Coupling and cooperativity in voltage activation of a limited-state BK channel gating in saturating Ca2+

Abstract

Voltage-dependent gating mechanisms of large conductance Ca(2+) and voltage-activated (BK) channels were investigated using two-dimensional maximum likelihood analysis of single-channel open and closed intervals. To obtain sufficient data at negative as well as positive voltages, single-channel currents were recorded at saturating Ca(2+) from BK channels mutated to remove the RCK1 Ca(2+) and Mg(2+) sensors. The saturating Ca(2+) acting on the Ca(2+) bowl sensors of the resulting BK(B) channels increased channel activity while driving the gating into a reduced number of states, simplifying the model. Five highly constrained idealized gating mechanisms based on extensions of the Monod-Wyman-Changeux model for allosteric proteins were examined. A 10-state model without coupling between the voltage sensors and the opening/closing transitions partially described the voltage dependence of Po but not the single-channel kinetics. With allowed coupling, the model gave improved descriptions of Po and approximated the single-channel kinetics; each activated voltage sensor increased the opening rate approximately an additional 23-fold while having little effect on the closing rate. Allowing cooperativity among voltage sensors further improved the description of the data: each activated voltage sensor increased the activation rate of the remaining voltage sensors approximately fourfold, with little effect on the deactivation rate. The coupling factor was decreased in models with cooperativity from approximately 23 to approximately 18. Whether the apparent cooperativity among voltage sensors arises from imposing highly idealized models or from actual cooperativity will require additional studies to resolve. For both cooperative and noncooperative models, allowing transitions to five additional brief (flicker) closed states further improved the description of the data. These observations show that the voltage-dependent single-channel kinetics of BK(B) channels can be approximated by highly idealized allosteric models in which voltage sensor movement increases Po mainly through an increase in channel opening rates, with limited effects on closing rates.

Figure 1.

Voltage activation of BK_B channels. (A) Representative single-channel currents recorded from a BK_B channel (DM4) in saturating 95 µM Ca²⁺_i. Arrows indicate the closed channel levels. (B) Plots of Po versus voltage for four separate BK_B channels, as indicated. The lines are fits with the Boltzmann equation Po = Po_max/(1 + exp[(V_0.5 − V)/b]), where b is the voltage sensitivity expressed as the voltage change (in millivolts) per e-fold change in Po. The parameters for the lines are given in Table I. (C and D) Voltage dependence of mean open and mean closed times for the same four channels as in B. The lines plot the predicted mean open and closed times for channels DM1 (continuous lines) and DM4 (dashed lines) calculated with Scheme V. A similar superposition of observed and predicted mean open and mean closed times was observed for channels DM2 and DM3. Parameters used in the predictions for channel DM4 in C and D of this figure and in Figs. 4–7 are given in Table S3.

Figure 2.

Estimating the partial charge associated with the opening and closing transitions for BK_B channels gating in saturating Ca²⁺_i. (A) Plot of Po versus voltage. Circles plot data obtained for BK_B channels expressed in oocytes for patches with a single channel (open circles) and from two to six channels per patch (closed circles). Squares plot data obtained from macro currents from BK_B channels expressed in HEK cells. (B) Voltage dependence of mean open times at negative potentials. The line is a linear fit to open times negative to −100 mV. Projecting to 0 mV gives an intrinsic channel closing rate (K in Schemes III, IV, and V) of 6,420 ± 680 s⁻¹ with a partial charge of −0.099 ± 0.015 e_o (257 mV/e-fold change). (C) Voltage dependence of mean closed times. The line is a linear fit to closed times negative to −100 mV. Projecting to 0 mV gives an estimate of the intrinsic opening rate (H in Schemes III, IV, and V) of 3.87 ± 1.88 s⁻¹ with a partial charge of 0.237 ± 0.06 e_o (108 mV/e-fold change). Data in B and C are a mean of the data obtained with single-channel recording.

Figure 3.

Open and closed dwell-time distributions for BK_B channel DM4 at the indicated voltages in saturating Ca²⁺_i. Lines are mixtures of exponential components fitted to the dwell times. Open time histograms were described by one to two significant exponential components, and closed time histograms were described by two to five significant exponential components. The time constants and areas of the exponentials for the four studied channels are given in Tables S1 and S2. A moving bin mean of three consecutive bins was used for the data at negative potentials because of the small numbers of intervals at the low Po. Channel DM4 is presented in Figs. 3–7 as a representative channel. Similar conclusions were reached with channels DM1–DM3.

Figure 4.

Comparison of the observed and predicted voltage dependence of Po for BK_B channel DM4 on linear and log-linear coordinates for the indicated gating mechanisms with saturating Ca²⁺_i. Open circles, observed voltage dependence; lines, predicted voltage dependence. A, linear coordinates; B, log-linear coordinates. Saturating Ca²⁺_i. The predictions of Schemes V and V_F (green and black lines) superimpose over most of the voltage range and give a somewhat more accurate description of the data at negative voltages than the other schemes.

Figure 5.

Open and closed dwell-time histograms for BK_B channel DM4 obtained at the indicated voltages with saturating Ca²⁺_i overlaid with the distributions predicted by the indicated kinetic schemes. Although all four schemes predicted the voltage-dependent shifts in the open dwell-time histograms, only Schemes V and V_F could predict the voltage dependence of the closed dwell-time histograms over the entire voltage range.

Figure 6.

Observed and predicted 2-D dwell-time distributions of open–closed- and closed–open-interval pairs for Scheme V for BK_B channel DM4 at 50 mV with saturating Ca²⁺_i. Scheme V approximated the 2-D distributions.

Figure 7.

Simulated single-channel currents for Scheme V for BK_B channel DM4 at the indicated voltages with saturating Ca²⁺_i. The simulated single-channel currents reproduce the kinetic properties of the experimental single-channel currents shown in Fig. 1.