Correspondence to: Brad S. Rothberg, Department of Neurobiology, Harvard Medical School, 220 Longwood Ave., Boston, MA 02115. Fax:617-734-7557 E-mail:brothberg{at}hms.harvard.edu.
![]() |
Abstract |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The voltage- and Ca2+-dependent gating mechanism of large-conductance Ca2+-activated K+ (BK) channels from cultured rat skeletal muscle was studied using single-channel analysis. Channel open probability (Po) increased with depolarization, as determined by limiting slope measurements (11 mV per e-fold change in Po; effective gating charge, qeff, of 2.3 ± 0.6 eo). Estimates of qeff were little changed for intracellular Ca2+ (Ca2+i) ranging from 0.0003 to 1,024 µM. Increasing Ca2+i from 0.03 to 1,024 µM shifted the voltage for half maximal activation (V1/2) 175 mV in the hyperpolarizing direction. V1/2 was independent of Ca2+i for Ca2+i 0.03 µM, indicating that the channel can be activated in the absence of Ca2+i. Open and closed dwell-time distributions for data obtained at different Ca2+i and voltage, but at the same Po, were different, indicating that the major action of voltage is not through concentrating Ca2+ at the binding sites. The voltage dependence of Po arose from a decrease in the mean closing rate with depolarization (qeff = -0.5 eo) and an increase in the mean opening rate (qeff = 1.8 eo), consistent with voltage-dependent steps in both the activation and deactivation pathways. A 50-state two-tiered model with separate voltage- and Ca2+-dependent steps was consistent with the major features of the voltage and Ca2+ dependence of the single-channel kinetics over wide ranges of Ca2+i (
0 through 1,024 µM), voltage (+80 to -80 mV), and Po (10-4 to 0.96). In the model, the voltage dependence of the gating arises mainly from voltage-dependent transitions between closed (C-C) and open (O-O) states, with less voltage dependence for transitions between open and closed states (C-O), and with no voltage dependence for Ca2+-binding and unbinding. The two-tiered model can serve as a working hypothesis for the Ca2+- and voltage-dependent gating of the BK channel.
Key Words: large-conductance Ca2+-activated K+ channel, KCa channel, Monod-Wyman-Changeux, Eigen, Markov
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Large conductance Ca2+-activated K+ channels (BK or maxi K+ channels)1 are activated by both intracellular calcium (Ca2+i) and depolarization of the membrane potential (
Some of the structural regions contributing to the voltage and Ca2+ sensitivity of BK channels have been identified. The pore-forming alpha subunits of BK channels, which are encoded by the gene at the Slo locus (
Gating mechanisms proposed to account for the Ca2+ and/or voltage sensitivity of BK channels have typically been based on the 10-state Monod-Wyman-Changeux model (MWC; 0 Ca2+i (
To overcome these limitations, we have extended the MWC and Eigen models to two-tiered gating mechanisms comprised of at least 50 states in their minimal theoretical form, with 25 closed states on the upper tier and 25 open states on the lower tier (0 Ca2+i (
0 Ca2+. It will now be crucial to test whether two-tiered gating mechanisms can also describe the complex interactions between Ca2+i and voltage (see commentary by
The purpose of the present study is to evaluate the ability of a two-tiered allosteric gating mechanism to describe both the Ca2+ and voltage-dependent activation of BK channels. Using single-channel recording techniques, we examine the effects of voltage on the open and closed interval durations over wide ranges of Ca2+i. The resulting dwell-time distributions and estimates of Po are analyzed to examine the relationship between activation by Ca2+i and voltage and estimate the charge movement associated with the voltage-dependent activation and deactivation of the channel. We find that two-tiered models provide a reasonable description of the Ca2+i and voltage dependence of the gating from 0 to saturating levels of Ca2+i over wide ranges of voltage and Po. In terms of the two-tiered mechanism, the voltage dependence of the gating arises mainly from voltage-dependent transitions between the closed (C-C) and open (O-O) states, with less voltage dependence for transitions between the closed and open states (C-O), and with no voltage dependence of the Ca2+-binding and -unbinding steps. Ca2+i modulates the voltage for half activation, while having little effect on the effective gating charge for activation. These findings on the voltage-dependent steps obtained with single-channel analysis over a range of voltage and Ca2+i are consistent with those obtained from macroscopic ionic and gating currents at
0 Ca2+i (
The two-tiered model provides a comprehensive gating mechanism for BK channels that can simultaneously describe the major features of the steady state activation by both Ca2+i and voltage over wide ranges Ca2+i, voltage, and Po.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Preparation and Single-Channel Recording
