Large conductance Ca2+-activated K+ channels (BK channels) gate open in response to both membrane voltage and intracellular Ca2+. The channel is formed by a central pore-gate domain (PGD), which spans the membrane, plus transmembrane voltage sensors and a cytoplasmic gating ring that acts as a Ca2+ sensor. How these voltage and Ca2+ sensors influence the common activation gate, and interact with each other, is unclear. A previous study showed that a BK channel core lacking the entire cytoplasmic gating ring (Core-MT) was devoid of Ca2+ activation but retained voltage sensitivity (Budelli et al. 2013. Proc. Natl. Acad. Sci. USA. http://dx.doi.org/10.1073/pnas.1313433110). In this study, we measure voltage sensor activation and pore opening in this Core-MT channel over a wide range of voltages. We record gating currents and find that voltage sensor activation in this truncated channel is similar to WT but that the coupling between voltage sensor activation and gating of the pore is reduced. These results suggest that the gating ring, in addition to being the Ca2+ sensor, enhances the effective coupling between voltage sensors and the PGD. We also find that removal of the gating ring alters modulation of the channels by the BK channel’s β1 and β2 subunits.

## Introduction

Large conductance BK potassium channels are activated by both voltage and intracellular calcium (Marty, 1981; Pallotta et al., 1981; Latorre et al., 1982). Opening of BK channels in muscle and neurons provides rapid efflux of potassium ion and thus hyperpolarizes the membrane potential, which provides a negative feedback to regulate membrane excitability and [Ca2+]i. These properties allow BK channels to play important roles in various physiological processes, such as neural excitation (Adams et al., 1982; Lancaster and Nicoll, 1987; Robitaille et al., 1993), smooth muscle contraction (Brayden and Nelson, 1992; Wellman and Nelson, 2003), hormone secretion (Petersen and Maruyama, 1984; Braun et al., 2008), hearing (Hudspeth and Lewis, 1988a,b; Wu et al., 1995), circadian rhythms (Meredith et al., 2006), and gene expression (Li et al., 2014).

BK channels are formed by four identical Slo1 subunits (Atkinson et al., 1991; Adelman et al., 1992; Shen et al., 1994; Wei et al., 1994). Each Slo1 subunit contains three distinct structural and functional domains: a voltage sensor domain (VSD) including the membrane spanning segments S1–S4 to sense membrane potential changes; a pore-gate domain (PGD), including the membrane spanning segments S5–S6 involved in opening and closing to control K+ ion permeation; and a large cytosolic domain (CTD), containing two Ca2+-binding sites (Schreiber and Salkoff, 1997; Bao et al., 2002; Shi et al., 2002; Xia et al., 2002; Zhang et al., 2010), to sense intracellular Ca2+. The Slo1 subunit also contains an additional transmembrane segment S0 at the N terminus of the VSD (Meera et al., 1997). A 20–amino acid peptide (the C-Linker) covalently links the PGD and the CTD. The membrane-spanning VSD and PGD are thought to form a structure with a central pore comprised of PGD contributions from all four Slo1 subunits and four VSDs located at the periphery (Long et al., 2005; Hite et al., 2015; Tao et al., 2017). The CTD from all four subunits forms a ring-like structure known as the gating ring (Wu et al., 2010; Yuan et al., 2010, 2011) that is covalently connected to the membrane-spanning channel structure with the four C-linkers. In addition, the gating ring also makes noncovalent interactions with the VSD (Hu et al., 2003; Yang et al., 2008, 2013; Hite et al., 2017; Tao et al., 2017).

Voltage can activate BK channels in the absence of intracellular Ca2+, and Ca2+ can activate the channel in the absence of voltage sensor activation (Meera et al., 1996; Cui et al., 1997; Horrigan et al., 1999; Horrigan and Aldrich, 2002; Yang et al., 2015). These results suggest that distinct mechanisms can control the voltage- and Ca2+-dependent opening of the BK channel. In contrast, Ca2+ affects voltage-dependent gating, whereas voltage alters Ca2+-dependent gating, suggesting an interrelationship between the two mechanisms of gating (Barrett et al., 1982; Cui et al., 1997). Allosteric models have been developed to integrate both Ca2+ and voltage-dependent activation (Cox et al., 1997; Horrigan et al., 1999; Horrigan and Aldrich, 2002), in which three structural domains, the PGD, VSD, and CTD, can undergo separate conformational changes but also are allosterically coupled to one another, i.e., the conformation of one domain affects conformational changes in the other two. Based on this mechanism, the cytosolic gating ring may affect voltage sensor movements and the voltage-dependent opening of the channel. The interactions among VSD, PGD, and CTD are further modulated by BK channel β subunits (Niu et al., 2004), which alter the voltage- and Ca2+-dependent activation (Tseng-Crank et al., 1996; Behrens et al., 2000; Orio et al., 2002).

Recently, Budelli et al. (2013) reported that a mutation of the mSlo1 channel, in which the entire CTD was replaced with an 11–amino acid Kv mini-tail (Core-MT channel), can open in response to membrane depolarization. Confirming the expectation (Xia et al., 2002, 2004), there was no Ca2+ sensitivity for the Core-MT channel because both proposed Ca2+-binding sites located in the CTD were removed. The voltage-dependent activation was also right shifted, as might be expected if the linkers apply a passive tension to the PGD, as proposed (Niu et al., 2004). The Core-MT channel provides a tool to study the function of the gating ring in voltage-dependent activation of BK channels. It also provides an excellent opportunity to reveal the allosteric action of the CTD on the VSD and the opening of the pore and to study the interaction of β subunits.

In this study, we measure voltage sensor activation and pore opening of the Core-MT channel for comparison with WT mSlo1 over a wide range of voltages. We find that removal of the gating ring greatly alters channel opening. The open probability of Core-MT is enhanced at negative voltages but reduced at positive voltages, resulting in a shallower voltage dependence of open probability as well as a pronounced 60-mV right shift to more positive potentials for half activation. In contrast, the voltage sensor activation in Core-MT channels measured with gating currents is left shifted a small amount (−21 mV) with little effect on the voltage dependence of activation. These results indicate that the coupling between voltage sensor activation and opening of the gate is reduced in Core-MT channels. We also studied the modulation of Core-MT by β1 and β2 subunits. Our results provide insights into the interactions among structural domains of BK channel α and β subunits. The results also shed light on the mechanisms underscoring these interactions.

## Materials and methods

### Mutagenesis and expression

All mutations were made by using overlap-extension PCR with Pfu polymerase (Agilent Technologies) from the mbr5 splice variant of mslo1 (Butler et al., 1993). All PCR-amplified regions were confirmed by sequencing. cRNA was synthesized in vitro with T3 polymerase (Ambion), and an amount of 0.05–50 or 150–250 ng/oocyte RNA for recording ionic and gating currents, respectively, was injected into oocytes (stage IV–V) from female Xenopus laevis. When α subunits were coexpressed with β subunits, the RNA ratio was 1:4. The WT human β1 subunit construct and inactivation-removed human β2 construct (Wallner et al., 1999; Xia et al., 2003) were used in this paper. The injected oocytes were incubated for 2–7 d at 18°C.

