Interaction Sites between the Slo1 Pore and the NH2 Terminus of the β2 Subunit, Probed with a Three-residue Sensor*

Calcium- and voltage-gated (BK) K+ channels encoded by Slo1 play an essential role in nervous systems. Although it shares many common features with voltage-dependent KV channels, the BK channel exhibits differences in gating and inactivation. Using a mutant in which FWI replaces three residues (FIW) in the NH2 terminus of wild-type β2-subunits, in conjunction with alanine-scanning mutagenesis of the Slo1 S6 segment, we identify that the NH2 terminus of β2-subunits interacts with the residues near the cytosolic superficial mouth of BK channels during inactivation. The cytosolic blockers did not share the sites with NH2 terminus of β2-subunits. A novel blocking-inactivating scheme was proposed to account for the observed non-competition inactivation. Our results also suggest that the residue Ile-323 plays a dual role in interacting with the NH2 terminus of β2-subunits and modulating the gating of BK channels.

K ϩ channels (K V channels). For K V channels, N-type inactivation arises from the cytosolic NH 2 terminus of the pore-forming ␣-subunits (7,8) or the auxiliary ␤-subunits (9) inserting into the ion permeation pathway thereby blocking conduction ion permeation. Previous studies show that the NH 2 terminus of either the ␣or ␤-subunit requires an inactivation domain (ID) composed of a hydrophobic head group to inactivate channels, followed by several positively charged amino acids (10,11). Xia et al. (12) reported that the uncharged hydrophobic head group (FIW) of the h␤2 NH 2 terminus results in the inactivation of BK channels and proves that it is the only structural determinant required for inactivation.
Evidence supporting the idea that the ID must insert into the pore is derived from the blocking experiments of K V channels by cytosolic blockers, which compete with the ID for channel occupancy (13,14), thus resulting in the slowing of inactivation kinetics. Another report from McKinnon's laboratory (15) demonstrated that the first four residues of the NH 2 terminus of an inactivating K V ␤ auxiliary subunit indeed interact with pore-lining residues of the K V 1.4 ␣-subunit. By contrast with K V channels, cytosolic blockers of BK channels do not slow the inactivation kinetics, indicating that there is no competition between these blockers and the ID of h␤2-subunits (3,16,17). For BK channels, there are two questions to be left, that is, how the ID interacts with the channel pore and why the cytosolic blocker of BK channels does not compete with the ID.
With a mutant FWI, which is obtained from substituting the initial three amino acids (FIW) of the h␤2-subunit NH 2 terminus with FWI, and a systematic alanine-scanning mutagenesis of the mSlo1 S6 segment, we demonstrate that the residue Ile-323 of mSlo1 ␣-subunits plays a dual role in interacting with the ID of h␤2-subunits and modulating the gating of BK channels. We examined the binding sites of both the cytosolic blockers and the ID of h␤2-subunits and developed a new model for explaining the non-competition mechanism of inactivating BK channels. The present findings may underlie the gating and inactivating mechanisms of BK channels.

EXPERIMENTAL PROCEDURES
Site-directed Mutagenesis-All mutations of mSlo1 and h␤2 were generated through PCR reactions, and all constructs were verified by sequencing. The FWI mutation of the wild-type h␤2 * This work was supported by the National Science Foundation of China (Grants 30470449, 30630020, 30670502, 30470646, 30500117, and 20132030), the Major State Basic Research Program of P. R. China (Grant 2004CB720000), and the Chinese Academy of Sciences (Grant KGCX2-SW-213-05). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. □ S The on-line version of this article (available at http://www.jbc.org) contains supplemental Figs. S1 and S2 and Tables S1 and S2. 1 Both authors contributed equally to this work. 2 To whom correspondence may be addressed: was generated by the traditional PCR reaction with the primers 5Ј-GCGCAAGCTTACCACCATGTTTTGGATAACCAGT-GGCCGGACCTCTTCATC-3Ј and 5Ј-GGCCCTCGAG-TTATCTATTGATCCGTTGGATCCTCTCAC-3Ј. The product was digested with HindIII and XhoI and then ligated into HindIII_XhoI vector pBF. Other point mutations of mSlo1 and h␤2 were generated by QuikChange protocol (Stratagene). For example, PCR reactions of mSlo1 were performed with mSlo1 as a template and a pair of complementary mutagenesis primers. The PCR reaction mixture was then cut with the enzyme DpnI to digest the template mSlo1. After DpnI digestion, the PCR mixture was used to transform competent bacterial cells to amplify the mutant plasmid of mSlo1.
