α + β channels, paired for the same level of filtering. In each case, the β subunit increased P _o by prolonging the bursts through increases in both the numbers of openings per burst and in the mean open time. Prolonging the bursts also decreased the fraction of shut intervals that were gaps between bursts by preventing the channel from entering the longer closed intervals that separate bursts.

Increasing P_o with the β Subunit Was Not Equivalent to Increasing Ca²⁺

Similar to the effects of the β subunit on increasing mean open time, increasing Ca²⁺ _i also increases mean open times for BK channels (Fig. 2 B; McManus and Magleby, 1991) and the numbers of openings per burst (Fig. 4 C; Magleby and Pallotta, 1983). Thus, a potential mechanism for the action of the β subunit is that it may increase the rates at which the channel binds the activating Ca²⁺ ions. If the addition of the β subunit increases all the Ca²⁺-binding rates proportionally, then α and α + β channels should display identical kinetics when the Ca²⁺ _i is adjusted to give the same P _o for both types of channels. To examine this possibility, we compared the dwell-time distributions of α and α + β channels at the same P _o.

Results are shown in Fig. 5, which presents open dwell-time distributions on the left and closed dwell-time distributions on the right for both α and α + β channels, each at two different Ca²⁺ _i. At 1.8 μM Ca²⁺ _i, the P _o for the α channel was 0.004 (Fig. 5 A), while the P _o for the α + β channel was 0.15 (Fig. 5 B). The increase in P _o induced by the β subunit was due to both a pronounced shift in the open intervals to longer durations and a marked decrease in the number of longer closed intervals (gaps between bursts), as indicated by a decrease in the amplitude of the component marked gaps.

Figure 5.

Dwell-time distributions obtained at the same P _o for α channels and for α + β channels indicate that the β subunit increases P _o differently than Ca²⁺ _i. The open and closed interval durations were log-binned and the square root of the number of intervals in each bin was plotted against the bin midtimes (see methods) for one α channel and one α + β channel at both 1.8 and 5.4 μM Ca²⁺ _i, as indicated. Compare A with C to see the effect of increasing Ca²⁺ _i on α channels and B with D to see the effect of increasing Ca²⁺ _i on α + β channels. Compare B with C to see the differences in distributions between α and α + β channels at the same P _o. Compare A with B to see the differences in the distributions between α and α + β channels at 1.8 μM Ca²⁺ _i, and C with D to see the differences in the distributions between α and α + β channels at 5.4 μM Ca²⁺ _i. To allow direct comparisons of the distributions, the number of intervals was normalized to 100,000 in each case. The mean durations of the gaps between bursts are indicated by the lines with long dashes for 1.8 μM Ca²⁺ _i and the lines with short dashes for 5.4 μM Ca²⁺ _i. The continuous lines are fits with sums of exponential components with time constants (ms) and areas of: (A, open) 0.066, 0.18; 0.32 0.40; 0.98, 0.42. (A, closed) 0.023, 0.51; 0.090, 0.22; 0.40, 0.074; 200, 0.12; 850, 0.079. (B, open) 0.031, 0.065; 0.19, 0.058; 4.30, 0.88. (B, closed) 0.023, 0.59; 0.15, 0.24; 0.77, 0.12; 85, 0.022; 490, 0.026. (C, open) 0.12, 0.22; 0.64, 0.30; 1.4, 0.49. (C, closed) 0.038, 0.54; 0.17, 0.23; 0.85, 0.061; 17.5, 0.14; 65, 0.020. (D, open) 0.032, 0.050; 0.21, 0.037; 5.2, 0.92. (D, closed) 0.018, 0.63; 0.10, 0.24; 0.50, 0.12; 2.13, 0.014; 13, 0.0021. Same experimental conditions and channels as used for Fig. 1.