### Electrophysiology

Inside-out patches were used to record Ionic currents with an Axopatch 200-B patch-clamp amplifier (Molecular Devices) and Pulse acquisition software (HEKA). Borosilicate pipettes with 0.5–1.5 MΩ resistance were used for inside-out patches from oocyte membrane. The current signals were then low-pass-filtered at 10 KHz and digitized at 20-µs intervals. A P/4 protocol with a holding potential of −120 mV was used to remove capacitive transients and leak currents. Solutions used in recording ionic currents were as follows. (a) Pipette solution (mM): 140 potassium methanesulfonic acid, 20 HEPES, 2 KCl, and 2 MgCl2, pH 7.2. (b) The nominal 0 µM [Ca2+]i solution (mM): 140 potassium methanesulfonic acid, 20 HEPES, 2 KCl, 5 EGTA, and 22 mg/liter (+)-18-crown-6-tetracarboxylic acid (18C6TA), pH 7.2. There is ∼0.5 nM free [Ca2+]i in the nominal 0 [Ca2+]i solution. (c) Basal bath (intracellular) solution (mM): 140 potassium methanesulfonic acid, 20 HEPES, 2 KCl, 1 EGTA, and 22 mg/liter 18C6TA, pH 7.2. CaCl2 was added to the basal solution to obtain the desired free [Ca2+]i, which was measured by a Ca2+-sensitive electrode (Thermo Fisher Scientific).

Gating currents were also recorded from inside-out patches and the currents sampled at 200 kHz and filtered at 20 kHz with leak subtraction using a −P/4 protocol. The pipette solution contained (mM) 127 TEA hydroxide, 125 methanesulfonic acid, 2 HCl, 2 MgCl2, and 20 HEPES, pH 7.2, and the internal solution contained (mM) 141 NMDG, 135 methanesulfonic acid, 6 HCl, 20 HEPES, and 5 EGTA, pH 7.2. All chemicals were from Sigma-Aldrich unless otherwise noted, and all the experiments were done at room temperature (22–24°C).

Single-channel currents for Fig. 3 (A–D) were recorded at room temperature (22–25°C) with an Axopatch 200B and sampled at 200 KHz with a Digidata 1322A (Molecular Devices). Filtering for analysis was at 5 kHz. The pipette solution contained (mM) 160 KCl, 10 HEPES, 10 MES, and 2 MgCl2, pH 7.0. The bath (intracellular) solution contained (mM) 160 KCl, 10 HEPES, 10 MES, and 5 HEDTA, pH 7.2. The calculated free Ca2+ was <3 nM based on 4.3 µM total Ca2+ in the solution determined by atomic absorption spectrophotometry from previous experiments. A free Ca2+ <3 nM is 30 times less than the 0.1 µM Ca2+ required to initiate activation of WT BK channels by Ca2+i (Nimigean and Magleby, 2000).

### Single-channel analysis for Fig. 3 (A–D)

Core-MT channel i-V plots are based on the fully open current level. Cursor lines in Axopatch Clampfit were adjusted by eye to measure the single-channel current amplitudes (Brelidze et al., 2003). The approach used to estimate POMax for Core-MT channels is detailed in the Results. We also tried estimating POMax for Core-MT with ensemble variance analysis. The PO was apparently too low at the highest voltage we could apply to obtain a sufficiently large number of sweeps to define a reliable fit, as might have been expected from theoretical studies (Alvarez et al., 2002; Lingle, 2006).

### Further analysis

Relative conductance was determined by measuring macroscopic tail current amplitudes at −80 or −120 mV. The conductance-voltage (G-V) relationship was fitted with the Boltzmann function:

$G/G Max =1/( 1+exp( −ze o ( V–V 1/2 )/kT ) )= 1/( 1+exp( ( V 1/2 –V )/b ) ),$
(1)

where G/GMax represents the ratio of conductance to maximal conductance, z is the number of equivalent charges, eo is the elementary charge, V is membrane potential, V1/2 is the voltage where G/GMax reaches 0.5, k is Boltzmann’s constant, T is absolute temperature, and b is the slope factor with units of millivolts, where b gives the change in millivolts required for an e-fold change in PO at very low PO. Each G-V relationship was averaged from 3–15 patches, and error bars in the figures represent SEMs. SEM estimates from the Boltzmann fitting are in the figure legends.

To measure NPO (total average open probability for all the channels N in a patch) at different negative voltage for Fig. 4 (B and C), we stimulated patches containing hundreds or thousands of channels with a long pulse (10 s) at each voltage. The currents (Fig. 4 A) were obtained by using the measured currents to subtract a baseline. All opening events were integrated (area = currents × time), which was then divided by single-channel current and total time to obtain NPO.

The estimation of the total number of channels expressed in a membrane patch has been described previously (Horrigan et al., 1999; Cui and Aldrich, 2000) and is based on the equation

$I=NγPO(V−EK)=Ni.$
(2)

In Eq. 2, i is single-channel current and i = γPO(V − EK). For WT mSlo1, N was estimated by measuring the macroscopic current at 100 mV in the presence of 100 µM [Ca2+]i, where the single-channel conductance is 273 pS and PO is ∼1.0 (Yang et al., 2010). For the Core-MT mutation, we used a single-channel conductance (220 pS) and macroscopic current at 250 mV to estimate N. The PO at this voltage was calculated based on the Boltzmann fitting of Core-MT G-V relation (Fig. 2 B; G/GMax = 0.61 at 250 mV; PO = (G/GMax)POMax), and POMax is PO at the voltage when G/GMax reaches the plateau of 1. POMax of Core-MT was assumed to be the same as E321A/E324A Core-MT (for details see Results and Fig. 3 [C and D]).

### Model fitting

The HCA model (Horrigan et al., 1999) has been successfully used to describe voltage-dependent activation of BK channels. However, the HCA model does not apply to the case where the maximum open probability (POMax) is <1. To use the HCA model to describe voltage-dependent gating of Core-MT that shows a POMax <1 (see Results), we propose an extended HCA model by adding “preopen” (intermediate) states, which are closed states immediately preceding open states in gating of BK channels (Ferguson et al., 1993; Rothberg and Magleby, 1998). The preopen state is connected to the open state with a voltage-independent equilibrium constant K1 (Scheme 1).

In Scheme 1, each square represents a voltage sensor at the resting state (R), whereas each solid circle in a square represents a voltage sensor in the active state. Open squares represent the closed state (C), gray squares represent the preopen state (C′), and dark squares represent the open state (O). The C-C′ equilibrium constant increases D-fold for each voltage sensor activated (R to A), and reciprocally, the R-A equilibrium constant increases D-fold when the channel moves from the closed state to the preopen state. Channels can be opened with an equilibrium constant K1 after reaching the preopen state.

PO-V curves of the WT and Core-MT channels (Figs. 4 C and 5, A–C) were fitted with the extended HCA model:

$P O =K 1 L 1 ( 1+JD ) 4 /( ( 1+K 1 )L 1 ( 1+JD ) 4 +( 1+J ) 4 ),$
(3)

where

$L 1 ( V )=L 1 exp( Z L V/kT )$
(4)
$J( V )=J 0 exp( Z J V/kT )=exp( ( V−V hc )Z J /kT )$
(5)
$D=exp( ( V hc −V ho )Z J /kT ).$
(6)

L1 is the equilibrium constant between the closed and the preopen channels ([C′]/[C]) at 0 mV, J represents the equilibrium constant for voltage sensor activation in each subunit, Vhc is the half-activation voltage at the closed state, Vho is the half-activation voltage at the preopen state, ZJ is the charge movement during a voltage sensor activation, ZL is the charge movement during the C to C′ transition, D is the allosteric factor coupling voltage sensor activation to channel opening, and eo, k, T, and V were defined as in Eq. 1, where kT/eo at 23°C = 25.5 mV. The Qon-voltage plots give Vhc and ZJ from Boltzmann fits.