Expression in Xenopus Oocytes-After DNA was linearized with MluI, SP6 RNA polymerase (Roche Applied Science) was used to synthesize cRNA for oocyte injection. The stage V-VI Xenopus oocytes were injected with 5-10 ng of cRNAs and then incubated in ND-96 solution at 18°C for 2-7 days. To keep ␤2 (or ␤2 mutants)-subunits at a saturating concentration, we coinjected mSlo1 ␣ (or ␣ mutants) and ␤2 (or ␤2 mutants) mRNAs into oocytes in a ratio of at least 1:2 by weight.
Electrophysiology-Macroscopic currents were recorded in inside-out patches at room temperature (22-25°C). Pipettes were filled with a solution containing the following (in millimolar): 160 MeSO 3 K, 10 H ϩ -HEPES, and 2 MgCl 2 , adjusted to pH 7.0 with MeSO 3 H. Intracellular solutions with different free [Ca 2ϩ ] were made by mixing 160 mM MeSO 3 K and 10 mM H ϩ -HEPES with Ca(MeS) 2 and 5 mM HEDTA (for 10 M) or 5 mM EGTA (for 0 M). Free [Ca 2ϩ ] was defined by the EGTAETC program (E. McCleskey, Vollum Institute, Portland, OR), with the pH adjusted to 7.0. Patch pipettes pulled from borosilicate glass capillaries had resistances of 2-6 M⍀ when filled with internal solution. Experiments were performed and recorded using an EPC-9 patch clamp amplifier and PULSE software (HEKA Elektronic, Lambrecht/Pfalz, Germany). Currents were typically digitized at 20 kHz. All macropatch records were filtered at 2.9-kHz during digitization. For displays, currents were filtered digitally at 2 kHz (Bessel 8-pole). All singlechannel currents were recorded at 10 kHz. During recording, solutions with or without the drugs QX-314 (2 mM) or tetraethylammonium (TEA, 50 mM) were puffed locally onto the insideout patches via a puffer pipette containing seven solution tubes. The tip (ϳ300 m diameter) of the puffer pipette was located about 120 m from the patches. As determined by the conductance tests, the solution around a patch under study was fully controlled by the application of a solution with a flow rate of 100 l/min or greater. All pharmacological experiments met this criterion. Chemicals were obtained from Sigma-Aldrich.
Data Analysis-Data were analyzed with IGOR (Wavemetrics, Lake Oswego, OR), Clampfit (Axon Instruments, Foster City, CA), and SigmaPlot (SPSS Science, Chicago, IL) software. Unless stated otherwise, the data are presented as mean Ϯ S.E., significance was tested by Student's t test, and differences between the mean values were considered significant at a probability of Յ0.05. G-V curves for activation were generated from steady-state currents, converted to conductance and then fitted by the single Boltzmann function with the form, 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. Recovery curves were fitted with the bi-exponential function (Equation 2), where a fast , fast , a slow , and slow are the percentages and time constants of fast and slow recovery components, respectively. The first term on the right of Equation 2 was used for the monoexponential recovery.