Currents flowing through single BK channels in patches of surface membrane excised from primary cultures of rat skeletal muscle (myotubes) were recorded using the patch-clamp technique (
Solutions
The solutions bathing both sides of the membrane contained 150 mM KCl and 5 mM TES [N-tris(hydroxymethyl)methyl-2-aminoethane sulfonate] pH buffer, with the pH of the solutions adjusted to 7.0. Contaminant Ca2+i was determined by atomic absorption spectrometry. Ca2+ (as CaCl2) was added to bring the Ca2+ concentration at the intracellular surface (Ca2+i) to the indicated levels. The solutions did not contain Ca2+ buffers unless indicated. Very low Ca2+i of 0.0003 and
0.03 µM was obtained by adding 2 mM EGTA and 0 or 266 µM Ca2+, respectively, to the solution. No Ca2+ was added to the extracellular (pipette) solution. Solutions were changed through the use of a microchamber (
Analysis Restricted to Activity in the Normal Mode
All data analyzed in this paper were restricted to activity in the normal mode, which typically includes 96% of the intervals (
Estimates of Po were obtained by dividing the observed open time by the sum of the observed open and closed times. Although missed events can have large effects on estimates of interval durations, they had negligible effect (<1%) on the estimates of Po. The reason for this is that, under the conditions of our experiments, the intervals that were missed were very brief compared with the mean durations of the intervals that were captured, so that missed events removed a negligible amount of the total time.
Estimating Rate Constants and Evaluating Kinetic Models
Estimates of the most likely rate constants, including their Ca2+ and voltage sensitivities, were made from the simultaneous (global) fitting of two-dimensional dwell-time distributions obtained at several different Ca2+i and voltages, using Q-matrix methods (
Normalized likelihood ratios (NLR1) were used to indicate how well any given kinetic scheme describes the 2-D dwell-time distributions when compared with a theoretical best description of the data (
![]() |
(1) |
where lnS is the natural logarithm of the maximum likelihood estimate for the observed 2-D dwell-time distributions given the kinetic scheme, lnT is the natural logarithm of the likelihood of the theoretical best description of the observed distributions, and n is the total number of fitted interval pairs (events) in the observed dwell-time distributions (
The NLR1 gives a measure of how well different kinetic schemes describe the distributions, but it cannot be used to directly rank schemes, since no penalty is applied for the number of free parameters. To overcome this difficulty, models were ranked using an information criteria approach (
![]() |
(2) |
then model g is ranked above model f, where mg and mf are the maximum likelihood estimates for models g and f, and kg and kf are the number of free parameters for each scheme.
Tests of whether linear regression slopes were significantly different from zero were made by first obtaining the regression coefficient by fitting with Sigma Plot, and then calculating a t statistic as described by
Estimating the Voltage Sensitivities of the Rate Constants
The voltage sensitivities of the rate constants were estimated using the simplifying assumption of an exponential relationship between the rate constants and membrane potential (
![]() |
(3) |
where rateij(V) is the effective rate constant (s-1) for the transition from state i to state j at voltage V (mV), Bij is the value of the base rate constant at +30 mV, qij is the partial charge (in units of eO) associated with transition ij, and kBT is 25.5 mV x units of electronic charge at 23°C. We estimated the value of the base rate at +30 mV to facilitate comparison with rate constants obtained at +30 mV in previous single-channel studies (
Since absolute rate theory (Equation 3) may not necessarily apply to conformational changes in proteins (
Estimating Effective Charge Movement qeff
Estimates of lower limits for the effective gating charge qeff were obtained by the limiting slope method (
![]() |
(4) |
where A is the maximal single-channel open probability, V0.5 is the voltage for half-maximal open probability, kB is the Boltzmann constant, and T is absolute temperature. In cases where a maximal open probability could not be defined due to low levels of activity, this value was fixed to a value of 0.95, which was typical of the maximal Po for the channel. The limiting slope method of estimating effective gating charge gives the equivalent number of charges for a linear model containing any number of closed states (
The effective gating charge qeff is given by Equation 5:
![]() |
(5) |
