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Molecular Cardiology Research Institute, New England Medical Center, and Department of Neuroscience, Tufts University School of Medicine, Boston, MA 02111

Correspondence to Daniel H. Cox: dan.cox{at}tufts.edu

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Large-conductance Ca²⁺-activated K⁺ channels (BK_Ca channels) are regulated by the tissue-specific expression of auxiliary ß subunits. ß1 is predominately expressed in smooth muscle, where it greatly enhances the BK_Ca channel's Ca²⁺ sensitivity, an effect that is required for proper regulation of smooth muscle tone. Here, using gating current recordings, macroscopic ionic current recordings, and unitary ionic current recordings at very low open probabilities, we have investigated the mechanism that underlies this effect. Our results may be summarized as follows. The ß1 subunit has little or no effect on the equilibrium constant of the conformational change by which the BK_Ca channel opens, and it does not affect the gating charge on the channel's voltage sensors, but it does stabilize voltage sensor activation, both when the channel is open and when it is closed, such that voltage sensor activation occurs at more negative voltages with ß1 present. Furthermore, ß1 stabilizes the active voltage sensor more when the channel is closed than when it is open, and this reduces the factor D by which voltage sensor activation promotes opening by 24% (16.812.8). The effects of ß1 on voltage sensing enhance the BK_Ca channel's Ca²⁺ sensitivity by decreasing at most voltages the work that Ca²⁺ binding must do to open the channel. In addition, however, in order to fully account for the increase in efficacy and apparent Ca²⁺ affinity brought about by ß1 at negative voltages, our studies suggest that ß1 also decreases the true Ca²⁺ affinity of the closed channel, increasing its Ca²⁺ dissociation constant from 3.7 µM to between 4.7 and 7.1 µM, depending on how many binding sites are affected.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Auxiliary subunits often tune ion channel behavior to the needs of a particular cell type (Isom et al., 1994; Gurnett and Campbell, 1996; Xu et al., 1998). This method of generating functional diversity is particularly well exploited by the large-conductance Ca²⁺-activated potassium channel, or BK_Ca channel, which is composed of pore-forming and auxiliary ß subunits (Knaus et al., 1994b; McManus et al., 1995). Four subunits are sufficient to form a fully functional channel complete with Ca²⁺ sensitivity, voltage sensitivity, and a large single-channel conductance (Shen et al., 1994; DiChiara and Reinhart, 1995; Cui et al., 1997). There is only a single gene for this subunit (Atkinson et al., 1991; Adelman et al., 1992; Butler et al., 1993). In different tissues, however, BK_Ca channels display different phenotypes, and this is thought to be due primarily to the tissue-specific expression of some subset of four homologous BK_Ca ß subunits (ß1–ß4) (Knaus et al., 1994a; McManus et al., 1995; Wallner et al., 1995, 1999; Meera et al., 1996, 2000; Tanaka et al., 1997; Xia et al., 1999, 2000; Behrens et al., 2000; Brenner et al., 2000a; Uebele et al., 2000; Weiger et al., 2000).

The ß2 subunit, for example, confers rapid inactivation upon the BK_Ca channels of adrenal chromaffin cells (Wallner et al., 1999; Xia et al., 1999), and ß4 renders many of the BK_Ca channels of the brain insensitive to the scorpion toxin charybdotoxin (Meera et al., 2000). Perhaps most profound, however, the BK_Ca ß1 subunit, which is predominately expressed in smooth muscle, slows the BK_Ca channel's kinetic behavior and dramatically increases its Ca²⁺ sensitivity (McManus et al., 1995; Wallner et al., 1995; Meera et al., 1996; Cox and Aldrich, 2000; Nimigean and Magleby, 2000). In fact, mice that lack ß1 have hypertension, because the BK_Ca channels of their vascular smooth muscle lack the Ca²⁺ sensitivity required for BK_Ca-mediated feedback regulation of smooth muscle contraction (Brenner et al., 2000b). Thus, ß1 is important in the vascular system and indeed in many other smooth muscle–dependent systems as well (Nelson and Quayle, 1995; Snetkov and Ward, 1999; Bayguinov et al., 2001; Niu and Magleby, 2002; Meredith et al., 2004; Morales et al., 2004). Four ß1 subunits associate with a single BK_Ca channel (Wang et al., 2002).

