The Contribution of RCK Domains to Human BK Channel Allosteric Activation*

Background: In BK channels, Ca2+ and voltage sensors are allosterically connected to the pore. Results: We optically resolved voltage sensor rearrangements, initiated by Ca2+ binding to the intracellular domains RCK1 and RCK2. Impairing the RCK2 abolished this allosteric effect. Conclusion: The RCK2 Ca2+ sensor is required for the allosteric facilitation of voltage sensor activation. Significance: RCK1 and RCK2 Ca2+ sensors are not functionally homologous. Large conductance voltage- and Ca2+-activated K+ (BK) channels are potent regulators of cellular processes including neuronal firing, synaptic transmission, cochlear hair cell tuning, insulin release, and smooth muscle tone. Their unique activation pathway relies on structurally distinct regulatory domains including one transmembrane voltage-sensing domain (VSD) and two intracellular high affinity Ca2+-sensing sites per subunit (located in the RCK1 and RCK2 domains). Four pairs of RCK1 and RCK2 domains form a Ca2+-sensing apparatus known as the “gating ring.” The allosteric interplay between voltage- and Ca2+-sensing apparati is a fundamental mechanism of BK channel function. Using voltage-clamp fluorometry and UV photolysis of intracellular caged Ca2+, we optically resolved VSD activation prompted by Ca2+ binding to the gating ring. The sudden increase of intracellular Ca2+ concentration ([Ca2+]i) induced a hyperpolarizing shift in the voltage dependence of both channel opening and VSD activation, reported by a fluorophore labeling position 202, located in the upper side of the S4 transmembrane segment. The neutralization of the Ca2+ sensor located in the RCK2 domain abolished the effect of [Ca2+]i increase on the VSD rearrangements. On the other hand, the mutation of RCK1 residues involved in Ca2+ sensing did not prevent the effect of Ca2+ release on the VSD, revealing a functionally distinct interaction between RCK1 and RCK2 and the VSD. A statistical-mechanical model quantifies the complex thermodynamics interplay between Ca2+ association in two distinct sites, voltage sensor activation, and BK channel opening.

tions, mutations, or changes in the environment. In ion channels, the gating mechanism(s) rely on the allosteric coupling between the pore and other modulatory domains, specialized to sense different stimuli, such as changes in membrane potential, temperature, mechanical stress, and the concentration of signaling molecules. Although the available atomic structures of ion channels or their functional domains are rapidly increasing, the mechanisms underlying allostery in these proteins are far from being fully understood. Several studies have provided experimental evidence of cooperative interactions in K ϩ channels (3)(4)(5)(6)(7)(8). An example of a highly allosteric membrane protein is the large conductance, voltage-and Ca 2ϩ -activated (BK, Slo1) K ϩ channel. BK channel open probability (P o ) is controlled by cooperative interactions between its four transmembrane voltage-sensing domains (VSDs), 2 an intracellular multiligand-sensing domain (gating ring), and the pore (6, 9 -12) (Fig. 1A). Functional BK channels are tetrameric proteins (13), each subunit composed of seven transmembrane segments (S0 -S6) and a large intracellular C terminus (14). As typical of voltage-activated K ϩ channels (15), the transmembrane region of BKchannels includes helices S5-S6, which contribute to the central, K ϩ -selective pore domain and a VSD including the charge-bearing segments S2-S3-S4 (16 -20) (Fig. 1A). BK sensitivity to Ca 2ϩ and other intracellular ligands (Mg 2ϩ , H ϩ , CO, Heme, etc.) is conferred by the large intracellular C-terminal region (10,11,21), which encompasses two tandem regulator of conductance of K domains, RCK1 and RCK2 (22)(23)(24)(25)(26)(27)(28)(29) (Fig. 1). RCK1 includes residues involved in both high affinity Ca 2ϩ sensing, such as Asp-362/Asp-367 (30), Met-513 (31), and Glu-535 (32), and low affinity divalent cation sensing (Glu-374 and Glu-399) (30,(33)(34)(35). RCK2 encompasses a high affinity Ca 2ϩbinding site (the "calcium bowl") consisting of five consecutive Asp residues (Asp-894 -Asp-898) (36 -38) (Fig. 1B). Recently resolved crystal structures of this intracellular domain (27)(28)(29) provided details of its structural organization, consisting of four pairs of RCK domains that assemble into a tetrameric complex ("gating ring") akin to those of bacterial MthK channels (23) (Fig. 1B). Our recent work has shown that the purified BK gat-ing ring selectively responds to Ca 2ϩ and Mg 2ϩ under physiologically relevant conditions, undergoing metal-driven conformational rearrangements, thus fulfilling its role as a chemomechanical transducer (39). Considering the highly allosteric nature of BK channel activation, these Ca 2ϩ -induced conformational changes are expected to propagate to the transmembrane functional domains. In thermodynamic terms, the activation of Ca 2ϩ sensors must alter the equilibrium isotherms of the pore and the VSD.
