Structural Basis for Calcium and Magnesium Regulation of a Large Conductance Calcium-activated Potassium Channel with β1 Subunits*

Background: Large conductance calcium-activated potassium (BK) channels are regulated by β1 subunits. Results: We identified two binding sites engaged in intersubunit interactions to regulate the sensitivity of BK to divalent ions. Conclusion: Both electrostatic and hydrophobic sites enhance the calcium sensitivity of BK, whereas the hydrophobic site selectively reduces the magnesium sensitivity. Significance: This work provides structural and mechanistic insights into the molecular mechanism of BK(β1) gating. Large conductance Ca2+- and voltage-activated potassium (BK) channels, composed of pore-forming α subunits and auxiliary β subunits, play important roles in diverse physiological activities. The β1 is predominately expressed in smooth muscle cells, where it greatly enhances the Ca2+ sensitivity of BK channels for proper regulation of smooth muscle tone. However, the structural basis underlying dynamic interaction between BK mSlo1 α and β1 remains elusive. Using macroscopic ionic current recordings in various Ca2+ and Mg2+ concentrations, we identified two binding sites on the cytosolic N terminus of β1, namely the electrostatic enhancing site (mSlo1(K392,R393)-β1(E13,T14)), increasing the calcium sensitivity of BK channels, and the hydrophobic site (mSlo1(L906,L908)-β1(L5,V6,M7)), passing the physical force from the Ca2+ bowl onto the enhancing site and S6 C-linker. Dynamic binding of these sites affects the interaction between the cytosolic domain and voltage-sensing domain, leading to the reduction of Mg2+ sensitivity. A comprehensive structural model of the BK(mSlo1 α-β1) complex was reconstructed based on these functional studies, which provides structural and mechanistic insights for understanding BK gating.

BK 4 channels play critical roles in modulating many physiological activities, such as neurotransmitter release and endo-crine secretion in neurons or endocrine cells, contraction of smooth muscle cells, and even frequency tuning in hair cells (1)(2)(3)(4)(5). These large conductance channels exhibit a considerable functional diversity with respect to their kinetic behavior, apparent Ca 2ϩ and Mg 2ϩ regulation, and pharmacological sensitivity to toxins (6,7). The cytosolic domain (CTD) of the BK channel contains multiple divalent ion binding sites, including two Ca 2ϩ binding sites with high and moderate affinity respectively as well as a low affinity Mg 2ϩ binding site (8 -10). Functional heterogeneity of native BK-type channels is often imparted by their association with tissue-specific auxiliary ␤1-␤4 subunits. For example, the mSlo1 ␣ subunits and ␤1 subunits are mostly co-localized in smooth muscle cells in heart and vascular tissues (11)(12)(13). These auxiliary subunits share a similar topology of two transmembrane (TM1 and TM2) segments, intracellular N and C termini, and a large extracellular loop (14 -18). One BK channel can associate with up to four auxiliary ␤ subunits in 1:1 stoichiometry with mSlo1 ␣ subunits (19,20). The ␤1 and ␤2 subunits of the ␤ family share the highest sequence homology and increase the apparent Ca 2ϩ sensitivity of BK channels (15,19,20). Several laboratories have reported that magnesium is also able to activate BK channels at the mSlo1(E374,E399) sites (9,10), and the locus of the Mg 2ϩ binding domain resides in the cytosolic terminal of S4 between the voltage-sensing domain (VSD) and the first C-terminal regulators of K ϩ conductance (RCK1) (21). Previous studies have reported that Mg 2ϩ sensitivity of BK is attenuated by ␤1 (22) and subsequently by ␤2 but to different extent (23). These reports imply that ␤ subtype-dependent differences in the sensitivity to Ca 2ϩ and Mg 2ϩ are possibly derived from their distinct structures.
In order to determine the intracellular activation sites between the mSlo1 ␣ and ␤1 subunits, we used double mutant cycle analysis to examine interaction based on the changes of free energy between the potential coupling residues. We found two crucial interaction sites on ␤1, namely an electrostatic enhancing (E) site and a hydrophobic (H) site in the cytosolic region for its coupling to mSlo1 ␣. We further constructed a computational model of the mSlo1-␤1 channel complex in the context of its structural and functional feasibility. Altogether, our results provided a putative working model of the mSlo1-␤1 complex, capable to explain both the Ca 2ϩ and Mg 2ϩ sensitivity of BK(␤1) channels.

