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Department of Physiology and Biophysics, University of Miami Miller School of Medicine, Miami, FL 33101

Correspondence to Xiang Qian: xiang.qian{at}ucsf.edu; or Karl Magleby: kmagleby{at}miami.edu

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The activation of BK channels by Ca²⁺ is highly cooperative, with small changes in intracellular Ca²⁺ concentration having large effects on open probability (Po). Here we examine the mechanism of cooperative activation of BK channels by Ca²⁺. Each of the four subunits of BK channels has a large intracellular COOH terminus with two different high-affinity Ca²⁺ sensors: an RCK1 sensor (D362/D367) located on the RCK1 (regulator of conductance of K⁺) domain and a Ca-bowl sensor located on or after the RCK2 domain. To determine interactions among these Ca²⁺ sensors, we examine channels with eight different configurations of functional high-affinity Ca²⁺ sensors on the four subunits. We find that the RCK1 sensor and Ca bowl contribute about equally to Ca²⁺ activation of the channel when there is only one high-affinity Ca²⁺ sensor per subunit. We also find that an RCK1 sensor and a Ca bowl on the same subunit are much more effective in increasing Po than when they are on different subunits, indicating positive intrasubunit cooperativity. If it is assumed that BK channels have a gating ring similar to MthK channels with alternating RCK1 and RCK2 domains and that the Ca²⁺ sensors act at the flexible (rather than fixed) interfaces between RCK domains, then a comparison of the distribution of Ca²⁺ sensors with the observed responses suggest that the interface between RCK1 and RCK2 domains on the same subunit is flexible. On this basis, intrasubunit cooperativity arises because two high-affinity Ca²⁺ sensors acting across a flexible interface are more effective in opening the channel than when acting at separate interfaces. An allosteric model incorporating intrasubunit cooperativity nested within intersubunit cooperativity could approximate the Po vs. Ca²⁺ response for eight possible subunit configurations of the high-affinity Ca²⁺ sensors as well as for three additional configurations from a previous study.

Abbreviations used in this paper: BK channel, large conductance Ca²⁺- and voltage-activated K⁺ channel; Ca²⁺_i, intracellular Ca²⁺; RCK, regulator of the conductance of potassium; WT, wild-type.

	INTRODUCTION

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Large conductance Ca²⁺-activated K⁺ (BK) channels are activated in a synergistic manner by intracellular Ca²⁺ (Ca²⁺_i) and depolarization (Barrett et al., 1982; Kaczorowski et al., 1996; Magleby, 2003). When opened, the efflux of K⁺ out of cells through the channels drives the membrane potential in the negative direction, which reduces excitability, shutting down Na⁺ and Ca²⁺ channels. By coupling membrane potential and Ca²⁺_i to excitability, BK channels modulate many processes, such as the contraction of smooth muscle and neurotransmitter release (Robitaille et al., 1993; Brenner et al., 2000; Petkov et al., 2001; Wang et al., 2001; Xu and Slaughter, 2005). Crucial in this coupling is the highly cooperative activation of BK channels by Ca²⁺_i that allows small changes in Ca²⁺_i to elicit large changes in open probability (Po), with Hill coefficients of typically 2–5 (Barrett et al., 1982; McManus et al., 1985; Golowasch et al., 1986; Cui et al., 1997; Nimigean and Magleby, 1999; Bian et al., 2001). In spite of its importance, the mechanism underlying the cooperative activation of BK channels by Ca²⁺_i remains unclear.

The high Hill coefficients of BK channels suggest that a minimum of 2–5 Ca²⁺ must bind to the channel for full activation (Barrett et al., 1982; McManus et al., 1985; Golowasch et al., 1986; Cui et al., 1997; Nimigean and Magleby, 1999; Bian et al., 2001). Consistent with a large number of Ca²⁺ binding sites, BK channels are tetramers (Shen et al., 1994), and studies have suggested at least three different types of Ca²⁺ sensors per subunit (for review see Magleby, 2003). These sensors are associated with the large intracellular COOH terminus of the channel, which is thought to form a Ca²⁺-activated gating ring comprised of eight RCK (regulators of the conductance of potassium) domains, two per subunit, designated RCK1 and RCK2 (Jiang et al., 2001, 2002; Niu et al., 2004). Two of the Ca²⁺ sensors are of high affinity (µM) and are defined by mutations to the Ca bowl and to D362/D367 (Schreiber and Salkoff, 1997; Schreiber et al., 1999; Xia et al., 2002; Zeng et al., 2005). The Ca²⁺ sensor silenced by the double mutation D362A/D367A will be referred to as the RCK1 sensor, since it is located on the RCK1 domain. Mutations to M513 may define the same high-affinity Ca²⁺ sensor as mutations to D362/D367 (Bao et al., 2002). The third Ca²⁺ sensor is low affinity (mM), binds Ca²⁺ and Mg²⁺, and is removed by mutations to E374/E399 (Shi and Cui, 2001; Zhang et al., 2001; Shi et al., 2002; Qian and Magleby, 2003). Under physiological conditions the low-affinity sensor would normally be occupied by Mg²⁺. Low concentrations of Ca²⁺ that maximally activate the two types of high-affinity sensors have little effect on the low-affinity sensor (Shi and Cui, 2001; Zhang et al., 2001; Shi et al., 2002). Mutating all the Ca bowls or RCK1 sensors reduces the Ca²⁺ response about an equivalent amount, with the Ca bowl having a somewhat lower Kd. Joint mutations to the Ca bowl and D362/D367 or to the Ca bowl and M513 essentially eliminate all of the high-affinity Ca²⁺ sensitivity (Bao et al., 2002; Xia et al., 2002).

Because BK channels are tetrameric proteins, with each subunit containing two high-affinity Ca²⁺ sensors, several different mechanisms are possible for the cooperative activation of the channel by these sensors. (1) Each Ca²⁺ sensor, whether located on the same or different subunit, could be independent of all the other Ca²⁺ sensors, with the cooperativity in Ca²⁺ activation arising from the joint action of the independent Ca²⁺ sensors on opening the gates. (2) The two Ca²⁺ sensors on each subunit could interact, but act independently of the Ca²⁺ sensors on other subunits. (3) Ca²⁺ sensors on different subunits could interact but be independent of Ca²⁺ sensors on the same subunit. (4) All Ca²⁺ sensors, whether on the same or different subunits could interact. Interaction between Ca²⁺ sensors, either directly or allosterically, could lead to cooperativity through, for example, changing the Kd for Ca²⁺ binding. Combinations of the above cooperative mechanisms would also be possible. An assumption of independent Ca²⁺ sensors that act jointly to open the gates of the channel (option 1 above) is generally consistent with previous studies (Cox and Aldrich, 2000; Cui and Aldrich, 2000; Shi and Cui, 2001; Zhang et al., 2001; Horrigan and Aldrich, 2002; Niu and Magleby, 2002; Xia et al., 2002).