In the present work, we tested these premises and attempted to experimentally investigate whether the Ca 2ϩ -induced conformational changes of the gating ring at the intracellular portion of the channel can propagate to, and be resolved as, structural rearrangements of the VSD. We combined the voltage-clamp fluorometry technique (40 -42) with the UV photolysis of a Ca 2ϩ cage compound, DM-Nitrophen (43)(44)(45)(46), to simultaneously trigger voltage-and Ca 2ϩ -dependent activations of BK channels. We found that rapid intracellular Ca 2ϩ release produced structural rearrangements that not only increased channel P o but also perturbed the conformation of the S4 helix of the BK VSD. In addition, impairing Ca 2ϩ sensing in RCK2 (calcium bowl neutralization), but not in RCK1, abolished the effect of the elevation of intracellular Ca 2ϩ concentration ([Ca 2ϩ ] i ) on VSD activation, underlining a functional difference of the two Ca 2ϩ sensors. These findings were included in a statistical-mechanical allosteric model of BK channel activation, based on that by Horrigan and Aldrich (6) but expanded to take into account that the two high affinity Ca 2ϩ sensors of the human BK channel are not functionally homologous. The fitting of experimental data to this new model allowed quantification of the distinct allosteric contribution of the two high affinity Ca 2ϩ -sensing sites in the gating ring to VSD activation and pore opening, resolving the network of allosteric interactions underlying voltage-and Ca 2ϩ -dependent BK channel activation.

Oocyte Preparation
Xenopus laevis (NASCO, Modesto, CA) oocytes (stages V-VI) were prepared as previously described (49) and then injected with 50 nl of cRNA solution (0.01-0.1 g/l) using a Drummond nano-injector. The injected oocytes were maintained at 18°C in an amphibian saline solution supplemented with 50 g/ml gentamycin (Invitrogen), 200 M DTT, and 10 M EDTA. 3-6 days after injection, the oocytes were labeled with 10 M membrane-impermeable, thiol-reactive fluorophore, tetramethylrhodamine-5Ј-maleimide (TMRM) (Molecular Probes, Eugene, OR) in a depolarizing K ϩ solution (120 mM K-MES, 2 mM Ca(MES) 2 , and 10 mM HEPES, pH 7). TMRM stock (100 mM) was dissolved in Me 2 SO and stored at Ϫ20°C. The oocytes were then thoroughly rinsed in a dye-free solution and injected with 100 nl of DM-Nitrophen precomplexed with Ca 2ϩ (2.5 mM final concentration in the oocyte), prior to voltage clamp fluorometry.

Electrophysiological Techniques
Voltage Clamp Fluorometry-The cut open oocyte vaseline gap technique (50) is a low noise, fast clamp technique. Changes in fluorescence signal and ionic currents were simultaneously measured from the same area of membrane isolated by the top chamber (20,42). The optical setup consists of a Zeiss Axioscope FS microscope with filters appropriate for TMRM (Omega Optical, Brattleboro, VT). The light source is a 100 W microscope halogen lamp. A TTL-triggered Uniblitz VS 25 shutter (Vincent Associates, Rochester, NY) is mounted on the excitation light path. The objective (Olympus LUMPlanFl, 40ϫ, water immersion) has a numerical aperture of 0.8 and a working distance of 3.3 mm (Olympus Optical). A Dagan Photomax 200 system is used for the amplification of the photocurrent and background fluorescence subtraction. A Xenon flash lamp system JML-C2 (Rapp Opto-electronik GmbH, Hamburg, Germany) delivering high energy UV flashes of adjustable intensity was used for the photolysis of caged Ca 2ϩ . An external trigger synchronized UV flashes with voltage clamp and optical recordings. A water-immersed quartz light guide was positioned ϳ0.5 mm away from the oocyte upper dome.