EXPERIMENTAL PROCEDURES
Constructs and Mutations-All ␣-subunit constructs were made from the mbr5 splice variant of mouse Slo1 (KCNMA1; GenBank TM accession number L16912). Human ␤1 (KCNMB1; GenBank TM accession number U25138.1) cDNAs were subcloned into pcDNA3.1. Mutations were introduced using the QuikChange site-directed mutagenesis kit (Stratagene). Specifically, the mutant mSlo1(D898N/D899N/D900N/D901N/D903N) (mSlo1(5D5N)) in the calcium bowl of RCK2 was constructed. All constructs and point mutations were verified by direct DNA sequence analysis. Fig. 1 shows the topological map of the constructs and mutations for all of the experiments.
Cell Culture and Transient Transfections in HEK293 Cells-HEK293 cells were cultured in DMEM supplemented with 10% fetal bovine serum (FBS), 100 units/ml penicillin, and streptomycin in incubators with 37°C and 5% CO 2 . One day before transfection, cells were transferred to 24-well plates. At 90% confluence, transfections could be performed with Lipofectamine 2000 (Invitrogen). 4 -6 h after transfection, the cells were transferred to a poly-D-lysine (Sigma)-coated slide for the patch clamp recordings. For all of the co-transfections, the ratio of ␣ to ␤ subunits was 1:2.
Patch Clamp Recording-For recordings, transfected HEK293 cells were transferred 1 day after transfection to 160 K ϩ solution containing 160 mM MeSO 3 K, 2 mM MgCl 2 , 10 mM HEPES (pH 7.0). All experiments were carried out with excised patches, in inside-out recording configuration. Patch pipettes were

BK channel act dea
ms ms Homology Modeling-The full models of BK channel were built by homology modeling combination with the known partial crystal structure of ion channels (i.e. RCK domains), and then the complex of mSlo1 and h␤1 were assembled manually. During the modeling process, the S1-S6 domains were built from MthK (Protein Data Bank entry 1LNQ) and KcSA (Pro- tein Data Bank entry 1K4C). The closed state RCK model was from previous reports (31, 32) (Protein Data Bank entry 3U6N). The S0 helix of BK and the TM1 of h␤1 was orientated manually according to another publication (29). The loosed loops of RCK and the linker of S0-S1 were also rebuilt and refined. The N-terminal 22-amino acid structure of ␤1 was constructed and refined by Amber12 with ff13 force field. First, the linear peptide was built with xleap of AmberTool13 and then minimized for 1000 steps, followed by 100,000 heating steps for 0 -325 K; finally, 50,000,000 equilibration steps were taken for the whole ensemble. The simulation time is 50 ns to make the conformation more stable. During the whole construction process, the 22-amino acid peptide was put into implicit generalized Born solvent with 1-fs time step. Then the combination of 22-amino acid N terminus and TM1 helix of ␤1 subunit was constructed manually and put into a pre-equilibrated 1-palmitoyl-2-oleoylphosphatidylcholine membrane ensemble with explicit SPC water model and refined for another 50 ns by Molecular Dynamics Suite, Desmond version 3.6 (33). Similar to the BK(␤2) complex, the combined model of full BK channel and partial ␤1 was assembled and embedded into an larger membrane ensemble with 1-palmitoyl-2-oleoyl-phosphatidylcholine, explicit SPC water model, and 160 mM KCl and then refined by a 5-ns standard molecular dynamics simulation with the Nosé-Hoover chain thermostat method and Martyna-Tobias-Klevin barostat method in Desmond version 3.6.

␤1 Modifies BK Channel Activation
Data Analysis-Recording data were analyzed with Clampfit (Axon Instruments, Inc.) and Sigmaplot (SPSS, Inc.) software. Unless otherwise stated, data are presented as mean Ϯ S.D. G-V curves for activation were fitted by the single Boltzmann function with the form, G/G max ϭ (1 ϩ exp((V Ϫ V 50 )/)) Ϫ1 , where V 50 is the voltage at which the conductance (G) is half the maximum conductance (G max ), and is a factor affecting the steepness of the activations.

