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Centro de Estudios Científicos, Valdivia, Chile and Facultad de Ciencias, Universidad de Chile, Santiago, Chile

Correspondence to Ramon Latorre: rlatorre{at}cecs.cl

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
High conductance, calcium- and voltage-activated potassium (BK) channels are widely expressed in mammals. In some tissues, the biophysical properties of BK channels are highly affected by coexpression of regulatory (ß) subunits. ß1 and ß2 subunits increase apparent channel calcium sensitivity. The ß1 subunit also decreases the voltage sensitivity of the channel and the ß2 subunit produces an N-type inactivation of BK currents. We further characterized the effects of the ß1 and ß2 subunits on the calcium and voltage sensitivity of the channel, analyzing the data in the context of an allosteric model for BK channel activation by calcium and voltage (Horrigan and Aldrich, 2002). In this study, we used a ß2 subunit without its N-type inactivation domain (ß2IR). The results indicate that the ß2IR subunit, like the ß1 subunit, has a small effect on the calcium binding affinity of the channel. Unlike the ß1 subunit, the ß2IR subunit also has no effect on the voltage sensitivity of the channel. The limiting voltage dependence for steady-state channel activation, unrelated to voltage sensor movements, is unaffected by any of the studied ß subunits. The same is observed for the limiting voltage dependence of the deactivation time constant. Thus, the ß1 subunit must affect the voltage sensitivity by altering the function of the voltage sensors of the channel. Both ß subunits reduce the intrinsic equilibrium constant for channel opening (L₀). In the allosteric activation model, the reduction of the voltage dependence for the activation of the voltage sensors accounts for most of the macroscopic steady-state effects of the ß1 subunit, including the increase of the apparent calcium sensitivity of the BK channel. All allosteric coupling factors need to be increased in order to explain the observed effects when the subunit is coexpressed with the ß2IR subunit.

Key Words: BK channel • ß subunits • allosteric model • voltage dependence • apparent calcium sensitivity

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The high conductance, voltage- and calcium-activated potassium channel (BK or MaxiK channel) is widely expressed among mammalian tissues (Toro et al., 1998). Its open probability increases on membrane depolarization or an increase in intracellular calcium concentration. As its activation leads to membrane hyperpolarization, it serves as a negative-feedback mechanism for the excitatory events that lead to increases in calcium concentration or raise the membrane potential. In vascular smooth muscle cells, BK channels play a key role in regulating the contractile tone (Nelson and Quayle, 1995; Brenner et al., 2000b); in chromaffin cells these channels help terminate the action potential and thus they modulate secretion (Neely and Lingle, 1992; Solaro et al., 1995), and in neurons BK channels colocalize with voltage-dependent calcium channels and are involved in the control of neurosecretion (Sah and Davies, 2000).

The BK channel is a homotetramer of its pore-forming subunit, which is coded by the gene Slo1 (KNCMA1) and is a member of the voltage-dependent potassium (Kv) channels superfamily. As in all other Kv channels, the S4 transmembrane segment is (or is part of) an intrinsic voltage sensor (Diaz et al., 1998; Cui and Aldrich, 2000). Gating and ionic currents in BK channels can be elicited by membrane depolarization in the absence of calcium, suggesting that this is a voltage-dependent channel (Stefani et al., 1997). The divalent cation acts as a modulator able to decrease the necessary energy to open the channel, promoting a leftward shift in the open probability (P_(O)) vs. voltage relationships. Therefore, as calcium is increased, less voltage is needed to activate the channel. The channel is also activated by intracellular Mg²⁺, whose binding sites are also low affinity binding sites for Ca²⁺ (Shi and Cui, 2001; Zhang et al., 2001).

Although only one gene codes for the BK channel (Slo1, KCNMA1), a wide variety of channel phenotypes has been found. These phenotypes differ in their calcium and voltage sensitivity as well as in their macroscopic kinetics. This variety is explained by several regulatory factors, including alternative splicing, protein phosphorylation, and, most importantly, coexpression of tissue-specific accessory proteins, called ß subunits (for review see Orio et al., 2002). Four ß subunits have been cloned, termed ß1–ß4 (Knaus et al., 1994; Wallner et al., 1999; Xia et al., 1999; Behrens et al., 2000; Brenner et al., 2000a; Meera et al., 2000; Uebele et al., 2000). The effects of the ß1 subunit coexpression include an increase of the apparent calcium sensitivity, a decrease of the voltage dependence of the channel, and a slow down of the macroscopic kinetics (McManus et al., 1995; Meera et al., 1996; Cox and Aldrich, 2000; Nimigean and Magleby, 2000; Qian and Magleby, 2003). The ß1 subunit also modulates the interaction of the channel with toxins and other activators (Dworetzky et al., 1996; Hanner et al., 1997; Valverde et al., 1999). The ß2 subunit has an N-type or fast inactivation motif in its NH₂ terminus, causing BK currents to inactivate when this subunit is present (Wallner et al., 1999; Xia et al., 1999). Besides this, the ß2 subunit also enhances BK channel's calcium sensitivity, in a very similar way to that of the ß1 subunit. The ß3 subunit has four splice variants. Three of them confer some degree of inactivation to BK currents, and they also produce an outward rectification of the open channel currents (Brenner et al., 2000a; Xia et al., 2000; Zeng et al., 2001). None of the ß3 subunits have any effect on the apparent calcium sensitivity of the channel. Finally, the ß4 subunit has the opposite effect as the ß1 subunit, decreasing the apparent calcium sensitivity of the BK channel (Brenner et al., 2000a; but see Ha et al., 2004). This subunit also slows down the macroscopic kinetics of the channel.