Voltage Clamp Fluorometry Recording Solutions-The external solution contained 60 mM Na-MES, 50 mM K-MES, 2 mM Ca(MES) 2 , 10 mM Na-HEPES (pH 7.0). The internal solution contained 120 mM potassium glutamate, 10 mM HEPES (pH 7.0). The solution for the intracellular pipette was 2700 mM Na-MES, 10 mM NaCl. Low access resistance to the oocyte interior was obtained by permeabilizing the oocyte with 0.1% saponin dissolved in the internal solution.
Analysis-The experimental data were analyzed with a customized program developed in our division and using fitting routines in Microsoft Excel. The data for the membrane conductance (G(V)) and the fluorescence (F(V)) curves were calculated from ionic current and fluorescence recordings, by averaging ϳ200 points (sampling frequency 50 s/point) up to 2 ms before and 20 ms after Ca 2ϩ -releasing UV flashes. The G(V) curves were calculated by dividing the current-voltage relationships (I-V curves) by the driving force (V m Ϫ E K ), where V m is the membrane potential, and E K is the equilibrium potential for K ϩ , estimated using the Nernst equation. F(V) and G(V) data points were fitted to one Boltzmann distribution of the following form, where G max and F max are the maximal G and F; F min is the minimal F; z is the effective valence of the distribution; V half is the half-activating potential; V m is the membrane potential; and F, R, and T are the usual thermodynamic values. The allosteric model is detailed in the supplemental data. Patch Clamp-Membrane patches from Xenopus oocytes in the inside-out configuration were perfused with bath solutions containing 115 mM K-MES, 5 mM KCl, 5 mM HEDTA, 10 mM HEPES, pH 7 (supplemental Fig. S1A). [Ca 2ϩ ] was varied by adding CaCl 2 . The free [Ca 2ϩ ] was theoretically calculated with WEBMAXC v2.10 and then measured using a Ca 2ϩ electrode (WPI, Sarasota, FL). The borosilicate glass pipettes (WPI) were filled with the bath solution at the lowest free [Ca 2ϩ ]. The holding potential was 0 mV. The data were filtered to one-fifth of the sampling frequency. G(V) curves for different BK clones (supplemental Fig. S1B) at different free [Ca 2ϩ ] i were constructed as described above. Plotting V half against [Ca 2ϩ ] produced calibration curves for the three BK clones used (supplemental

Statistical Analysis
Scatter plots of ⌬V half versus ⌬kTln[Ca 2ϩ ] i were tested for monotonicity using Spearman's rank order correlation coefficient () using the statistical software SigmaStat (Aspire Software, Ashburn, VA). Analysis using Pearson's coefficient for linear dependence yielded similarly significant measures of correlation and therefore are not included. ⌬V half data were normalized to unitless quantities by multiplying by the fitted values for charge displacement (z L for ⌬GV half and 4z J for ⌬FV half ) and dividing by the change in chemical potential for calcium ⌬ ϭ ⌬kTln[Ca 2ϩ ] i . The collective mean of these normalized quantities, which can be interpreted as a measure of thermodynamic linkage between Ca 2ϩ -and voltage-sensing elements of the channel, was assessed for nonzero value using Student's t test. Of a total of 36 initially considered experiments, six were excluded either because: (i) ⌬ did not exceed a post hoc threshold of 8 meV established to minimize error from insufficient calcium release (five experiments); or (ii) [Ca 2ϩ ] i was near the positive saturated range (ϳ10 3 M and higher), limiting the effect on ⌬V half (1 experiment). Including these experiments introduced outliers in the normalized data points but did not affect statistical outcomes.