RESULTS
The Mutation FWI Is a More Sensitive Probe for Screening the Interaction Sites-The pore-forming segment (S6) of the ␣-subunits of BK channels shares homology with the K ϩ channels, several of whose crystal structures have been well resolved (18 -20). After aligning the sequences of mSlo1 with the potassium channels KcsA, K V 1.2, and MthK ( Fig. 1A), we inferred by structural homology that the pore-lining residues in BK channels were Ile-323, Val-319, Phe-315, and Leu-312 (18). The h␤2-subunit of the BK ␣-subunit has two proposed transmembrane (TM) segments with an intracellular NH 2 terminus of 46 amino acids (3). The sequence of the h␤2 NH 2 terminus followed by the predicted first transmembrane (TM1) segment is given in Fig. 1B.
To determine interaction between the ID and pore, the wildtype h␤2 (FIW) usually serves for detecting the interacting residues in the pore by means of alanine mutagenesis of mSlo1 ␣-subunits. The time constant of recovery from inactivation is a good character for this purpose. On the basis of our preliminary results, however, it is difficult to use the FIW to determine the interacting sites due to its doubtful time constants in recovery from inactivation (data not shown). Therefore, it is necessary to find a more sensitive probe for the goal mentioned previously.
After examining wild-type h␤2 (FIW) and three rearranged constructs FWI, IWF, and WIF, we find that they largely share FIGURE 1. Multisequence alignment within the pore region of mSlo1 and three other K V channels and a sequence of the NH 2 terminus of h␤2 used in this study. A, the predicted domains of the P loop and the pore region of the S6 segment of the mSlo1 gene are marked with lines above. Residues in which the nature of the side chain is preserved (Ͼ50% similarity) are marked in gray and homologous residues in black. The arrows in the mSlo1 S6 domain refer to the amino acids we mutated into alanine. The sequences are: mSlo1, Mus musculus, accession number (acc) PIR A48206; K V 1.2, Rattus norvegicus, acc PIR NM_012970; KcsA, Streptomyces lividans, acc PIR S60172; MthK, Methanothermobacter thermautotrophicus, acc PIR AAB85995. B, sequence of NH 2 terminus of the mSlo1 auxiliary h␤2-subunits. TM1 designates the proposed beginning of the first TM segment. The first three hydrophobic residues FIW, which induce inactivation of BK channels (12), are shown in gray. The sequence is: h␤2, human KCNMB2, acc PIR NM_005832. most of kinetic characteristics in activation, inactivation, and recovery, except that the construct FWI exhibits a bi-exponential recovery different from the other mutations (12) (supplemental Fig. S1). For recovery from inactivation, the wild-type h␤2 and IWF and WIF exhibited similar time constants in a mono-exponential recovery (average r ϭ 18.5 Ϯ 4.4 ms at Ϫ140 mV), whereas the mutation FWI exhibited bi-exponential recovery components with a fast component ( r-fast ϭ 6.5 Ϯ 0.6 ms at Ϫ140 mV) and a slow component ( r-slow ϭ 323 Ϯ 46 ms at Ϫ140 mV), ϳ50-fold slower (Fig. 2, A and C, and supplemental Table S1). We infer that the bi-exponential kinetics of FWI in recovery from inactivation mostly results from the residue Trp-3, because tryptophan is bulky and may have significant impact on the pore-lining residues in the S6 region during the recovery process. Despite the differences in the recovery kinetics, we believe that FWI interacts with a similar region of the channel as FIW, because their kinetic characteristics are very similar except for recovery.
Considering that the FWI as an infrequent mutation of the native h␤2 (FIW) exhibits a bi-exponential recovery, we infer that there should be a specific residue in the pore interacting with the FWI more strongly to induce the slow recovery. Furthermore, two components of FWI, especially the slow one, can be used to identify the interaction sites, and these are much better than one component of h␤2 (FIW). Comparing with the results from native h␤2 (FIW), we found in this study that the FWI was a better sensor for exploring interaction sites.
