Measuring the Influence of the BK_Ca β1 Subunit on Ca²⁺ Binding to the BK_Ca Channel

Large-conductance Ca²⁺-activated potassium (BK_Ca) channels are crucial for the regulation of arterial tone, where they facilitate a negative feedback mechanism that opposes vasoconstriction (Nelson et al., 1995; Nelson and Quayle, 1995; Brenner et al., 2000). Intravascular pressure increases arterial tone by a complex process that includes membrane depolarization and the subsequent elevation of cytoplasmic Ca²⁺ via voltage-dependent Ca²⁺ channels. This global increase in Ca²⁺ leads to vasoconstriction, but it also triggers localized Ca²⁺ release events from ryanodine receptors on the smooth muscle sacroplasmic reticulum. These release events, termed Ca²⁺ sparks, activate nearby BK_Ca channels that then create a hyperpolarizing K⁺ current known as a STOC. STOCs then oppose further constriction (Nelson et al., 1995; Perez et al., 1999). The BK_Ca channel's accessory β1 subunit has been show to be critically important in this regulatory process, as mice that lack β1 have greatly reduced STOCs in response to sparks as well as hypercontractile smooth muscle and hypertension (Brenner et al., 2000; Pluger et al., 2000). In heterologous expression systems β1 subunits, four of which assemble with a single channel (Shen et al., 1994), make the BK_Ca channel substantially more Ca²⁺ sensitive (McManus et al., 1995; Meera et al., 1996; Cox and Aldrich, 2000a). Thus, in the absence of β1 it appears that BK_Ca channels lack the Ca²⁺ sensitivity required for BK_Ca-mediated feedback regulation of smooth muscle tone.

The mechanism by which β1 enhances the BK_Ca channel's Ca²⁺ sensitivity has been the subject of many studies (Wallner et al., 1996; Nimigean and Magleby, 1999b, 2000; Cox and Aldrich, 2000b; Qian et al., 2002; Qian and Magleby, 2003; Bao and Cox, 2005; Orio and Latorre, 2005; Morrow et al., 2006; Orio et al., 2006; Wang and Brenner, 2006; Yang et al., 2008), but it is still unclear. Nimigean and Magleby (1999a,b, 2000) found that β1 increases the length of time that the BK_Ca channel spends in bursting states and that this effect persists in the absence of Ca²⁺ (Nimigean and Magleby, 1999a). They suggested that a Ca²⁺-independent effect underlies most of the channel's increased Ca²⁺ sensitivity. In support of this notion, Bao and Cox (2005) found, when studying gating currents, that β1 stabilizes voltage sensor activation such that activation occurs at more negative voltages with β1 present. At most voltages this decreases the work that Ca²⁺ must do to open the channel and thereby increases the channel's apparent Ca²⁺ affinity. However, to account for the full change in Ca²⁺ sensitivity brought about by β1, Bao and Cox (2005) also proposed that β1 alters the true affinities of the channel's high-affinity Ca²⁺ binding sites (Bao et al., 2004), a conclusion supported by the earlier study of Cox and Aldrich (2000).

A recent paper by Yang et al. (2008), however, suggests that this may not be the case. Their experiments revealed that mutation of the voltage sensor residue R167 eliminates the ability of β1 to enhance the BK_Ca channel's Ca²⁺ sensitivity, implying that β1 enhances Ca²⁺ sensitivity solely by altering the conformation or movements of the voltage sensor. Here, to clarify this issue, we have used high-resolution Ca²⁺ dose–response curves to determine directly whether or not β1 alters the BK_Ca channel's affinity for Ca²⁺ at either of its two types of high-affinity Ca²⁺ binding sites. We find effects of β1 on the real affinities of both sites.

TSA 201 cells (modified human embryonic kidney cells) were transiently transfected with expression vectors (pcDNA 3; Invitrogen) encoding the mouse α subunit (mslo-mbr5) (Butler et al., 1993), the mouse β1 subunit of the BK_Ca channel, enhanced green fluorescent protein (eGFP-N1; BD), and the empty pcDNA 3.1+ vector (Invitrogen) to control for the total amount of transfected DNA. Cells were transiently transfected using the Lipofectamine 2000 reagent (Invitrogen). The eGFP was used to monitor successfully transfected cells. For transfection, cells at 80–90% confluence in 35-mm falcon dishes were incubated with a mixture of the plasmids (total of 4 μg DNA) Lipofectamine and Optimem (Invitrogen) according to the manufacturer's instructions. In brief, the mixture was left on the cells 4–8 h after which the cells were replated into recording Falcon 3004 dishes in standard tissue culture media: DMEM with 1% fetal bovine serum, 1% L-glutamine, and 1% penicillin-streptomycin solution (all from Invitrogen). The cells were patch clamped 1–3 d after transfection.