By increasing Ca²⁺ _i from 1.8 to 5.4 μM, the P _o of the α channel was increased from 0.004 to 0.16 (Fig. 5 C) to approximate the P _o of 0.15 for the α + β channel at 1.8 μM Ca²⁺ _i (Fig. 5 B). A comparison of the dwell-time distributions for the α and α + β channels at the same P _o showed marked differences in the kinetics: both the mean open times and the mean durations of the gaps between bursts were approximately an order of magnitude less for the α channel (Fig. 5 C) than for the α + β channel (Fig. 5 B), while the relative numbers of gaps between bursts were greater for the α channel than for the α + β channel. These marked differences in the kinetics of α and α + β channels at the same P _o exclude the possibility that the β subunit acts by the same proportional increases in all the rate constants for Ca²⁺ binding.

The β Subunit Has Little Effect on the Durations of the Gaps between Bursts

One reason why increasing P _o with the β subunit was not equivalent to increasing Ca²⁺ _i in the absence of the β subunit was the differential effects of the β subunit and Ca²⁺ _i on the gaps between bursts. Fig. 4, B and D, shows that the β subunit had little effect on the durations of the gaps between bursts, while decreasing their relative numbers. This can also be seen in Fig. 5, where the addition of the β subunit at a fixed Ca²⁺ _i had little effect on the mean durations of the gaps between bursts (positions of the peaks labeled gaps) while it decreased the relative numbers of the gaps, as indicated by the decrease in amplitude of the peaks in the presence of the β subunit (compare Fig. 5 A to B for 1.8 μM Ca²⁺ _i and Fig. 5 C to D for 5.4 μM Ca²⁺ _i).

Ca²⁺ _i Decreases the Durations of the Gaps between Bursts

In contrast to the little effect of the β subunit on the durations of the gaps between bursts, increasing P _o by raising Ca²⁺ _i decreased the durations of gaps between bursts for both α and α + β channels. This decrease is shown in Fig. 4 B, where increasing Ca²⁺ _i reduced the durations of gaps between bursts for both types of channels. This effect of Ca²⁺ _i in reducing the durations of gaps between bursts for both the α and α + β channels can also be seen in the dwell-time distributions in Fig. 5, where increasing Ca²⁺ _i from 1.8 to 5.4 μM shifted the peaks labeled gaps to briefer durations (compare Fig. 5 A to C for α channels and Fig. 5 B to D for α + β channels). Thus, a major means by which Ca²⁺ _i increases P _o for both α and α + β channels is to drive the channels from the gaps between bursts into the bursting states, decreasing the durations of the gaps between bursts.

The β Subunit Acts Specifically to Stabilize Bursting Activity

The results in Figs. 1 and 4 A showed that burst duration was markedly greater for α + β channels than for α channels for data obtained at the same Ca²⁺ _i. The results also showed that increasing P _o by increasing Ca²⁺ _i increased burst duration for both α and α + β channels. Since the β subunit increases P _o (Fig. 2 A), the greater burst duration for α + β channels could have been a consequence of the increased P _o, rather than a specific effect of the β subunit on lengthening the bursts.

To distinguish between these two possibilities, the effects of the β subunit on the bursting kinetics were studied at the same P _o for α and α + β channels over a wide range of P _o, obtained by changing Ca²⁺ _i. The results are shown in Fig. 6, where the parameters describing bursting kinetics are plotted against P _o. When α and α + β channels were compared at the same P _o (the Ca²⁺ _i was higher for the α channels to obtain the same P _o), mean burst duration was still greatly increased for α + β channels when compared with α channels (Fig. 6 A), due mainly to increases in both mean open times (Fig. 6 C) and the mean number of openings per burst (Fig. 6 D). Thus, the β subunit directly facilitates bursting, as its effects on bursts are greater than if the P _o were elevated to the same level in the absence of the β subunit by increasing Ca²⁺ _i.

Figure 6.