Detailed studies of the modulation of the apparent calcium sensitivity have been carried on for the ß1 subunit. These studies strongly suggest that the ß1 subunit affects the functional coupling between calcium binding and channel opening rather than the calcium binding affinity (Cox and Aldrich, 2000; Nimigean and Magleby, 2000). It is unclear at present whether or not the other ß subunits modify the apparent Ca²⁺ sensitivity through a mechanism similar to that proposed for the ß1 subunit.

The synergistic activation of the BK channel by two different stimuli (increases in intracellular calcium and membrane depolarization) has been shown to be rather complex, leading to the proposition of different kinetic schemes of up to 250 states and even more (for review see Magleby, 2003). One of the key features that define the behavior of BK channel is that neither calcium nor voltage is strictly necessary for channel activation. In the virtual absence of calcium, the channel is activated by large depolarization (Meera et al., 1996; Cui et al., 1997; Stefani et al., 1997), and when all voltage sensors are resting, the open probability of the channel can be increased by augmenting intracellular calcium (Horrigan and Aldrich, 2002). Even in the absence of both stimuli (in very low calcium and at very negative potentials), the channel still opens with a very low, but measurable, open probability (10^–6) and a low voltage dependence not related to the voltage sensor (Horrigan et al., 1999; Horrigan and Aldrich, 2002). This, and several other observations, including macroscopic and single channel kinetics, led to the idea that both calcium and voltage increase the open probability by an allosteric mechanism (Horrigan et al., 1999; Rothberg and Magleby, 1999, 2000; Cui and Aldrich, 2000; Talukder and Aldrich, 2000; Horrigan and Aldrich, 2002). In this type of mechanism, neither voltage sensor movement nor calcium binding are strictly coupled to channel opening; these three processes are independent equilibriums that interact allosterically with each other. The existence of at least two and maybe three calcium binding sites with different affinities (Zhang et al., 2001; Xia et al., 2002) makes the picture more complicated and raises, almost exponentially, the number of states in a model.

The best compromise between simplicity and reproduction of the voltage and calcium dependence in a wide range of voltages and calcium concentrations, including very low open probabilities, is probably achieved by a 70-state allosteric activation model (Horrigan and Aldrich, 2002). This model (also explained in Fig. 1) takes into account two voltage dependences, one for the channel opening itself and one for the voltage sensor movement, and only the high-affinity calcium dependence. It also includes some allosteric interaction between calcium binding and voltage sensor movement. The open probability at any voltage and calcium concentration is given by the equation

(1)

where

View larger version (33K): [in this window] [in a new window]   FIGURE 1. Allosteric activation model for BK channel. (A) The allosteric activation by calcium originates a 10-state Monod-Wymann-Changeaux (MWC) activation model. For each calcium binding site occupied, the equilibrium constant for channel opening (L) is multiplied by the allosteric factor C. The same factor multiplies the calcium binding equilibrium constant (K) when the channel is open. (B) The allosteric activation by voltage also originates a 10-state MWC model. In this case, the allosteric factor is D and the equilibrium constant for voltage sensor activation is J. (C) The combination of A and B originates a two-tiered, 50-state model. (D) The complete 70-state model takes into account some interaction between voltage sensor activation and calcium binding (allosteric factor E). Note that when E = 1, the model reduces to 50-state as in C (modified from Horrigan and Aldrich, 2002).

In this paper, we present a detailed study of the effects of the ß1 subunit and the ß2 subunit without the inactivation domain (ß2IR) on the calcium and voltage dependence of the BK channel. We focus on how the ß subunits affect the voltage dependence of channel activation, as no previous study has shown whether the ß1 subunit affects either the voltage sensor–associated or the voltage sensor–independent voltage dependence of the BK channel. Our results show that the ß1 subunit, but not the ß2IR subunit, has an important effect on the voltage sensor–associated voltage dependence of the channel. This effect is very likely to be a reduction in the number of effective gating charges per voltage sensor or the voltage dependence of the sensors activation (from 0.51 to 0.3). Contrary to a previous report (Cox and Aldrich, 2000), only this reduction of the voltage dependence can account for most of the ß1 subunit effects on the macroscopic steady-state behavior of the channel, including the enhanced apparent calcium sensitivity. In the case of the ß2IR subunit, an increase of the allosteric coupling factors is needed to account for its effects, as well as some change in the calcium binding affinity. We also found that both ß subunits reduce the intrinsic equilibrium constant for channel opening (L₀).