where z is the effective valence of the moved charge, eo is the value of an electronic charge (eo = 1.6 x 10-19 C), and d is the fractional distance the charge moves in the electric field of the membrane. The voltage sensitivity of the channels, expressed as the change in membrane potential required for an e-fold change in Po, can be calculated from qeff with:
![]() |
(6) |
(
Online Supplemental Material
Fig. S1 presents single-channel currents simulated over a range of Ca2+i and voltage using Scheme 2. The noise and filtering used in the simulation was equivalent to that in the experimental current records to allow direct comparison to the experimental records in Fig 1. The simulated single-channel current records in Fig. S1 were essentially indistinguishable from the experimental current records in Fig 1, except for stochastic variation and a slightly more stable baseline in the simulated data. Thus, comparison of simulated to experimental data shows that Scheme 2 predicted the characteristic features of the single-channel current records over wide ranges of voltage (-80 to +70 mV) and Ca2+i (0 to 1,024 µM). Fig. S1 is available online at http://www.jgp.org/cgi/content/full/116/1/75/DC1
|
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Currents through a single large-conductance Ca2+-activated K+ channel at two different Ca2+i, each at three different voltages ranging from +30 to +50 mV, are shown in Fig 1 A. These traces illustrate the activation of the channel by both Ca2+i and depolarization. The activating effect of Ca2+i at three different voltages can be seen by comparing each trace on the left with the corresponding trace on the right at higher Ca2+i. At +30 mV, increasing Ca2+i from 5.5 to 12.3 µM increased Po 8.3-fold, from 0.024 to 0.20. Similarly, the activating effect of voltage can be seen by comparing the top traces with the traces below. For example, at 5.5 µM Ca2+i, changing the voltage from +30 to +50 mV increased Po 9.2-fold, from 0.024 to 0.22.
Voltage also modulated BK channels at the extremes of very high and very low Ca2+i. Fig 1 C shows that depolarizing from -80 to -50 mV in very high (1,024 mM) Ca2+i increased Po 8.5-fold, from 0.026 to 0.22. Fig 1B and Fig D, presents examples of data recorded at very low Ca2+i, of 0.0003 (C) and 0.03 µM (D). Such low Ca2+is are effectively equivalent to 0 Ca2+i (
25-fold in the overall records from which the examples shown in Fig 1B and Fig D, were taken.
Voltage Dependence of BK Channel Activation
Insight into the voltage dependence of channel opening can be obtained from fitting the steady state Po vs. voltage relation with a Boltzmann distribution (
Examples of data used to estimate limiting slope are shown in Fig 2A and Fig B, which plots on linear and logarithmic coordinates steady state Po vs. voltage for single-channel data recorded from five different single-channel patches at each of four different Ca2+i. Boltzmann fits to the data (Equation 4) are plotted as thick continuous lines. Increasing Ca2+i shifts the PoV relation leftward on the voltage axis (
|
The limiting slopes are more clearly seen in Fig 2 B, where the logarithmic coordinates emphasize the data obtained at low Po. Changing Ca2+i 30,000-fold had little apparent effect on the limiting slope over the examined range of Pos. Fig 2 C plots 17 estimates of qeff against Ca2+i for data from five different single BK channels and also from two patches containing four BK channels each. The mean estimate of qeff was 2.3 ± 0.6 eo (thick line), giving an e-fold increase in Po per 11.1 mV depolarization. There was little effect of Ca2+i on qeff, as the slope of a linear regression line (-0.025 e0/10-fold increase in Ca2+i, not shown) was not significantly different from zero (P > 0.45), and the correlation coefficient (r2 = 0.006) was negligible. These results suggest that changes in Ca2+i have little effect on the effective gating charge, as measured in these experiments. This mean estimate of qeff of 2.3 eO obtained from limiting slope measurements of single-channel data can be compared with the estimates for hSlo of 1.6 eO (
2 eO (
10-4, the limiting slope becomes more shallow (
0 Ca2+i.
The effect of Ca2+i on V1/2 values (the voltage for half-maximal activation) estimated from the same data used for Fig 2 C is shown in Fig 2 D. In the range of 41,000 µM, increasing Ca2+i shifted V1/2 towards more hyperpolarized voltages with a slope of -50 mV per 10-fold increase in Ca2+i (thick line). In contrast, V1/2 was independent of Ca2+i at very low Ca2+i, where a 100-fold increase in Ca2+i from 0.3 to 30 nM had little effect on the V1/2 of 150 mV (horizontal thick line). This apparent lack of effect of Ca2+i on V1/2 at very low Ca2+i is consistent with observations in previous studies using macroscopic currents recorded from hSlo (
100 µM. Our observations in Fig 2 D are not sufficient to confirm this decrease in slope because of the scatter in the data.