Automated fitting in Excel of the PO-V data with Eqs. 3, 4, and 5 and fixed parameters K1, ZJ, and Vhc determined directly from the experimental data then gave estimates of the fitting parameters D, ZL, and L1. The fitting was done by using Solver in Excel (Microsoft) with the GRC nonlinear search routine to minimize the squares of the errors between the observed and predicted PO. ZL and L1 were converted to log10 for fitting and then converting back. Each fit was typically started several times with different starting parameters for D, ZL, and L1 to assure that the least squared error was obtained.

Estimates for the SEMs for D, ZL, and L1 for both WT and Core-MT channels were obtained by automated fitting of individual experiments with n = 4 for Core-MT and n = 6 for WT. Significance was determined with the t test. The data points plotted in the figures in the paper are the averages of data points from multiple experiments, and it is averaged data points that were fitted to obtain the means of the parameters presented in the paper.

## Results

### The effects of gating ring removal on gating charge movements in BK channels

Activation of the WT mSlo1 channel depends on intracellular Ca2+ and voltage, and positive voltages can activate the channel in the absence of Ca2+ (Cui et al., 1997). The deletion of the gating ring in the Core-MT channel completely eliminated Ca2+ dependence of channel activation and turned the channel into a voltage-gated K+ (Kv) channel (Budelli et al., 2013). This mutation provides an excellent opportunity to reveal the effects of the gating ring on the voltage-dependent gating of mSlo1. Voltage-dependent gating in Kv channels starts with voltage sensor activation in response to membrane depolarization. We first studied voltage sensor activation of both the WT and Core-MT channels by recording gating currents (Fig. 1). Large gating currents could be recorded from membrane patches expressing Core-MT channels (Fig. 1 A), likely reflecting the expression of a large number of the channels. The voltage for half-activation (V1/2) of gating charge movements (Q) of Core-MT shifted 21 mV to more negative voltages relative to WT, but the slope of the Q-V relation for mutant and WT channels remained the same (Fig. 1 B). Thus, removal of the gating ring produces a small left-shift in the voltage required for voltage sensor activation, with little change in the voltage sensitivity of activation.

### Deletion of the gating ring alters voltage-dependent opening of BK channels

Core-MT channels showed robust macroscopic currents at positive voltages (Fig. 2 A). Compared with WT mSlo1 channels, the voltage for half activation (V1/2) of Core-MT channels right shifted 60 mV to more positive voltages, with a reduction in slope factor from 20.5 to 27.6 mV (Fig. 2 B). These results are consistent with those in the original study of Core-MT function (Budelli et al., 2013).

The 60-mV right shift of V1/2 for the G-V curves of Core-MT made it technically difficult to observe the plateau of the Core-MT G-V relation because the extremely positive voltages required to reach the maximum open probability disrupted the membrane. The lack of a clear plateau made it difficult to reliably estimate V1/2 and the slope factor by fitting the Boltzmann equation to the G-V relation (see Materials and methods). Previous work indicated that the double mutation E321A/E324A applied to WT channels left-shifted V1/2 ∼100 mV with no effect on the slope (Zhang et al., 2014). If this same mutation applied to Core-MT channels gives a similar left shift, then this would shift the activation of WT and Core-MT channels into a voltage range where the plateaus of the G-V relations of both channel types could be determined. To investigate this possibility, we measured the G-V relations of WT and Core-MT channels with the added mutations E321A/E324A.

For both WT and Core-MT channels, the E321A/E324A mutations left-shifted V1/2 ∼100 mV with no change in slope (Fig. 2, B and D). These large left shifts allowed us to clearly observe the plateaus of the G-V curves to improve the reliability of the Boltzmann fits. For E321A/E324A mutated channels, removing the gating ring reduced the slope factor from 19.5 to 28.9 mV and right-shifted V1/2 73 mV (Fig. 2 D). These findings were essentially the same as for channels without the E321A/E324A mutations (Fig. 2 B). Thus, these observations indicate that with or without the E321A/E324A mutations to improve accuracy of measurement, removing the gating ring decreased the voltage sensitivity of activation and right-shifted the V1/2 for activation. Thus, the removal of the gating ring shifts the G-V relation to more positive voltages with a reduced slope but shifts the Q-V relation in the opposite direction to more negative voltages with little change in slope.

### Deleting the gating ring decreases single-channel current amplitude

Converting G-V plots to PO-V plots requires knowing the single-channel conductance (see Materials and methods). To estimate single-channel conductance, single-channel current records were obtained from WT and Core-MT channels over a range of voltages (representative records in Fig. 3 A). For WT channels, single-channel conductance was 316 ± 5 pS at 80 mV, decreasing to 281 ± 3 pS at 160 mV; for Core-MT channels, single-channel conductance was 243 ± 3 pS at 80 mV, decreasing to 226 ± 9 pS at 160 mV (Fig. 3 B). The plot of the i-V data indicate that removing the gating ring decreased single-channel conductance a mean of 22.6 ± 1.6% over the examined voltage range of 80–160 mV. A reduced single-channel conductance for Core-MT channels has been reported previously (Budelli et al., 2013). The decline in single-channel conductance at positive voltages for WT channels mainly arises from voltage-dependent block of the pore by protons from the intracellular side (Brelidze and Magleby, 2004); a similar blocking mechanism may also apply to the Core-MT channels.

### Deletion of the gating ring reduces POMax for E321A/E324A Core-MT channels

An observation that a G-V curve reaches a plateau does not indicate that the PO of the underlying single-channels approaches 1.0 but only that the PO has reached a maximum steady-state value, POMax. The 60-mV right shift in the G-V curve for Core-MT compared with WT (Fig. 2 B) was sufficiently large that it was not possible to collect macroscopic currents and single-channel data at sufficiently high voltages to obtain a clear plateau to estimate the POMax for Core-MT. Consequently, we took advantage of the added double mutation E321A/E324A to the Core-MT channel to left-shift the G-V curve by 90 mV (Fig. 2 D). We then measured NPO from the single-channel current records over a range of voltages (Fig. 3, C and D), where N is the number of channels in the patch. Dividing NPO at each voltage by the maximum number of channels simultaneously open at the highest voltage recording (≥200 mV) in the same patch then gave estimates of PO, which was 0.21 at 200–220 mV. We then fit this PO versus voltage relationship with a Boltzmann equation to obtain a projected POMax of 0.27 for the E321A/E324A Core-MT channel (Fig. 3 D). The observation that the macroscopic G-V curve (Fig. 2 D) and the single-channel PO-V curve (Fig. 3 D) for E321A/E324A Core-MT channels activate and saturate over the same voltage range supports that the less well defined single-channel PO is saturating; if the current is saturating in the macro currents, it also would be saturating in the single-channel currents. The POMax for E321A/E324A mutated WT channels approached 0.95 with Boltzmann fitting (Fig. 3 D), which is the same as POMax for WT (Horrigan et al., 1999) and in agreement of our present measurement of ∼0.94 in 0 [Ca2+]i), indicating that the E321A/E324A mutation added to WT did not increase, and more importantly, did not decrease POMax. If the E321A/E324A mutation added to Core-MT also does not alter POMax, then the POMax for Core-MT channels would be the same as for E321A/E324A Core-MT channels, which was 0.27. This estimate of 0.27 would place an upper limit on POMax for Core-MT channels, as estimating N by counting current levels, even for prolonged recordings, can underestimate N when PO is small.