Bursting kinetics for α + β channels differ from α channels at the same P _o. The indicated bursting parameters are plotted against P _o for an α channel and an α + β channel. At any given P _o, the Ca²⁺ _i would be higher for the α channel than for the α + β channel. The presence of the β subunit led to increases in burst duration (A), mean open time (C), and the number of openings per burst (D), all factors that would increase P _o for the α + β channels. The decreased durations of the gaps between bursts (B) for α channels then allowed the two types of channels to have the same P _o. The α channel was recorded with symmetrical 175 mM KCl, while the α + β channel was recorded with 175 mM intracellular KCl and 150 mM extracellular KCl. With symmetrical 175 mM KCl, similar findings were obtained for both α and α + β channels, but over a narrower examined range of P _o. Effective filtering of 5.1 kHz. α Channel, C57; α + β channel, C34.

In contrast to the β subunit–induced increases in the burst parameters, the mean durations of the gaps (closed intervals) between bursts were about an order of magnitude less for α channels than for α + β channels at the same P _o (Fig. 6 B). Since the β subunit has little effect on the durations of the gaps between bursts (Figs. 4 B and 5), this difference reflects the fact that the data from α channels were obtained at a higher Ca²⁺ _i to obtain the same P _o. The higher Ca²⁺ _i for the α channels reduced the durations of the gaps between bursts.

Consistency of Bursting Kinetics as a Function of P_o

Fig. 7, A and B, plots the mean burst duration and the mean duration of the gaps between bursts against P _o for five α and five α + β channels. P _o ranged from ∼0.0003 to ∼0.85. The points cluster around the lines (linear least squares fits to the log of the points), indicating a relative lack of variability when these bursting parameters are plotted against P _o. This can be compared with the data in Fig. 4, E and F, where the variability is greater when the same bursting parameters are plotted against Ca²⁺ _i. Nevertheless, for both types of plots, the variability among channels of the same type was less than the effect of the β subunit on the indicated bursting parameters.

Figure 7.

Bursting kinetics of native BK channels from cultured rat skeletal muscle tissue suggest that the channels are composed of α subunits alone. (A and B) The indicated bursting parameters are plotted vs. P _o for 10 patches, 5 containing a single α channel (open symbols) and 5 containing a single α + β channel (filled symbols). (C and D) The indicated bursting parameters for six patches, each containing a single native BK channel from cultured rat skeletal muscle, are plotted vs. P _o. The dotted lines replot the continuous lines from A and B. The bursting kinetics of native BK channels from rat skeletal muscle cluster close to the line for channels composed of α subunits alone. Each symbol type plots data from a different channel.

A variability in the Ca²⁺ dependence of BK channels has been described previously for native, purified, and cloned channels (Moczydlowski and Latorre, 1983; Singer and Walsh, 1987; McManus and Magleby, 1991; Giangiacomo et al., 1995; Silberberg et al., 1997). Plotting the bursting parameters against P _o rather than Ca²⁺ _i may provide a means to remove much of this variability when studying the detailed single-channel kinetics.

Native BK Channels from Cultured Rat Skeletal Muscle Have Bursting Kinetics Like α Channels

The significant separation of the bursting parameters between α and α + β channels, together with the relative lack of variability in the parameters for channels of the same type (Fig. 7, A and B), makes it possible to functionally identify whether native BK channels are composed of α subunits alone, of both α and β subunits, or of a mixture of the two. Bursting parameters for data from six patches from cultured rat skeletal muscle, each containing a single BK channel, are plotted in Fig. 7, C and D. The dotted lines replot the continuous lines from Fig. 7, A and B, defining the bursting parameters for the cloned α and α + β channels.