	MATERIALS AND METHODS

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Channel Expression
cDNAs coding for BK channel subunit (KCNMA) from myometrium (GenBank/EMBL/DDBJ accession no. U11058), human ß1 and ß2 subunits (KCNMB1 and KCNMB2, GenBank/EMBL/DDBJ accession no. U25138 and AF099137) and ß2 subunit without inactivation domain (ß2IR) (Wallner et al., 1999) were provided by L. Toro (University of California at Los Angeles [UCLA], Los Angeles, CA). mMESSAGE mMACHINE (Ambion) in vitro transcription kit was used to obtain mRNAs. Channels were expressed in Xenopus oocytes using standard techniques (Stühmer and Parekh, 1995). For macroscopic current recordings, 0.75–2 ng of subunit cRNA or a mixture of 0.5–1.5 ng ( subunit) and 2–3 ng (ß subunit) was injected per oocyte. For limiting voltage dependence experiments, 30 ng ( subunit) or 12.5 ng ( subunit) + 25 ng (ß subunit) was injected. The approximate molar ratio was at least 6:1 (ß:), ensuring saturation of ß subunit.

Electrophysiological Recordings and Solutions
1–5 d after cRNA injection, currents were recorded using the inside-out configuration of the patch-clamp technique. All recordings were performed at room temperature (20–22°C). Intracellular (bath) and extracellular (pipette) solutions contained (in mM) 110 KOH, 10 HEPES, and 2 KCl, and were adjusted to pH 7.4 with methanosulfonic acid. Depending on the desired free calcium concentration, 1.8–3.5 mM CaCl₂ and 5 mM EGTA (5–200 nM), HEDTA (0.68–12 µM), or NTA (22–150 µM) was added. Free calcium concentrations were calculated using the WinMaxChelator Software (http://www.stanford.edu/~cpatton/maxc.html) and checked with a calcium electrode (World Precision Instruments). For the solution designated as 5 nM, this is an upper estimation based on contaminating calcium. Depending on the magnitude of currents, and in order to minimize voltage drops due to series resistance, some experiments were done with solutions containing 36 mM KOH and 74 mM NMDG. The pipette solution contained 100 nM or lower free calcium.

Pipettes were pulled in a horizontal pipette puller (Sutter Instruments) from Corning 7740 (Pyrex) or Custom 8250 (Warner Instruments) borosilicate capillary glass. Pipette resistance was 0.8–2 M in 110 K⁺, and series resistance error was always <10 mV.

Data were acquired with an Axopatch 200B (Axon Instruments) or an EPC-7 (List Medical) amplifier, filtered with an 8-pole Bessel filter (Frequency Devices) at 1/5 of the acquisition rate and sampled with a 16-bit A/D converter (NI-6036; National Instruments). Typical acquisition rates for macroscopic current recordings ranged from 66.6 to 100 kHz ( subunit alone) or from 16.6 to 40 kHz ( + ß subunits). For unitary events quantification, recordings were sampled at 50 kHz for and 20 kHz for + ß channels. A homemade acquisition software was developed in the LabView programming environment (National Instruments). Primary data analysis was performed with Analysis (UCLA) and Clampfit 9 (Axon Instruments) software.

Steady-state Activation Analysis
The Solver function of Microsoft Excel was used to fit instantaneous tail currents to a Boltzmann function of the form

(2)

where I_max is the maximum obtained tail current, z is the voltage dependency of activation, V_0.5 is the half-activation voltage, T is the absolute temperature (typically 295 K), F is the Faraday's constant, and R is the universal gas constant. When [Ca²⁺] was <500 nM, only low conductances were achieved and the estimation of I_max became unreliable. In those cases, G_max was fixed using the value obtained with higher calcium concentrations in the same patch. All the analyses that follow were performed using I/I_max values.

G values were calculated for each experiment as –zFV_0.5. Mean G values were plotted against calcium concentration and fitted to a concentration-effect sigmoid equation (Eq. 6). As we used calcium concentrations uniformly distributed in a logarithmic scale, the fit was performed using log([Ca²⁺]).

Statistical Analysis
To test whether a fit parameter was statistically different between two (or more) datasets, a global fit (null hypothesis, in which the parameter of interest was restricted to be equal among all datasets) was compared against an independent fit of each dataset (alternative hypothesis). Comparison between independent and global fits was done by an extra sum-of-squares F test, using the formula

where SS and DF are the sum-of-squares and the degrees of freedom of the fit, respectively. glb and ind denote the global and the independent fit, respectively. All the analysis and the conversion of the F value to a P value were done with the GraphPad Prism software (GraphPad Software Inc.).