### Deleting the gating ring increases PO/POMax at negative potentials

G-V relations obtained from macroscopic currents (Fig. 2) can measure voltage activation for voltages where G/GMax is greater than a few percent. However, previous studies have shown that the PO of WT BK channels increases five orders of magnitude, from ∼10−7 to ∼0.01, when voltages increase from −140 to 100 mV in 0 Ca2+ (Horrigan et al., 1999; Yang et al., 2010; Zhang et al., 2014). To examine to what extent the removal of the gating ring alters channel activity over these potentials, currents were recorded from membrane patches containing large numbers of WT or Core-MT channels. For such conditions, the PO of individual channels in the membrane patch was low, but because of the large number of channels in the patch, single-channel opening events were frequently observed (Fig. 4 A). The single-channel records for WT and Core-MT channels were converted to PO/POMax as described in the Materials and methods and plotted against membrane potential in Fig. 4 B. Deleting the gating ring increased PO/POMax 30-fold at very negative potentials for Core-MT compared with WT.

### Deletion of the gating ring reduces voltage sensor–pore coupling

In Fig. 4 C, we combine the results of the voltage dependence of channel opening measured from single-channel currents in Fig. 4 B with the macroscopic currents in Fig. 2, assuming that POMax for Core-MT channels is 0.27. Over the voltage range of ∼400 mV, PO for WT increased ∼107-fold, whereas PO for Core-MT increased ∼105-fold. This ∼100-fold reduction in the total increase in PO comes from an increased PO at negative voltages (Fig. 4 B) and a reduced PO at positive voltages. Hence, removal of the gating ring greatly reduces the voltage dependence of channel opening. This is most easily seen by looking at the shallower slope for Core-MT compared with WT in the middle voltage range (Fig. 4 C). This marked reduction in the voltage dependence of channel opening is in contrast to the small change in the voltage-dependent gating charge movements (Fig. 1 B). These results (Figs. 1, 2 B, and 4 C) indicate that the voltage sensor movements in Core-MT promote the opening of the gates less effectively than in WT. Thus, the deletion of gating ring reduces the coupling between the voltage sensor movements and gate opening in BK channels.

### A quantitative description of the reduced VSD-PGD coupling in Core-MT

The experimental data in Fig. 4 clearly show that the deletion of gating ring results in an overall reduction of the VSD-pore coupling, such that the increase of channel open probability over the entire voltage range of VSD activation is reduced to ∼1% of that for WT channel. It has been shown previously that voltage-dependent gating of BK channels follows an allosteric mechanism involving several molecular processes that can be well described by an allosteric HCA model (Horrigan et al., 1999). We considered using the HCA model to fit our experimental data to quantitatively describe the changes in voltage-dependent gating caused by the removal of gating ring to dissect the underlying molecular processes involved. However, the original HCA model was developed based on the WT channel in which the POMax reaches 1 so that the model does not include any mechanism that describes BK channel gating with a POMax <1.

To adopt the HCA model to fit the data from both WT and Core-MT channels, we introduce a preopen state to extend the HCA model. The experimental data are then fitted with this extended HCA model (see Materials and methods). The extended HCA model includes voltage sensor activation from the resting state to the activated state ((R-A)4, for four subunits), channel opening through a preopen state C′ (C-C′-O), and the voltage sensor–pore coupling factor (D), as shown in Scheme 1. The added preopen state is a straightforward extension of the HCA model that is consistent with the experimental results of a reduced POMax for the Core-MT channel and is supported by previous experimental observations suggesting a preopen state (Ferguson et al., 1993; Rothberg and Magleby, 1998). The model assumes that activation of the VSD does not open the channel directly but increases the occupancy of the preopen state, which increases PO via an intrinsic voltage-independent transition.

At high voltage where G/GMax reaches a plateau, (1 + J)4 << (1 + JD)4, then

$P OMax =K 1 /( 1+K 1 ).$

From our measurements where POMax = 0.94 for WT channels and 0.27 for Core-MT channels, we obtain K1= 15.7 for WT channels and 0.37 for Core-MT channels (Table 1). Estimates of Vhc and ZJ were obtained from the Q-V plots in Fig. 1 B, and then the PO-V data were fit to the extended HCA model with an automatic fitting algorithm (see Materials and methods) to obtain estimates of the free parameters L1, ZL, and D (Table 1), which are generally similar for WT to those from previous HCA model fittings (Horrigan et al., 1999; Zhang et al., 2010), considering that the models could have different constraints. Comparing the values of the fitted parameters of the WT and Core-MT channels, we found that the removal of gating ring alters various aspects of voltage-dependent gating of the channels (Fig. 4 C and Table 1). Most notably, D, the equilibrium factor that drives the gating from the closed to the preopen closed states in Scheme 1 and also facilitates voltage sensor activation for preopen states, decreased significantly from 32.2 ± 3.0 for WT to 4.4 ± 1.1 (P < 0.0001) for Core-MT. L1, the intrinsic equilibrium between the closed and preopen state, increased significantly from 3.10−8 ± 0.4 × 10−8 in WT to 4.4 × 10−5 ± 0.7 × 10−5 in Core-MT (P < 0.005). Removing the gating ring had an insignificant effect on ZL, the effective charge movement associated with transitions from the closed to the preopen (intermediate) state, which was 0.32 ± 0.02 eo in WT and 0.38 ± 0.10 eo in Core-MT (P > 0.11).

For Fig. 4 C, we used an indirect estimate of 0.27 for POMax for Core-MT based on studies with E321A/E324A mutations of WT and Core-MT channels (Fig. 3, C and D). To explore to what extent potential errors in estimating POMax would have on estimates of the coupling factor D and other parameters, we present three plots for assumed POMax for Core-MT channels of 0.99, 0.1, and 0.01 (Fig. 5). In all three plots, the slopes of the Core-MT channel were similar and less than for WT, indicating reduced voltage sensitivity over the wide range of explored values for POMax. The plots were then fitted with the extended HCA model. We found that the value of POMax for Core-MT did not affect the D factor (Fig. 5 and Table 1) but altered L1 and K1 to shift the plots up and down. These results further support our observations (Fig. 4 C and Table 1) that the removal of gating ring reduces D, the voltage sensor–gate coupling.

To explore whether potential errors in estimating ZL could give rise to apparent uncoupling of voltage sensors from gates, we fixed ZL to various values and then refit the PO versus V curve of Core-MT with L1 and D as free parameters. Fixing ZL from its best-fit value of 0.38 eo to 0.1, 0.2, 0.5, or 0.8 eo and refitting changed D from its best-fit value of 4.4 to 10.5, 7.7, 3.0, and 1.1, respectively. Consequently, over a greater range of values of ZL for Core-MT than might be expected, estimates of D for Core-MT remained greatly reduced compared with 32.2 for WT, indicating that the observed uncoupling does not arise from possible errors in estimating ZL. It also should be noted that the fits became worse when ZL was fixed away from its best-fit value.

We also explored whether possible errors in determining L1 could have induced the decrease in D for Core-MT channels. Fixing L1 threefold higher or threefold lower than the best fitting value for Core-MT data and refitting the Core-MT data changed D to 1.86 or 9.2, respectively, compared with 32.2 for WT. Consequently, for a wide range of possible errors in estimating L1, removing the gating ring still uncoupled the voltage sensors from the gates. Hence, the extended data analyses in these sections and the SEM of the fitted parameters and t tests in a previous section all quantitatively indicate that removal of the gating ring uncoupled the PGD from the VSD in terms of the extended HCA model.

### Deletion of gating ring increases the intrinsic open probability, POInt, of BK channels at negative voltage

BK channels can still open at very negative voltages (less than or equal to −100 mV) where the voltage dependence of the open probability becomes shallower (Fig. 4 C; Horrigan et al., 1999; Yang et al., 2010). These observations suggest that the channel has an intrinsic open probably, POInt, at very negative potentials that is not dependent on voltage sensor activation. Based on our estimate of POMax for Core-MT channels of 0.27, the intrinsic POInt at negative voltages for Core-MT was 15-fold higher than that of WT (Fig. 4 C).