To test further the mechanism of cooperativity we now compare the Ca²⁺-dependent activation of BK channels in which the high-affinity Ca²⁺ sensors on the gating ring are studied in different combinations on the same and different subunits. We find that channels with four high-affinity Ca²⁺ sensors distributed at one sensor per subunit were approximately equivalent in their ability for Ca²⁺ activation of the channel, independent of whether the four sensors were four RCK1 sensors, four Ca bowls, or two RCK1 sensors plus two Ca bowls. Thus, the two types of high-affinity Ca²⁺ sensors when distributed at one high-affinity Ca²⁺ sensor per subunit are approximately equivalent. It has previously been found that four RCK1 sensors are approximately equivalent to four Ca-bowl sensors (Bao et al., 2002; Xia et al., 2002). Our observations extend the equivalence to mixtures of the two types of high-affinity Ca²⁺ sensors, provided there is only one high-affinity sensor per subunit. In addition, we find that two high-affinity Ca²⁺ sensors located on the same subunit are much more effective in activating the channel than when located on different subunits, indicating positive intrasubunit cooperativity.

An extension of previous allosteric models (Cox and Aldrich, 2000; Cui and Aldrich, 2000; Shi and Cui, 2001; Zhang et al., 2001; Xia et al., 2002; Niu and Magleby, 2002) to incorporate intrasubunit cooperativity in which high-affinity Ca²⁺ sensors on the same subunit are more effective than when on separate subunits could approximate the Po vs. Ca²⁺ response for eight possible subunit configurations of the high-affinity Ca²⁺ sensors as well as three additional configurations from a previous study. In this extended model the intrasubunit cooperativity is nested within the intersubunit cooperativity. If it is assumed by analogy to MthK channels (Jiang et al., 2002) (a) that BK channels have a gating ring comprised of eight RCK domains that are separated by alternating fixed and flexible interfaces, and (b) that the Ca²⁺ sensors must work at a flexible interface, then a comparison of the possible configurations of the Ca²⁺ sensors on the subunits of BK channels in our experiments with the observed Ca²⁺ responses suggests that the flexible interfaces are intrasubunit and the fixed interfaces are intersubunit. On this basis, intrasubunit cooperativity arises because a pair of high-affinity Ca²⁺ sensors working across a flexible interface within a subunit gives a greater shift in the equilibrium toward the open state than when the sensors act separately on separate subunits.

	MATERIALS AND METHODS

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Clones, Mutagenesis, and Channel Expression
Experiments were performed using the mouse Slo1 subunit of the BK channel provided by Merck Research Laboratories. This subunit was initially cloned by Pallanck and Ganetzky (1994), GenBank/EMBL/DDBJ accession no. U09383, before modification by Merck Research Laboratories (McManus et al., 1995). Alpha subunits with mutations to the Ca²⁺ sensors in the Ca bowl (5D5N mutant: FLDQDDDDDPD to FLDQNNNNNPD) and in the RCK1 sensor (D362A/D367A mutant: FLKDFLHKDRDD to FLKAFLHKARDD), and with mutations of both 5D5N and D362A/D367A were provided by X. Xia and C. Lingle (Washington University School of Medicine, St. Louis, MO) (Xia et al., 2002). Using these constructs, we made two additional mutant subunits that were insensitive to block by extracellular TEA by mutating a site in the pore region of the channel (Y294V: GYGDVYAKT to GYGDVVAKT), as described previously (Niu and Magleby, 2002) to obtain Y294V/5D5N and Y294V/5D5N/D362A/D367A mutant subunits. (The numbering differs from our previous paper [Niu and Magleby, 2002] because the counting starts 40 amino acids later at the second methionine.) Mutations were made by using Stratagene's QuikChange Site-Directed Mutagenesis Kit and were checked by sequencing. The cDNA was transcribed in vitro by using the mMESSAGE mMACHINE Kit (Ambion) to obtain cRNA for injection into Xenopus oocytes. Oocytes were microinjected with 0.5–20 ng of cRNA 2–8 d before recording. When expressing channels with two different types of subunits, the cRNA was injected in a 1:1 ratio.

Electrophysiology and Solutions
Single-channel currents were recorded with the patch clamp technique (Hamill et al., 1981) from inside-out patches of membrane excised from Xenopus oocytes using an Axopatch 200B amplifier (Axon Instruments, Inc.). The pipette solution contained 158 mM KCl and 5 mM N-[tris(hydroxymethyl)methyl]-2-aminoethanesulfonic acid (TES) pH buffer. The bath solution contained 158 mM KCl, 5 mM TES, 1 mM EGTA, 1 mM N-(2-hydroxyethyl) ethylenediamine-N,N',N'-triacetic acid (HEDTA), and sufficient added CaCl₂ to obtain the desired free Ca²⁺ concentrations of 1–1,000 µM. All solutions were adjusted to pH 7.0. Solutions with a calculated free Ca²⁺ of 10^–8 M will be referred to as 0 Ca²⁺ solutions because Ca²⁺_i at these concentrations has essentially no effect on the gating of the channel (Nimigean and Magleby, 2000). Voltages refer to the intracellular potential. Experiments were performed at room temperature (20–23°C).

Data Analysis
Single-channel data were sampled at 200 kHz and typically filtered to 2–5 kHz using pClamp8 or pClamp9 (Axon Instruments, Inc.). Analysis of the digitized records was then performed using custom programs and Clampfit 9.0 (Axon Instruments, Inc.), as described previously (McManus et al., 1987; McManus and Magleby, 1988; Nimigean and Magleby, 1999). Fitting of equations to the Po vs. Ca²⁺_i plots was accomplished with the nonlinear least squares fitting routines in SigmaPlot 2000 (Systat Software Inc.). Data are expressed as the mean ± SEM.

	RESULTS

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Two Different High-affinity Ca²⁺ Sensors Contribute to the Cooperative Activation of BK Channels by Ca²⁺_i
To investigate the mechanism for cooperative activation of BK channels by Ca²⁺_i, we constructed and identified modified BK channels with different configurations of the high-affinity Ca²⁺ sensors on the subunits. Fig. 1 A presents a cartoon of a single subunit from a wild type (WT) BK channel. Similar to the super family of voltage-activated channels, the subunit contains transmembrane segments S1–S6, including a positively charged S4 domain that functions as a voltage sensor (Atkinson et al., 1991; Adelman et al., 1992; Butler et al., 1993; Diaz et al., 1998; Cui and Aldrich, 2000), and a P-loop to form the selectivity filter of the channel (Doyle et al., 1998). In addition, BK channels have an S0 domain that places the NH₂ terminus extracellular (Meera et al., 1997) and a large intracellular COOH terminus that has two high-affinity Ca²⁺ sensors: the Ca bowl located at the end of the RCK2 domain near the end of the COOH terminus (Schreiber and Salkoff, 1997) and a Ca²⁺ sensor defined by the mutation D362A/D367A (to be referred to as the RCK1 sensor) located upstream of the Ca bowl in the RCK1 domain of the COOH terminus (Xia et al., 2002). The schematic notation used to represent the tetrameric structure of the WT channel with its eight high-affinity Ca²⁺ sensors, two per subunit, is also shown in Fig. 1 A, where the blue squares are RCK1 sensors (R) and the red hexagons are Ca bowls (B). The alphanumeric notation for WT channels is then 4(RB), indicating that each of the four subunits have an RCK1 sensor (R) and a Ca bowl (B). When RCK1 sensors or Ca bowls are eliminated by mutation, the sensor designation letter is replaced with a .