The symbols for the native channels are in the immediate vicinity of the line for the bursting parameters of α channels. The simplest explanation of these observations is that native BK channels from cultured rat skeletal muscle are composed of α subunits alone. This conclusion is consistent with the studies of Tseng-Crank et al. (1996) and Chang et al. (1997) who found low or no β mRNA expression in human, canine, or rat skeletal muscle. We cannot exclude, however, that the native channels may have one or more β subunits per channel, but appear to gate like α channels because of other factors. For example, the alternative splice structure of BK channels can alter gating (Lagrutta et al., 1994). Since the structure of the studied native BK channels is not known, they may be of a different splice variant than the cloned channels.

The β Subunit Inhibits Entry into Subconductance States

Ion channels can enter subconductance levels during gating, reflecting the entry of the channel into conformations that are not fully open or are perhaps partially blocked (Barrett et al., 1982; Chapman et al., 1997; Premkumar et al., 1997; Zheng and Sigworth, 1997). Fig. 8 shows a typical example of gating to a subconductance level that was observed in α channels, but was seldom observed in α + β channels. To examine the subconductance gating, 210 min of current records from 24 α channels and 230 min from 15 α + β channels were visually inspected for transitions to subconductance levels with durations longer than 50 ms. There were 382 transitions to such subconductance levels with a mean duration of 0.4 s for the α channels, 9 transitions with a mean duration of 0.3 s, and 1 transition with a duration of 9 s for the α + β channels. The total time spent in subconductance levels for each channel was divided by the total time of the recording for that channel and converted to percentage for the plots in Fig. 8 C.

Figure 8.

The β subunit stabilizes the channel in the fully open conductance level rather than in subconductance levels. Representative single-channel current traces from an α channel with subconductance gating and from an α + β channel without subconductance gating are presented on a slower time base in A and a faster time base in B. The fully open conductance level for both the α and α + β channels shown was ∼315 pS. The subconductance level typically had an amplitude of about half the value of the full conductance level. Ca²⁺ _i was 18 μM for the α channel and 5.4 μM for the α + β channel. Same channels and filtering as used for Fig. 1. (C) Percent time spent in subconductance gating for 24 α channels and 15 α + β channels with a P _o > 0.7. The data were visually screened for transitions to subconductance gating with a duration longer than 50 ms. The membrane potential was +30 mV and the Ca²⁺ _i (3–100 μM) gave a P _o of 0.70–0.96. The first 14 α channels and first 9 α + β channels were recorded with 175 mM intracellular KCl and 150 mM extracellular KCl, while the next 10 α channels and 6 α + β channels were recorded with symmetrical 175 mM KCl.

The mean percentage of time that α channels spent gating to subconductance levels (1.1 ± 1.2%, mean ± SD) was decreased 32-fold (P < 0.0003, Mann-Whitney test) in the α + β channels (0.034 ± 0.097%). While 20 of 24 α channels spent >0.1% of their time gating to subconductance levels, only 1 of 15 α + β channels did. Thus, the β subunit inhibits entry into partially conducting states that give subconductance levels of the type shown in Fig. 8.

discussion

The accessory β subunit of mammalian BK channels greatly increases Ca²⁺ sensitivity (McManus et al., 1995; Dworetzky et al., 1996; Meera et al., 1996; Tseng-Crank, et al., 1996). The single-channel analysis in our study provides insight into the mechanism for this apparent increase in Ca²⁺ sensitivity. We found that the β subunit increased burst duration 20–100-fold by increasing both the number of openings per burst and the mean open times, while having little effect on the mean durations of the gaps (closed intervals) between bursts.

The bursting kinetics of channels can be described by the highly simplified Scheme I, where k ₁ is the rate constant for entering bursts and k ₋₁ is the rate constant for leaving bursts. For simple models that describe the basic single-channel properties of the gating of BK channels, the gaps between bursts in Scheme SI are generated by potential transitions among three to eight closed states, and the bursts in Scheme SI are generated by potential transitions among three to four open states and three to six brief closed states (Magleby and Pallotta, 1983; McManus and Magleby, 1991; Wu et al., 1995; Rothberg and Magleby, 1998). Because the data in our study were recorded from patches containing a single BK channel, each gap between bursts represents the sum of the dwell times in the closed states entered between bursts for that single channel. Some of the closed states contributing to the gaps between bursts would be expected to bind Ca²⁺, with the binding driving the channel through one or more closed states towards the first open state that terminates the gap between bursts. It is this Ca²⁺ dependence of the closed states entered between bursts that produces long gaps between bursts at low Ca²⁺ and brief gaps at high Ca²⁺.