Ca 2ϩ Binding to BK Gating Ring Induces Structural Rearrangements in VSD-
The human BK channel (Slo1) VSD has been studied using voltage clamp fluorometry and shown to undergo voltage-dependent molecular rearrangements (19,20,48,51). In this work, BK channels were engineered to allow for specific fluorescent labeling of the extracellular side of the S4 transmembrane segment at position 202 (this BK construct is referred to as pseudo WT or pWT throughout this paper). As we have previously shown, TMRM labeling position 202 reports conformational changes related to BK VSD activation (19,20,48). Also, the TMRM fluorescence reported from the adjacent position 201 shares an almost identical voltage dependence with that of gating currents (Q(V) curve) (20).
To probe for Ca 2ϩ -induced conformational changes of the VSD, Xenopus oocytes expressing pWT BK (prelabeled with TMRM) were injected with DM-Nitrophen, a caged Ca 2ϩ compound that undergoes UV photolysis, releasing Ca 2ϩ . Thus, under voltage clamp (using the cut-open oocyte vaseline gap technique (50) modified for epifluorescence measurement (40 -42)), we induced rapid increase of [Ca 2ϩ ] i by delivering UV flashes focused on the upper exposed oocyte membrane. Simultaneous recordings of K ϩ currents and fluorescence emissions from an oocyte expressing pWT channels are shown in Fig. 2A. Ca 2ϩ release was induced by UV flash triggered 60 ms after the onset of each depolarizing pulse. The rapid elevation of [Ca 2ϩ ] i increased the BK channel P o , manifested by a downward or upward deflection of the ionic current traces (according to the K ϩ reversal potential, Ϫ20 mV) ( Fig. 2A, black  traces). Notably, UV-induced Ca 2ϩ uncaging also induced an increase of the simultaneously recorded TMRM fluorescence emission ( Fig. 2A, red traces), suggesting that the Ca 2ϩ -dependent activation of BK channels involves VSD conformational changes. The voltage dependence of the fluorescence deflections (F(V)) and macroscopic K ϩ conductance (G(V)) were calculated from the fluorescence and ionic current recordings, 2 ms before and 20 ms after Ca 2ϩ -releasing UV flashes (Fig. 2B). The rapid increase in [Ca 2ϩ ] i produced a hyperpolarizing shift of the G(V) curve (⌬GV half Ϸ Ϫ50 mV) associated with a smaller, but well resolved, translation of the F(V) curve in the same direction (⌬FV half Ϸ Ϫ25 mV). Note that the Ca 2ϩ release induced a crossover of G(V) and F(V) curves (Fig. 2B), evidence for BK channels undergoing conformational transitions while in the open state (5,6,16,52).
The effects observed in BK channels were genuinely produced by Ca 2ϩ , as confirmed by the lack of detectable changes in ionic current and fluorescence recordings when Ca 2ϩ -insensitive Shaker K ϩ channels, fluorescently labeled to resolve their S4 movements, were similarly subjected to UV-induced Ca 2ϩ release (supplemental Fig. S2, A and B). Moreover, ionic current and fluorescence recordings from pWT BK channels expressed in oocytes not injected with DM-Nitrophen were unaffected by UV flashes (supplemental Fig. S2, C and D). The reproducibility of Ca 2ϩ photo release during sequential pulses is demonstrated in supplemental Fig. S3, A and B, which also shows that [Ca 2ϩ ] i returned to its basal level in less than 1 s (supplemental Fig.  S3C).
To estimate the local intracellular free [Ca 2ϩ ] i before and after UV photolysis, we exploited the BK intrinsic Ca 2ϩ sensing properties (i.e. the dependence of the half activation potential GV half on [Ca 2ϩ ] i ), as previously utilized in motor neurons and hair cells (53,54). GV half versus free [Ca 2ϩ ] calibration curves were constructed from excised patch experiments (see "Experimental Procedures" and supplemental Fig. S1). Note that in the pWT background, Ca 2ϩ sensitivity was reduced by the well documented mutations in RCK1 and RCK2 domains, recapitulating the effect observed in WT BK channels (30,36).