How ß1 enhances the BK_Ca channel's Ca²⁺ sensitivity is not well understood. Perhaps the simplest mechanism would be for it to increase the affinities of the channel's Ca²⁺-binding sites, but this does not appear to be the case. Nimigean and Magleby (1999)(2000) found that ß1 increases the length of time that the BK_Ca channel spends in bursting states and that this effect persists in the absence of Ca²⁺. They suggested that it is this Ca²⁺-independent effect that underlies most of the channel's increased Ca²⁺ sensitivity. Furthermore, we found previously that as the Ca²⁺ concentration is raised, the concentration at which the BK_Ca channel's conductance–voltage relation begins to shift leftward is essentially unaffected by ß1 (Cox and Aldrich, 2000), a result that suggests that, at least when it is open, the channel's affinity for Ca²⁺ is not greatly altered by ß1. In fact, this study leads us to suggest that, rather than greatly altering the channel's Ca²⁺-binding properties, ß1 may be enhancing its voltage-sensing properties by shifting the equilibrium for voltage sensor activation, and therefore the channel's gating charge vs. voltage relation (Q–V relation) 100 mV toward more negative voltages. This would be expected to decrease the work that Ca²⁺ binding must do to open the channel at most voltages and thereby bring about an apparent increase in Ca²⁺ affinity at most voltages as well. Contrary to this hypothesis, however, Orio and Latorre (2005) have recently proposed that it is a decrease in effective gating charge, rather that a shift in the channel's Q–V relation, that accounts for the effects of ß1.

Here, to distinguish between these possibilities, we have measured gating currents from heterologously expressed BK_Ca channels with and without ß1 coexpression. Our results indicate that the channel's Q–V relation does shift dramatically leftward upon ß1 coexpression, with no change in gating charge. Thus, ß1 stabilizes the active conformation of the channel's voltage sensors, and this has a large effect on the Ca²⁺ sensitivity of the channel. In addition, however, in order to fully account for the increase in apparent Ca²⁺ affinity brought about by ß1, we have also found it necessary to suppose that ß1 decreases the true affinity of the closed channel for Ca²⁺.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Channel Expression
Experiments were done with a BK_Ca channel subunit clone from mouse mSlo-mbr5 (Butler et al., 1993) and a ß1 subunit clone from bovine (bß1) (Knaus et al., 1994a). In vitro transcription was performed with the mMessage mMachine kit with T3 or T7 RNA polymerase (Ambion). 0.05–250 ng of total cRNA was injected into Xenopus laevis oocytes 2–6 d before recording. Different amounts of cRNA were injected for different purposes, 0.05–0.2 ng for single channel recording, 10–50 ng for macroscopic current recording, and 150–250 ng for gating currents and limiting P_open recordings. bß1 and mSlo cRNA were mixed in a molar ratio of 2:1 before injection.

Electrophysiology
All recording were done in the inside-out patch clamp configuration (Hamill et al., 1981). Patch pipettes were made of borosilicate glass (VWR micropipettes) with 0.5–4 M resistances that were varied for different recording purposes. The tips of the patch pipettes were coated with sticky wax (Sticky Wax) 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 (Instrutech) and Pulse acquisition software (HEKA Electronik). For macroscopic current recording, data were sampled at 50 kHz and filtered at 10 kHz.

In most macroscopic current experiments, capacity and leak currents were subtracted using a P/5 subtraction protocol with a holding potential of –120 mV and leak pulses opposite in polarity to the test pulse, but with BK_+ß1 currents recorded at 10 and 100 µM Ca²⁺ no leak subtraction was performed.

Unitary currents were sampled at 100 kHz and filtered at 10 kHz. For gating current recordings, voltage commands were filtered at 7.5 kHz to limit the size of fast capacity transients, and the data were sampled at 100 kHz and filtered at 5–10 kHz. Capacity and leak currents were subtracted using a P/5 protocol with a holding potential of –120 mV and leak pulses opposite in polarity to the test pulse. All experiments were performed at room temperature, 22–24°C.

Solutions
Gating current solutions were made according to Horrigan and Aldrich (1999). Pipette solutions contained (in mM) 127 TEA-OH, 125 HMeSO₃, 2 HCl, 2 MgCl₂, 20 HEPES, pH 7.2 (adjusted with HMeSO₃ or TEA-OH). The 0.5 nM Ca²⁺ internal solution contained (in mM) 141 NMDG, 135 HMeSO₃, 6 HCl, 20 HEPES, 40 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA), 5 EGTA, pH 7.2 (adjusted with NMDG and HMeSO₃).

K⁺ current recording solutions were composed of the following (in mM): pipette solution, 80 KOH, 60 NMDG, 140 HMeSO₃, 20 HEPES, 2 KCl, 2 MgCl₂ (pH 7.20); internal solution, 80 KOH, 60 NMDG, 140 HMeSO₃, 20 HEPES, 2 KCl, 1 HEDTA or 1 EGTA, and CaCl₂ sufficient to give the appropriate free Ca²⁺ concentration (pH 7.20). EGTA (Sigma-Aldrich) was used as the Ca²⁺ buffer for solutions containing <1 µM free [Ca²⁺]. HEDTA (Sigma-Aldrich) was used as the Ca²⁺ buffer for solutions containing between 1 and 10 µM free Ca²⁺, and no Ca²⁺ chelator was used in solutions containing 100 µM free Ca²⁺. 50 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA) was added to all internal solutions to prevent Ba²⁺ block at high voltages (Cox et al., 1997b).