From Scheme 1, it can be seen that a decreased coupling factor D would have no effect at very negative voltages. Consequently, the extended HCA model accounts for the 15-fold increase in POInt at very negative potentials through changes in the parameters K1, L1, and ZL, with the major change being a large increase in L1, the equilibrium for the C-C′ transition at 0 mV. As the voltage is increased, the decreased coupling between voltage sensors and gate (D) in Core-MT gives a decreased voltage sensitivity, so PO increases at a slower rate in Core-MT reaching a lower PO. The extended HCA model tells us how K1, L1, and ZL change in terms of the highly simplified model but gives little information about the multiple transduction pathways and energy barriers thought to be involved in voltage sensor–PGD coupling (Horrigan and Aldrich, 2002; Niu et al., 2004; Sweet and Cox, 2008; Hite et al., 2017) and how these would be altered by removing the gating ring.

Setting the model aside, the experimental observations are that removing the gating ring increases PO at negative voltages and decreases PO at positive voltages and decreases the coupling between voltage sensors and gates. As a possible mechanism, at very negative voltages the intrinsic open probability of Core-MT channels is higher than for WT channels because the fully resting (held down) voltage sensors are only partially coupled to the gates, so the gates are not held as fully closed. Hence, the decreased coupling between voltage sensors and gates after removing the gating ring would have a dual effect on BK channel gating, decreasing PO at positive potentials and increasing PO at negative potentials.

### Deletion of gating ring alters β subunit modulation

β1 and β2 subunits of BK channels interact with mSlo1 to alter Ca2+ and voltage-dependent activation. Their modulation of voltage-dependent activation of mSlo1 can be measured in 0 [Ca2+]i, with a different phenotype for the β1 and β2 subunits (Orio et al., 2002; Lee and Cui, 2009; Lee et al., 2010). The β1 subunit shifts the G-V relationship to the right and reduces slope, whereas the β2 subunit does not alter the G-V relation (Figs. 6 B and 7 B; Orio et al., 2002). In contrast, both β subunits alter gating charge movements by shifting the Q-V relation to more negative voltages (Figs. 6 D and 7 D; Sun et al., 2013). Previous studies suggest that β1 and β2 subunits also modify voltage-dependent activation via different mechanisms. It is thought that β1 mainly interacts with the voltage sensor of Slo1 to alter Q-V directly, whereas β2 primarily interacts with the cytosolic gating ring to alter Q-V indirectly (Lee and Cui, 2009; Lee et al., 2010; Sun et al., 2013). Here, we study the Core-MT channel to further test these previously proposed mechanisms.

Fig. 6 A shows the current traces of WT and Core-MT with the coexpression of human β1 subunit (hβ1). Compared with WT + hβ1, Core-MT + hβ1 currents activated with faster kinetics. However, β1 altered the G-V relation of Core-MT and WT in a similar manner, by reducing the steepness and shifting the G-V to more positive voltages (Fig. 6 B). β1 left-shifted the Q-V of both WT and Core-MT to more negative voltages (Bao and Cox, 2005). The −50-mV left shift for Core-MT Q-V was less than the −70 mV left shift for WT Q-V (Fig. 6, C and D; and Fig. 1 B). Interestingly, the Q-V of WT + hβ1 and that of Core-MT + hβ1 were nearly superimposable. This result could indicate that the gating ring has no effect on β1–voltage sensor interactions.

The β2 subunit had no effects on the G-V relation of WT or Core-MT (Fig. 7, A and B). β2 left-shifted the Q-V relation of Core-MT to more negative voltages by −22 mV, which was less than the left shift of −65 mV for WT (Fig. 7, C and D; and Fig. 1 B). Thus, the removal of the gating ring had a small effect on the modulation of G-V and Q-V relations by β1 but a larger effect on the modulation of Q-V relation by β2. These results are consistent with the previously proposed mechanisms that β1 mainly interacts with the voltage sensor of mSlo1 to modify voltage-dependent gating, whereas β2 primarily interacts with the gating ring to indirectly modify voltage-dependent gating.

## Discussion

We have studied voltage-dependent activation of the Core-MT mutation and found that the deletion of the gating ring from mSlo1 channels had a small effect on voltage sensor movement, left-shifting V1/2 of the QOn-V relation −21 mV with negligible change in slope (Fig. 1). In contrast, the deletion of the gating ring decreased the voltage dependence of channel opening. The open probability of the WT mSlo1 channel increased ∼4 × 106–fold over the 400-mV test potential range of −140 to 260 mV, whereas the open probability of the Core-MT mutation increased ∼5 × 104–fold over the same voltage range, being reduced ∼100-fold (Fig. 4 C). This result indicates that the deletion of the gating ring weakens the coupling between the VSDs and the PGD to reduce the influence of voltage sensor activation on pore opening. Fitting the data with an extended HCA model showed a significant reduction of the D factor, which measures the VSD-pore coupling, from 32.2 in WT to 4.4 in Core-MT (Fig. 4 C and Table 1).

The change in channel open probability caused by the removal of gating ring was observed over the wide examined voltage range, with an increase of intrinsic opening of BK channels at voltages where the voltage sensors would be in the resting state and a decrease in the maximum open probability that the channel can attain at high voltages where the voltage sensors would be fully activated (Fig. 4 C). These results are consistent with a proposed model in which the PGD coupled with the VSD has an intrinsic open probability for negative potentials in 0 Ca2+i and that, normally in WT channels, the VSD-pore coupling suppresses pore opening, decreasing the intrinsic opening probability when the VSDs are in the resting state at negative potentials but promotes pore opening when the VSDs are at the activated state at positive potentials. Because the gating ring in WT BK channels facilitates the VSD-pore coupling, the removal of the gating ring in Core-MT shows the dual effect of increasing PO at more negative potentials and decreasing PO at more positive potentials. This is evident in the crossing of the PO/voltage curves for WT and Core-MT channels at ∼40 mV in Fig. 4 C.

The BK channel gating ring contains eight Ca2+-binding sites that mediate Ca2+-dependent opening of the channel (Schreiber and Salkoff, 1997; Shi et al., 2002; Xia et al., 2002, 2004; Wu et al., 2010; Yuan et al., 2010, 2011; Zhang et al., 2010; Hite et al., 2017; Tao et al., 2017). Previous studies have shown that, although depolarizing voltages and Ca2+ binding can independently open BK channels (Cui et al., 1997), Ca2+ binding affects voltage-dependent opening, and likewise, voltage depolarization alters Ca2+-dependent opening (Horrigan and Aldrich, 2002; Sweet and Cox, 2008). This interdependence of voltage and Ca2+-dependent channel opening could be caused by a direct interaction between the voltage sensor and Ca2+ binding site, or alternatively, linked by the interactions among VSD, PGD, and gating ring that are responsible for the facilitation of VSD-pore coupling by the gating ring. Therefore, a conformational change in VSD could affect the conformation of the gating ring and vice versa.

What are the interactions among VSD, PGD, and gating ring that are responsible for the facilitation of VSD-pore coupling by the gating ring? Previous studies have revealed three types of interactions among the three domains. The first interaction is a direct pull between gating ring and the pore-gate through C-linkers. This interaction is supported by the observation that a shortening or lengthening of C-linkers from the PGD to the gating ring by deletion or addition of amino acid residues altered voltage and Ca2+ dependences of BK channel opening; the alteration was dependent on the length of the C-linker and could be explained as if the C-linker–gating ring complex behaved like a passive spring in 0 Ca2+, pulling on the PGD to open the channels (Niu et al., 2004). Recently solved structures of the BK channel in both apo and Ca2+-bound states showed that Ca2+ binding expands the top of the gating ring, consistent with the idea that C-linkers from the gating ring to the S6 helices in the PGD are pulled upon Ca2+ binding (Yuan et al., 2010, 2011; Hite et al., 2017; Tao et al., 2017).