RESULTS
Determination of the Enhancing Site of mSlo1(␤1) Channels-Both ␤1 and ␤2 subunits can enhance the Ca 2ϩ sensitivity of BK channels (34 -37). In previous work, we determined the complementary paired residues mSlo1(K392,R393)-␤2(E44,D45) as an enhancing (E) site of BK (␤2) channels (26). After comparing the sequences of ␤1 and ␤2, we found that a pair of conserved residues, ␤1(E13,T14), may play a role similar to that of ␤2(E44,D45). To explore the possible interaction between two groups of residues, we performed thermodynamic double mutant cycle analysis (38 -41). Changes of free energy coupling between mutations in pairs of residues located in different subunits were respectively calculated by using a thermodynamic square composed of the WT complex (␣␤), the two single mutants (␣*␤ and ␣␤*), and the corresponding double mutant (␣*␤*) (asterisks denote a mutation). The thermodynamic square was described as follows, ⌬⌬G ϭ ⌬G ␣␤* ϩ ⌬G ␣*␤ Ϫ ⌬G ␣*␤* . A distinct change of ⌬⌬G Ն 1 kcal/mol would be judged to be coupled; otherwise it was not.
Non-electrostatic Interaction between ␤1(K3,K4) and Calcium Binding Bowl-There are two different types of residues in the N terminus of the ␤1 subunit, namely electrostatic typelike ␤1(K3K4) and hydrophobic type-like ␤1(L5,V6,M7). There are many potential residues in the RCK domain of the BK ␣ subunit that may couple with two types of binding sites, but we reason that two prerequisites must be satisfied: accessibility and associability. For the basic residues ␤1, the acidic ones in the RCK domain of BK ␣ subunit near the ␤1(K3K4) are strong candidates, whereas the hydrophobic ones in the RCK domain probably bind to hydrophobic residues ␤1(L5,V6,M7).
We previously reported that the Ca 2ϩ bowl exerted a force onto the S6 gate of BK(␤2) via the calcium bowl site (19), raising the possibility that there may be another pathway in ␤1, distinct from that in ␤2. To this end, it is necessary to examine the second calcium binding site mSlo1(D362,D367)of BK channel (9). In other words, the mSlo1(D362,D367)-␤1(K3,K4) may play a role in regulating the BK gating similar to that of mSlo1(5D5N)-␤2(K33,R34,K35) (26). Contrary to our expectation, we found that their ⌬⌬G was about 0.1 kcal/mol (Fig. 3C), suggesting that there was no significant interaction between the mSlo1(D362,D367) and the ␤1 (K3,K4).
Taken together, there was no electrostatic interaction between the mSlo1 and the ␤1 (K3,K4).
A Putative Structural Model of BK(␤1) Channels-As we described the above, both the E and H sites enhanced the calcium sensitivity of BK channels. To further verify their feasibilities in space structure, we constructed a model of BK channel by homology modeling using the known partial crystal structure of BK channels (i.e. the published crystal structure of RCK domains) and manually assembled mSlo1 and ␤1 complex (see "Experimental Procedures"), in which the location of ␤1(TM1) is placed next to both S1 and S2 of Slo1 (Fig.  5A) (29). Based on this information, we noticed in molecular dynamics simulations that the ␤1(E13,T14) was just located at the top of mSlo1(K392,R393) with a mean distance of about 3.8 -4.4 Å in between and that the side chains of three residues ␤1(L5,V6,M7) were lined in parallel with that of mSlo1(L906,L908), co-localized within close proximity of the residues mSlo1(L906,L908) (Fig. 5B). This suggests that the enhancing force by Ca 2ϩ binding was possibly coming from H 3 E 3 PGD, forming a pathway of enhancing Ca 2ϩ sensitivity of BK channels. Along with our experimental results, these simulations led us to suggest that both electrostatic and hydrophobic effects appear to be synergistic for Slo1 ␣ and ␤1 interactions.
H Site Reducing Magnesium Sensitivity of BK(␤1) Channel-Previous studies revealed that the Mg 2ϩ binding site was located in the VSD and cytosolic domain (CTD) interface of mSlo1 (7) and that the ␤1 reduced the Mg 2ϩ sensitivity by directly altering the structural configuration of the Mg 2ϩ binding site (23). To examine which site, ␤1(L5,V6,M7) or ␤1(E13,T14), could affect the Mg 2ϩ sensitivity of BK(␤1) channels, we performed experiments in a variety of Mg 2ϩ concentrations and found that the G-V curve showed a leftward shift of 28.5 and 57.1 mV in 10 mM Mg 2ϩ , in the presence and absence of ␤1 subunits, respectively, compared with 0 Mg 2ϩ (Fig. 6, A-C). This indicates that the ␤1 reduces the Mg 2ϩ sensitivity of BK channels. Here we noticed that the peak currents of BK in Mg 2ϩ experiments varied widely due to the blockage of Mg 2ϩ while the Mg 2ϩ concentrations were elevated. The G-V curve showed a leftward shift of 56.7 mV in 10 mM Mg 2ϩ in the presence of ␤1(L5Q,V6Q,M7Q) (Fig. 6, B and C). Similarly, the G-V curve of mSlo1(L906Q,L908Q)-␤1 channels had a leftward shift of 50.4 mV. These results suggest that both the mutants ␤1(L5Q,V6Q,M7Q) and mSlo1(L906Q,L908Q) could eliminate the ␤1-induced reduction of Mg 2ϩ sensitivity of BK(␤1) channels. Correspondingly, the G-V curve of ␤1(E13K,T14K) only showed a leftward shift of 30 mV in 10 mM Mg 2ϩ , similar to that of the WT ␤1 (Fig. 6C), indicating that the H site but not the E site affected the Mg 2ϩ sensitivity of BK(␤1) channels (Fig.  6D). When Mg 2ϩ was increased to 50 mM, we found even greater leftward shifts of V 50 (Fig. 6, A-D), again demonstrating that only the H site affected the Mg 2ϩ sensitivity of BK(␤1) channels.