The molar ratio of β1 to α-expressing plasmids transfected was 1 β1 plasmid to between 0.6 and 2 α plasmids for all experiments. These ratios were determined to be well above that required to maximize the effects of β1 on channel gating in experiments in which the relative amount of β1 to α plasmid was titrated until no further effect of β1 was observed. The minimal saturating ratio was determined to be 1 β1 plasmid to 6.8 α plasmids, as determined by the magnitudes of β1-induced G-V shifts at 100 µM [Ca²⁺]. This is likely due to more efficient transcription and or translation of β1 relative to the much larger α subunit.

All recordings were done in the inside-out patch clamp configuration (Hamill et al., 1981). Patch pipettes were made of borosilicate glass (VWR micropipettes) with 0.8–5-MΩ resistances that were varied for different recording purposes. The tips of the patch pipettes were coated with sticky wax (KerrLab) and fire polished. Data were acquired using an Axopatch 200B patch clamp amplifier and a Macintosh-based computer system equipped with an ITC-16 hardware interface and Pulse acquisition software (HEKA). For macroscopic current recordings, data were sampled at 50 kHz and filtered at 10 kHz. In most macroscopic current recordings, capacity and leak current were subtracted using a P/5 subtraction protocol with a holding potential of −120 mV and leak pulses in opposite polarity to the test pulse, but with BK_Ca currents recorded with >100 µM Ca²⁺, no leak subtraction was performed. Unitary–current recordings acquired at 0 mV were sampled at 100 kHz and filtered at 2 kHz. All experiments were performed at room temperature, 22–24°C.

The pipette solution for macroscopic current recordings contained the following (in mM): 118 KMeSO₃, 20 N-methyl-glucamine-MeSO₃, 2 KCl, 2 MgCl₂, and 2 HEPES, pH 7.20. The pipette solution for current recordings at 0 mV contained the following (in mM): 3 KMeSO₃, 135 N-methyl-glucamine-MeSO₄, 2 KCl, 2 MgCl₂, and 2 HEPES, pH 7.20. 10 µM GdCl₃ was added to both pipette solutions to block endogenous stretch-activated channels (Yang and Sachs, 1989; Qian and Magleby, 2003). The bath solution for all recordings contained the following (in mM): 118 KMeSO₃, 20 N-methyl-glucamine-MeSO₃, 2 KCl, and 2 HEPES, pH 7.20. 1 mM EGTA (Fluka) was used as the Ca²⁺ buffer for solutions containing 3–500 nM free [Ca²⁺], 1 mM HEDTA (Sigma-Aldrich) was used as the Ca²⁺ buffer for solutions containing 0.8–20 µM free [Ca²⁺], and no Ca²⁺ chelator was used as the Ca²⁺ buffer in solutions containing between 20 µM and 2.5 mM free Ca²⁺. 50 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA) was added to all internal solutions to prevent contaminant Ba²⁺ block at high voltages. Both internal and external solutions were brought to pH 7.20.

The appropriate amount of total Ca²⁺ (100 mM CaCl₂ standard solution; Orion Research, Inc.) to add to the buffered solutions to yield the desired approximate free Ca²⁺ concentrations of 3 nM to 2.5 mM was calculated using the program MaxChelator (see Online supplemental material below), and the solutions were prepared as described previously (Bao et al., 2002). The Ca²⁺ concentrations reported above were determined with an Orion Ca²⁺-sensitive electrode. The solutions bathing the intracellular side of the patch were changed by means of a DAD valve controlled pressurized superfusion system (ALA Scientific Instruments).

All data analysis was performed with Igor Pro graphing and curve-fitting software (WaveMetrics, Inc.), and the Levenberg-Marquardt algorithm was used to perform nonlinear least-square curve fitting. Values in the text are given ± the standard error of the mean.

G-V relations were determined from the amplitude of tail currents measured 200 µs after repolarizations to −80 mV following voltage steps to the test voltage. Each G-V relation was fitted with a Boltzmann function,

and normalized to the maximum of the fit.

Under conditions where the open probability (Popen) is small (<10⁻²), single-channel openings were observed in patches containing hundreds of channels and I_K was measured from steady-state recordings 30 s in duration. NPopen was determined from all-points histograms by measuring the fraction of time spent (P_K) at each open level (k) using a half-amplitude criteria and summing their contributions NPopen = Σ kP_K, where N is the number of channels in the patch.

The effect of Ca²⁺ on Popen was determined from the ratio of NPopen at a given [Ca²⁺] to NPopen at 0.88 or 5.4 µM Ca²⁺ for all [Ca²⁺] tested on a given patch. In the presence of β1, the range of total activity per patch obtained over the range of [Ca²⁺] tested (3 nM to 2.5 mM) was greater than could be covered with a single normalization point. Therefore, in patches with many channels from which we were most interested in making low Popen measurements, the NPopen data at each [Ca²⁺] was normalized by the NPopen value measured at 0.88 µM [Ca²⁺]. Such curves were then averaged. Likewise, in patches with fewer channels, from which we were most interested in making higher Popen measurements, the NPopen data at each [Ca²⁺] was normalized by the NPopen value measured at 5.4 µM [Ca²⁺], and these curves were then averaged. The curve normalized to 0.88 µM was then adjusted so as to have the same value at 0.88 µM [Ca²⁺] as the curve normalized to 5.4 µM [Ca²⁺]. To yield a single curve at the [Ca²⁺] at which the two curves overlapped, the two values present were subjected to a weighted average, weighted by the number of measurements in each of the two curves being brought together. This yielded a Ca²⁺ dose–response curve with a value of 1 at 5.4 µM. This curve was then rescaled vertically so that the bottom of the curve equaled 1, or 0 on a log scale. This final curve we plotted as (NPopen/NPopen_min).