Residue Ile-323 in the Cavity of the mSlo1 Channel Interacts with the ID of the FWI-Because the ID produced inactivation through hydrophobic interaction, we systematically mutated each hydrophobic residue in S6 of BK channel to alanine. Each mutant of the mSlo1 coexpressed with the mutation FWI was termed "mutant mSlo1-FWI," for example, I323A-FWI in this study. For each coexpression such as mutant mSlo1-FWI, all the recovery experiments were performed from inside-out patches by the paired-pulse recovery protocol shown at the bottom of Fig (Fig. 2B). The slow recovery time constant of I323A-FWI r-slow ϭ 43.6 ms is the closest to the monoexponential recovery time constant of the wild-type mSlo1-h␤2 ( r ϭ 21.9 ms). Considering the fact that the residue Ile-323 is a pore-lining residue, thus, we infer that Ile-323 possibly plays a significant role as one of the interaction sites in prolonging recovery from the inactivation. The fast recovery time constants of M314A-FWI and V319A-FWI ( r-fast M314A ϭ 1.9 Ϯ 0.4 ms; r-fast V319A ϭ 1.8 Ϯ 0.5 ms) were significantly faster than those of any other mutations (supplemental Table S2). Both the amino acids Val-319 and Ile-323 probably contribute to the lining toward the inner wall of the pore, whereas the residue Met-314 may not (18). One explanation may be that the mutation M314A allosterically translocates the pore-lining residue Phe-315, which then may alter its contact with the ID of h␤2. Unfortunately, we failed to express mutant F315A (21), which may indicate an unusual structure between the Met-314 and Phe-315. An NMR structure of the h␤2 NH 2 -terminal peptide (22) indicates that the first ten residues of h␤2 are flexible and extendable into a linear peptide structure. Making a rough estimate on the basis FIGURE 2. Mutational analysis of the ID of h␤2-subunits and hydrophobic residues in the S6 pore region of mSlo1 channels. A, currents resulting from mSlo1-h␤2, mSlo1-FWI, I323A-FWI, and mSlo1-FWQ as indicated were activated by a paired pulse protocol with 10 M Ca 2ϩ . The voltage protocol is shown at the bottom. T is the variable time interval between the two pulses. The scale for currents is in arbitrary units. The dotted line is zero-current line. B, for all the mSlo1 mutants coexpressed with FWI, the ratio i / r-fast is referred as K d-fast (fast dissociation constant) and the ratio of i / r-slow as K d-slow (slow dissociation constant). i is the inactivation time constant measured at 100 mV with 10 M Ca 2ϩ , r-fast is the fast component of the recovery time constant at Ϫ140 mV with 10 M Ca 2ϩ and r-slow is the slow one. C, the fractional recovery as a function of recovery time is plotted for the set of traces in A. A single exponential function was fitted through the recovery points of h␤2-mSlo1 (E, r ϭ 21.9 Ϯ 4.8 ms; i ϭ 23.7 Ϯ 2.9 ms; n ϭ 10) and mSlo1-FWQ (OE, r ϭ 10.0 Ϯ 1.7 ms; i ϭ 9.6 Ϯ 1.2 ms; n ϭ 8), and a bi-exponential function was fitted through the points of mSlo1-FWI (⌬, r-fast ϭ 6.5 Ϯ 0.6 ms; r-slow ϭ 323.0 Ϯ 46.0 ms; i ϭ 29.9 Ϯ 2.7 ms; n ϭ 5) and I323A-FWI (F, r-fast ϭ 4.4 Ϯ 1.6 ms; r-slow ϭ 43.6 Ϯ 22.3 ms; i ϭ 27.0 Ϯ 8.0 ms; n ϭ 8). The scale for currents is in arbitrary units.
of an assumed linear inactivation peptide docked within the mSlo1 ion conduction pathway, we hypothesize that Phe-2 in the ID of mutation FWI makes contact with Met-314, Trp-3 with Val-319, and Ile-4 with Ile-323 during the inactivation process.