The Calcium Bowl Is Required for Ca 2ϩ -mediated Effect on VSD Movements-Two high affinity Ca 2ϩ -sensing sites are located within the BK gating ring ligand binding apparatus: one, in the RCK2 domain, coordinates Ca 2ϩ via the five Asp residues (Asp-894 -Asp-898) comprising the calcium bowl (27,29,36); the other, in RCK1, includes residue Asp-367, which is critical for Ca 2ϩ sensing (30) (its Ca 2ϩ -coordinating role has been suggested (32) but not yet experimentally demonstrated (25,27,29)). These Ca 2ϩ -sensing sites differ in several respects, including: structure and relative positions within the gating ring and RCK domains (Fig. 1) (27)(28)(29); affinity and selectivity for divalent cations (34); apparent voltage dependence of Ca 2ϩ binding (55); and role in epilepsy/dyskinesia-causing BK channel mutants (56). Given these established differences, we asked whether the two high affinity Ca 2ϩ sensors also exert different contributions to the pore and VSD activation. To assess the role of these modules in the allosteric interaction between the gating ring and the VSD, the two high affinity Ca 2ϩ -sensing sites were separately neutralized by introducing mutations D362A/ D367A (in RCK1) (30) and D894N/D895N/D896N/D897N/ D898N (in RCK2) (36). In individual experiments measuring D362A/D367A channels, following UV flash photolysis, the rapid increase of [Ca 2ϩ ] i induced a detectable shift toward more negative potentials in both the G(V) and F(V) curves. The shift was in the same direction as was observed in pWT channels, but smaller (Fig. 3, A and B), suggesting that residues Asp-362/Asp-367 are not necessary to mediate the propagation of Ca 2ϩ -induced gating ring rearrangements to the VSD.
On the other hand, in D894N/D895N/D896N/D897N/ D898N channels, there was no obvious effect of intracellular Ca 2ϩ release on the F(V) curve (Fig. 3, C and D). Still, the P o of FIGURE 2. Intracellular Ca 2؉ photo release induces conformational changes of the VSD of BK channels. A, K ϩ current and fluorescence traces simultaneously recorded during depolarizations to the indicated potentials from an oocyte expressing pWT channels are shown superimposed. Caged Ca 2ϩ release was triggered 60 ms after the onset of depolarization by UV light flashes delivered onto the oocyte. In this experiment [Ca 2ϩ ] i increased from 10 to 84 M. Ionic current and fluorescence signals increased following UV flashes. The photodiode amplifier was blanked for 3 ms during the UV flash to prevent overload. B, normalized fluorescence (F) and K ϩ conductance (G) data from the experiment in A, before and after UV flashes, were fit to a single Boltzmann distribution. Both curves were leftward-shifted at high [Ca 2ϩ ] i : before UV, GV half ϭ 0 mV and FV half ϭ Ϫ37 mV; after UV, GV half ϭ Ϫ51 mV and FV half ϭ Ϫ63 mV. Note the crossing of G(V) and F(V) curves after Ca 2ϩ release, consistent with the view that Ca 2ϩ can open BK channels at membrane potentials where VSDs are not activated (5,6,16,52). this mutant was increased by the elevation of [Ca 2ϩ ] i , as demonstrated by the leftward-shifted G(V) curve following Ca 2ϩ release (Fig. 3D). The absence of detectable Ca 2ϩ -induced VSD conformational changes excludes a direct effect of Ca 2ϩ on the BK VSD (e.g., mediated by a charge screening effect), implying a functional, allosteric coupling between the calcium bowl and VSD.