In some cases, Popen rather than (NPopen/NPopen_min) was reported as a function of [Ca²⁺]. This was done by determining Popen for each channel type at a single [Ca²⁺] in separate experiments, and then adjusting the average log (NPopen/NPopen_min) versus log [Ca²⁺] curve vertically, such that Popen was correct at the [Ca²⁺] at which Popen was known. This Popen, used for calibration, was determined at 2.5 mM [Ca²⁺] from patches whose channel content was apparent (n = 1–4).

The amount of Ca²⁺ to add to internal solutions to yield the desired free Ca²⁺ concentrations was calculated using the program MaxChelator, which was downloaded from http://www.stanford.edu/∼cpatton/maxc.html and is included as executable files.

The BK_Ca channel is both Ca²⁺ and voltage sensitive, and the effects of these stimuli are often displayed as a series of G-V relations determined over a series of Ca²⁺ concentrations. Such a series, determined from current families recorded from BK_Ca channels expressed in TSA 201 cells, is shown in Fig. 1 C. Representative data used to construct such a series are shown in Fig. 1 A. The data are from an excised inside-out macropatch expressing the mouse BK_Ca α subunit (mSlo1). Increasing intracellular Ca²⁺ shifts the channels' G-V curve leftward, an effect that is generally known to be due to three types of Ca²⁺ binding sites, two of high affinity and one of low affinity (Schreiber and Salkoff, 1997; Bian et al., 2001; Bao et al., 2002, 2004; Shi et al., 2002; Xia et al., 2002). The channels in these patches, however, contained the mutation E399N, which eliminates low-affinity Ca²⁺ sensing (Shi et al., 2002; Xia et al., 2002). So here only the effects of Ca²⁺ binding at the channel's high-affinity Ca²⁺ binding sites are evident. We refer to the mSlo1 channel carrying this mutation as ΔE. Increasing Ca²⁺ from 3 nM to 2.5 mM shifts the ΔE G-V relation ∼200 mV leftward.

When the mouse BK_Ca β1 subunit is expressed with the α subunit (see currents in Fig. 1 B), the Ca²⁺-induced leftward shifting evident in Fig. 1 C becomes more pronounced (Fig. 1 D), and thus it may be said that β1 increases the Ca²⁺ sensitivity of the BK_Ca channel in that it increases its G-V shift in response to a given change in [Ca²⁺] (McManus et al., 1995). On a plot of half-maximal activation voltage (V_1/2) versus [Ca²⁺], this effect is seen as an increase in slope (Fig. 1 E). At a single membrane voltage, 0 mV for example, it appears as an increase in both the efficacy and the apparent affinity of the channel for Ca²⁺ (Fig. 1 F). These data reveal that Ca²⁺ binding to the BK_Ca channel's low-affinity Ca²⁺ binding sites (eliminated by the E399N mutation) is not required for β1's effects on Ca²⁺ sensing. β1 has similar effects on the ΔE channel as it does on wild-type mSlo1 (McManus et al., 1995; Cox and Aldrich, 2000a; Bao and Cox, 2005).

In a previous study we found that much of β1's effects on Ca²⁺ sensing are due to its effects on voltage sensor movement, but to completely account for our data, we suggested that β1 also has effects on Ca²⁺ binding (Bao and Cox, 2005). Here, to test this hypothesis we sought to estimate the channel's Ca²⁺ dissociation constants at each high-affinity Ca²⁺ binding site in the presence and absence of β1. To do this we used high-resolution Ca²⁺ dose–response curves (Horrigan and Aldrich, 2002; Sweet and Cox, 2008). The channel's Popen was measured at a single voltage over a large range of [Ca²⁺]. Fig. 2 (A and B) shows unitary currents recorded from membrane patches expressing either ΔE or ΔE + β1. Both patches were held at 0 mV and exposed to a range of [Ca²⁺]. Although each patch contained many channels, Popen was low at 3 nM [Ca²⁺], such that activity was observed as the infrequent and brief openings of single channels. Increasing intracellular Ca²⁺ then caused an increase in Popen. From data like these we derived the ΔE and ΔE + β1 channels' Popen versus [Ca²⁺] relations (Fig. 2 C). So that all parts of each curve could be well determined, Popen was measured over seven orders of magnitude with 21 Ca²⁺ concentrations. To do this, many patches were used and normalized by their values of NPopen at 5.3 µM, where N is the number of channels in a given patch. The resulting curve was then either normalized to its minimum to yield curves like those in Fig. 3 C or adjusted so as to have the proper Popen at 2.5 mM [Ca²⁺] (determined in separate single-channel experiments; see Materials and methods). This yielded curves like those in Fig. 2 D.