Single Channel Analysis
All-points amplitude histograms were obtained from 20–45 s recordings. For each histogram, NP_(O) was calculated by measuring the fraction of time (P_k) spent at each open level (k) using a half-amplitude criteria and summing their contributions NP_(O) = kP_k. In some experiments, it was checked that the half-amplitude criteria method yields a similar result (<5% difference in NP_(O)) than a Gaussian fit of the histograms. For voltages >50 mV, NP_(O) was calculated from the macroscopic tail current measurement, dividing by the unitary conductance (220 pS) and the tail voltage. In some experiments, the number of channels in the patch (N) was calculated by raising the calcium concentration and performing a nonstationary noise analysis (Sigworth, 1980; Alvarez et al., 2002) or measuring total patch conductance between –10 and 10 mV when all channels were open. In this way, an absolute P_(O) was obtained and was used to normalize and average the experiments.

Fit to the Allosteric Activation Model
For each calcium concentration, a mean V_0.5 (<V_0.5>) value was obtained. All the corresponding G/G_max vs. V curves were displaced in the voltage axis by V_0.5 – <V_0.5>, allowing us to construct an average curve that preserved the shape of the individual curves at every [Ca²⁺]. Each of these curves comprised three to eight sets of 30 to 35 points that were converted to a 40-point set by a smoothing function in Sigmaplot 8.0. The families of G/V curves were simultaneously fitted to Eq. 1 by minimizing least-squares with a mixture of Marquardt-Levenverg and Simplex iterations in Origin Pro (OriginLabs). Several fits were attempted with different initial parameters and the fits with lower chi-squared were chosen.

	RESULTS

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Effect of ß1 and ß2IR Subunits on Steady-state Activation Parameters of BK Channel
Fig. 2 summarizes the voltage- and calcium dependence of the BK channel and how it is affected by the ß1 and ß2 subunits. We studied a truncated ß2 subunit (2-19ß2, ß2IR) that lacks the inactivation peptide. In the presence of the ß2IR subunit, BK currents are sustained (compare Fig. 2 A, +ß2wt and +ß2IR) and therefore the effects of this subunit in the activation parameters of the BK channel are best studied.

View larger version (33K): [in this window] [in a new window]   FIGURE 2. Effects of ß1 and ß2IR subunits on BK channel steady-state activation parameters. (A) Macroscopic currents recorded in the inside-out configuration at 5 nM (left) and 2.8 µM (right) intracellular calcium. The respective voltage protocols are shown at the bottom. (B) Averaged P(O)/V curves at 2.8 µM (triangles) and 5 nM Ca2+ (circles). n = 4–9. Lines are the best fit to a Boltzmann distribution (Eq. 2). Fit parameters are: , V0.5 = 209 mV, z = 0.89 (5 nM); V0.5 = 42 mV, z = 1.54 (2.8 µM). +ß1, V0.5 = 244 mV, z = 0.67 (5 nM); V0.5 = –5 mV, z = 1.15 (2.8 µM). +ß2IR, V0.5 = 190 mV, z = 0.96 (5 nM); V0.5 = –33 mV, z = 1.59 (2.8 µM) (C) Average of the obtained V0.5 values plotted against calcium concentration. (D) Average of the obtained z values plotted against calcium concentration. Error bars are SD, n = 4–7.

As the calcium concentration is increased >200 nM, the voltage dependence of the BK channel increases in the 0.1–10 µM range and then decreases again as the calcium concentration is further increased (Fig. 2 D). In the presence of the ß1 and ß2IR subunits, this behavior is maintained, but the ß1 subunit shows lower z at all calcium concentrations (P < 0.0001 when compared with with a two-way ANOVA test; P = 0.008 for [Ca²⁺] 100 nM). On the contrary, the ß2IR subunit does not modify the voltage sensitivity of the channel (P = 0.27).

ß1 and ß2IR Subunits Do Not Change Calcium Binding Affinity
The changes in the V_0.5/[Ca²⁺] relationships may be interpreted as a change in the calcium binding affinity of the channel. It has been already proposed, however, that the ß1 subunit acts by a mechanism different than enhancing the calcium binding to the channel (Cox and Aldrich, 2000; Nimigean and Magleby, 2000). The data we present below suggest that this is true for the ß2IR subunit as well.