Pull on the C-linkers is coupled in the gating ring with an elevation of the α-B helix of each subunit of the gating ring (Yuan et al., 2010, 2011; Hite et al., 2017; Tao et al., 2017). This elevated α-B helix could push directly on the VSD-PGD providing a second type of interaction among the three domains. Push on the VSD-PGD may activate the channel directly. This push by the α-B helix on the VSD-PGD could also push the gating ring away from the VSD-PGD increasing the pull of the C-linkers on the S6 helices to further activate the channel through a push-pull mechanism.

The third type of interaction involves electrostatic interaction directly between the gating ring and the VSD. In studies of Mg2+-dependent activation of BK channels, it was found that the putative Mg2+-binding site was located in the interface between the VSD and gating ring, with two residues from each of the domains (D99 and N172 from the VSD and E374 and E399 from the gating ring) forming Mg2+ coordinators (Yang et al., 2008). The bound Mg2+ activates the channel by electrostatic interaction with R213 in the S4 transmembrane segment of the VSD (Hu et al., 2003). These studies indicate a close proximity between the gating ring and the VSD and identified interactions between pairs of residues in the two domains, including spontaneously formed disulfide bond between C99 and C397, residues D99–E374, and charges at 172–399 (Yang et al., 2008, 2013). The crystal structures of BK channel gating ring show that E374 and E399 locate at the top surface of the gating ring, which faces the membrane, providing further support to these functional findings (Wu et al., 2010; Yuan et al., 2010, 2011).

With any of the above mechanisms, the interaction between the gating ring and the membrane-spanning domains could have a profound effect on the conformations of the membrane-spanning domain because removal of the gating ring not only reduces the VSD-PGD coupling but also alters the intrinsic energy for channel opening. Our gating current measurements showed that removal of the gating ring shifted Vhc, the half activation voltage for the closed states, −21 mV, from 159 mV for WT to 138 mv for Core-MT. This shift would arise from changes in the VSD movements when the channels were still closed (Scheme 1 [top row], Fig. 1, and Table 1). To determine the effect of gating ring removal on Vho, the voltage for half activation for the preopen states (second row in Scheme 1), Eq. 6 (see Materials and methods) was arranged to obtain:

$V ho =V hc –( kT/Z J )lnD.$

The large decrease in D upon removing the gating right-shifted Vho 73 mV, from −11 mV for WT to 62 mV for Core-MT. The much larger shift in Vho compared with the shift in Vhc suggests that removal of the gating ring may primarily affect the conformation of the preopen states rather than that of the closed states. This idea is consistent with the changes of the intrinsic energy for transitions of the preopen state to the closed (L1) or open (K1) state. In terms of the extended HCA model, it is mainly the shift in Vho for the preopen states that shifts the G/GMax-V curve.

The effect of the mini tail (11 amino acids of C-linker) remaining after removing the gating ring (see Materials and methods) on the voltage-dependent gating of Core-MT channels is not known. For example, the mini tails might themselves interact, altering the gating process. The contribution of the mini tail to our observed Core-MT behavior needs to be examined when a method is devised to express Core channels without the mini tail, to fully evaluate the effects of the gating ring in BK channel gating.

In summary, removing the gating ring of the BK channel had profound effects of reducing the increase of probability of channel opening while only inducing a small leftward shift in the voltage required for activation of the gating current. These observations indicate that removing the gating ring decreases coupling between voltage sensors and the gates. Thus, the gating ring normally contributes to coupling, even in the absence of Ca2+. Our results also support the mechanism that the β2 subunit, but not the β1 subunit, alters BK channel voltage sensor movements primarily by interacting with the gating ring.

## Acknowledgments

This work was supported by National Institutes of Health grants R01 HL70393 and R01 NS092570 to J. Cui and R01 GM114694 to L. Salkoff and K.L. Magleby and National Natural Science Foundation of China grant 31271143 to J. Cui.

The authors declare no competing financial interests.

Richard W. Aldrich served as editor.