Fig. 2 C shows a comparison of the Popen/Popen_min versus [Ca²⁺] relations at 0 mV of the ΔE channel in the presence (filled circles) and absence (open circles) of β1. The magnitude of the change in Popen induced by Ca²⁺ (the range the data spans on the ordinate) is ∼100-fold larger for the ΔE + β1 channel than it is for the ΔE channel. This magnitude is determined by the energy Ca²⁺ binding imparts to the channel's central closed-to-open conformational change, which in turn is determined by the open- and closed-state Ca²⁺ binding affinities of each binding site. Thus, that this magnitude changes with β1 coexpression indicates that β1 alters Ca²⁺ binding.

To analyze this effect more rigorously, Popen versus [Ca²⁺] relations were determined for the ΔE (open circles) and ΔE + β1 (filled circles) channels (Fig. 2 D), and these data were then analyzed as follows. If one assumes that there are four of each type of Ca²⁺ binding site and that each site influences channel opening by altering the equilibrium constant of a single conformational change between closed and open—as much evidence suggests (McManus and Magleby, 1991; Cox et al., 1997; Cui et al., 1997; Horrigan et al., 1999; Horrigan and Aldrich, 1999, 2002; Rothberg and Magleby, 1999, 2000; Cox and Aldrich, 2000a)—and that there are no interactions between binding sites and no interactions between binding sites and voltage sensors (not rigorously true [Sweet and Cox, 2008], but see below), then at constant voltage the channel's Popen as a function of voltage can be written as

where K_C1 and K_C2 represent the dissociation constants of binding sites 1 and 2 in the closed conformation, K_O1 and K_O2 represent the dissociation constants of binding sites 1 and 2 in the open conformation, and M represents the closed-to-open equilibrium constant when no Ca²⁺ are bound. As relates to the BK_Ca channel, M is voltage dependent and incorporates all effects of voltage on opening.

In the absence of Ca²⁺, Eq. 1 reduces to:

which can be rearranged to

Further, at voltages where Popen is much less than 1 (∼10⁻² or lower, such as 0 mV, which we have used here), Eq. 3 may be simplified to

Thus, in the absence of Ca²⁺, M can be determined directly from Popen.

Conversely, at saturating Ca²⁺, Eq. 1 reduces to

where

and

and, therefore, the top of the Popen versus [Ca²⁺] curve is determined by M and the ratios (C1 and C2) of the open- and closed-state Ca²⁺ dissociation constants at the two types of sites.

The ΔE channel's Popen versus [Ca²⁺] curve at 0 mV (Fig. 2 D, open circles) was fitted with Eq. 1 (solid line). The fit yielded the following values:

Note the large standard errors of the dissociation constants. This suggests that the fit is not unique and that the RCK1 and Ca²⁺ bowl sites likely have similar affinities at 0 mV, such that changes in the parameters governing one site can be compensated for by changes in the parameters governing the other site. Indeed, the fit was almost as good when we supposed that the two types of sites had identical binding properties (gray curve).

Also shown in Fig. 2 D is the Popen versus [Ca²⁺] curve we determined for the ΔE channel in the presence of β1. β1 reduces M by 235-fold, which moves the 0 [Ca²⁺] data point well down the ordinate. This indicates that some of β1's effects are on channel properties that are unrelated to Ca²⁺ binding, as has been demonstrated (Nimigean and Magleby, 1999b, 2000; Bao and Cox, 2005; Orio and Latorre, 2005; Wang and Brenner, 2006). Fitting this curve with Eq. 1 yielded:

The fit is better determined than the fit to the ΔE (α only) curve, and it suggests that in addition to decreasing M ∼200-fold, β1 increases the affinity of both binding sites when the channel is open, and it reduces the affinity of one site when the channel is closed. This increases C at both sites and thereby the effect of Ca²⁺ binding on channel opening.

To test more directly whether β1 affects Ca²⁺ binding, and if so, at which sites and to what extent, we examined β1's effects on each type of binding site individually using mutations that selectively eliminate the effect of Ca²⁺ at each type of site. D367A eliminates Ca²⁺ sensing via RCK1 sites (Xia et al., 2002), and D898A/D900A eliminates Ca²⁺ sensing via Ca²⁺ bowls (Bao et al., 2004). Before using these mutations, however, it was important to confirm that in conjunction with E399N, they completely eliminate the effect of Ca²⁺ on Popen. Shown in Fig. 3 are Ca²⁺ dose–response relations at 0 mV determined from a patch expressing the triple mutant (E399N)(D367A)(D898A/D900A), which we refer to as ΔEΔRΔB, in the presence and absence of β1. As is evident, the triple mutant shows no response to Ca²⁺, which demonstrates that the three sites targeted by these mutations can together account for all Ca²⁺ sensing. Importantly, ΔEΔRΔB + β1 also shows no response to Ca²⁺. Thus, in our hands, β1 does not restore the Ca²⁺ sensitivity of one or more of the sites, as has been suggested (Qian and Magleby, 2003), nor does β1 contain Ca²⁺ binding sites of its own that are coupled to channel opening.