The appropriate amount of total Ca²⁺ (100 mM CaCl₂ standard solution; Orion Research Inc.) to add to the base internal solution containing 1 mM HEDTA to yield the desired free Ca²⁺ concentration was calculated using the program Max Chelator (http://www.stanford.edu/~cpatton/maxc.html), and the solutions were prepared as previously described (Bao et al., 2004). To change Ca²⁺ concentration, the solution bathing the cytoplasmic face of the patch was exchanged using a sewer pipe flow system (DAD 12) purchased from Adams and List Assoc. Ltd.

Data Analysis
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-squares curve fitting. Values in the text are given ± SEM.

G–V Curves
Conductance–voltage (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

(1)

and normalized to the maximum of the fit. The half-activation voltage (V_1/2) and the effective gating charge (z) were determined from the fitting.

Q–V Curves
The amount of activated gating charge (Q) at a given voltage was determined from the area under the gating current trace between 0 and 300 µs after the initiation of the voltage step. Repolarizations were to –80 mV. Each Q–V relation was fitted with a Boltzmann function and normalized to the maximum of the fit. The voltage sensor's half-activation voltage V_hc and the gating charge z_J were determined from the fitting.

Limiting P_open Analysis
P_open measurements <10^–3 were made in 3 nM Ca²⁺ with patches that contained hundreds of channels. The number of channels in a given patch (N) was determined by switching the patch into a solution that contained either 100 µM Ca²⁺ () or 10 µM Ca²⁺ (+ß1) and recording macroscopic currents at moderate to high voltages. N was than calculated as N = I/(iP_O), where i represents the single channel current at a given voltage and P_O represents the open probability at that same voltage. Both i and P_O were determined previously in separate experiments. In some experiments P_O was estimated from the G–V relation determined from the same patch. After determining the number of channels in a given patch, the membrane voltage was moved to lower voltages, the patch was superfused with a 3 nM Ca²⁺ solution, and unitary currents were recorded for 5–30 s at progressively more negative voltages. All-points histograms were then used to determine the probability of observing 0, 1, 2, 3, ... open channels at a given time, and true channel P_open was then determined as

(2)

where Ft_{open_n} represents the fraction of time n channels are open during the recording.

Fitting –V Curves Based on the Model of Horrigan et al. (1999)
Relaxation time constants as a function of voltage were calculated for Scheme I (see Fig. 5) assuming its horizontal steps equilibrate much more rapidly than its vertical steps, such that they are always at equilibrium (Cox et al., 1997a; Cui et al., 1997; Horrigan et al., 1999; Horrigan and Aldrich, 2002). Under this assumption, (V) can be calculated as a weighted average of all the vertical rate constant in Scheme I as follows:

(3)

where _x and _x represent closed-to-open and open-to-closed rate constants, respectively, and f_cx and f_ox represent the fraction of closed or open channels occupying the state that precedes each transition. These fractions for the closed channel were calculated as follows:

(4)

For the open channel, f_O0–f_O4 were calculated in the same way but using Jo rather than Jc. Each vertical rate constant was also assigned a voltage dependence as follows

(5)

where x = (0, 1, 2, 3, 4, 5) and z + z = z_L.. For a given vertical step, once the forward rate was specified, the backward rate was determined by the equilibrium parameters of the model.

(6)

Thus, to fit the –V curves in Fig. 7, 11 independent parameters were required: L, V_hc, D, z_J, z_L, z, ₀(0), ₁(0), ₂(0), ₃(0), and ₄(0). For definitions of L, V_hc, D, z_J, and z_L see RESULTS.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Steady-state Effects of ß1
The BK_Ca channel is both Ca²⁺ and voltage sensitive, and the effects of these stimuli together are often displayed as a series of conductance–voltage (G–V) relations determined over a series of Ca²⁺ concentrations (Barrett et al., 1982). Such a series, determined from currents recorded from channels expressed in Xenopus oocyte macropatches is shown in Fig. 1 C. These G–V curves were derived from channels composed of subunits alone. When the BK_Ca ß1 subunit is coexpressed with the subunit, the Ca²⁺-induced leftward shifting evident in Fig. 1 C becomes more pronounced (Fig. 1, D and E; see also Table I) (McManus et al., 1995; Wallner et al., 1995; Meera et al., 1996; Cox and Aldrich, 2000), and thus it may be said that ß1 increases the Ca²⁺ sensitivity of the BK_Ca channel in that it increases its G–V shift in response to changes in Ca²⁺ concentration (McManus et al., 1995).