Both Y318A-FWI and V305A-FWI show slow recovery time constants of over 80 ms, which are 4-fold that of mSlo1-h␤2 (22 ms) or 2-fold that of I323A-FWI (40 ms) (see supplemental  Table S2). As the residue Tyr-318 is next to the pore-lining residue Val-319, we reckoned that it could interact with the ID also. For V305A, its influences were not so significant as the ones of the I323A or V319A in either slow or fast recovery components (Fig. 3). Secondly, the ID should interact with the residues clustering in a small group, not an isolated residue as Val-305 does. Finally, the structure model of mSlo1 shows that the Val-305 in S6 might indirectly affect the slow recovery rate through forming a hydrophobic cluster with the neighboring residues in the S5 and S6. Thus, there is little possibility that Val-305 is one of the interaction sites with the ID.
To confirm the interaction between Ile-4 and Ile-323, we attempted to alter the hydrophobic residue Ile-4 in the FWI to a hydrophilic residue, i.e. a new mutant FWQ, to eliminate the slow recovery process. The fractional recovery from inactivation for mSlo1-FWQ and three other combinations of constructs are shown in Fig. 2C. Clearly, both the mSlo1-FWQ and mSlo1-h␤2 have only a single exponential recovery, but mSlo1-FWI exhibits two obvious exponential recovery components. Because the FWQ has the lesser hydrophobicity, the time constants of both recovery and inactivation of mSlo1-FWQ are faster than that of mSlo1-h␤2. The mono-exponential recovery curves of mSlo1-FWQ and mSlo1-h␤2 demonstrate a specific steric requirement for Ile-4 in the ID to directly interact with the pore-lining residue Ile-323.
We also compared the G-V curves of each pore mutation with the wild-type mSlo1 and found that the V 50 of I323A shifted only about ϩ20 mV with 10 M Ca 2ϩ (Fig. 3B) relative to the mSlo1. Furthermore, we noticed that the relative V 50 of the pore mutations compared with mSlo1 shifted variously at 10 M Ca 2ϩ (Fig. 3C). Comparing Fig. 3C with Fig. 2B, we found that the slow recovery component was not tightly related to the changes of V 50 , but mainly depended on the interaction between the pore and the ID. Taking L312A as an example, even though its V 50 shifted ϳϪ130 mV, the recovery of L312A still contained a slow recovery component.
No  (17) reported that the cytosolic blockers of BK channels did not slow the inactivation process and further inferred that they did not share the binding sites with the ID based on the competition model of K V channels. However, it is still unknown whether the blockers of BK channels have specific binding sites in pore and why they do not compete with the ID.
To determine whether blockers slow the inactivation process and where their binding sites are at the same time, we examined the inactivating currents of coexpression of the mSlo1 mutants and FWI in most experiments. Cytosolic application of 2 mM QX-314 reduced the averaged peak currents to 20 -50% but caused insignificant differences in inactivation time constants i (Fig. 4, A and B). The inactivation time constants i varied from 20 to 36 ms with an average time constant i ϭ 25.3 Ϯ 4.3 ms. According to competition model, the 20 -50% unblocking currents are predicted to produce a 2-to 4-fold slowing of i (3,13,14). In Fig. 4 (A and B), however, 2 mM QX-314 resulted in no significant changes in i for all the mSlo1 mutants. Similar results were obtained by cytosolic application of 50 mM TEA (Fig. 4, C and D). It seems unnecessary to use the FWI for determining the binding affinity of blockers. However, we will find something interesting after comparing how they differ. In Fig. 4B, 2 mM QX-314 showed less inhibition on the currents of the mSlo1-h␤2, M314A-FWI, and V319A-FWI than that of the mSlo1, M314A, and V319A, respectively, which suggests that the ID prevents QX-314 from entering the cavity. In Fig. 4D, however, 50 mM TEA did not show the statistic difference on inhibition probably due to a very high concentration used in this experiment. No matter whether we have used FWI or not, there is no significant difference in their binding affinities. It indicates that no mutations along the ion conduction pathway significantly affect the binding affinities of QX-314 or TEA.