We analyzed results from all experiments, as depicted in Fig.  4. The Ca 2ϩ -induced shift of the half-activation potential of G(V) curves (⌬GV half ) was consistently associated with a shift of the F(V) curves (⌬FV half ) in the same direction, but only with an intact calcium bowl (Fig. 4A). To quantify the dependence of observed shifts in G(V) and F(V) curves upon Ca 2ϩ release in pWT and mutants channels, we performed a statistical analysis as described under "Experimental Procedures." We found a strong monotonic correlation between Ca 2ϩ release (⌬kTln[Ca 2ϩ ]) and G(V) and F(V) voltage shifts in pWT and in the D362A/D367A mutant (Fig. 4, B and C). This was also true for the D894N/D895N/D896N/D897N/D898N mutant in the case of z L *GV half (p Ͻ 0.001), but not in the case of 4z J *⌬F Ϫ V half (p ϭ 0.705). Furthermore, normalizing the voltage shifts by the change in Ca 2ϩ chemical potential (⌬) abolished the correlation between shifts of FV half and GV half as shown by theclustering of the data points (Fig. 4, E-G). We interpreted these data as a demonstration of the obligatory dependence of FV half and GV half on [Ca 2ϩ ]. The normalized voltage shift FIGURE 3. RCK1 and RCK2 are not functionally equivalent Ca 2؉ sensors. A, K ϩ current and fluorescence traces simultaneously recorded during depolarizations to the indicated potentials from a representative oocyte expressing BK channels with neutralized high affinity Ca 2ϩ sensing in RCK1 (D362A/D367A) are shown superimposed. Caged Ca 2ϩ release was triggered 35 ms after the onset of depolarization by challenging the oocyte with UV light to produce [Ca 2ϩ ] i increase from 137 to 320 M. As in the pWT channels, ionic current and fluorescence increased following UV flash. The photodiode amplifier was blanked for 3 ms during the UV flash to prevent overload. B, normalized fluorescence (F) and K ϩ conductance (G) data from the experiment in A, before and after UV flashes, were fit to a single Boltzmann distribution. Both curves were leftward-shifted at high [Ca 2ϩ ] i : before UV, GV half ϭ Ϫ21 mV and FV half ϭ Ϫ85 mV; after UV, GV half ϭ Ϫ35 mV and FV half ϭ Ϫ101 mV. C, as in A, from an oocyte expressing BK channels with neutralized calcium bowl in RCK2 (D894N/D895N/D896N/  D897N/D898N, D894 -898N). Following UV flash, [Ca 2ϩ ] i increased from 105 to 210 M. Only ionic currents were affected by Ca 2ϩ uncaging. D, as in B, for data from calcium bowl mutant in C. Before UV, GV half ϭ 3 mV and FV half ϭ Ϫ79 mV; after UV, GV half ϭ Ϫ26 mV and FV half ϭ Ϫ78 mV.
was statistically different from zero for all channels in the case of G(V) and also for pWT and RCK1 mutant D362A/ D367A in the case of F(V) (Fig. 4, E and F), but there was no significantly detectable shift in 4z J *⌬FV half /⌬ in the case of RCK2 mutant D894N/D895N/D896N/D897N/D898N (Fig.  4G). Thus, with the exception of the RCK2 mutant, an increase in intracellular [Ca 2ϩ ] consistently produced a leftward shift in the activation curves (⌬GV half ) associated with a statistically significant shift of the voltage sensor activation (⌬FV half ) in the same direction.
These results suggest that RCK1 and RCK2 employ different allosteric pathways to bring about Ca 2ϩ -mediated activation. To quantify the mechanistic interpretation of the experimental results, we fit the data with an allosteric statistical-mechanical model.
An Allosteric Model of BK Channel That Accounts for Presence of Two High Affinity Ca 2ϩ Sensors per Subunit-The experimental data suggest that Ca 2ϩ binding to RCK1 and RCK2 high affinity Ca 2ϩ sensors results in different effects on BK activation. To interpret our data in the context of an allosteric scheme, we constructed a statistical-mechanical model inspired by the equilibrium Horrigan and Aldrich model of BK channel activation (6). The Horrigan and Aldrich model describes the allosteric interactions linking voltage sensing, Ca 2ϩ binding, and pore opening in BK channels. We expanded on the Horrigan and Aldrich model to include two Ca 2ϩ -sensing domains per subunit ( Fig. 5 and supplemental data), each capable of interacting with the Pore (allosteric factors C 1 and C 2 ), with the VSD (allosteric factors E 1 and E 2 ), and with each other (allosteric factor F). The normalized G(V) and F(V) data obtained at two different [Ca 2ϩ ] (before and after UV photolysis) from pWT, RCK1 mutant, and RCK2 mutant channels were simultaneously fit to the model ( Fig. 6 and Table 1): F(V) data were fit to the model prediction of VSD activation, whereas G(V) data were fit with P o , as previously (19). As a further constraint, we simultaneously fit averaged values of GV half as a function of [Ca 2ϩ ] for the three BK channel clones (supplemental Fig. S1C and Fig. 6D). In fitting the mutant channels, we minimized the number of parameters needed to obtain good fits while constraining the remaining variables to their pWT equivalent. Because it appears that RCK1 retains its high affinity Ca 2ϩ binding properties when D362/D367 are neutralized (25), K d1 in the RCK1 mutant was constrained to be equal to the corresponding pWT value. Intersubunit interactions between BK regulatory domains were forbidden; previous work has indicated that such interactions do not play a major role (57).