View larger version (34K): [in this window] [in a new window]   Figure 1. ß1 increases the Ca2+ sensitivity of the BKCa channel. (A and B) Macroscopic currents recorded from BK channels (A) and BK+ß1 channels (B). Currents are from inside-out Xenopus oocyte macropatches exposed to 10 µM internal Ca2+. (C and D) G–V relations determined at the following Ca2+ concentrations: 0.003, 1, 10, and 100 µM for the BK channel (C) and BK+ß1 channel (D). Each curve represents the average of between 4 and 22 individual curves. Error bars indicate SEM. The solid curves are Boltzmann fits with the following parameters: BK, 3 nM Ca2+: Q = 0.93 e, V1/2 = 200.3 mV; 1 µM Ca2+: Q = 1.36 e, V1/2 = 120.6 mV; 10 µM Ca2+: Q = 1.18 e, V1/2 = 32.8 mV; 100 µM Ca2+: Q = 1.15 e, V1/2 = –2.4 mV. BK1ß1, 3 nM Ca2+: Q = 0.62 e, V1/2 = 213.1 mV; 1 µM Ca2+: Q = 0.94 e, V1/2 = 82.1 mV; 10 µM Ca2+: Q = 1.02 e, V1/2 = –59.5 mV; 100 µM Ca2+: Q = 0.96 e, V1/2 = –101 mV. (E) Plots of half-maximal activation voltage (V1/2) vs. Ca2+ concentration. The V1/2 values are from Table I. Error bars represent SEM.

View larger version (34K): [in this window] [in a new window]   Figure 2. The effects of ß1 are both Ca2+ and voltage dependent. (A–C) Ca2+ dose–response curves determined for the BK and BK+ß1 channel at (A) –40, (B) 0, and (C) +40 mV. Curves are fitted with the hill equation: =. Fit parameters are as follows: –40 mV, BK (Kd = 36.5 µM, n = 1.24); BK+ß1(Kd = 6.89 µM, n = 2.7); 0 mV, BK (Kd = 22.1 µM, n = 1.5); BK+ß1 (Kd = 3.4 µM, n = 1.9); +40 mV, BK (Kd = 7.25 µM, n = 1.6); BK+ß1(Kd = 3.68 µM, n = 1.5). (D–G) G–V relations are shown for the BK and the BK+ß1 channel at (D) 100 µM Ca2+, (E) 10 µM Ca2+, (F) 1 µM Ca2+, and (G) 3 nM Ca2+. The curves are fitted with Boltzmann functions as described in the legend to Fig. 1.

ß1's Effects on BK_Ca Gating Currents
What does the ß1 subunit do to the normal process of BK_Ca channel gating that creates these large and physiologically important effects? Previously, we addressed this question by comparing the effects of ß1 to what happens to simulated currents when various parameters in models of BK_Ca channel gating were altered (Cox and Aldrich, 2000). From this work we concluded that multiple aspects of gating are likely altered by ß1, including small changes in Ca²⁺ binding, gating charge, and the intrinsic energetics of channel opening. One large change we predicted, however, was a large ß1-induced leftward shift in the channel's charge–voltage (Q–V) relation. This, we supposed, would lower the free energy difference between open and closed states at most voltages, and thus lower as well the work Ca²⁺ binding must do to open the channel (Cox and Aldrich, 2000).

Here, to directly test this prediction we have examined BK_Ca gating currents in the absence and presence of ß1. A family of gating currents for the BK channel is shown in Fig. 3 A. These currents were recorded in the essential absence of Ca²⁺ (0.5 nM) with 1-ms voltage steps. Most notable, they are small and fast, 500–1,000 times smaller than the ionic currents we typically observe under the same conditions of channel expression (Fig. 1 A), and at +160 mV (Fig. 3 A, fourth trace down) the ON gating current decays with a time constant of 57.2 ± 4.0 µs (n = 16), and the OFF gating current at –80 mV is similarly fast ((off) = 31.2 ± 3.3 µs, n = 20). Thus, care had to be taken to ensure that what we were observing was in fact gating current and not the result of capacity current subtraction errors. We are confident, however, that these currents are indeed gating currents, as they are not seen in uninjected oocytes (second trace down). They are not seen in response to voltage pulses of equal magnitude but opposite polarity (third trace down), and they have characteristics very similar to those reported previously for the BK channel (Horrigan and Aldrich, 1999, 2002) (Table II).

View larger version (33K): [in this window] [in a new window]   Figure 3. BKCa gating currents. (Top traces) Gating current families recorded from BK (A) and BK+ß1 (B) channels with 0.5 nM internal Ca2+. The second and third traces in A and B demonstrate that gating currents are not observed in patches from oocytes that were not injected with BKCa cRNA (second) or with hyperpolarizing voltage steps (third). The lowest traces in A and B are gating currents recorded with pulses to +160 mV. Repolarizations are to –80 mV. Exponential fits to the on and off currents are indicated with dashed line. (C and D) Comparisons of on-gating current (Ig) and potassium current (IK) from BK (C) and BK+ß1 (D) channels. Pulses were to +160 mV. Ca2+ = 0.5 nM. The gating and ionic currents compared in C and D are from different patches.

The gating currents we have recorded from both BK and BK_+ß1 channels have relaxation time constants close to the theoretical time resolution of our recording system 40 µs, and so we have not analyzed the kinetics of these currents further, as they may be distorted by our hardware. What is clear, however, is that both with and without ß1, BK_Ca gating currents are very fast.