Scheme I.

Inspection of Scheme SI suggests that the β subunit could promote bursting by facilitating the entry of the channel into bursts (by increasing k ₁) or by preventing the channel from leaving the bursts once entered (by decreasing k ₋₁), or by both actions. If the β subunit acts to facilitate entry into bursts, then the durations of the gaps (closed intervals) between bursts should be decreased by the β subunit. Alternatively, if the β subunit acts by retaining the channel in bursts once entered, then the β subunit should have little effect on the durations of the gaps between bursts, but should decrease their relative numbers since the channel would enter the gaps between bursts less often.

Our observations that the β subunit increased burst duration and decreased the numbers of gaps between bursts (Figs. 1, 4 A, and 5) while having little effect on the durations of the gaps between bursts (Figs. 4 B and 5) suggest that the β subunit had little effect on k ₁. Thus, the β subunit increases P _o mainly by slowing k ₋₁ to retain the channel in the bursting states.

In contrast to the relative lack of effect of the β subunit on the durations of the gaps between bursts, increasing Ca²⁺ _i decreased the durations of gaps between bursts for both α and α + β channels (Figs. 1, 4 B, and 5). Thus, a major means by which Ca²⁺ _i increased P _o for both α and α + β channels was to increase k ₁ to drive the channels from the gaps between bursts into the bursting states. Increasing Ca²⁺ _i also increased the durations of the bursts, but not as much as the increase induced by the β subunit for the same increase in P _o (Figs. 1, 4, and 6).

How might the β subunit effectively slow k ₋₁ to retain the channel in the bursting states? One possibility would be for the β subunit to add additional states that are entered during the bursting. Gating in these additional states could then retain the channel in the bursts. Another possibility would be for the β subunit to add additional Ca²⁺ binding sites that would act to retain the channel in bursts. Our observations that the β subunit did not change the numbers of exponential components in the dwell-time distributions (Fig. 3) or the Hill coefficients (Fig. 2) suggest that the β subunit does not act by changing either the numbers of kinetic states entered during gating or the effective number of Ca²⁺ binding sites. (Our observations that the number of subunits per channel could be doubled, from four for α channels to eight for α + β channels, without changing the numbers of detected kinetic states, indicate that the number of states entered during gating is not necessarily related to the total number of subunits comprising the α channel.)

The above findings, when coupled with previous observations that the β subunit does not appear to change the effective gating charge (McManus et al., 1995; Meera et al., 1996), suggest that the β subunit acts not by fundamental changes in the gating mechanism, such as alterations in either the number of Ca²⁺-binding sites or the number of major conformational changes, but rather through modulation of the gating of the α subunits.

One possible way the β subunit might modulate the gating of the α subunits would be through changes in the Ca²⁺ binding rates. If the β subunit increased all the Ca²⁺-binding rates to the α subunits proportionally, then increasing Ca²⁺ _i sufficiently to obtain the same P _o for α channels as for α + β channels should give the same single-channel kinetics for both types of channels. This was found not to be the case, as the durations of the bursts, the mean open times, the mean numbers of openings per burst, and the durations of the gaps between bursts were all considerably less for α channels than for α + β channels at the same P _o (Figs. 5 and 6).