The best set of fitting parameters that accounts for the experimental data is reported in Table 1. The valence of the VSD charge is z J ϭ 0.6 e 0 , similar to what has been reported for the R207Q BK channel (18). The opening of the channel (C-O transition) is also intrinsically voltage-dependent (z L ϭ 1 e 0 ), in general agreement with previous works (6,18). During the simultaneous fitting, the intrinsic Ca 2ϩ dissociation constants for RCK1 (K d1 ) and RCK2 (K d2 ) were constrained to within the range reported by a recent study (55), resulting in K d1 ϭ 10.03 M and K d2 ϭ 2.98 M for pWT channels (Fig. 6A). We also   Table 1.

TABLE 1
Fitting parameters for the model predictions shown in Fig. 6 For the mutants only parameters different from pWT are reported. found that, in the Ca 2ϩ -bound state, RCK1 strongly stabilized VSD activation (E 1 ϭ 10) and, to a lesser extent, the conducting state (C 1 ϭ 2.84). On the other hand, RCK2 efficiently facilitated pore operation (C 2 ϭ 10.41) and exerted a positive cooperativity on VSD activation (E 2 ϭ 2.28). A negative cooperativity was exhibited between the two Ca 2ϩ -sensing domains (F ϭ 0.02), as also suggested by a previous investigation (55).

DISCUSSION
BK channels combine properties of both voltage-and ligandgated ion channels, a feature that allows them to integrate information on membrane potential and [Ca 2ϩ ] i to control key physiological processes such as the smooth muscle tone, cochlear hair cell tuning, neuronal excitability, neurotransmitter release, insulin secretion, and oxygen sensing (10, 11, 59 -63). The interaction between voltage and Ca 2ϩ sensing mechanisms was proposed for native BK channels reconstituted in lipid bilayer (52) and further investigated in cloned BK channels, demonstrating the allosteric nature of the dual activation mechanism (6,9,12,55,64). In this work, the interplay between transmembrane VSD and intracellular gating ring with the BK pore was investigated using voltage-clamp fluorometry combined with UV flash photolysis of DM-Nitrophen to elicit a fast, reversible, and reproducible increase in intracellular free [Ca 2ϩ ] ( Fig. 2 and supplemental Figs. S2 and S3). In the human BK channel (Slo1), we provided experimental evidence that the rapid increase of [Ca 2ϩ ] i induces a conformational change that, originating in the gating ring, propagates to the VSD, facilitating its activation ( Figs. 2A and 4). Indeed, the purified BK gating ring in solution can undergo Ca 2ϩ -driven structural rearrangements, resulting in an overall decrease of its hydrodynamic radius (39). Likely, both RCK1 and RCK2 contribute to the Ca 2ϩ -induced rearrangements of the gating ring, based on the sensor/transducer properties of isolated RCK1 and RCK2 homomers (24,25).
Moreover, a physical proximity of VSD and gating ring is suggested by their mutual coordination of Mg 2ϩ (10,11,35,65). Atomic structures of the BK gating ring (27)(28)(29), have pinpointed the locations of the calcium bowl (in RCK2) and Asp-362/Asp-367 residues (in RCK1) that, in the whole channel, could face the intracellular portion of the VSD (Fig. 1).