An important consequence of the speed of the BK and BK_+ß1 channels' gating charge movement is illustrated in Fig. 3 (C and D). In response to a strong depolarization, both channels' voltage sensors move almost completely (I_g) before the channels begin to open (I_K). The time constants of channel opening are 18 (BK) and 177 (BK_+ß1) times larger than those of gating charge movement. Thus, for both channels, rapid ON gating currents reflect voltage sensor movement in the channel's closed conformation (Stefani et al., 1997; Horrigan and Aldrich, 1999).

To determine Q–V relations we integrated both ON and OFF gating currents and plotted these integrals separately as a function of test potential. These integrals report the amount of gating charge that moves rapidly during each voltage pulse. Examples of Q–V curves from individual BK and BK_+ß1 patches are shown in Fig. 4 (A and B), and as is evident, both with and without ß1, there is very little difference between the BK_Ca channels' rapid ON and OFF Q–V curves. Thus, charge is not immobilized by depolarization in either case.

View larger version (21K): [in this window] [in a new window]   Figure 4. The ß1 subunit shifts the closed channel's charge–voltage (Q–V) relation leftward without changing its shape. (A) On and Off Q–V relations determined from a single BK channel patch. (B) On and Off Q–V relations determined from a single BK+ß1 channel patch. (C) Normalized averaged Qon–V relations for the BK (11 curves averaged) and BK+ß1 channels (14 curves averaged). Each curve in C is fitted with a Boltzmann function. The fit parameters are as follows: BK: zJ = 0.577 ± 0.023e, Vhc = 151 ± 1.9 mV; BK+ß1: zJ = 0.571 ± 0.025 e, Vhc = 80 ± 2.4 mV. The error bars in C represent SEM.

+ß1

+ß1

+ß1

The Current View of BK Voltage-dependent Gating

(7)

(8)

where R, T, and F have their usual meanings, z_J is the gating charge associated with a single voltage sensor, and V_hc and V_ho are the half-maximal activation voltages of the channel's Q–V relation, when the channel is either closed (V_hc) or open (V_ho). In order for voltage sensor movement to promote opening, V_ho must be more negative than V_hc.

View larger version (35K): [in this window] [in a new window]   Figure 5. The allosteric model of BKCa voltage-dependent gating of Horrigan et al. (1999). Horizontal transitions represent voltage senor movement. Vertical transitions represent channel opening. For details of the model see RESULTS and MATERIALS AND METHODS.

(9)

where L is the equilibrium constant between open and closed at 0 mV when no voltage sensors are active, and z_L is a small amount of gating charge associated with the closed-to-open conformational change.

As is the case for other voltage-gated K⁺ channels, it is fairly clear that the S4 region, and probably part of S3, forms the BK_Ca channel's voltage sensor, whose gating charge is designated here z_J (Stefani et al., 1997; Diaz et al., 1998; Horrigan and Aldrich, 1999; Hu et al., 2003). The physical basis for z_L, however, has yet to be determined, but without assigning some voltage dependence to the closed-to-open conformational change, it is not possible to fit the BK ionic current data at all well (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999; Cox and Aldrich, 2000; Cui and Aldrich, 2000; Rothberg and Magleby, 2000). Thus, the equilibrium voltage dependence of BK gating in the absence of Ca²⁺ is well described by five parameters, V_hc, V_ho, z_J, L, and z_L, and to this point our data allows us to specify two of them V_hc and z_J. To fully determine the effects of ß1 on the voltage-dependent aspects of BK_Ca channel gating at equilibrium, however, requires that we specify V_ho, L, and z_L for both channels as well. To do this we have performed the experiments described below.

Estimating ß1's Effects on the Closed-to-Open Conformational Change
At far negative voltages, where no voltage sensors are active, Eq. 9 reduces to Eq. 10 (Horrigan et al., 1999)

(10)

which can be rewritten as

(11)

Eq. 11 states that as we make the membrane voltage more and more hyperpolarized, a plot of log(P_open) vs. voltage will begin to turn away from the voltage axis, and it will reach a limiting slope that is less than the maximum slope and reflects the voltage dependence of just the closed-to-open conformational change (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999). That is, in this voltage range, the slope of the log(P_open)–V relation will be determined only by z_L, and the position of the curve on the vertical axis will be determined only by L. Thus, as has been discussed previously (Horrigan and Aldrich, 1999, 2002), by determining the BK_Ca channel's P_open vs. voltage relation at far negative potentials we can estimate z_L and L directly.