We then used the mutant (E399N)(D367A), which we refer to as ΔEΔR, to examine β1's effect on Ca²⁺ sensing at the Ca²⁺ bowl. Fig. 4 displays BK_Ca currents from individual patches expressing ΔEΔR in the absence (A) or presence (B) of β1. Each patch was held at 0 mV and exposed to various [Ca²⁺]. For the ΔEΔR channels, application of Ca²⁺ caused an increase in Popen, but the increase was not as great (∼10²-fold) as it was with the ΔE channel (∼10⁵-fold), likely because the ΔR mutation eliminates half of the channels high-affinity Ca²⁺ binding sites. But more importantly, expression of β1 increased the Ca²⁺ dependence of Popen for the ΔEΔR channels. Fig. 4 C shows a comparison of the Popen/Popen_min versus [Ca²⁺] relations for the ΔEΔR channel in the presence (filled circles) and absence (open circles) of β1 at 0 mV. Remarkably, for the ΔEΔR channel, the change in Popen produced by saturating Ca²⁺ is ∼50 times larger in the presence of β1 than it is in its absence. This indicates that β1 increases C at the Ca²⁺ bowl site and therefore that it affects Ca²⁺ binding at this site.

To determine the extent to which β1 affects Ca²⁺ binding, in Fig. 4 D, the Popen versus [Ca²⁺] relations for the ΔEΔR channels (open circles) and ΔEΔR + β1 channels (filled circles) are plotted. These data are the same as those in Fig. 4 C, except they have been plotted as absolute Popen. The affinities of the intact Ca²⁺ bowl site in the presence and absence of β1 were then determined from fits with Eq. 8 below, which is analogous to Eq. 1, but represents the case where there is only one type of Ca²⁺ binding site.

Importantly, the bottom of the curve is still determined by M, but once M is specified, the top of the curve is determined only by C. That is, at saturating Ca²⁺,

where

.

Thus, when there is a single type of binding site, determining the top and bottom of the channel's Popen versus [Ca²⁺] curve greatly constrains the fitting. In fact, in leaves only one parameter free, either of the two dissociation constants, to determine the shape of the curve.

Fitting the ΔEΔR channel's Popen versus [Ca²⁺] curve yielded the fit shown in Fig. 4 D (solid line). Gratifyingly, even with these constraints the fit closely approximated the data and yielded the following parameters (see also Table I):

Next, we fitted the ΔEΔR + β1 curve (Fig. 4 D, dashed line), and again the fit appeared to well approximate the data. This suggests that β1 does not likely alter the assumptions underlying Eq. 8: a single conformational change between opened and closed; four binding sites; and binding at one site does not affect binding at the other sites, except via promoting opening. The fit yielded the following parameter values:

Note that the fit is well constrained and suggests that β1 reduces the affinity of the Ca²⁺ bowl site for Ca²⁺ both in the opened and the closed channel. The effect on K_O however is smaller than on K_C and not clearly significant. The effect on K_C, however, is large (2.8-fold), and it is predominately this change that increases C for this site and accounts for the expanded Popen range spanned by the ΔEΔR channel's Ca²⁺ dose–response relation in the presence of β1.

Thus, β1 does alter Ca²⁺ binding at the Ca²⁺ bowl site. It lowers the Ca²⁺ bowl's affinity when the channel is closed. Unexpectedly, however, the loss of the channel's RCK1 sites also had a dramatic effect on β1's influence on the Ca²⁺-independent properties of channel gating. The β1-induced change in M, which was 235-fold for the ΔE channel (Fig. 2 D), is absent in ΔEΔR channel. Indeed, with the D367A mutation present, it appears β1 no longer effects M. The bottoms of the two curves in Fig. 2 D are at the same place on the log (Popen) axis. This result argues that functional RCK1 sites are required for β1's effect on the intrinsic equilibrium constant between open and closed, usually referred to as L (for an analysis of mouse β1's effects on L see Wang and Brenner 2006).

To examine β1's effect on Ca²⁺ sensing at the RCK1 sites we used the mutant (E399N)(D898A/D900A), which we refer to as ΔEΔB. In Fig. 5, BK_Ca currents from individual patches expressing ΔEΔB channels in the absence (A) or presence of β1 (B) are displayed. Patches were held at 0 mV and exposed to various [Ca²⁺]. For ΔEΔB channels application of Ca²⁺ caused an increase in Popen, but again the increase is not as great (∼10⁴-fold) as it is with the ΔE channel (∼10⁵-fold), presumably because the ΔEΔB channel had lost half of its high-affinity Ca²⁺ binding sites. More importantly, however, coexpression of β1 increased the maximal effect of Ca²⁺ on Popen. Fig. 5 C shows a comparison of the Popen/Popen_min versus [Ca²⁺] relations for the ΔEΔB channel in the presence (filled circles) and absence (open circles) of β1. The effect of β1 on Ca²⁺ sensing via the RCK1 sites is substantial. For the ΔEΔB channel, the change in Popen produced by saturating Ca²⁺ is ∼400 times larger in the presence of the β1. This again requires that β1 increase C (K_C1/K_O1) at the RCK1 site and therefore that it affects Ca²⁺ binding at this site as well.