A Kinetic Model for the Cytoplasmic Blocker QX-314 Blocking the Inactivating BK Channels-On the basis of our experiments, a schematic, which is presented with only two opposite subunits and one inactivation domain, illustrates a kinetic process that includes both the inactivation and the blocking and inactivation of BK channels (Fig. 5). For a competition model of K V channels, the channel can only alter from the open state to the inactivated state or to the blocked state, but not to the blocked and inactivated state, because the cytosolic blockers and the ID compete for binding to the same site (14).
In our non-competitive scheme for BK channels, the channel cannot only go from the open state to either the blocked state or the inactivated state, but also from the blocked state to the blocked and inactivated state. Therefore, the one-step noncompetitive scheme for BK channels ("one-step" means one inactivation step) can be modeled as in Scheme 1, where states are represented by: O, open; I, inactivated; B, blocked; and BI, blocked-inactivated. Rate constants are: k 1 , inactivation; k Ϫ1 , returning from inactivation; k B , binding; and k ϪB , dissociation.
The transition rates between the B and the BI states are same to that between the open (O) and the inactivated (I) states. There is no link between the BI and I states, because the charged blockers cannot penetrate through cell membrane. Therefore, blockers are trapped in the cavity of the pore when the inactivation site is occupied. Following Choi et al. (14), we also ignore the voltage-dependent activation steps, which are rapid and thus do not complicate measurements of inactivation at the positive voltages studied. For a complete inactivation, we make the assumption that k Ϫ1 is close to zero. The blockers association and dissociation is typically much more rapid than the inactivation process (i.e. k B and k ϪB Ͼ Ͼ k 1 ). The channel goes to the inactivated state from the open state or to the blockedinactivated state from the blocked state with the same inactivation time constant i ϭ 1/(k 1 ϩ k Ϫ1 ) (for the case k 1 Ͼ Ͼ k Ϫ1 , i Ϸ 1/k 1 ). The difference between the competitive and the noncompetitive model is that the blocked channels are protected from rapid equilibrium with the pool of open channels and return to the blocking-inactivation state and "permanently" lost with the same rate as that between the open and inactivation state. Therefore, this scheme can predict that the inactivation time constant with and without blockade will be the same (the unblocked fraction of channels f ϭ k ϪB /(k B ϩ k ϪB ) and the inactivation time constant in the presence of blockers i blocker ϭ 1/k 1 ). A similar consideration can be directly used to describe the two-step inactivation model. Two-step inactivation model (O 7 O* 7 I) is revised from the one-step inactivation model (O 7 I) (13)(14)(15)(16). O, O*, and I are the open, pre-inactivation, and inactivation states, respectively. However, the twostep inactivation model can be simplified into a one-step inactivation model when the transition rate between O and O* is much larger than between O* and I (15,23).