To do this, we recorded BK and BK_+ß1 macroscopic currents at depolarized voltages (+10 to +80 mV) and 10 or 100 µM Ca²⁺. From these currents we could determine the number of channels in a given patch (N) (see MATERIALS AND METHODS). Then, we lowered the Ca²⁺ concentration to 3 nM and the membrane voltage to negative values where the channels are rarely open, and recorded unitary currents. Such currents are shown in Fig. 6 (A and B). Notice, the BK channels appear to open more frequently than the BK_+ß1 channels, but the burst times of the BK_+ß1 channels appear on average longer (expanded traces). From data like that in A and B, the probabilities of observing 1, 2, 3 ... open channels at a given time were determined with all-points histograms, and these probabilities and N were then used to determine the true mean open probability of the channels in each patch (see MATERIALS AND METHODS). In this way, we could measure open probabilities as low as 10^–6.

View larger version (46K): [in this window] [in a new window]   Figure 6. Estimating L and zL from Popen at negative voltages. Unitary currents were recorded with 3 nM internal Ca2+ from BK (A) and BK+ß1(B) channels. The patch in A contained 2,859 channels. The patch in B contained 3,270 channels. Mean log(Popen)–voltage relations determined from patches like that in A (12 patches) and B (15 patches) are shown in C for the BK channel and D for the BK+ß1 channel. In C, the bottom of the curve is fitted with the following function: log(Popen) = log(L) + 0.4342zLFV/RT. The resulting parameters were log(L) = –5.66 ± 0.13, zL = 0.410 ± 0.065. In D, no submaximal limiting slope was identified.

+ß1

+ß1

+ß1

+ß1

-Relaxation vs. Voltage Relations Suggest No Change in z_L
But for a brief delay, the onset and offset of BK ionic currents can be well fitted with a simple exponential function over a very wide voltage range. ß1 does not change this; however, at 0 Ca²⁺ it does slow both activation and deactivation. On a plot of log(-relaxation) vs. voltage this is seen as an upward shift in the channel's log()–V curve (Fig. 7 C). The general shapes of the BK and the BK_+ß1 curves, however, remain similar. At far negative voltages there is a shallow region of positive slope. This transitions into a steeper region that persists until the plots reach a peak, and after the peak, -relaxation falls often steadily at high voltages. According to the Horrigan, Cui, and Aldrich model (Fig. 5, bottom), the phases of these plots are understood as follows. At far negative voltages, no voltage sensors are active, and -relaxation is determined by the rate constant of the O₀ to C₀ transition and its voltage dependence (z). At far positive voltages a similar situation obtains, and -relaxation is determined by the C₄ to O₄ rate constant and its voltage dependence (z); where z + z = z_L. In the middle, no single transition determines the time constant of relaxation; but rather, as voltage sensors become active, a weighted average of all the vertical rate constants in Scheme I prevails. Thus, just as with the log(P_open)–V relation, the model predicts that there will be a transition or inflection point in the channel's log()–V relation at the voltage where voltage sensors start to become activated, and at voltages more negative than this the plot will reach a limiting slope that reflects now the portion of z_L associated with the closing transition (z) (Horrigan and Aldrich, 2002).

View larger version (35K): [in this window] [in a new window]   Figure 7. The ß1 subunit does not alter the voltage dependence of the closed-to-open conformational change. Macroscopic ionic currents were recorded from BK (A) and BK+ß1 (B) channels in excised oocyte macropatches. Voltage steps were varied as indicated, and the time courses of relaxation were fitted with single-exponential functions. Time constants () from the fits are plotted in C. For voltages of +100 mV and greater, activation time constants are plotted. Otherwise deactivation time courses are plotted. The –V curves in C were fitted (solid lines) to a function that approximates the kinetics of Scheme I in the limit that voltage sensor movement is fast relative to channel opening and closing (see MATERIALS AND METHODS). The fit parameters were as follows: BK: held Vhc=151 mV, L = 2.2 x 10–6, zJ = 0.58 e, zL = 0.41 e, fitting yielded D = 12.6 ± 0.43, z = 0.10 ± 0.002 e, 0(0) = 7452.3 s–1, 1(0) = 4121.4 s–1, 2(0) = 5645.8 s–1, 3(0) = 851 s–1, 4(0) = 1025 s–1, 0(0) = 0.016 s–1, 1(0) = 0.114 s–1, 2(0) = 1.98 s–1, 3(0) = 3.76 s–1, 4(0) = 57.12 s–1; BK+ß1: held Vhc = 80 mV, zJ = 0.57 e, fitting yielded L = 3.3 x 10–6 ± 6.4 x 10–6, zL = 0.46 e, D = 10.4 ± 6.4, z = 0.17 e, 0(0) = 931.7 s–1, 1(0) = 213.2 s–1, 2(0) = 547.8 s–1, 3(0) = 333.5 s–1, 4(0) = 126.7 s–1; 0(0) = 0.003 s–1, 1(0) = 0.007 s–1, 2(0) = 0.198 s–1, 3(0) = 1.251 s–1, 4(0) = 4.934 s–1. Both curves are also fitted (dashed lines) at far negative voltages with the following function: =. Fit parameters are as follows: BK (voltages <–180 mV) (0) = 6940.8 s–1, z = 0.11 e; BK+ß1 (voltages <–280 mV) (0) = 1808.7 s–1, z = 0.11 e.