Since the β subunit does not increase all of the Ca²⁺-binding rates proportionally, could it act by increasing a subset of the Ca²⁺-binding rates? Our observation that the β subunit had little effect on the durations of the gaps between bursts suggests that the β subunit has little effect on the Ca²⁺-binding rates to the closed states that dominate the gaps between bursts. This observation does not exclude the possibility that the β subunit may increase some of the Ca²⁺-binding rates in the bursting states, but such an effect would require a differential effect of the β subunit on the bindings of successive Ca²⁺.

If the β subunit does act by retaining the channel in the bursting states, then this is functionally equivalent to imposing a barrier to prevent the channel from leaving the bursting states. If this is the case, then the deactivation from the bursting states that occurs in the presence of Ca²⁺ after a step to negative membrane potentials might be expected to be slowed by the β subunit. Consistent with this possibility, the β subunit does slow deactivation after steps to negative membrane potentials (Dworetzky et al., 1996; Meera et al., 1996: Tseng-Crank et al., 1996).

The β subunit of the BK channel bears no sequence homology with accessory subunits from other channels (Knaus et al., 1994), suggesting that modulatory subunits may have evolved separately as needed to modulate specific channels. It also appears that the β subunit of the BK channel works differently from the modulatory subunits of other channels that increase expression levels and speed activation and inactivation rates (Lacerda et al., 1991; Varadi et al., 1991; Isom et al., 1992; Rettig et al., 1994; Makita et al., 1994; Heinemann et al., 1995; Morales et al., 1995; Shi et al., 1996). However, the actions of the β subunit for the BK channel seem to have some features in common with the actions of the accessory Ca²⁺ channel β_2A subunit on Ca²⁺ channels in the presence of a dihydropyridine derivative; both subunits increase burst duration, although in the case of the Ca²⁺ channel this increase occurs only when the Ca²⁺ channel is in a high P _o mode. Interestingly, these increases in burst duration by the different subunits on different channels occur even though the β subunit of BK channels has two putative transmembrane segments (Knaus et al., 1994), while the β_2A subunit of Ca²⁺ channels is cytoplasmic (Takahashi et al., 1987).

A comparison of the bursting kinetics of BK channels from cultured rat skeletal muscle to the bursting kinetics of α channels and α + β channels indicated that BK channels in cultured rat skeletal muscle have bursting kinetics similar to α channels (Fig. 7). Thus, BK channels in cultured rat skeletal muscle gate as if they are composed of α subunits alone. This conclusion is consistent with the studies of Tseng-Crank et al. (1996) and Chang et al. (1997), who found low or no β mRNA expression in human, canine, and rat skeletal muscle. In contrast to skeletal muscle, BK channels in tracheal smooth muscle are composed of α + β subunits, and most BK channels in human coronary artery smooth muscle function as if they are composed of α + β subunits (Tanaka et al., 1997). The β subunit would confer a greater Ca²⁺ sensitivity to BK channels in smooth muscle.

Our observation that the β subunit of BK channels decreases the percentage of time spent in gating to subconductance levels (Fig. 8) suggests that the β subunit of BK channels stabilizes the full conductance level of the open states. Similar to our observation for BK channels, the presence of an auxiliary subunit for the ryanodine receptor also decreases the percentage of time spent in gating to subconductance levels (Ondrias et al., 1996).

Conclusion

From a functional viewpoint, it is the retention of the BK channel in the bursting states by the β subunit that increases the apparent Ca²⁺ sensitivity of the channel. In the presence of the β subunit, each burst of openings is greatly amplified in duration through increases in both the numbers of openings per burst and in the mean open times. The physical mechanism by which the β subunit retains the channel in the bursting states is not known, but one possibility is that selective allosteric effects of the β subunits on the α subunits facilitate some conformational changes and/or inhibit others. This selective facilitation and/or inhibition would work to increase the effective energy barrier for leaving the bursting states, through increases in both mean open time and the numbers of openings per bursts.

Abbreviations used in this paper

BK channel

large conductance Ca²⁺-activated K⁺ channel

GFP

green fluorescent protein

HEK cells

human embryonic kidney cells