View larger version (34K): [in this window] [in a new window]   Figure 1. Structure and function of four homotetrameric configurations of high-affinity Ca2+ sensors used to investigate cooperativity among Ca2+ sensors. (A) Cartoon of a single WT subunit (upper left) and a schematic diagram of a WT channel formed from four of these subunits (upper right). Each WT subunit has two high-affinity Ca2+ sensors on the intracellular COOH terminus, an RCK1 sensor (R) and a Ca-bowl sensor (B), giving an (RB) subunit. WT channels are comprised from four such subunits, designated 4(RB). WT channels were fully activated with 100 µM Ca2+i at + 50 mV, as indicated by the single-channel current record (upper current trace). Addition of 1.5 mM extracellular TEA, (TEAO) completely blocked the currents (lower trace). Arrows indicate the closed current level. (B) Mutation of the RCK1 site produces a B subunit, where indicates a mutated sensor. Homomeric 4(B) channels expressed from B subunits have greatly reduced activation with 100 µM Ca2+i (upper current trace) and can be blocked by 1.5 mM TEAO. (C) Mutation of the Ca-bowl site produces an R subunit. Homomeric 4(R) channels expressed from R subunits also have greatly reduced activation with 100 µM Ca2+i. The channel is not blocked by TEAO because of the presence of a Y294V pore mutation (lower trace). (D) Mutation of both the RCK1 sensor and the Ca bowl produce subunits. Homomeric 4() channels are Ca2+ insensitive up to 1,000 µM Ca2+. The channel is not blocked by TEAO because of the presence of a Y294V pore mutation (lower trace). Current traces in this and the following figures are representative excerpts from longer records.

When both high-affinity Ca²⁺ sensors on each subunit were removed by mutation, producing 4() channels, then 100 µM Ca²⁺ had little effect on channel activity, giving a Po of <0.01, (Fig. 1 D, top trace). Results from a series of experiments over a range Ca²⁺_i for the four types of modified channels shown in Fig. 1, WT 4(RB), 4(B), 4(R), and 4(), are presented in Fig. 2 together with data from a another type of modified channel, 2(B) +2(R), to be discussed later. The curves are fits with the Hill function,

(1)

where P_max is the maximum Po, 0.92, K_d is an apparent K_d indicating the Ca²⁺_i required for half activation, and n is the Hill coefficient that reflects the slope of the dose–response relationship. Because the response from the 4(B) channels, the 4(R) channels, and the 2(B)+2(R) channels (to be discussed later) was similar, the data from these three types of channels were fitted with a single curve. The K_d for WT channels was 2.01 µM with a Hill coefficient of 3.30 (dashed line) compared with a K_d of 94.4 µM and a Hill coefficient of 1.05 for the 4(B), 4(R), and 2(B)+2(R) channels (continuous line). Thus, removing either the four Ca bowls (plotted blue squares) or the four RCK1 sensors (plotted red hexagons) shifted the K_d to the right by 92 µM and decreased the Hill coefficient by 2.2. The similar response for 4(B) channels and 4(R) channels in Fig. 2 indicates that four RCK1 sensors or four Ca bowls are about equally effective in activating the channel. Removing all eight of the high-affinity Ca²⁺ sensors to obtain 4() channels removed all of the Ca²⁺ sensitivity up to 1,000 µM (green triangles). Thus, RCK1 sensors or Ca bowls are required for the channel to detect micromolar concentrations of Ca²⁺_i. The small response with Ca²⁺_i >1000 µM for the 4() channels reflects a separate low-affinity Ca²⁺/Mg²⁺ sensor (Shi and Cui, 2001; Zhang et al., 2001; Xia et al., 2002; Shi et al., 2002). These single-channel observations on the contributions of four Ca-bowl sensors, four RCK1 sensors, and four low-affinity sensors to the Ca²⁺ activation of the channel are generally consistent with previous studies using macroscopic recordings (Bao et al., 2002; Xia et al., 2002).

View larger version (13K): [in this window] [in a new window]   Figure 2. RCK1 sensors and Ca bowls are approximately equivalent in activating BK channels when distributed on separate subunits. Po vs. Ca2+i plots for 4(RB), 4(R), 4(B), 2(B)+2(R), and 4() channels. Data for each plotted point is from 5–7 single-channel patches. The lines are fits with the Hill equation (Eq. 1). The data from the 4(R), 4(B), and 2(B)+2(R) channels cluster together, and consequently these data were simultaneously fit to obtain the continuous line through the data. The Kd for the 4(RB) and combined 4(R), 4(B), and 2(B)+2(R) channels are 2.01 and 94.4 µM, respectively, with Hill coefficients of 3.30 and 1.05, respectively. In this and the following figures data that were obtained for a free Ca2+ 0.01 µM are plotted at 0.01 µM to save space, as there was no difference in response at such low Ca2+. Points at 0.01 have been displaced slightly so they can be seen.

Expressing and Identifying Channels with Different Subunit Distributions of the Two High-affinity Ca²⁺ Sensors
To determine whether the greatly enhanced response when both the RCK1 sensors and Ca bowls were present might arise from interactions of these two types of high-affinity Ca²⁺ sensors within or between subunits, we studied channels constructed with a total of four high-affinity sensors distributed to either facilitate intrasubunit interactions, 2(RB)+2(), or intersubunit interactions, 2(B)+2(R). Schematic diagrams of the subunit composition of these channels are shown in Fig. 3 A, together with diagrams for the other channels examined in this paper. The 2(RB)+2() channels would facilitate exploration of intrasubunit interactions of the Ca²⁺ sensors because two of the subunits have two high-affinity Ca²⁺ sensors on the same subunit and the other two subunits have no high-affinity Ca²⁺ sensors. The 2(B)+2(R) channels would facilitate exploration of intersubunit interactions because each subunit has only one high-affinity Ca²⁺ sensor per subunit. The fact that each of these channel types has two RCK1 sensors and two Ca bowls facilitates comparison of the results. Because it is not known whether there would be a preferential assembly of the two types of subunits in each channel either adjacent or diagonal to one another, both types of assembly are shown in Fig. 3 A.

View larger version (28K): [in this window] [in a new window]   Figure 3. Identification of the subunit stoichiometry of the heteromeric channels used to explore intrasubunit cooperativity. (A) Presentation of the channels examined in this study, their channel designation, and distributions of the high-affinity Ca2+ sensors on the subunits, where blue squares are RCK1 sensors and red hexagons are Ca bowls. For 2(RB)+2() and 2(B)+2(R) channels, both adjacent and diagonal subunit configurations are shown. (B) 2(RB)+2() channels were obtained by coexpressing RB subunits together with subunits that had the Y294V pore mutation to relieve TEAO block. Each expressed channel had one of five distinct current amplitudes in the presence of 1.5 mM TEAO. Examples of single-channel currents (+50 mV) from channels with one of the four nonzero current amplitudes are presented. (An example of the zero current amplitude is presented in Fig. 1 A where the channel was first identified in the absence of TEAO.) The deduced subunit stoichiometry for each of the current amplitudes is shown at the right, with both possible configurations for the 2(RB)+2() channel shown. The 2(RB)+2() channel can be identified by a current level of 5 pA at + 50 mV. (C) Plot of single-channel current amplitude against the number of subunits, assuming that the current amplitude is proportional to the number of subunits with the pore site mutation that removes TEAO block. (D and E) 2(B)+2(R) channels were obtained by coexpressing (B) subunits together with R subunits that had the Y294V pore mutation that relieved TEAO block. 2(B)+2(R) channels were identified by a current level of 5 pA at + 50 mV, following the same strategy as used above.