To determine how much each dissociation constant is affected, we plotted (Fig. 5 D) the Popen versus [Ca²⁺] relations for the ΔEΔB (open circles) and ΔEΔB + β1 (filled circles) channels and fit these relations with Eq. 8. The affinities of the intact RCK1 sites in the presence and absence of β1 were then determined from the fits. The fit to the ΔEΔB data (solid line) yielded the following values (see also Table I):

And the fit to the ΔEΔB + β1 data (dashed curve) yielded the following values (see also Table I):

Thus, there is a small β1-induced change in the affinity of the RCK1 sites when the channel is closed, and a much larger relative change when the channel is open, the opposite of what we observed at the Ca²⁺ bowl. Most important, however, the changes are diametric and consequently the change in C is large (7.5→36), and it is this change that drives the expansion of the channel's Ca²⁺ dose–response curve along the ordinate in Fig. 5 C upon β1 coexpression. Interestingly, the β1-induced change in M is ∼200-fold for the ΔEΔB channel, similar to what is observed with the ΔE channel. Thus, unlike functional RCK1 sites, functional Ca²⁺ bowls are not required for β1's effects on the Ca²⁺-independent gating properties of the BK_Ca channel.

Although β1 has very large effects on the ΔEΔB channel's Ca²⁺ dose–response relation, there is a complicating factor that makes our conclusions about the effects of β1 on this site less than definitive. Our analysis assumes that there are no direct interactions between Ca²⁺ binding sites and voltage sensors. We have however shown previously (Sweet and Cox, 2008) that Ca²⁺ binding at the RCK1 site is voltage dependent, an effect that is most reasonably attributed to a direct intrasubunit interaction between voltage sensor and RCK1 Ca²⁺ binding site. Further, we have estimated the allosteric factor by which voltage sensor activation alters the equilibrium constant for Ca²⁺ binding at the RCK1 site (E) to be ∼2.8, and Horrigan and Aldrich (2002) arrived at a similar value, 2.4, based on the effect of Ca²⁺ on voltage sensor movement measured with gating currents. This means that Eq. 8 is not strictly correct for the ΔEΔB channel because as Ca²⁺ binds and the channels open, more voltage sensors will become active, even if the voltage is held constant, and this could lead to enhanced binding not accounted for by Eq. 8. The magnitude of this effect will depend on E and on the properties of the channel's voltage sensors. In terms of the Horrigan and Aldrich (HA) model, it will depend on L and V_hc, and V_ho, z_L, and z_J (Horrigan and Aldrich, 2002). Furthermore, if β1 changes any of these parameters this could alter the channel's Ca²⁺ dose–response curve in a way that looks like an increase in C, when no real change in C has occurred.

Ideally, our experiments would have been performed at a negative voltage where the channel's voltage sensors are very rarely active; however, in the presence of the β1 subunit voltage sensors become active at far negative voltages where Popen at 3 nM [Ca²⁺] is too low to measure well, making this approach impractical. However, we examined whether the effects of β1 on the BK_Ca channel's voltage sensing parameters could account for its effects on the ΔEΔB channel's Popen versus [Ca²⁺] curve as follows. We simulated ΔEΔB Popen versus [Ca²⁺] curves using the HA model and voltage-sensing parameters that have been well established for the wild-type mSlo1 channel (V_ho = 27 mV, V_hc = 151 mV, z_J = 0.58, z_L = 0.41, L0 = 2 × 10⁻⁶, and E = 2.8) and Ca²⁺ dissociation constants we determined for the RCK1 site (K_C = 23.2 µM and K_O = 4.9 µM). This led to the Popen versus [Ca²⁺] curve shown in Fig. 6 B (dark curve). We then simulated the effects of β1 on the voltage-sensing parameters of the channel by lowering L from 2 × 10⁻⁶ to 2 × 10⁻⁹ to account for the large decline in M (Popen at 3 nM Ca²⁺), and we altered V_hc to +80 mV and V_ho to −34 mV, parameters we have determined previously for α+β1 channels (Bao and Cox, 2005). The resulting curve is also shown in Fig. 6 B (gray curve), and as anticipated, altering these voltage-sensing parameters did increase the maximum effect of Ca²⁺ on Popen. The change in Popen brought about by saturating [Ca²⁺] increased 1.55-fold. Thus, some of the changes we have observed in the ΔEΔB channel's Popen versus [Ca²⁺] curve upon β1 expression likely arise from β1's effects on voltage sensing rather than Ca²⁺ binding. However, as seen in Fig. 6 A, β1 increases the maximum effect of Ca²⁺ on Popen 708-fold—far greater than the effect we anticipate due to the linkage between Ca²⁺ binding and voltage sensing (1.55-fold). In fact the anticipated effect is <1% of the true effect of β1. Thus, this complication not withstanding, it does appear that β1 alters the true Ca²⁺ affinities of the RCK1 sites as well as the Ca²⁺ bowl sites.