DISCUSSION
BK channels function differently due to their auxiliary ␤ subunits, which underlie their diverse physiological roles in a variety of cells. A lack of detailed structural information of the mSlo1 ␣-␤1 complex has precluded us from fully understanding their coupling mechanisms. It was hypothesized that ␤1 somehow altered the structural conformation of the Mg 2ϩ site to weaken the action of VSD to PGD (Fig. 7A) (18). In this study, we demonstrated two complementary pairs of residues located in the CTD, of which the E site only modulated the Ca 2ϩ sensitivity, and the H site modulated both the Ca 2ϩ and Mg 2ϩ sensitivity of BK(␤1) channels. Our findings indicated that the H site might play a role as a pivot in transferring a Ca 2ϩ -binding force from the calcium bowl in the CTD, which might disturb the structural configuration of the Mg 2ϩ site to decrease the Mg 2ϩ -binding force onto VSD, ultimately weakening the channel gating. At the same time, the E site served as a scaffold between the membrane-spanning and RCK domains of mSlo1, boosting the force from the H site to enhance channel gating (Fig. 7B).
Surprisingly, we found that the H site of ␤1 was composed of hydrophobic residues, different from the electrostatic site as in ␤2, although they share similar basic residues at the corresponding position of their N-terminal sequences, indicating that these two subunits have different N-terminal structures. The structure derived from molecular dynamics simulation indicates that the N terminus of ␤1 has a looplike conformation with no secondary structure, which makes ␤1(L5,V6,M7) interact with mSlo1(L906/L908) more readily. Unlike the corresponding basic residues ␤2(K33,R34,K35) the basic residues ␤1(K3,K4) are located far from the calcium bowl site, suggesting that there is a marked spatial difference in structural arrangement between the N termini of ␤1 and ␤2 (26). Given that both the ␤1 and ␤2 subunits reduce Mg 2ϩ sensitivity (23), we deduce that the perturbation of the Mg 2ϩ binding sites ultimately attenuates the Mg 2ϩ sensitivity of BK(␤1) and BK(␤2) channels, because the N termini of ␤1 and ␤2 binding to the cytosolic domain may enlarge the distance between VSD and CTD.
In conclusion, we demonstrated that the N terminus of ␤1 contained an H site in addition to the electrostatic sites as previously described in the N terminus of ␤2 (26). This novel H site of ␤1 imparts unique function distinct from that of ␤2, despite their similar sequences, impacting BK gating with a different mechanism. Additionally, our methods developed in this study may help to further explore how other subunits, such as ␤3 and ␤4, differentially regulate the sensitivity of BK channels to divalent ions.