To obtain 2(RB)+2() channels, we coexpressed WT (RB) subunits (homomeric response in Fig. 1 A) with () subunits in which the RCK1 sensor, the Ca bowl, and the TEA blocking site were all mutated (homomeric response in Fig. 1 D). In the absence of TEAo, all of the channels from this coexpression had the same current level of 13.0 pA. In the presence of 1.5 mM TEAo, the current amplitudes from different channels could be different, but the response from any single channel remained constant (Fig. 3 B). Responses from 20 patches indicated four different levels of unitary current amplitude: 2.0, 4.3, 7.5, and 9.4 pA (Fig. 3 C), with the zero current level coming from experiments like that in Fig. 1 A. Because single-channel current amplitudes increase with the number of subunits that have mutated TEA binding sites (Shen et al., 1994; Niu and Magleby, 2002; Tian et al., 2004), the subunit composition of the channel can be deduced, as indicated in Fig. 3 B, where current amplitudes of 4–5 pA indicate 2(RB)+2() channels. The same approach was used to obtain 2(B)+2(R) channels. B subunits (homomeric response in Fig. 1 B) were coexpressed with (R) subunits (homomeric response in Fig. 1 C), and the 2(B)+2(R) channels were then indicated by a current level of 5 pA (Fig. 3 E). Previous studies have shown that the Po of BK channels is not affected by mutations to the TEA sites (Niu and Magleby, 2002) or by the presence of TEA_O (Langton et al., 1991). We have also observed for inside-out patches that WT channels in the absence of TEA_O have a Po vs. Ca²⁺ response similar to channels in the presence of 1.5 mM TEA_O expressed from a combination of WT subunits and subunits with the TEA site mutated. In some experiments that were carried out with outside-out patches so that the extracellular solution could be changed, a small TEA_O-induced decrease in Po (5 mV right shift of the Po-V curve) could be observed (to be presented elsewhere). Why TEA_O appears to have a small effect in some studies and little or no effect in others is unclear. Nevertheless, all these observations when taken together indicate that any possible effects of TEA_O on Po are expected to be small, suggesting that the assay system used to identify subunit composition of channels should be suitable for the needs of the present study.

4(R), 4(B), and 2(B)+2(R) Channels Have a Similar Ca²⁺ Response
The data in Figs. 1 and 2 showed a similar Ca²⁺ response for homomeric channels with four Ca bowls (4(B) channels) or four RCK1 sensors (4(R) channels). A common feature between these two types of channels is one high-affinity Ca²⁺ sensor per subunit. If the RCK1 sensors and Ca bowls are approximately equivalent in Ca²⁺ activation, as the data in Fig. 2 suggest, then heteromeric 2(B)+2(R) channels, which also have one high-affinity Ca²⁺ sensor per subunit, but a mixture of high-affinity sensors, should respond to Ca²⁺ the same as the homomeric 4(R) channels and the homomeric 4(B) channels. Using the methods outlined in Fig. 3 (D and E), we identified 2(B)+ 2(R) channels and plotted their response to Ca²⁺ in Fig. 2 (open circles). As indicated above, the Ca²⁺ response for 2(B)+2(R) channels was generally similar to that for 4(R) channels and also for 4(B) channels. Thus, the relative equivalence of RCK1 sensors and Ca bowls for Ca²⁺ activation extends to channels with a mixture of both types of high-affinity Ca²⁺ sensors, provided that there is only one high-affinity Ca²⁺ sensor per subunit.

From the differential distributions of high-affinity Ca²⁺ sensors on the subunits of the 4(B), 4(R), and 2(B)+2(R) channels (Fig. 3 A), it seems unlikely that the high-affinity Ca²⁺ sensors on these different channels would directly interact with each other in a consistent manner for all three channels. Yet, these channels display similar responses to Ca²⁺_i, suggesting that the high-affinity Ca²⁺ sensors on different subunits act relatively independently of one another.

High-affinity Ca²⁺ Sensors on the Same Subunit Display Intrasubunit Cooperativity
If high-affinity Ca²⁺ sensors always act independently of one another, then the Ca²⁺ response of the channel should depend only on the number of high-affinity Ca²⁺ sensors in the channel, independent of whether they are on the same or different subunits. To test for independence, we compared two different configurations of the high-affinity Ca²⁺ sensors, each with a total of four high-affinity Ca²⁺ sensors per channel, but distributed differently. For 2(RB)+2() channels, two of the subunits have two high-affinity Ca²⁺ sensors each and the other two subunits have no high-affinity Ca²⁺ sensors. For 2(B)+2(R) channels, there is one high-affinity Ca²⁺ sensor for each subunit. Both of these channel types have two RCK1 sensors and two Ca bowls.

Representative single-channel currents recorded at four different Ca²⁺_i for these two types of channels are shown in Fig. 4. For both channel types Po increased as Ca²⁺_i was increased, but the Po was higher at each examined Ca²⁺_i for 2(RB)+2() channels (Fig. 4 A) than for 2(B)+2(R) channels (Fig. 4 B). Data from a series of experiments of this type are presented in Fig. 4 C as Po vs. Ca²⁺_i plots. Clearly, four Ca²⁺ sensors distributed so that two of the subunits have two Ca²⁺ sensors each (as RCK1/Ca-bowl pairs) and two of the subunits have no Ca²⁺ sensors (2(RB)+2() channels) gave a greater response to Ca²⁺ (filled diamonds) than when the same four Ca²⁺ sensors were distributed separately as one Ca²⁺ sensor per subunit (open circles, 2(B)+2(R) channels). The K_d for the 2(RB)+2() channels (29.7 µM) was 3.9-fold less than the K_d for 2(R)+2(B) channels (114.4 µM), with Hill coefficients of 1.35 and 1.04, respectively. For comparison, the response of the WT channel with its four pairs of RCK1/Ca-bowl Ca²⁺ sensors is indicated as a dashed line. The greater Ca²⁺ response for 2(RB)+2() channels when compared with 2(R)+2(B) channels indicates a positive cooperativity in activation between the Ca bowl and the RCK1 sensor when they are located on the same subunit.

View larger version (26K): [in this window] [in a new window]   Figure 4. Two high-affinity Ca2+ sensors on the same subunit are more effective than when on different subunits, indicating intrasubunit cooperativity. (A and B) Representative single-channel currents recorded from a 2(RB)+2() channel (A) and a 2(B)+2(R) channel (B) at four different Ca2+i at +50 mV. The Po is higher at each level of Ca2+i when two of the four subunits have two high-affinity Ca2 sensors each, rather than when each of the four subunits has a single high-affinity Ca2+ sensor. TEAO (1.5 mM) was present for both channels. (C) Plots of Po vs. Ca2+i for the indicated channel types: 2(RB)+2() channels (filled diamonds, Kd = 29.7µM, Hill coefficient = 1.35) require less Ca2+i for the same Po than 2(B)+2(R) channels (open circles, Kd = 114.4 µM, Hill coefficient = 1.04). The dashed line is the response for WT channels from Fig. 2. Data for each plotted point is from 5–7 single-channel patches.