The Boltzmann distribution used to obtain the V_0.5 and z values is based on the simplifying assumption of a two-state model. In this model, the difference in free energy (G) between the open and closed states of the channel is given by

(3)

Although the BK channel has more than two states, we can use Eq. 3 to obtain the overall energy difference between open and closed states. The V_0.5 and z values from Fig. 2 (C and D), as well as Eq. 3, were used to obtain the G values plotted in Fig. 3 against calcium concentration (symbols). The G/[Ca²⁺] relationship shows that calcium affects this energy difference in a simple concentration-dependent fashion. Therefore, the G/[Ca²⁺] relationship can be fitted to an equation of the form

(4)

where G⁰ is G in absence of calcium, G_Ca is the change in G produced by calcium binding to the channel (in saturating calcium, G = G⁰ + G_Ca), EC₅₀ is the half-effect concentration, and n is the slope or concentration dependence of the change. As our data span several orders of magnitude of calcium concentration and are evenly distributed in a logarithmic scale, it is more appropriate to express the calcium concentration and EC₅₀ as log[Ca²⁺] and logEC₅₀, respectively. Then

(5)

which can be reordered to

(6)

View larger version (17K): [in this window] [in a new window]   FIGURE 3. G vs. [Ca2+] relationships for BK channel. G was calculated for each individual experiment as –zFV0.5. Plotted values are mean ± SD (n = 4–9). Lines represent the best fit to a sigmoid concentration-effect curve (Eq. 6). Best-fit values are listed in Table I.

View this table: [in this window] [in a new window]   TABLE I Parameters for the Best Fit of G vs. [Ca2+] Values to Eq. 6

The ß Subunits and the Limiting Slope for Voltage-dependent Activation
In voltage-dependent channels, the lnP_(O)/V relationship becomes linear and reaches a maximum slope (known as limiting slope) at very low open probabilities. It has been shown (Almers, 1978; Sigg and Bezanilla, 1997) that for any linear voltage-dependent model

(7)

where q is the voltage sensor charge effectively coupled to channel activation and F, R, and T have their usual meanings. The BK channel departs from this behavior; it reaches a maximum slope of 2 at P_(O) 10^–3, but when the P_(O) is further lowered, a lower slope of 0.3 is reached at P_(O) < 10^–6. This is one of many observations that led to the proposition of an allosteric mechanism for the voltage-dependent activation of the BK channel (Horrigan et al., 1999; Rothberg and Magleby, 1999). In this model, the opening of the channel has an intrinsic voltage dependence unrelated to the movement of the voltage sensors. The allosteric model is depicted in Fig. 1 B, where both the L (for channel opening) and J (for voltage sensor activation) equilibrium constants are voltage dependent. In the absence of calcium and at very negative potentials, all voltage sensors are in the resting state. In this condition, the model is confined to the C₀–O₀ equilibrium, governed by the equilibrium constant L. Then,

(8)

As L << 1, we can approximate P_(O) L, and then

(9)

Therefore, for the BK channel the limiting slope is actually given by

(10)

where z_L is the voltage dependence for the equilibrium constant L or the voltage dependence for channel opening.

We studied whether the ß1 or the ß2IR subunit have any effect on this behavior of the BK channel. To determine the limiting slope of the voltage dependence, we quantified single unitary opening events in patches containing hundreds and even thousands of channels, in conditions of very low open probabilities. Fig. 4 A shows the single channel activity of a patch containing 10,000 BK channels ( subunit alone) at three holding voltages. The opening events become less frequent at negative potentials as evidenced in the all-points histograms in Fig. 4 B (compare the 200 pS peaks at –60 vs. –120 mV). In the presence of the ß1 and ß2IR subunits (Fig. 4, C–F), a similar behavior was observed.

View larger version (45K): [in this window] [in a new window]   FIGURE 4. Unitary events quantification at very low open probabilities. Inside-out patches containing hundreds of (A), +ß1 (C), or +ß2IR (E) channels were exposed to the indicated membrane potentials in the virtual absence of intracellular calcium (5 nM). All-points histograms were constructed from 20–45-s recordings for (B), +ß1 (D), and +ß2IR (F) channel containing patches. Amplitudes are expressed as conductance in pS.

View larger version (36K): [in this window] [in a new window]   FIGURE 5. Limiting voltage dependence for , +ß1, and +ß2IR channels. Semilogarithmic P(O)/V plots for (A), +ß1 (B), and +ß2IR (C) channels, obtained from unitary events quantification (V < 60 mV) or macroscopic recordings (V > 30 mV). Values shown are mean ± SD of 3–9 points, obtained from 8 ( and +ß2IR) or 9 (+ß1) different patches. In some cases, the SD bars fall within the symbols. Linear intervals were fitted to Eq. 9 and the corresponding z values are shown beside the plots. The inset in B shows a smoothed differential of the lnP(O)/V data, expressed as electronic equivalents (scaled by RxT/F). The straight dotted line marks the Y = 0.3 position while the dotted curve is a simple exponential fit of the data added as visual reference. (D) Simultaneous fit of the P(O)/V data to Eq. 11 restricting a shared zL value for all datasets (lines). Parameters for the best fit are listed in Table II. Symbols are the same experimental data shown in A–C.

(11)

where L = L₀exp(z_LFV/RT) and J = exp(z_JF(V – V_h(J))/RT). The parameters to be fitted are L₀, V_h(J), z_L, z_J, and D (see INTRODUCTION).