## References

,
P.R.
,
A.
Constanti
,
D.A.
Brown
, and
R.B.
Clark
.
1982
.
Intracellular Ca2+ activates a fast voltage-sensitive K+ current in vertebrate sympathetic neurones
.
Nature.
296
:
746
749
.
,
J.P.
,
K.Z.
Shen
,
M.P.
Kavanaugh
,
R.A.
Warren
,
Y.N.
Wu
,
A.
Lagrutta
,
C.T.
Bond
, and
R.A.
North
.
1992
.
Calcium-activated potassium channels expressed from cloned complementary DNAs
.
Neuron.
9
:
209
216
.
Alvarez
,
O.
,
C.
Gonzalez
, and
R.
Latorre
.
2002
.
Counting channels: a tutorial guide on ion channel fluctuation analysis
.
26
:
327
341
.
Atkinson
,
N.S.
,
G.A.
Robertson
, and
B.
Ganetzky
.
1991
.
A component of calcium-activated potassium channels encoded by the Drosophila slo locus
.
Science.
253
:
551
555
.
Bao
,
L.
, and
D.H.
Cox
.
2005
.
Gating and ionic currents reveal how the BKCa channel’s Ca2+ sensitivity is enhanced by its β1 subunit
.
J. Gen. Physiol.
126
:
393
412
.
Bao
,
L.
,
A.M.
Rapin
,
E.C.
Holmstrand
, and
D.H.
Cox
.
2002
.
Elimination of the BKCa channel’s high-affinity Ca2+ sensitivity
.
J. Gen. Physiol.
120
:
173
189
.
Barrett
,
J.N.
,
K.L.
Magleby
, and
B.S.
Pallotta
.
1982
.
Properties of single calcium-activated potassium channels in cultured rat muscle
.
J. Physiol.
331
:
211
230
.
Behrens
,
R.
,
A.
Nolting
,
F.
Reimann
,
M.
Schwarz
,
R.
Waldschütz
, and
O.
Pongs
.
2000
.
hKCNMB3 and hKCNMB4, cloning and characterization of two members of the large-conductance calcium-activated potassium channel β subunit family
.
FEBS Lett.
474
:
99
106
.
Braun
,
M.
,
R.
Ramracheya
,
M.
Bengtsson
,
Q.
Zhang
,
J.
Karanauskaite
,
C.
Partridge
,
P.R.
Johnson
, and
P.
Rorsman
.
2008
.
Voltage-gated ion channels in human pancreatic β-cells: electrophysiological characterization and role in insulin secretion
.
Diabetes.
57
:
1618
1628
.
Brayden
,
J.E.
, and
M.T.
Nelson
.
1992
.
Regulation of arterial tone by activation of calcium-dependent potassium channels
.
Science.
256
:
532
535
.
Brelidze
,
T.I.
, and
K.L.
Magleby
.
2004
.
Protons block BK channels by competitive inhibition with K+ and contribute to the limits of unitary currents at high voltages
.
J. Gen. Physiol.
123
:
305
319
.
Brelidze
,
T.I.
,
X.
Niu
, and
K.L.
Magleby
.
2003
.
A ring of eight conserved negatively charged amino acids doubles the conductance of BK channels and prevents inward rectification
.
100
:
9017
9022
.
Budelli
,
G.
,
Y.
Geng
,
A.
Butler
,
K.L.
Magleby
, and
L.
Salkoff
.
2013
.
Properties of Slo1 K+ channels with and without the gating ring
.
110
:
16657
16662
.
Butler
,
A.
,
S.
Tsunoda
,
D.P.
McCobb
,
A.
Wei
, and
L.
Salkoff
.
1993
.
mSlo, a complex mouse gene encoding “maxi” calcium-activated potassium channels
.
Science.
261
:
221
224
.
Cox
,
D.H.
,
J.
Cui
, and
R.W.
Aldrich
.
1997
.
Allosteric gating of a large conductance Ca-activated K+ channel
.
J. Gen. Physiol.
110
:
257
281
.
Cui
,
J.
, and
R.W.
Aldrich
.
2000
.
Allosteric linkage between voltage and Ca2+-dependent activation of BK-type mslo1 K+ channels
.
Biochemistry.
39
:
15612
15619
.
Cui
,
J.
,
D.H.
Cox
, and
R.W.
Aldrich
.
1997
.
Intrinsic voltage dependence and Ca2+ regulation of mslo large conductance Ca-activated K+ channels
.
J. Gen. Physiol.
109
:
647
673
.
Ferguson
,
W.B.
,
O.B.
McManus
, and
K.L.
Magleby
.
1993
.
Opening and closing transitions for BK channels often occur in two steps via sojourns through a brief lifetime subconductance state
.
Biophys. J.
65
:
702
714
.
Hite
,
R.K.
,
P.
Yuan
,
Z.
Li
,
Y.
Hsuing
,
T.
Walz
, and
R.
MacKinnon
.
2015
.
Cryo-electron microscopy structure of the Slo2.2 Na+-activated K+ channel
.
Nature.
527
:
198
203
.
Hite
,
R.K.
,
X.
Tao
, and
R.
MacKinnon
.
2017
.
Structural basis for gating the high-conductance Ca2+-activated K+ channel
.
Nature.
541
:
52
57
.
Horrigan
,
F.T.
, and
R.W.
Aldrich
.
2002
.
Coupling between voltage sensor activation, Ca2+ binding and channel opening in large conductance (BK) potassium channels
.
J. Gen. Physiol.
120
:
267
305
. (published erratum appears in J. Gen. Physiol. 2002. 120:599)
Horrigan
,
F.T.
,
J.
Cui
, and
R.W.
Aldrich
.
1999
.
Allosteric voltage gating of potassium channels I. Mslo ionic currents in the absence of Ca2+
.
J. Gen. Physiol.
114
:
277
304
.
Hu
,
L.
,
J.
Shi
,
Z.
Ma
,
G.
Krishnamoorthy
,
F.
Sieling
,
G.
Zhang
,
F.T.
Horrigan
, and
J.
Cui
.
2003
.
Participation of the S4 voltage sensor in the Mg2+-dependent activation of large conductance (BK) K+ channels
.
100
:
10488
10493
.
Hudspeth
,
A.J.
, and
R.S.
Lewis
.
1988
a
.
Kinetic analysis of voltage- and ion-dependent conductances in saccular hair cells of the bull-frog, Rana catesbeiana
.
J. Physiol.
400
:
237
274
.
Hudspeth
,
A.J.
, and
R.S.
Lewis
.
1988
b
.
A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, Rana catesbeiana
.
J. Physiol.
400
:
275
297
.
Lancaster
,
B.
, and
R.A.
Nicoll
.
1987
.
Properties of two calcium-activated hyperpolarizations in rat hippocampal neurones
.
J. Physiol.
389
:
187
203
.
Latorre
,
R.
,
C.
Vergara
, and
C.
Hidalgo
.
1982
.
Reconstitution in planar lipid bilayers of a Ca2+-dependent K+ channel from transverse tubule membranes isolated from rabbit skeletal muscle
.
79
:
805
809
.
Lee
,
U.S.
, and
J.
Cui
.
2009
.
β subunit-specific modulations of BK channel function by a mutation associated with epilepsy and dyskinesia
.
J. Physiol.
587
:
1481
1498
.
Lee
,
U.S.
,
J.
Shi
, and
J.
Cui
.
2010
.
Modulation of BK channel gating by the β2 subunit involves both membrane-spanning and cytoplasmic domains of Slo1
.
J. Neurosci.
30
:
16170
16179
.
Li
,
B.
,
W.
Jie
,
L.
Huang
,
P.
Wei
,
S.
Li
,
Z.
Luo
,
A.K.
Friedman
,
A.L.
Meredith
,
M.H.
Han
,
X.H.
Zhu
, and
T.M.
Gao
.
2014
.
Nuclear BK channels regulate gene expression via the control of nuclear calcium signaling
.
Nat. Neurosci.
17
:
1055
1063
.
Lingle
,
C.J.
2006
.
Empirical considerations regarding the use of ensemble-variance analysis of macroscopic currents
.
J. Neurosci. Methods.
158
:
121
132
.
Long
,
S.B.
,
E.B.
Campbell
, and
R.
Mackinnon
.
2005
.
Voltage sensor of Kv1.2: structural basis of electromechanical coupling
.
Science.
309
:
903
908
.
Marty
,
A.
1981
.
Ca-dependent K channels with large unitary conductance in chromaffin cell membranes
.
Nature.
291
:
497
500
.
Meera
,
P.
,
M.
Wallner
,
Z.
Jiang
, and
L.
Toro
.
1996
.
A calcium switch for the functional coupling between α (hslo) and β subunits (KV, Ca β) of maxi K channels
.
FEBS Lett.
382
:
84
88
.
Meera
,
P.
,
M.
Wallner
,
M.
Song
, and
L.
Toro
.
1997
.
Large conductance voltage- and calcium-dependent K+ channel, a distinct member of voltage-dependent ion channels with seven N-terminal transmembrane segments (S0-S6), an extracellular N terminus, and an intracellular (S9-S10) C terminus