Both Adjacent and Diagonal Subunit Orientations of Identical Subunits are Likely to be Expressed for Both 2(RB)+2() and 2(B)+2(R) Channels

Predicting the Ca²⁺ Response with Combined Intra- and Intersubunit Cooperativity
The Ca²⁺ activation of BK channels has been described by models with two high-affinity Ca²⁺ sensors and one low-affinity Ca²⁺/Mg²⁺ sensor on each subunit. In these models the three types of Ca²⁺ sensors work independently of one another to control the gating, with the cooperativity in activation by Ca²⁺_i arising from the joint action of the three types of Ca²⁺ sensors on the opening–closing transitions, and not from interactions among the Ca²⁺ sensors (Cox et al., 1997; Cox and Aldrich, 2000; Shi and Cui, 2001; Zhang et al., 2001; Xia et al., 2002; Niu and Magleby, 2002; Hu et al., 2003). For a fixed voltage, these interactions can be described by

(SCHEME 1)

where Po is the open probability, P_max is the maximum observed Po, K_RC and K_RO are the equilibrium constants for the binding of Ca²⁺ to the closed and open states of each high-affinity RCK1 site, K_BC and K_BO are the equilibrium constants for the binding of Ca²⁺ to the closed and open states of each high-affinity Ca bowl, K_MC and K_MO are the equilibrium constants for binding of Ca²⁺ to the closed and open states of each low-affinity Ca²⁺/Mg²⁺ site, n₁, n₂, and n₃ are the number of RCK1 sensors, Ca bowls, and low-affinity sensors, respectively, each with a value of four in WT channels, and L(V), with a value of 2,500 at +50 mV, is the allosteric gating factor that is determined directly in the absence of Ca²⁺_i (Cox et al., 1997; Niu and Magleby, 2002; Xia et al., 2002). In Scheme 1, the equilibrium constants do not change with the number of bound Ca²⁺, indicating independent (noninteracting) Ca2⁺ sensors. In addition, based on Scheme 1, the Ca²⁺ response of the channel should depend only on the number of Ca²⁺ sensors of each type in the channel, independent of whether they are on the same or different subunits.

However, as shown in Fig. 4, two high-affinity Ca²⁺ sensors on the same subunit are more effective in activating the channel than when on different subunits. Thus, the implicit assumption of independence between high-affinity Ca²⁺ sensors in Scheme 1 requires modification. To approach this problem, we examined whether an expanded model that includes positive cooperative interactions between RCK1 sensors and Ca bowls located on the same subunit can account for the data. This model is described by Scheme 2, where W is an empirical factor that indicates the intrasubunit cooperativity for RCK1 sensors and Ca bowls located on the same subunit, n₁ is the number of subunits with both a Ca bowl and an RCK1 sensor, n₂ is the number of subunits with an RCK1 sensor and without a Ca bowl, n₃ is the number of subunits without an RCK1 sensor and with a Ca bowl, and n₄ is the number of subunits with a low-affinity sensor. For WT channels, n₁ = 4, n₂ = 0, n₃ = 0, and n₄ = 4. For 2(RB)+2() channels, n₁ = 2, n₂ = 0, n₃ = 0, and n₄ = 4. For 2(B)+2(R) channels, n₁ = 0, n₂ = 2, n₃ = 2, and n₄ = 4.

To test the ability of Scheme 2 to describe intra- and intersubunit cooperativity, we replotted the data from Figs. 2 and 4 in Fig. 5 A for the six different types of examined channels 4(RB), 2(RB)+2(), 2(B)+2(R), 4(R), 4(B), and 4(), and then simultaneously fitted all the data. The Po versus Ca²⁺ response for all these channel types was approximated by Scheme 2 (continuous lines, Fig. 5 A). The fitting was done with identical parameters for all channel types, except for the values of n, which were fixed by the stoichiometry of the Ca²⁺ sensors. The value of W, the empirical intrasubunit cooperativity factor, was 1.19, indicating positive cooperativity between the RCK1 sensor and the Ca bowl when they are on the same subunit.

(SCHEME 2)

The fitted equilibrium constants for the binding of Ca²⁺ to the RCK1 sensor and the Ca bowl were similar but not identical (see figure legend), giving rise to the three clustered lines for the 4(R), 4(B), and 2(B)+2(R) channels.

View larger version (15K): [in this window] [in a new window]   Figure 5. A gating model incorporating both intra- and intersubunit cooperativity (Scheme 2) can describe the Ca2+-dependent activation of BK channels comprised of subunits with different numbers and distributions of high-affinity Ca2+ sensors. (A) Po vs. Ca2+i plots for the six different channel types, as indicated. The continuous lines are simultaneous fits with Scheme 2 to all the plotted data and were calculated with L(V) = 2500 (from Niu and Magleby, 2002), KBC = 6.3 µM, KBO = 1.0 µM, KRC = 7.8 µM, KRO = 1.3 µM, KMC = 3000 µM; KMO = 644 µM, W = 1.19, Pmax = 0.90. An assumption that the two high-affinity Ca2+ sites were identical gave an equally good fit (not shown) with L(V) = 2500, KBC = KRC = 6.9 µM, KBO = KRO = 1.1 µM, KMC = 3000 µM, KMO = 644 µM, W = 1.19. The values of n for each curve were set by the subunit composition (see text). KMC was poorly defined and was set to the same value of both fits. (B) Po vs. Ca2+i plots for the data from Niu and Magleby (2002) for BK channels with different numbers of Ca bowls. From left to right the subunit composition was 4(RB), 3(RB)+1(R), 2(RB)+2(R), 1(RB)+3(R), and 4(R). The continuous lines are simultaneous fits with Scheme 2 to all the data in part B, and were calculated with L(V) = 2500, KBC = 7.18 µM, KBO = 1.00 µM, KRC = 110.35 µM, KRO = 18.98 µM, KMC = 3000 µM; KMO = 961 µM, W = 1.63, and Pmax = 0.95.

The dose–response curve for the 4(R) channels in the study of Niu and Magleby (2002) was steeper and right shifted (Fig. 5 B, filled circles) compared with the 4(R) channels in Fig. 5 A (blue squares). The steeper response in Fig. 5 B would be expected because the dose–response data for each channel of the same type was plotted after shifting the data for each individual channel to align the K_d to the average K_d for channels of the same type. Such shifting removes the variation in K_d that typically occurs among BK channels, leading to steeper slopes (discussed in Niu and Magleby, 2002). For Fig. 5 A, the data were averaged without shifting in order to obtain error bars and because of data at a limited number of Ca²⁺_i for some of the channels contributing to the averaged data, which did not allow determination of the individual K_d required for shifting. The right shift most likely reflects that different Ca-bowl mutations were used in the two studies, which can produce somewhat different effects (Schreiber and Salkoff, 1997; Bao et al., 2002). Consequently, the best-fitted parameters for Scheme 2 were somewhat different for the two studies.

Although Scheme 2 could approximate the Po vs. Ca²⁺_i response for a wide range of distribution and number of high-affinity Ca²⁺ sensors on the subunits (Fig. 5), the intrasubunit cooperativity factor W in this equation is an empirical parameter, and consequently, Scheme 2 becomes an empirical equation when W differs from 1.0. Furthermore, since both high-affinity Ca²⁺ sensors on the same subunit would not always have a bound Ca²⁺, then the number of paired sensors is not given strictly by the number of subunits with two high-affinity Ca²⁺ sensors. This is currently incorporated into the fitted value of W, but an expanded version of Scheme 2 would be required to explicitly take this into account. Scheme 2, of course, is only one of many different schemes that could be proposed to incorporate intrasubunit cooperativity. For example, we also examined some models in which intrasubunit interactions occurred through changes in the binding affinities for the two high-affinity sensors rather than through the empirical W cooperativity factor. These models could also approximate the data but were more complex with a larger number of free parameters. Scheme 2 is a simple equilibrium model. Any actual physical model for cooperativity is likely to be more complex than Scheme 2. Nevertheless, Scheme 2 demonstrates that a model in which intrasubunit cooperativity is nested within intersubunit cooperativity can approximate the experimental data over a wide range of configurations of high-affinity Ca²⁺ binding sensors on the subunits.