P_(O) values from Fig. 5 (A–C) were fitted to Eq. 11. Before allowing the parameters to vary freely during the fit, we noted that previous works (Horrigan and Aldrich, 1999, 2002) showed that the half-activation voltage for voltage sensors (V_h(J)) is around 150 mV. This assumption is confirmed in our study by the maximum of the _act/V plot (see Fig. 9 B), which is highly dependent on V_h(J) (Horrigan et al., 1999). Moreover, this maximum is not affected by ß subunit coexpression (Fig. 9 B). Therefore, we restricted V_h(J) to be between 140 and 160 mV in all the fits. Based on the measured limiting slope, z_L was restricted to be >0.25. Two fits were performed: one in which z_L was free to vary in each dataset (, +ß1, and +ß2IR) and a second one in which z_L was restricted to be equal for the three datasets. An extra sum-of-squares F test yielded that a common z_L cannot be discarded (P = 0.22) and was preferred for the following analysis. Fig. 5 D (lines) shows the best simultaneous fit with the same z_L value and the parameters are listed in Table II.

View larger version (33K): [in this window] [in a new window]   FIGURE 6. The maximum slope of the ln(P(O))/V relationship is highly affected by the zJ parameter. (A) Semilogarithmic P(O)/V plots for , +ß1, and +ß2IR channels. This is the same data as in Fig. 5 D, showing the P(O) > 10–5 range for a better appreciation of the maximum slope. Duplicate points correspond to data obtained by two different methods (unitary events quantification and macroscopic recordings). Lines represent the fit of the maximum slope found in the 0–100-mV range. (B) P(O)/V curves (dotted lines) simulated with Eq. 11 are plotted in the P(O) > 3 x 10–5 range. In each plot, the thicker dotted line is the same, corresponding to the following parameters: Vh(J) = 140 mV, zJ = 0.61, L0 = 4.7 x 10–6, zL = 0.28, and D = 14.4. Thinner dotted lines were constructed varying zJ (top left), D (top right), zL (bottom left), L0 (bottom right, gray), or Vh(J) (bottom right, black) in the indicated ranges. Continuous straight lines represent the maximum d(lnP(O))/dV value of each simulated curve.

Fig. 7 A shows representative current traces for channel deactivation at –60 mV after a 200-mV depolarizing pulse. Both ß subunits slow down the deactivation process of the channel, and the time course of the current induced by +ß1 channels is slower than that promoted by +ß2IR channels. Current traces are well fitted by a single exponential time course, and Fig. 7 B shows the deactivation time constants (_deact) obtained in a wide range of voltages. In the voltage range from –220 to 0 mV, the deactivation time (_deact) constant for +ß1 channels is higher (slower) than that for +ß2IR. At 0 mV, this tendency is inverted. Moreover, the semilogarithmic _deact/V plots for and + ß2IR clearly show two slopes, while the +ß1 plot apparently shows only one slope.

View larger version (21K): [in this window] [in a new window]   FIGURE 7. The ß subunits and the voltage dependence of the deactivation kinetics in the absence of calcium. (A) Tail current traces evoked by a –60-mV pulse after opening the channels with a 200-mV activation pulse. Current magnitude of each trace was normalized by the mean current at the 200-mV steady state. Over the traces, the best fit to an exponential decay is shown. (B) Deactivation time constant (deact) plotted against voltage. Symbols represent mean ± SD. n = 3–4. For the subunit, most of the SD bars fall within the symbols. (C) The range from –220 to –190 mV of each plot was fitted to Eq. 15 (dotted lines). The fit shown is with a shared value of z (0.13). The range from 20 to 100 mV (), –50 to 100 mV (+ß1), and 0 to 75 mV (+ß2IR) was fit to the same equation (continuous lines). Obtained z values were 0.46, 0.23, and 0.47, respectively.

_deact

(12)

View larger version (35K): [in this window] [in a new window]   FIGURE 8. Proposed kinetic scheme for BK channel in the absence of calcium. (A) Kinetic scheme proposed by Horrigan et al. (1999). = (0)exp(zFV/RT), ß = ß(0)exp(–zßFV/RT), n = n(0)exp(zFV/RT), and n = n(0)exp(–zFV/RT). The correspondence with the scheme in Fig. 1 B is verified by the following equalities: J = /ß, L0 = 0/0, zJ = z + zß, zL = z + z, and D = (n+1/n+1)/(n/n) = f2. (B) Abbreviated kinetic scheme that considers the movement of the voltage sensors as in instantaneous equilibrium.

(13)

At very negative potentials, all voltage sensors will be in their resting state and therefore the only (or prevailing) open state will be O₀. Then,

(14)

(15)

(16)

In other words, the _deact/V plot will exhibit an exponential dependence to voltage (linear in a semilogarithmic plot) whenever the voltage sensors for the open channel are all in the resting state. Thus, the limiting voltage dependence of the macroscopic kinetics reveals a process unrelated to voltage sensor movements.