Simulations in Fig. 6 illustrate two different cases, i.e. onestep non-competition and two-step non-competition. c is defined as the control inactivation time constant (without

Residue Ile-323 Plays a Dual Role in BK Channels
blocker), b is defined as the inactivation time constant at 2 mM QX-314, and f ϭ max (unblocked)/max (control). In the simulation, we chose k OB ϭ 16,000, k BO ϭ 7,500 or 8,600 (24), k OO * ϭ 1,000, and k O * O ϭ 2,000 (25). As long as the rates k OB and k BO are much larger than the other rates, the simulation always yields a non-competition result. Residue Ile-323 Modulates the Gating of BK Channels-By analogy to the shaker-type K ϩ channel K V 1.4-IR, residue Ile-323 in BK channels corresponds to Tyr-569 in K V 1.4-IR channels (15). Closer examination of I323A macroscopic and singlechannel currents reveals additional critical differences from the wild-type BK channels. The I323A tail currents exhibit an outward rectified current, strikingly different from the wild-type channels (Fig. 7, A and B) (26). The results of the macroscopic currents are consistent with the outward rectification of unitary conductance measured from the maximum single-channel level shown in Fig. 7 (C and D). In contrast, the single-channel currents of the wild-type mSlo1 show little rectification in Fig. 7  (C (right) and D). Resembling a dSlo-like flickery behavior (27,28), the single channel of I323A shows very noisy opening in contrast to the mSlo1 single-channel opening shown in Fig. 7C. We also observed that the open probability of the largest level reduced more rapidly at negative voltages. Consequently, the rectification property of the I323A mutant was possibly caused by the very short open time, the very low open probability, and the relatively low filtering frequency. More detailed work is clearly required to illuminate the nature of rectification. In addition, rectification will not affect the G-V curve due to very low open probability at negative voltages under conditions we currently used (Fig. 3B).
As the corresponding residue in the flickery dSlo (A2, C2, E2, G5, 10 splice variant) is Thr-337 rather than Ile (28,29), we substituted Thr for Ile-323 in wide-type mSlo1 and found that I323T induced the flickery single-channel currents similar to the flickery dSlo. 5 This mechanism may help us to understand the behavior of the flickery dSlo single channels.
Simulation of an Interaction between h␤2 (FIW and FWI) and mSlo1 Subunits of BK Channels-To further understand the molecular basis for interaction between the h␤2 subunit and BK-type channels, docking simulations were performed with the wild-type h␤2 (FIW) NH 2 terminus and its mutant FWI interacting with mSlo1 ␣-subunits, using the bimolecular complex program 3D-DOCK (see also "Methods" in the supplemental materials). The most favorable docking conformations were guided by our experimental results described above (Fig.  8) based on the K V 1.2 channel data (PDB code 2A79) and the NMR data (PDB code 1JO6) of the h␤2 NH 2 terminus (22,30). The computational models for complexes of FIW-mSlo1 and FWI-mSlo1 were further analyzed, using the LIGPLOT program (31,32) (Fig. 9). As shown in Fig. 8, the FIW and FWI side chains of the h␤2 subunits are tightly packed together to form a hydrophobic core. Each component of the hydrophobic core makes close contact to a corresponding residue of the mSlo1 S6 segment and fully blocks the mouth of the BK channels. The interactions in the mSlo1-h␤2 (mSlo1-FIW) structural model mainly involved hydrophobic contacts, which include Phe  . Blocking-and-inactivation models for the blockade of QX-314 on the BK currents arising from the mutation F307A co-expressed with FWI. A, for the one-step inactivation models, triangles and circles represent the currents evoked by a voltage step to 100 mV in the presence of 10 M Ca 2ϩ before and after applying 2 mM QX-314, respectively. The long dash, dotted, and solid lines represent the simulation traces calculated from the inactivation (right top), competition (right middle), and non-competition (right bottom) models, respectively. B, all the simulations were calculated from the two-step inactivation models shown on the right side. Other parameters are the same as those described in A. amino acid Thr-5 of the h␤2 in the mSlo1-FWI complex also predicts hydrophobic contacts with Ile-323 (C).

DISCUSSION
In this study, we show that the ID of the h␤2-subunit does not occupy the same site with channel blockers, which directly leads to a non-competitive inactivation. However, two critical questions need to be answered: why the channels in this work did not show any reopening during the deactivation process and by what pathway the ID can access the conducting entrance of the pore.