	DISCUSSION

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Small changes in Ca²⁺_i can lead to large changes in the Po for BK channels (Barrett et al., 1982; McManus et al., 1985; Golowasch et al., 1986; Cui et al., 1997; Nimigean and Magleby, 1999; Bian et al., 2001). This highly cooperative activation involves at least three Ca²⁺ sensors per subunit. Two of these are high-affinity (µM) Ca²⁺ sensors defined by mutations to D362/D367 (RCK1 sensor) and to the Ca bowl, and the third is a low-affinity Ca²⁺/Mg²⁺ sensor defined by mutations to E374/E399 (see INTRODUCTION). The objective of our study was to determine the contributions of the two high-affinity Ca²⁺ sensors to the cooperative activation of BK channels by Ca²⁺. The approach was to examine BK channels with different configurations of the high-affinity Ca²⁺ sensors on the subunits. We found that the two high-affinity Ca²⁺ sensors contributed about equally to activating the channel when there was only one high-affinity Ca²⁺ sensor per subunit. We also found that two high-affinity Ca²⁺ sensors on the same subunit were much more effective in increasing open probability (Po) than when they were on separate subunits, indicating positive intrasubunit cooperativity. An empirical model incorporating intrasubunit cooperativity nested within intersubunit cooperativity could approximate the Po vs. Ca²⁺ response for eight possible subunit configurations of the high-affinity Ca²⁺ sensors, as well as three additional configurations from a previous study. The question then arises as to possible mechanisms for the intra- and intersubunit cooperativity.

Intrasubunit Cooperativity Appears To Be Nested within Intersubunit Cooperativity
Previous studies for the gating of BK channels have found that the Ca²⁺ activation of the channel could be described by assuming that each considered Ca²⁺ sensor acts independently but jointly to activate the channel (Cox and Aldrich, 2000; Cui and Aldrich, 2000; Shi and Cui, 2001; Zhang et al., 2001; Horrigan and Aldrich, 2002; Niu and Magleby, 2002; Xia et al., 2002). Such a model is described by Scheme 1 in which the affinity of each Ca²⁺ sensor is independent of Ca²⁺ binding at other sensors. In Scheme 1 the cooperativity arises from joint action of independent Ca²⁺ sensors on the gates.

To account for our observations that two high-affinity Ca²⁺ sensors on the same subunit are more effective in activation of the channel than when they are on separate subunits, we introduced an empirical intrasubunit cooperativity factor W in Scheme 2 that facilitates the ability of two high-affinity Ca²⁺ sensors on the same subunit to activate the channel. The physical basis for the intrasubunit cooperativity is not known but, in terms of Scheme 2, is consistent with the possibility that intersubunit cooperativity comes from the independent but joint action of each subunit to open the gates of the channel, with intrasubunit cooperativity facilitating the independent contribution of the individual subunits. Thus, intrasubunit cooperativity appears to be nested within intersubunit cooperativity. Suggestions of cooperative interactions that go beyond Scheme 1 have been inferred from previous studies (Cox et al., 1997; Rothberg and Magleby, 1999, 2000; Cui and Aldrich, 2000; Horrigan and Aldrich, 2002; Xia et al., 2002, 2004; Horrigan et al., 2005), so it is to be expected that Scheme 1 would need to be expanded.

Why BK channels have evolved such an elaborate mechanism for high-affinity Ca²⁺ activation that uses eight high-affinity sites of two different types is not clear but may reflect mechanical/energetic factors related to extracting sufficient energy from Ca²⁺ binding for Ca²⁺ activation of the channel over a wide range of both Ca²⁺ and voltage. Mg²⁺_i activates BK channels by binding to low-affinity sites and can also modulate BK channel activity through inhibitory action on the high-affinity sites (Shi and Cui, 2001; Zhang et al., 2001; Xia et al., 2002; Qian and Magleby, 2003; Kubokawa et al., 2005; Zeng et al., 2005). To what extent Mg²⁺ inhibition may act by altering intrasubunit cooperativity between the two high- affinity sites will need to be investigated.

Possible Gating Ring Structures of BK Channels
To gain insight into possible mechanisms for intra- and intersubunit cooperativity, we now examine our findings in light of what is known about the structural basis for the Ca²⁺-dependent gating of K⁺ channels. It has been proposed, based on analogy to the crystal structure of a Ca²⁺-modulated bacterial K⁺ channel, MthK, that the intracellular COOH terminus of BK channels forms a large intracellular gating ring comprised of eight RCK (regulator of the conductance of K⁺) domains (Jiang et al., 2001; Jiang et al., 2002). It has also been proposed that binding of Ca²⁺ to the gating ring may increase Po by expanding the gating ring to open the gates (Jiang et al., 2002; Niu et al., 2004; Dong et al., 2005). Based on these proposals, cartoons of hypothetical gating ring structures for WT BK channels are presented in Fig. 6. RCK1 and RCK2 domains are included in the cartoons based on the structure of MthK (Jiang et al., 2002), but it must be emphasized that these are assumed structures, as the actual structure of BK channels is unknown. It should also be noted that the RCK1 and RCK2 domains in MthK channels are identical, whereas the presumed RCK1 and RCK2 domains of BK channels have limited sequence identity. Nevertheless, for purposes of discussion, it will be assumed that BK channels have a gating ring comprised of RCK1 and RCK2 domains, similar to MthK.

View larger version (45K): [in this window] [in a new window]   Figure 6. If the assumptions are made that the high-affinity Ca2+ sensors act at a flexible interface and that the interfaces between RCK domains in the gating ring alternate between fixed and flexible, then the data are consistent with a flexible, rather than a fixed, interface between the RCK1 and RCK2 domains of a single subunit. Schematic diagrams of WT BK channels and their gating rings are presented with different distributions of the high-affinity Ca2+ sensors assuming (A1–A3) a flexible intrasubunit interface or (B1–B3) a fixed intrasubunit interface. Transmembrane segments S0–S5 are removed in the side views of the BK channels in A1 and B1 to show the S6 gates. RCK1 domains are ellipses, RCK2 domains are squares, RCK1 sensors are blue squares, Ca bowls are red hexagons, RCK domains from the same subunit are of the same color, fixed interfaces are indicated by a bar across the interface, and flexible interfaces are indicated by contact between the RCK1 and RCK2 domains. The distributions of the RCK1 sensors and Ca bowls on the subunits are indicated in the stick diagrams for each channel type. The four channel types in A2 (for flexible intrasubunit interfaces) had similar Ca2+ response curves and required 3.9-fold more Ca2+ for half activation than the channel types in A3. These same channel types are repeated in B2 and B3 for fixed intrasubunit interfaces. The consistent distributions of high-affinity Ca2+ sensors in A2 and A3 assuming a flexible intrasubunit interface can be contrasted to the inconsistent distributions in B2 and B3 assuming a fixed intrasubunit interface, suggesting a flexible intrasubunit interface.