Using a statistical-mechanical model inspired by the Horrigan and Aldrich model (6) but accounting for two distinct Ca 2ϩ sensors (Fig. 5), we quantified the allosteric interactions between pore, VSD, and the two RCK domains. In pWT channels, the model predicted salient differences in the allosteric coupling between RCK1 and RCK2 with the VSD and the pore ( Table 1), suggesting that they are functionally separable, despite their structural homology. RCK1 and RCK2 are allosterically coupled by negative cooperativity, such that the activation of one domain disfavors the activation of the other, recapitulating the findings of Sweet and Cox (55). The functional impairment of Ca 2ϩ sensing either in RCK1 or in RCK2 highlighted their functional diversity. In D362A/D367A mutants, a rapid increase in [Ca 2ϩ ] i significantly facilitated pore and VSD activation (Figs. 3A and 4), as indicated by the consistent leftward shifts of both G(V) and F(V) curves at the highest [Ca 2ϩ ] i (Figs. 3B and 4). This effect was likely mediated by intact calcium bowls in RCK2 domains. The effect of the D362A/D367A is largely accounted for by the loss of cooperativity between RCK1 and the pore (allosteric factor C 1 ) ( Table 1 and Fig. 6B). It is interesting that the model can account for the effects of the D362A/D367A mutation without reducing the intrinsic Ca 2ϩ affinity of the RCK1 domain (K d1 ). This prediction would be in agreement with the lack of direct experimental evidence that Asp-362/Asp-367 residues are essential for Ca 2ϩ coordination. However, a potential Ca 2ϩ -binding site involving Asp-367 and other residues has been proposed based on electrophysiological evidence (30,34,55) and inference from the gating ring crystal structure (28,32). Interestingly, the neutralization of calcium bowl abolished the Ca 2ϩ -induced facilitation of the VSD activation; indeed, the F(V) curves were not significantly modified by the Ca 2ϩ release (Figs. 3D and 4). To account for these experimental data, three model parameters were considerably altered compared with the corresponding pWT values ( Table  1), suggesting that the neutralization of the five Asp residues not only abolished a high affinity Ca 2ϩ -binding site (calcium bowl) but also altered the energetics of gating ring operation, likely because of a structural perturbation.
Recent work has pointed out an important functional difference between RCK1 and RCK2: Ca 2ϩ binding to the RCK1 domain (but not to RCK2) is voltage-dependent (55). To test the validity of our model prediction, we computed the steadystate occupancy of the Ca 2ϩ -bound state for RCK1 and RCK2. We found that, for a wide range of membrane potentials, the occupancy of RCK1 Ca 2ϩ -bound state was voltage-dependent, whereas RCK2 Ca 2ϩ binding was weakly affected by membrane potential (supplemental Fig. S4). Thus, despite their structural homology, RCK1 and RCK2 domains provide different contribution to the Ca 2ϩ -dependent activation of BK channels.
The importance of achieving a deeper understanding of the BK channel biophysical properties resides in its involvement in several diseases, such as hypertension, epilepsy, schizophrenia, and diabetes (11,62,63,66). In particular, elucidating the mechanisms underlying the functional coupling between VSD and the two distinct Ca 2ϩ sensors is fundamental for the physiology and pathophysiology of excitable cells. For instance, the Slo1 epilepsy/dyskinesia-causing mutation affects Ca 2ϩ -dependent activation originating from the Ca 2ϩ -binding site in RCK1, but not in RCK2, by altering the coupling mechanism between Ca 2ϩ binding and gate opening (56).
In summary, we have directly probed the allosteric nature of BK channel Ca 2ϩ -dependent activation by optically tracking VSD movements perturbed by Ca 2ϩ binding to the gating ring, under voltage clamp. By investigating channels impaired in high affinity Ca 2ϩ -sensing sites, we revealed that the two BK Ca 2ϩ sensors are not functionally equivalent: although both contribute to Ca 2ϩ -dependent channel activation, the efficiency of the allosteric interactions appears different. A functional calcium bowl (RCK2) is required to observe the propagation of Ca 2ϩ -induced "wave" of rearrangements from the cytoplasmic portion to the transmembrane VSD. The results were fit with a statistical-mechanical allosteric model to quantify the cooperative interactions among the prominent BK regulatory domains. Although this approach was successful in dissecting the allosteric contributions of high affinity Ca 2ϩsensing domains to BK channel activation, it did not explore the role of low affinity Ca 2ϩ -sensing sites (30,(33)(34)(35), because the experimental [Ca 2ϩ ] range was limited to prevent their significant engagement. Nevertheless, it would be of great interest to further investigate their allosteric contribution to BK channel operation to better understand the complex mechanism of BK channel activation.