In K V channels, once the ID occupies its blocking position, it impedes closure of the channels to lead channels to reopen during the deactivation process (8,13). In BK channels, during the process of deactivation, the fully inactivated channels with a hydrophobic inactivation domain such as h␤2 do not show reopening but do show reopening with some lesser hydrophobic inactivation domains such as h␤3b. It seems to depend on whether the recovery time constant is comparable to the closing time constant. Because the recovery process of h␤2 from complete inactivation (e.g. 20 ms) is usually much slower than its closing process (e.g. 0.1 ms), thus it can fully conceal the reopen process of BK channels. By contrast, we can anticipate that the reopening appears from the incomplete inactivated BK channels by h␤3b with a recovery time constant of r ϭ 0.38 ms. 5 Moreover, recent work from a few laboratories has shown that the ID reaches the ion-conducting pore through lateral "side portals" in the cytoplasmic portion of the channel (20,33,34). In our modeling, we cannot exclude any pathway accessing to or withdrawing from the ionconducting pore.
Here we also want to emphasize that the models for both the competitive and non-competitive case may give a bi-exponential inactivation if the blocking rates are relatively smaller, that is, one of the inactivation time constants is faster  and the another slower than the control. Slow blockers such as peptides used to be an example of the competition model. They clearly share the same sites with the NH 2 terminus and typically induce a bi-exponential inactivation due to their low blocking rates.
It is interesting to know why the mutated construct FWI gives different dynamics in the period recovering from inactivation compared with the wild-type h␤2 (FIW). For FIW, the residue Trp-4, as the last residue involved in the inter-molecular interaction, is the most hindered component of the hydrophobic core maybe due to its large volume. It has less contact with the mouth of the channel (only one Ile-323) and is exposed to solvent. For construct FWI, the residue Trp-3 before Ile-4 as the second residue is also the most hindered component of the hydrophobic core. In comparison with FIW, the residue Trp-3 in FWI makes more contacts with the channels (interacting with two Ile-323 residues), is buried deeply and is less exposed to solvent. This kind of arrangement of the hydrophobic side chains in FWI might account for its distinct recovery behavior after inactivation. We expect that the last residue Ile-4 will firstly leave the pore at the beginning of the recovery, and then the buried residue Trp-3 will dissociate slowly with the Ile-323, which results in a slow recovery process. For construct FIW, the most hindered residue Trp-4 dissociates quickly due to the exposure to solvent and less interaction with the channel, and the residues Phe-2 and Ile-3 leave simultaneously to show monoexponential recovery process. This analysis may also explain why the complex mSlo1-FWQ shows identical recovery dynamics to that of the mSlo1-h␤2 complex. Because the glutamine (Gln) in the construct FWQ is a hydrophilic residue, the residue Trp-3 becomes solvent-exposed and so leads to a single exponential recovery. In complex I323A-FWI, the residue Ile-323 is replaced with a relatively weaker hydrophobic residue alanine, which leads to a reduced interaction between Trp-3 and Ile-323. Compared with the complex mSlo1-h␤2, the recovery of I323A-FWI shows a slight difference, which may be attributed to the shield effect of a following hydrophobic residue Ile-4.
It is interesting to consider why FWI shows a bi-exponential recovery with a 50:50 ratio. This feature may implicate that FWI has two interacting styles in the pore. At the recovery voltage of Ϫ140 mV with 10 M Ca 2ϩ , the ϳ50% of FWI may be trapped in a fast dissociating substate, which was not indicated in the present simulations of interaction between mSlo ␣ and h␤2 subunits (Fig. 9), and the remaining half in a slow dissociating sub-state to lead to a bi-exponential recovery with a ratio of about 50:50. However, FIW has only one stable interaction style. The reason for that is probably that the rhombus-like FWI acts in an "unstable" style with two sub-states, but the cone-like FIW acts in a "stable" style with one state. Actually, the wide-type r␤2 (FIW) in rat chromaffin cells showed a much weaker bi-exponential recovery with a ratio of, on average, 25 (fast):75 (slow) at voltages more positive than Ϫ100 mV, 6 although the bi-exponential recovery of h␤2 (FIW) is extraordinarily rare. Obviously, more experiments are needed to verify whether the bi-exponential phenomena are ubiquitous in inactivating BK channels.