Here, we have examined the mechanism by which the BK_Ca channel's β1 subunit increases the Ca²⁺ sensitivity of channel activation. To be as accurate as possible, we used unitary–current recordings from patches containing from a few hundred to just a few channels. This allowed us to determine Popen over seven orders of magnitude. To be as model independent as possible, we made measurements at constant voltage, and where possible low Popen, such that the amplitudes and shapes of the resulting Ca²⁺ dose–response curves were dependent primarily, if not exclusively, on the channel's Ca²⁺ binding parameters. The essential assumptions we made in fitting our data were as follows: (1) that there is a single conformational change between open and closed that can occur with any number of Ca²⁺ bound, an idea that is consistent with a great many single-channel and macroscopic BK_Ca channel studies and all current models (McManus and Magleby, 1991; Cox et al., 1997; Cui et al., 1997; Horrigan et al., 1999; Horrigan and Aldrich, 1999, 2002; Rothberg and Magleby, 1999, 2000; Cox and Aldrich, 2000a); (2) that there are four of each type of high-affinity site. This has been established for the Ca²⁺ bowl (Niu and Magleby, 2002), and given the fourfold symmetry of the channel, this seems likely to be the case for the RCK1 site as well; and (3) that there are no interactions between binding sites of the same type or between Ca²⁺ binding and voltage sensor movement.

We found that the 0 mV Ca²⁺ dose–response curve of BK_Ca channels containing only functional RCK1 sites could be well fitted by supposing that each site independently influences opening, and that each site has a dissociation constant of 15.8 µM when the channel is closed and 2.1 µM when the channel is open. These values produce a C value of 7.5, which allows us to calculate that each Ca²⁺ bound to a Ca²⁺ bowl site decreases the energy difference between open and closed by 4.9 KJ/mol.

In the presence of β1, the RCK1 site's dose–response curve at 0 mV could also be well fitted with a simple model and yielded values for K_C and K_O of 18.5 and 0.52 µM, respectively. These values produce a substantial C value of 36 (8.8 KJ/mol per binding event), which we think is in large part responsible for the dramatic increase in the influence of Ca²⁺ on Popen brought about by β1 in the ΔEΔB channels. As discussed above, however, our estimates of these values are complicated by an interaction between Ca²⁺ binding and voltage at the RCK1 sites. But we have simulated the influence that this complication will likely have on Ca²⁺ binding in the presence of β1, and it turns out to very small compared with the effect of β1 observed. Thus, we do not think this linkage has greatly distorted our measurement of K_C and K_O.

Ca²⁺ binding to the Ca²⁺ bowl is not voltage sensitive (Sweet and Cox, 2008); thus, our conclusions drawn from data for the Ca²⁺ bowl sites are more clear. We found that the Ca²⁺ bowl's dose–response curve at 0 mV could be well fitted by supposing that each Ca²⁺ bowl independently influences opening, and that each site has a dissociation constant for Ca²⁺ of 2.1 µM when the channel is closed and 0.56 µM when the channel is open. These values produce a C of 3.75, which allows us to calculate that each Ca²⁺ bound at a Ca²⁺ bowl site decreases the energy difference between open and closed by 3.2 KJ/mol. These numbers may be compared with previous estimates of K_C and K_O for this site. Xia et al. (2002) estimated K_C = 4.5 ± 1.7 µM and K_O = 2.0 ± 0.7 µM (C = 2.25), and Bao et al. (2002) estimated K_C = 3.8 ± 0.2 and K_O = 0.94 ± 0.06 µM (C = 4.0). And in Sweet and Cox (2008), we estimated K_C = 3.13 ± 0.28 µM and K_O = 0.88 ± 0.06 µM (C = 3.55). Thus, our current estimates are close to our previous estimates, especially in terms of C.

More interestingly, we found that coexpression of β1 changed the ΔEΔR channel's Popen versus [Ca²⁺] relation in a manner that indicated that the affinity of the Ca²⁺ bowl site for Ca²⁺ is changed in the presence of β1. In the presence of β1, the ΔEΔR channel's dose–response curve at 0 mV could be well fitted by supposing that each Ca²⁺ bowl independently influences opening, and that each site has an affinity of 5.9 µM when the channel is closed and 0.67 µM when the channel is open. These values produce a C value of 8.8, which allows us to calculate that with β1 present, each Ca²⁺ bound at a Ca²⁺ bowl decreases the energy difference between open and closed by 5.3 KJ/mol.