.
94
:
14066
14071
.
Meredith
,
A.L.
,
S.W.
Wiler
,
B.H.
Miller
,
J.S.
Takahashi
,
A.A.
Fodor
,
N.F.
Ruby
, and
R.W.
Aldrich
.
2006
.
BK calcium-activated potassium channels regulate circadian behavioral rhythms and pacemaker output
.
Nat. Neurosci.
9
:
1041
1049
.
Nimigean
,
C.M.
, and
K.L.
Magleby
.
2000
.
Functional coupling of the β1 subunit to the large conductance Ca2+-activated K+ channel in the absence of Ca2+. Increased Ca2+ sensitivity from a Ca2+-independent mechanism
.
J. Gen. Physiol.
115
:
719
736
.
Niu
,
X.
,
X.
Qian
, and
K.L.
Magleby
.
2004
.
Linker-gating ring complex as passive spring and Ca2+-dependent machine for a voltage- and Ca2+-activated potassium channel
.
Neuron.
42
:
745
756
.
Orio
,
P.
,
P.
Rojas
,
G.
Ferreira
, and
R.
Latorre
.
2002
.
New disguises for an old channel: MaxiK channel β-subunits
.
News Physiol. Sci.
17
:
156
161
.
Pallotta
,
B.S.
,
K.L.
Magleby
, and
J.N.
Barrett
.
1981
.
Single channel recordings of Ca2+-activated K+ currents in rat muscle cell culture
.
Nature.
293
:
471
474
.
Petersen
,
O.H.
, and
Y.
Maruyama
.
1984
.
Calcium-activated potassium channels and their role in secretion
.
Nature.
307
:
693
696
.
Robitaille
,
R.
,
M.L.
Garcia
,
G.J.
Kaczorowski
, and
M.P.
Charlton
.
1993
.
Functional colocalization of calcium and calcium-gated potassium channels in control of transmitter release
.
Neuron.
11
:
645
655
.
Rothberg
,
B.S.
, and
K.L.
Magleby
.
1998
.
Kinetic structure of large-conductance Ca2+-activated K+ channels suggests that the gating includes transitions through intermediate or secondary states. A mechanism for flickers
.
J. Gen. Physiol.
111
:
751
780
.
Schreiber
,
M.
, and
L.
Salkoff
.
1997
.
A novel calcium-sensing domain in the BK channel
.
Biophys. J.
73
:
1355
1363
.
Shen
,
K.Z.
,
A.
Lagrutta
,
N.W.
Davies
,
N.B.
Standen
,
J.P.
, and
R.A.
North
.
1994
.
Tetraethylammonium block of Slowpoke calcium-activated potassium channels expressed in Xenopus oocytes: evidence for tetrameric channel formation
.
Pflugers Arch.
426
:
440
445
.
Shi
,
J.
,
G.
Krishnamoorthy
,
Y.
Yang
,
L.
Hu
,
N.
Chaturvedi
,
D.
Harilal
,
J.
Qin
, and
J.
Cui
.
2002
.
Mechanism of magnesium activation of calcium-activated potassium channels
.
Nature.
418
:
876
880
.
Silberberg
,
S.D.
,
A.
Lagrutta
,
J.P.
, and
K.L.
Magleby
.
1996
.
Wanderlust kinetics and variable Ca2+-sensitivity of Drosophila, a large conductance Ca2+-activated K+ channel, expressed in oocytes
.
Biophys. J.
70
:
2640
2651
.
Sun
,
X.
,
J.
Shi
,
K.
Delaloye
,
X.
Yang
,
H.
Yang
,
G.
Zhang
, and
J.
Cui
.
2013
.
The interface between membrane-spanning and cytosolic domains in Ca2+-dependent K+ channels is involved in β subunit modulation of gating
.
J. Neurosci.
33
:
11253
11261
.
Sweet
,
T.-B.
, and
D.H.
Cox
.
2008
.
Measurements of the BKCa channel’s high-affinity Ca2+ binding constants: effects of membrane voltage
.
J. Gen. Physiol.
132
:
491
505
.
Tao
,
X.
,
R.K.
Hite
, and
R.
MacKinnon
.
2017
.
Cryo-EM structure of the open high-conductance Ca2+-activated K+ channel
.
Nature.
541
:
46
51
.
Tseng-Crank
,
J.
,
N.
Godinot
,
T.E.
Johansen
,
P.K.
Ahring
,
D.
Strøbaek
,
R.
Mertz
,
C.D.
Foster
,
S.P.
Olesen
, and
P.H.
Reinhart
.
1996
.
Cloning, expression, and distribution of a Ca2+-activated K+ channel beta-subunit from human brain
.
93
:
9200
9205
.
Wallner
,
M.
,
P.
Meera
, and
L.
Toro
.
1999
.
Molecular basis of fast inactivation in voltage and Ca2+-activated K+ channels: a transmembrane β-subunit homolog
.
96
:
4137
4142
.
Wei
,
A.
,
C.
Solaro
,
C.
Lingle
, and
L.
Salkoff
.
1994
.
Calcium sensitivity of BK-type KCa channels determined by a separable domain
.
Neuron.
13
:
671
681
.
Wellman
,
G.C.
, and
M.T.
Nelson
.
2003
.
Signaling between SR and plasmalemma in smooth muscle: sparks and the activation of Ca2+-sensitive ion channels
.
Cell Calcium.
34
:
211
229
.
Wu
,
Y.C.
,
J.J.
Art
,
M.B.
Goodman
, and
R.
Fettiplace
.
1995
.
A kinetic description of the calcium-activated potassium channel and its application to electrical tuning of hair cells
.
Prog. Biophys. Mol. Biol.
63
:
131
158
.
Wu
,
Y.
,
Y.
Yang
,
S.
Ye
, and
Y.
Jiang
.
2010
.
Structure of the gating ring from the human large-conductance Ca2+-gated K+ channel
.
Nature.
466
:
393
397
.
Xia
,
X.M.
,
X.
Zeng
, and
C.J.
Lingle
.
2002
.
Multiple regulatory sites in large-conductance calcium-activated potassium channels
.
Nature.
418
:
880
884
.
Xia
,
X.M.
,
J.P.
Ding
, and
C.J.
Lingle
.
2003
.
Inactivation of BK channels by the NH2 terminus of the β2 auxiliary subunit: an essential role of a terminal peptide segment of three hydrophobic residues
.
J. Gen. Physiol.
121
:
125
148
.
Xia
,
X.M.
,
X.
Zhang
, and
C.J.
Lingle
.
2004
.
Ligand-dependent activation of Slo family channels is defined by interchangeable cytosolic domains
.
J. Neurosci.
24
:
5585
5591
.
Yang
,
H.
,
J.
Shi
,
G.
Zhang
,
J.
Yang
,
K.
Delaloye
, and
J.
Cui
.
2008
.
Activation of Slo1 BK channels by Mg2+ coordinated between the voltage sensor and RCK1 domains
.
Nat. Struct. Mol. Biol.
15
:
1152
1159
.
Yang
,
H.
,
G.
Zhang
, and
J.
Cui
.
2015
.
BK channels: multiple sensors, one activation gate
.
Front. Physiol.
6
:
29
.
Yang
,
J.
,
G.
Krishnamoorthy
,
A.
Saxena
,
G.
Zhang
,
J.
Shi
,
H.
Yang
,
K.
Delaloye
,
D.
Sept
, and
J.
Cui
.
2010
.
An epilepsy/dyskinesia-associated mutation enhances BK channel activation by potentiating Ca2+ sensing
.
Neuron.
66
:
871
883
.
Yang
,
J.
,
H.
Yang
,
X.
Sun
,
K.
Delaloye
,
X.
Yang
,
A.
Moller
,
J.
Shi
, and
J.
Cui
.
2013
.
Interaction between residues in the Mg2+-binding site regulates BK channel activation
.
J. Gen. Physiol.
141
:
217
228
.
Yuan
,
P.
,
M.D.
Leonetti
,
A.R.
Pico
,
Y.
Hsiung
, and
R.
MacKinnon
.
2010
.
Structure of the human BK channel Ca2+-activation apparatus at 3.0 Å resolution
.
Science.
329
:
182
186
.
Yuan
,
P.
,
M.D.
Leonetti
,
Y.
Hsiung
, and
R.
MacKinnon
.
2011
.
Open structure of the Ca2+ gating ring in the high-conductance Ca2+-activated K+ channel
.
Nature.
481
:
94
97
.
Zhang
,
G.
,
S.-Y.
Huang
,
J.
Yang
,
J.
Shi
,
X.
Yang
,
A.
Moller
,
X.
Zou
, and
J.
Cui
.
2010
.
Ion sensing in the RCK1 domain of BK channels
.
107
:
18700
18705
.
Zhang
,
G.
,
H.
Yang
,
H.
Liang
,
J.
Yang
,
J.
Shi
,
K.
McFarland
,
Y.
Chen
, and
J.
Cui
.
2014
.
A charged residue in S4 regulates coupling among the activation gate, voltage, and Ca2+ sensors in BK channels
.
J. Neurosci.
34
:
12280
12288
.

Abbreviations used:

• CTD

cytosolic domain

•
• PGD

pore-gate domain

•
• VSD

voltage sensor domain