+ß1

+ß1

+ß1

Estimating L and V_ho With and Without ß1
To this point then we have specified V_hc, z_J, and z_L for both channels, and left to specify are V_ho for the BK channel, and V_ho and L for the BK_+ß1 channel. One way we have attempted to estimate these parameters is to fit the two curves in Fig. 7 C with Eq. 12 below, which approximates Scheme I's –V relation in the limit that voltage sensor movement is much faster than channel opening and closing (Cox et al., 1997a; Horrigan and Aldrich, 2002; for details of the approximation see MATERIALS AND METHODS). As this condition applies for both channels over much of the voltage range, such an approximation is likely to be reasonably good. Indeed, Eq. 12 fits both curves quite well (Fig. 7 C, solid lines).

(12)

Here _i and _i are the forward and backward rate constants enumerated in Fig. 7 (bottom) and f_Oi and f_Ci represent the fraction of open channels or closed that occupy state O_i or C_i respectively. In fitting the BK log()–V curve we held V_hc, z_J, L, and z_L to the values we estimated from gating current and limiting P_open measurements, leaving only V_ho to vary along with z and five rate constants, one for each vertical step in Scheme I. The resulting fit yielded z = 0.11 and V_ho = +39 mV. For the BK_+ß1 fit we adjusted V_hc to the value we obtained from our BK_+ß1 gating current measurements, +80 mV, z_J was again fixed, and L was now allowed to vary freely along with z_L, V_ho, z, and again five rate constants. The resulting fit yielded V_ho = –25 mV, z = 0.15, and L = 3.3 x 10^–6, z_L = 0.46 (for standard deviations of fit parameters see figure legend). Thus, this analysis suggests, as we surmised above, that z_L and z change little, if any, with ß1 coexpression, but that V_ho moves 64 mV leftward, while L perhaps increases slightly (2.2 x 10^–63.3 x 10^–6) but remains on the order of 10^–6.

A more direct way to measure V_ho for either channel would be to measure gating charge movement exclusively when the channel is open. This, however, requires large prolonged depolarizations that we have found technically unfeasible. Another way we can estimate V_ho, however, and indeed also L for the BK_+ß1 channel, is to simply fit each channel's P_open–V relation with Eq. 9, while holding the parameters we have already determined constant. Since for the BK channel we have specified four of five parameters, and for the BK_+ß1 channel three of five, we expect such fits to be very well constrained.

To do this we combined our limiting P_open data (Fig. 6) with macroscopic current data (Fig. 2 G) to obtain P_open–V curves that are well determined over large ranges of both voltage and P_open. Fig. 8 shows these curves fitted with Eq. 9. For the BK fit in A, V_hc, z_J, L, and z_L were set to the following values: z_J = 0.58 e, V_hc = 151 mV, z_L = 0.41 e, L = 2.2 x 10^–6, and D was allowed to vary freely. This yielded D = 16.8, which indicates a V_ho value of +27 mV, similar to a previous report (Horrigan and Aldrich, 1999) (Table II). Similarly, for the BK_+ß1 fit (Fig. 8 B, solid line), V_hc, z_J, and z_L were set as follows: z_J = 0.57 e, V_hc = 80 mV, z_L = 0.41 e, and the fit yielded a D value of 12.8 that equates to V_ho = –34 mV, and L = 2.5 x 10^–6. Thus ß1 is estimated here to shift V_ho leftward 61 mV (see simulations in Fig. 8 C) but it has almost no effect on L.

View larger version (23K): [in this window] [in a new window]   Figure 8. Estimating L and Vho from Popen–V curve fits. (A) The Po–V relation of the BK channel at 3 nM Ca2+ is shown over a wide range of voltages. At +60 mV and below, the data points are from unitary current measurements; above +60 mV, the data are from macroscopic current measurements. The curve displayed represents the average of 35 experiments, and error bars represent SEM. The data are fitted with Eq. 9 as described in RESULTS. Free parameters: D = 16.8 ± 0.28. (B) The Po–V relation of the BK+ß1 channel. The curve displayed represents the average of 43 experiments, and error bars represent SEM. As in A, the data are fitted with Eq. 9. Free parameters: D = 12.8 ± 0.55, L = 2.53 x 10–6 ± 0.55 x 10–6. The dashed red curve is the fit from A placed here for ease of comparison. (C) Simulated Q–V relations for the open BK and BK+ß1 channels demonstrating the –61 mV shift induced by ß1 that the fits in A and B predict. The functions displayed are =, with Vho equal to 27 mV (BK) and –34 mV (BK+ß1) and zJ = 0.58 (BK), zJ = 0.57 (BK+ß1).