When the points from –220 to –190 of each plot are fitted to Eq. 15, a curve is defined (dotted lines in Fig. 7 C) that overlaps very well the points up to –35 mV for , up to –160 mV for +ß1, and up to –120 mV for +ß2IR. These curves have the same value for z, 0.13 (P = 0.17 for different values). This indicates that the ß1 and ß2IR subunits do not affect the voltage dependence of the kinetic rate for channel closure (z). Since z_L = z – z, it is expected that ß subunits do not affect the voltage dependence of the kinetic rate for channel opening, z.

The fit of the _deact/V plots to Eq. 15 also evidences that the +ß1 plot has two slopes. This second slope of the ln(_deact)/V relationship obeys to a more complex relation than the first slope, involving all the _n (n > 0) kinetic constants (Eq. 13), and it is highly dependent on the voltage dependence of the voltage sensor activation. As expected, the z value for the second slope in +ß1 is much lower (0.23) compared with (0.46) and +ß2IR (0.47).

Fig. 9 A shows representative current traces for BK channel activation at 200 mV in the absence and presence of the ß1 and ß2IR subunits. Both ß subunits slow down channel activation, though the effect of the ß2IR subunit is more pronounced. Like the deactivation time course, all traces are well fitted by a single exponential rise, and Fig. 9 B shows the activation time constant (_act) obtained at several activation voltages. The _act for channels formed by +ß1 and +ß2IR subunits are always higher than the subunit alone, and the _act for +ß2IR currents are higher than for +ß1. In the voltage range presented here, the limiting voltage dependence is not reached and the only approximation that can be made from Eq. 12 is _n >> . Thus, the linear range in this plot obeys the expression

(17)

which involves voltage sensor equilibriums within closed states. The fit of this linear range to a simple exponential equation is shown in Fig. 9 C. As expected for a voltage sensor–related relationship, the z value for +ß1 (0.11) is lower than for (0.19) and +ß2IR (0.24).

View larger version (20K): [in this window] [in a new window]   FIGURE 9. The ß subunits and the voltage dependence of the activation kinetics in the absence of calcium. (A) Current traces evoked by a 200-mV pulse after a –80-mV prepulse. Current magnitude of each trace was normalized by the mean current at steady state. Over the traces, the best fit to an exponential raise is shown. For and +ß1, the fit was extrapolated (segmented lines) to show that the traces are effectively normalized to the same maximum. (B) Activation time constant (act) plotted against activation voltage. Symbols represent mean ± SD. n = 3–5. (C) The lineal range of each plot was fit to Eq. 15 with a negative z.

_act

In summary, the study of the voltage dependence of the macroscopic channel kinetics is consistent with our previous conclusions: (a) only the ß1 subunit affects the voltage sensor–associated voltage dependence of BK channel, presumably decreasing the voltage dependence of the voltage sensor activation, (b) none of the studied ß subunit affects the voltage dependence for the C–O transition, and (c) both ß subunits enhance the allosteric coupling between voltage sensor activation and channel opening (allosteric factor D).

The ß Subunits and the 70-state Allosteric Activation Model
We have established how the voltage sensitivity of the BK channel is affected by the ß1 and ß2IR subunits by looking at the channel behavior in the absence of calcium. Our next step is to evaluate the impact of these calcium-independent changes on the apparent calcium sensitivity of the channel, i.e., the behavior of the channel when the calcium concentration is increased. To do so, we fitted the P_(O)/V relationships in the whole 5 nM–150 µM range to Eq. 1. P_(O)/V curves for , +ß1, and +ß2IR channels and at different calcium concentrations were averaged in a way that preserved the average V_0.5 and shape of the individual data obtained (see MATERIALS AND METHODS). It is important to note that we and others (Horrigan and Aldrich, 2002) have noticed that a simple least-squares fit of the data to Eq. 1 can yield parameters far from those obtained by direct measurements. Therefore, before attempting such a fit, it is important to collect as much data as possible about realistic parameter values and introduce them as restrains in the fitting procedure. Also, we will refrain from drawing conclusions about the absolute values obtained with this procedure and will focus on the qualitative comparison between the different sets of parameters.

First, we obtained a satisfactory fit of the P_(O)/V curves for channels. Based on the maximum of the _act/V plots, as well as on previous data by others (Horrigan et al., 1999; Horrigan and Aldrich, 2002), we restricted V_h(J) to be between 140 and 160 mV. After the results of the fit to the voltage-dependent activation in the absence of calcium (Table II), we applied the restrictions 0.5 < z_J < 0.6, 0.25 < z_L < 0.35, and 10^–6 < L₀ < 10^–5. K_d, C, D, and E were only restricted to be higher than 0. The best fit obtained under these conditions is shown on Fig. 10 A, together with the best-fit parameters. The parameters obtained are in a reasonable agreement with those obtained in the absence of calcium (Table II) and with previous fits (Horrigan and Aldrich, 2002). The predicted V_0.5 and z values are plotted together with the experimental values in Fig. 10 (C and D) (continuous line and filled triangles, respectively), showing that these parameters reproduce very well the voltage- and calcium-dependent steady-state activation of the BK channel.