In MthK, there are a total of eight interfaces (contacts) between the eight RCK domains that alternate between fixed and flexible around the gating ring (Jiang et al., 2002), although the "fixed" interfaces may also have some flexibility (Dong et al., 2005). If BK channels have a gating ring similar to MthK channels, then BK channels would also have alternating fixed and flexible interfaces (Jiang et al., 2002). Consequently, alternating fixed interfaces (bars) and flexible interfaces (contacts) are shown in Fig. 6, A1 and B1. Notice that each interface, whether fixed or flexible, occurs between an RCK1 domain on the upper part of the gating ring and an RCK2 domain on the lower part of the gating ring. For BK channels, each proposed RCK2 domain would be attached to an RCK1 domain with a nonconserved RCK1–RCK2 linker (Schreiber and Salkoff, 1997; Schreiber et al., 1999). Neither the expression nor the function of BK channels requires that the RCK1–RCK2 linker be intact, as functional channels are obtained by injecting separate messenger RNA for the core (S0–S6 plus RCK1) and tail (RCK2) of the channel (Meera et al., 1997; Schreiber and Salkoff, 1997; Schreiber et al., 1999; Moss and Magleby, 2001; Qian et al., 2002; Schmalhofer et al., 2005). Because an intact RCK1–RCK2 linker is not required for function, RCK1–RCK2 linkers are not shown in Fig. 6.

Support for the gating ring model depicted in Fig. 6 (A1 and B1) comes from the observations that RCK domains isolated from MthK can form either dimers or octamers in solution depending on the ionic conditions, with comparison of crystal structures indicating movement at the flexible interfaces (Dong et al., 2005), although not as large as expected, suggesting that the "fixed" interfaces may also have some flexibility (Dong et al., 2005). Further support for a gating ring model for BK channels comes from the observations that shortening the linkers between the gating ring and the S6 gates increases Po and lengthening the linkers has the opposite effect, and this is the case over a wide range of Ca²⁺ (Niu et al., 2004).

Is the Intrasubunit Interface Fixed or Flexible?
When considering possible mechanisms for intra- and intersubunit cooperativity in BK channels, it would be most useful to know whether the interface formed between the proposed RCK1 and RCK2 domains on the same subunit is fixed or flexible. Analogy to MthK channels cannot be used to answer this question because the RCK2 domains of MthK channels are not directly attached to the RCK1 domains but are separate subunits assembled from solution (Jiang et al., 2002; Dong et al., 2005). Consequently, we explored if examination of our experimental data could give insight into whether the intrasubunit interfaces for BK channels were fixed or flexible.

Our approach was to compare the theoretical distributions of high-affinity Ca²⁺ sensors for assumed flexible or fixed intrasubunit interfaces to the Ca²⁺ response of the channels to determine whether either type of interface could be excluded because of inconsistency between the distributions of Ca²⁺ sensors and response. The locations of the high-affinity Ca²⁺ sensors on the gating ring are shown in Fig. 6 for the various configurations of channels considered in this paper. In Fig. 6 (A1–A3) the intrasubunit interfaces are assumed to be flexible and the intersubunit interfaces fixed. In Fig. 6 (B1–B3), the opposite configuration is assumed. Fig. 6 A1 and Fig. 6 B1 are side views of simplified WT channels, as discussed above, and A2–A3 and B2–B3 are schematic diagrams of only the gating ring looking into the channel from below. In these drawings RCK1 domains are ellipses, RCK2 domains are rectangles, RCK1 Ca²⁺ sensors are blue squares, Ca bowls are red hexagons, each fixed interface between RCK1 and RCK2 domains is indicated by a stabilizing bar across the interface, each flexible interface between RCK1 and RCK2 domains is indicated by contact between the two domains, and RCK1 and RCK2 domains from the same subunit are of the same color. For both flexible and fixed intrasubunit interfaces, it is expected that the 2(B)+2(R) channels and the 2(RB)+2() channels will be expressed in two different assemblies: with the same type of subunit adjacent and with the same type of subunit diagonal. Consequently, both adjacent and diagonal configurations are presented, but it should be noted that the same conclusions would be reached if only the adjacent or the diagonal configurations were expressed. It will be argued in the sections below that our data are fully consistent with a flexible intrasubunit interface. The key assumptions in this analysis are that BK channels have a gating ring comprised of RCK domains, that the interfaces between the RCK domains alternate between fixed and flexible, and that the high-affinity Ca²⁺ sensors act at the flexible interfaces. These assumptions are based on analogy to the MthK channel, which has a gating ring comprised of RCK domains with alternating fixed and flexible interfaces, and the further observation that the binding of Ca²⁺ across the flexible interface of MthK channels induces the gating ring to expand (Jiang et al., 2002; Dong et al., 2005).

One High-affinity Ca²⁺ Sensor per Subunit.
We found that channels with one high-affinity Ca²⁺ sensor per subunit, independent of whether the Ca²⁺ sensors were RCK1 sensors, Ca bowls, or a mixture of both, gave approximately the same Po versus Ca²⁺ response (Fig. 1, B and C; Fig. 2, continuous line). The subunit locations of the high-affinity Ca²⁺ sensors for the four possible configurations of these functionally equivalent channels are presented in Fig. 6 A2 for an assumed flexible intrasubunit interface and in Fig. 6 B2 and for an assumed fixed intrasubunit interface. For an assumed flexible intrasubunit interface, each of the four configurations of the channel with one high-affinity Ca²⁺ sensor per subunit also had one high-affinity Ca²⁺ sensor per flexible interface (Fig. 6 A2). On this basis, each of the channels examined in Fig. 6 A2 gave the same Ca²⁺ response because each of the channels had a consistent distribution of one high-affinity Ca²⁺ sensor (either an RCK1 sensor or Ca bowl) per flexible interface.

In contrast, for an assumption of a fixed intrasubunit interface for one high-affinity Ca²⁺ sensor per subunit, there was an inconsistent distribution of Ca²⁺ sensors at the flexible interfaces (Fig. 6 B2). Two of the configurations (Fig. 6 B2, top row) had one Ca²⁺ sensor per flexible interface. Another configuration (Fig. 6 B2, bottom left) had two flexible interfaces with one Ca²⁺ sensor each, one flexible interface with two Ca²⁺ sensors, and one flexible interface with no Ca²⁺ sensors. The remaining configuration (Fig. 6 B2, bottom right) had two flexible interfaces with two Ca²⁺ sensors each and two flexible interfaces without Ca²⁺ sensors. Such diversity in the distribution of high-affinity Ca²⁺ sensors at the flexible interfaces of the channels in Fig. 6 B2 is inconsistent with the experimental observations that channels with one high-affinity Ca²⁺ sensor per subunit gave approximately the same response to Ca²⁺. This inconsistency argues against a fixed intrasubunit interface.

Two High-affinity Ca²⁺ Sensors on Each of Two Subunits and No High-affinity Ca²⁺ Sensors on the Other Two Subunits.
When the configuration of four high-affinity Ca²⁺ sensors per channel was two Ca²⁺ sensors on each of two subunits and no Ca²⁺ sensors on each of two subunits, as in Fig. 6 (A3 and B3), then the Ca²⁺ required to half activate the channel was decreased 3.9-fold (Fig. 4). Hence, two high-affinity Ca²⁺ sensors on each of two subunits were much more effective than when there was one Ca²⁺ sensor on each of four separate subunits. For an assumption of a flexible intrasubunit interface (Fig. 6 A3), each of the two configurations of the channel with two Ca²⁺ sensors on each of two subunits and no Ca²⁺ sensors on each of two subunits would have two Ca²⁺ sensors at each of two flexible interfaces and no Ca²⁺ sensors at the other two flexible interfaces. Thus, the same Ca²⁺ response for both configurations in Fig. 6 A3 would be expected if the response depended on the distribution of paired Ca²⁺ sensors at the flexible interfaces and not on whether identical subunits were adjacent or diagonal.