ß1 Affects Ca²⁺ Binding
The question still remains, however, as to whether these changes are enough to explain the changes in Ca²⁺ sensitivity described in Figs. 1 and 2. To address this issue we have incorporated our findings into a model of BK_Ca channel gating that takes into account both Ca²⁺ and voltage sensing.

Our recent work suggests that the BK_Ca channel has two sets of four high-affinity Ca²⁺ binding sites, which are structurally distinct but have similar binding properties (Bao et al., 2002, 2004; Xia et al., 2002). Assuming one site does not affect another, and the channel's voltage sensors and Ca²⁺ binding sites also act independently, this information can be combined with Scheme I to produce a model of BK_Ca channel gating that considers both Ca²⁺ binding and voltage sensing (Cox and Aldrich, 2000; Cui and Aldrich, 2000; Rothberg and Magleby, 2000; Zhang et al., 2001; Horrigan and Aldrich, 2002). The open probability of such a model is given by Eq. 13:

(13)

where now, as compared with Eq. 9, two terms has been added to the denominator that each contain a set of Ca²⁺ dissociation constants, one set for each binding site (K_C1, K_O1; K_C2, K_O2). Here, Ca²⁺ binding promotes opening by binding more tightly to the open channel than the closed, and thus two constants are specified for each type of site. The c subscript denotes the closed channel and the o subscript, the open channel. Because, both types of binding sites appear to have similar binding properties, we may simplify Eq. 13 to Eq. 14:

(14)

where now eight equivalent binding sites are considered with binding constants K_C and K_O.

To see, then, if the changes in V_hc and V_ho that we have observed upon ß1 coexpression are sufficient to account for the BK channel's enhanced Ca²⁺ response, for each channel type, we fitted a series of G–V relations with Eq. 14 (Fig. 9). For the BK fit (Fig. 9 A), V_hc, V_ho, z_J, L, and z_L were held at the values we determined from our experiments in the absence of Ca²⁺ (Table II), and only K_C and K_O were allowed to vary. Still a reasonably good fit was obtained that captured well the shifting nature of the BK channel's G–V relation as a function of Ca²⁺ concentration. This fit yielded K_C = 3.71 µM and K_O = 0.88 µM, similar to our previous estimates (Bao et al., 2002).

View larger version (64K): [in this window] [in a new window]   Figure 9. ß1 also affects Ca2+ binding. (A) BK G–V relations at a series of Ca2+ concentrations fitted simultaneously (solid curves) with Eq. 14. Only KC and KO were allowed to vary. The fit yielded KC = 3.71 µM and KO = 0.88 µM. The other parameters of the fit were determined from experiments performed with nominally 0 Ca2+ (3 nM) (Vhc = 151 mV, L = 2.2 x 10–6, Vho = 27 mV, zJ = 0.58, zL = 0.41). (B) The fit from A is superimposed on a series of BK+ß1 G–V curves. (C) The voltage-sensing parameters of the model were altered to reflect the changes that occur as ß1 binds, Vho = (27–34 mV), Vhc = (15180 mV), L = (2.2 x 10–62.5 x 10–6). (D) With BK+ß1 voltage-sensing parameters KC and KO were allowed to vary freely, yielding the fit shown and KC = 4.72 µM, KO = 0.82 µM. (E) Here, the BK+ß1 voltage-sensing parameters were used for the fit, and ß1 was allowed to influence only half of the channels' eight Ca2+-binding sites. The data are fit with Eq. 13. KC1 and KO1 were held at 3.71 µM and 0.88 µM, respectively. KC2 and KO2 were allowed to vary freely, yielding KC2 = 5.78 µM, KO2 = 0.73 µM. (F) The data are again fit with Eq. 13 but now KO2 was held at 0.88 µM and only KC2 was allowed to vary. This yielded KC2 = 7.14 µM.

+ß1

+ß1

To determine then what is required to fully account for the BK_+ß1 G–V relation as a function of Ca²⁺, we fit the BK_+ß1 G-V relations with Eq. 14, now fixing the voltage-sensing parameters to their BK_+ß1 values (V_hc = 80 mV and V_ho = –34 mV, L = 2.5 x 10^–6, z_L = 0.41) and allowing K_C and K_O to vary. The resulting fit is shown in Fig. 9 D. To account for the additional leftward shifting K_C increases from 3.71 to 4.72 µM, while K_O declines slightly from 0.88 to 0.82 µM. This causes the ratio K_C/K_O to increase from 4.2 to 5.7.

Thus, our analysis suggests that ß1 has a very small effect (<10%) or perhaps no affect on Ca²⁺ binding when the channel is open, consistent with our earlier study (Cox and Aldrich, 2000), and it reduces the affinity of each binding site for Ca²⁺ when the channel is closed, increasing K_C 27%. It is perhaps surprising that such small changes in affinity can have such a dramatic effect on the position of the channel's G–V relation at high Ca²⁺ concentrations, but in fact this should be expected, as at saturating Ca²⁺ the equilibrium constant between open and closed depends on