These numbers are difficult to compare with previous estimates of the affinities of the BK_Ca channel in the presence of β1. Bao and Cox (2005) estimated the affinities of the channel in the presence of β1 to be K_C = 3.71 µM and K_O = 0.88 µM (C = 4.2) for site 1 and K_C = 5.78 µM and K_O = 0.73 µM (C = 7.9) for site 2. These estimates, however, were based on the assumption that β1 affected the affinity of only one of the two binding sites (site 2), which we now think is not the case. But interestingly, and of relevance here, Cox and Aldrich (2000) observed that the affinity of the channel for Ca²⁺ in the open conformation must not change upon expression of β1, as β1 does not alter the critical [Ca²⁺] required to begin to see a leftward shift in the channel's G-V relation (Cox and Aldrich, 2000a). This is in agreement with our data that show that expression of β1 does not appreciably alter K_O for the higher-affinity site (Ca²⁺ bowl: Ko_α = 0.56 µM, K_Oα+β1 = 0.67 µM).

In considering the effects of β1 on Ca²⁺ binding, it is interesting to note that the BK_Ca β1 subunit has very little intracellular sequence, just its N and C termini—15 and 13 amino acids long, respectively. The rest of the protein is comprised of two transmembrane domains and a large extracellular loop—118 amino acids. Thus, if β1 subunits alter the channel's affinity for Ca²⁺ by interacting directly with Ca²⁺ binding sites, generally accepted to be contained within the cytoplasmic C terminus of the channel, they seemingly must do so through these short intracellular termini. Supporting this idea, chimera experiments with β1 and β2 (Orio and Latorre, 2005) and β1 N- and C-terminal deletion experiments (Wang and Brenner, 2006) have shown that these termini play a critical role in transmitting β1's effects to the channel proper.

In addition to β1's effects on Ca²⁺ binding, and in agreement with the previous findings of Wang and Brenner (2006), we found that mouse β1 reduces Popen at 0 mV in the absence of Ca²⁺, presumably by lowering L. Strikingly, our results show that a mutation at a Ca²⁺ binding site (D367A) not only eliminates Ca²⁺ binding at the RCK1 sites, but it also eliminates β1's ability to reduce Popen at 0 mV in the absence of Ca²⁺. That is, a single Ca²⁺ binding site mutation affects both the mechanism by which the channel senses Ca²⁺ and also the mechanism by which β1 influences the intrinsic energetics of opening.

We also found that when we combine mutations at all three types of Ca²⁺ binding sites—E399N (low-affinity site), D367A (RCK1 site), and D898/D900 (Ca²⁺ bowl)—we see no effect of Ca²⁺ on channel gating in the α-only channel, and we see no restoration of an effect of Ca²⁺ on channel gating by β1. This in contrast to the work of Qian and Magleby (2003), who found that coexpression of β1 restored some Ca²⁺ sensitivity to a similar triple mutant. We do not know why we did not see the restorative effect of β1 observed by Qian and Magleby. The most straightforward explanation is that the Ca²⁺ binding sites were disabled by the mutations and could not be fixed by β1. However, the main differences between the two studies were as follows: our recordings were made at 0 mV, whereas theirs were conducted at +50 mV. The mutations used at each binding site were not exactly the same between the two studies, and Qian and Magleby recorded from single-channel patches, whereas the patches we used typically contained many channels. Furthermore, Qian and Magleby did not see the restorative effect of β1 in every experiment, but rather they reported a large variability from patch to patch. This would seem to suggest that perhaps there is a subtle environmental factor required for the effect they observed that was absent from our experiments.

Our measurements of the effects of β1 on Ca²⁺ binding also stand in some contrast to the recent paper of Yang et al. (2008). They found that the mutation R167A in the voltage-sensing domain of the mSlo1 channel eliminates β1's ability to alter the channel's G-V curve at all [Ca²⁺]. This result suggests that by altering just voltage sensor movement one can disrupt the β1-induced enhancement of Ca²⁺ sensitivity altogether. It seems hard to imagine how such a mutation could simultaneously eliminate β1's effects on voltage sensor movement and Ca²⁺ binding at both binding sites, unless these processes are physically more intertwined than previously thought.

Perhaps rather than affecting Ca²⁺ binding directly, the β1 subunit might be affecting a linkage between Ca²⁺ binding and voltage sensing, which in turn affects Ca²⁺ binding. Indeed, we have shown recently (Sweet and Cox, 2008) that such a linkage exists between the RCK1 sites and the voltage sensors, so it is possible that an enhancement of the allosteric factor at this linkage, E, could create enhanced binding affinity. It would be interesting to explore this linkage in α+β1 channels. However, we found no such linkage between Ca²⁺ bowl sites and the channel's voltage sensors (Sweet and Cox, 2008); thus, we do not think that such an effect is involved in the β1-induced changes in the binding affinity we observed at the Ca²⁺ bowl sites.

In conclusion, we have shown that the BK β1 subunit has effects on the affinities of the BK_Ca channel's high-affinity Ca²⁺ binding sites. It primarily increases the affinity of the RCK1 sites when the channel is open, and it primarily decreases the affinity of the Ca²⁺ bowl sites when the channel is closed. Both of these modifications increase the difference in affinity between open and closed, such that Ca²⁺ binding at either site has a larger effect on channel opening when β1 is present.

This work was supported by program project grant P01-HL077378 and predoctoral fellowship F31 NS047823 from the National Institutes of Health.

Edward N. Pugh Jr. served as editor.