For an assumption of a fixed intrasubunit interface (Fig. 6 B3), one of the configurations of channels with two Ca²⁺ sensors on each of two subunits and no Ca²⁺ sensors on each of two subunits would have two Ca²⁺ sensors at one flexible interface, one Ca²⁺ sensor at each of two flexible interfaces, and no Ca²⁺ sensors at one flexible interface (Fig. 6 B3, left). The other configuration would have one Ca²⁺ sensor at each of the four flexible interfaces (Fig. 6 B3, right). Such a pronounced difference in the distribution of high-affinity Ca²⁺ sensors at the flexible interfaces of the two possible channel configurations in Fig. 6 B3 might be expected to produce a large difference in response. Yet, there was no indication that this was the case. Furthermore, both of the channel configurations in Fig. 6 B3 are essentially equivalent to channel configurations in Fig. 6 B2, yet the channels for Fig. 6 B3 required 3.9-fold less Ca²⁺ for half activation than those in Fig. 6 B2. These inconsistencies between the distributions of the Ca²⁺ sensors and the Ca²⁺ responses for an assumed fixed intrasubunit interface (Fig. 6, B2 and B3) are in marked contrast to the consistent relationships observed for an assumed flexible intrasubunit interface (Fig. 6, A2–A3). Consequently, the data suggest a flexible intrasubunit interface for BK channels, and such an interface will be assumed for further discussion of mechanism. It should be emphasized that this conclusion is based on the assumptions that BK channels have a gating ring comprised of RCK domains similar to MthK channels, that the interfaces between RCK1 and RCK2 domains alternate between fixed and flexible, and that the high-affinity Ca²⁺ sensors act at the flexible interfaces. Alternatively, if the interfaces do not alternate between fixed and flexible, or if the Ca²⁺ sensors act at the fixed interfaces (although it would be difficult to see how Ca²⁺ sensors could have any action at a fixed interface or have cooperative interactions across a fixed interface), then the conclusion would have been just the opposite.

Possible Mechanisms for Intrasubunit Cooperativity
We observed that two high-affinity Ca²⁺ sensors on the same subunit were much more effective in activating the channel then when on separate subunits (Fig. 4), indicating intrasubunit cooperativity. If the interface between RCK1 and RCK2 domains on the same subunit is flexible, as considered above, then taken together, these observations indicate that two high-affinity Ca²⁺ sensors acting on either side of a flexible intrasubunit interface are far more effective at opening the channel than two high-affinity Ca²⁺ sensors located singly on separate subunits, giving the conditions for intrasubunit cooperativity.

Scheme 2, which incorporates intrasubunit cooperativity nested within intersubunit cooperativity, could approximate the Ca²⁺ response of the different examined configurations of the high-affinity Ca²⁺ sensors on the subunits. In terms of the diagrams of the gating rings in Fig. 6 (A1–A3), intersubunit cooperativity would arise from independent but joint action of the Ca²⁺ sensors on different subunits to expand the gating ring and open the channel, whereas intrasubunit cooperativity would arise from cooperative action of Ca²⁺ sensors located on either side of the flexible interface of a single subunit, leading to a more effective expansion of the gating ring than if the Ca²⁺ sensors were located on different subunits. The molecular machinery in BK channels that makes two Ca²⁺ sensors on the same subunit more effective than two Ca²⁺ sensors on separate subunits is unknown, but for MthK channels, the two Ca²⁺ binding sites located across each flexible interface are separated by only 11 Å (Dong et al., 2005), such that expansion of the interface induced by Ca²⁺ binding at one site might be expected to influence the neighboring Ca²⁺ binding site.

Whereas the Ca bowl and the RCK1 sensors are both of high affinity with similar effects on the Po vs. Ca²⁺ response in our relatively low resolution experiments, these sites are not identical, as they have differential cation sensitivity, somewhat different K_d, and differential effects on the activation and deactivation properties of the channel (Schreiber and Salkoff, 1997; Bao et al., 2002; Xia et al., 2002; Zeng et al., 2005). Furthermore, whereas the RCK1 and RCK2 domains of MthK are essentially identical, the proposed RCK1 and RCK2 domains of BK channels have only very limited sequence identity, and the Ca bowl appears as an additional structure downstream of the proposed RCK2 domain (Schreiber and Salkoff, 1997; Schreiber et al., 1999; Bian et al., 2001; Jiang et al., 2001). Thus, it is expected that the locations of the high-affinity Ca²⁺ binding sites in BK channels will differ from the symmetrical structure of the low-affinity Ca²⁺ binding sites in MthK. Consequently, whereas Scheme 2 and the schematic diagrams of the BK channel in Fig. 6 (which are based on an assumed structure) can serve to summarize the data and should be useful for designing future experiments, the actual structure is likely to differ significantly from the structure assumed for purposes of discussion, and it is also anticipated that the gating mechanism will be more complex than Scheme 2.

Cooperativity in Other Channels
Various types of intersubunit cooperativity have been described previously. For example, glycine receptors comprised of homomeric 1 subunits can bind a glycine molecule on each of five subunits, with interaction between the binding sites when the channel is still closed, giving intersubunit cooperativity before the conformational change associated with channel opening (Beato et al., 2004). For NMDA receptors, a steric interaction exists between NR1 and NR2 subunits that modulates glycine affinity (Regalado et al., 2001). For voltage-gated potassium channels, the S4 voltage sensors can first move independently and then move cooperatively to open the channel (Smith-Maxwell et al., 1998a,b; Schoppa and Sigworth, 1998a,b,c; Ledwell and Aldrich, 1999; Patlak, 1999; Mannuzzu and Isacoff, 2000; Pathak et al., 2005; Tombola et al., 2005). The voltage sensors in BK channels act mainly independently but jointly to open the gates (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999; Cox and Aldrich, 2000). For cyclic nucleotide-gated channels, it has been proposed that the four subunits may associate and activate as two independent dimers with independent binding of ligand to each subunit that forms a dimer, but the conformational changes of the two subunits within the dimer upon ligand binding can be cooperative and concerted (Liu et al., 1998; Richards and Gordon, 2000; Craven et al., 2006). For the above examples of intersubunit cooperativity, there are two general types of mechanisms: cooperativity arising from independent but joint action of the subunits to open the gates and cooperativity arising from interactions among the binding sites or subunits.

BK channels may also have these two types of cooperative action, with intrasubunit cooperativity being a likely candidate for interactions among the high-affinity Ca²⁺ sensors located on the same subunit, and intersubunit cooperativity arising from independent but joint action of high-affinity Ca²⁺ sensors on different subunits. We found that two high-affinity Ca²⁺ sensors on a single subunit were much more effective at activating the channel than two high-affinity Ca²⁺ sensors on separate subunits, indicating positive intrasubunit cooperativity. A model with intrasubunit cooperativity nested within intersubunit cooperativity was consistent with the experimental observations.

	ACKNOWLEDGMENTS

 
Supported in part by grants from the National Institutes of Health (AR32805) and the Muscular Dystrophy Association.

Olaf S. Andersen served as editor.

Submitted: 3 January 2006
Accepted: 13 September 2006

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