View larger version (41K): [in this window] [in a new window]   FIGURE 10. A change in zJ can account for the increase of the apparent calcium sensitivity in the presence of the ß1 subunit. (A) Averaged experimental P(O)/V curves (symbols) and predictions of the best fit to Eq. 1 (lines) for channels. Within the plot, the parameters of the best fit are shown. See the text for the restrictions applied. (B) Averaged experimental P(O)/V curves (symbols) and predictions of the best fit to Eq. 1 (lines) for +ß1 channels. In the left plot, the fit was done with the same parameters obtained in A (best fit parameters for ) and varying only zJ. In the right plot, L0 was fixed to 3 x 10–7 and zJ, C, and D were varied. (C and D) Families of predicted P(O)/V curves were fitted to a Boltzmann distribution (Eq. 2) and the obtained V0.5 (C) and z (D) values are plotted against calcium concentration (lines). Symbols represent the experimental values (these are the same values plotted in Fig. 2, C and D).

From the analysis of the data in the absence of calcium, we concluded that the ß1 subunit reduces the voltage dependence of the activation of the voltage sensors. The fit to the allosteric model for the voltage- and calcium-dependent activation shows that this reduction can account for most of the characteristic increase of the apparent calcium sensitivity that the ß1 subunit induces on the channel. The model predicts that an effect completely unrelated to the calcium-dependent activation parameters is almost sufficient to affect the apparent calcium sensitivity.

The fit of the P_(O)/V curves for +ß2IR channels to Eq. 1 was first attempted with the following constraints: 0.25 < z_J < 0.6; 0.25 < z_L < 0.4; V_h(J) =140; 10^–8 < L₀ < 10^–6 and K_d, C, D, and E > 0. These are similar to the constraints applied to the fit for except for a different range for L₀ (see Table II) and a wider range for z_J. Fig. 11 A, left, plots the predictions of the best fit (lines) together with the experimental averaged P_(O)/V curves (symbols) and the list of the best-fit parameters (fit 1). This fit predicts a z_J value similar to that of +ß1 and much lower than for , suggesting that the ß2IR subunit also reduces the voltage dependence for voltage sensor activation. This result is incompatible with the maximum slope measurements (Fig. 6) and its deviation from the experimental data is clearly reflected in the failure of fit 1 to reproduce properly the z/[Ca²⁺] relationship (Fig. 11 C, continuous line). We ultimately restricted conditions so as to match best our previous experimental results. Therefore, we applied the following restrictions: from the fit of the P_(O)/V curve in the absence of calcium we fixed V_h(J) = 140 mV, 10^–7 < L₀ < 10^–6, z_L = 0.3, and D = 29. From the same result, z_J was restricted to be only slightly lower than the value for , therefore the restriction was 0.45 < z_J < 0.6. Finally, K_d, C, and E > 0. One of the best fits obtained in this way is shown in Fig. 11 A, right (fit 2). Though fit 2 does not accurately characterize the P_(O)/V relationships at all calcium concentrations, it does predict a higher voltage dependence (higher z values) than +ß1 channels (Fig. 11 C, dotted line). This is the key difference between ß1 and ß2IR subunits and should not be disregarded. Moreover, in the absence of calcium, the parameters from fit 2 predict a maximum dln(P_(O))/dV value similar to that of the fit and higher than the +ß1 fits (not depicted). Unlike the ß1 subunit, this fit predicts the increase of the allosteric coupling factors for both calcium- and voltage-dependent activation (C and D, respectively). Remarkably, fit 2 also predicts an increase of the allosteric factor that relates the activation of voltage sensors with calcium binding (E). The above analysis suggests that the ß2IR subunit enhances the calcium sensitivity of the BK channel by a different mechanism than the ß1 subunit, involving changes in the allosteric coupling factors.

View larger version (40K): [in this window] [in a new window]   FIGURE 11. Fit of the P(O)/V curves for +ß2IR to Eq. 1. (A) Averaged experimental P(O)/V curves (symbols) and predictions of the best fit to Eq. 1 (lines) for channels. Fit 1 was performed using the following restrictions: 140 < Vh(J) < 160, 0.25 < zL < 0.4, 0.25 < zJ < 0.6. Fit 2 was performed using the following restrictions: 140 < Vh(J) < 160, zL = 0.3, 0.45 < zJ < 0.6, E > 0. In each case, the best-fit parameters obtained are listed to the right of the plot. (B and C) Families of predicted P(O)/V curves were fitted to a Boltzmann distribution (Eq. 2) and the obtained V0.5 (B) and z (C) values are plotted against calcium concentration (lines). Symbols represent the experimental values for +ß2IR (these are the same values plotted in Fig. 2, C and D).

	DISCUSSION

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