Voltage-dependence of Mean Open and Closed Intervals
To gain further insight into the voltage dependence of the gating transitions, the mean durations of open and closed intervals were measured over a range of voltages and Ca2+i. Fig 3A and Fig B, presents such data at three different Ca2+i from three representative channels. Both depolarization and Ca2+i increased mean open times and decreased mean closed times. The voltage dependence of mean open times could be approximated by single exponentials over the examined range of Ca2+i and voltage (thick lines). In contrast, the mean closed times were first approximated by a single exponential, and then approached a minimum of 180 µs under conditions of voltage and Ca2+i when Po > 0.95 (thick lines). As will be shown in a later section, a minimum mean closed time is reached because the dominant closed intervals at high Po are the flickers (brief closings within bursts), which have observed mean lifetimes that are little affected by voltage.
|
The slopes of the exponential part of the thick lines in Fig 3A and Fig B, give a measure of the voltage dependence of the apparent mean closing and opening rates, respectively (see METHODS). Estimates of the effective charge movement qeff determined from plots of this type are presented in Fig 3 C. The mean qeff associated with channel closing, as determined from the open durations, was -0.5 eO, giving an e-fold decrease in closing rate per 50-mV depolarization (dashed line through open symbols in Fig 3 C), and the mean qeff associated with channel opening, as determined from the closed durations, was 1.8 eO, giving an e-fold increase in opening rate per 14-mV depolarization (dashed line through filled symbols). The plots in Fig 3A-C, show that the effective charge movement associated with opening and closing is relatively independent of voltage or Ca2+i over the examined range of conditions.
Fig 3 D plots the apparent mean closing and opening rates at +30 mV as a function of Ca2+i. The apparent mean opening rate (determined from the inverse of the closed-interval durations) was steeply Ca2+ dependent over the examined range of 150 µM Ca2+i. Outside of this range, the apparent mean opening rate was little affected by Ca2+i, reaching an observed minimum of
0.5/s at very low Ca2+i and an observed maximum of
5,500/s at high Ca2+i. The maximum Ca2+ dependence of the apparent mean closing rate (determined from the inverse of the open interval durations) was considerably less than for the apparent mean opening rate, as indicated by the open symbols in Fig 3 D. The results in Fig 3 D are consistent with previous observations (
Voltage Shifts the Open and Closed Dwell-time Distributions
To obtain further insight into the effects of voltage on the transitions among states, the open and closed intervals were binned into dwell-time distributions and fitted with sums (mixtures) of exponential components. The numbers of significant exponential components give an estimate of the minimal number of states entered during gating (
|
The fits to the open distributions obtained at +30 mV in Fig 4A and Fig B, are plotted as dashed lines on the open distributions obtained at +50 mV in Fig 4C and Fig D, at the same Ca2+i. It can be seen that the major effects of the additional depolarization were to increase the number and duration of the longer openings while decreasing the number of the briefer open intervals.
Closed dwell-time distributions from the same experiment are shown in Fig 4EH. The closed distributions at the lower Pos of 0.024, 0.20, and 0.22 (EG) were best fit by the sums of five exponential components, and the distribution at the higher Po of 0.81 (H) was best fit with the sum of four exponential components (thin continuous lines), suggesting that a minimum of four to five closed states are entered during gating over the wide examined range of Po.
The fits to the closed distributions obtained at +30 mV (Fig 4E and Fig F) are plotted as dashed lines on the closed distributions obtained at +50 mV (G and H) at the same Ca2+i. The major effects of further depolarization were to greatly decrease the durations and frequency of the longer closed intervals, shifting the area to the briefer closed intervals. The shifts in the closed distributions with depolarization were more pronounced than for the open distributions, consistent with the greater voltage dependence of the mean closed-interval duration when compared with the mean open-interval duration (Fig 3).
For data obtained from six additional channels with one to four different Ca2+i for each channel, at least three to four open and four to six closed states were typically entered during gating over the examined ranges of Po. In these additional experiments, as was the case for Fig 4, there was no obvious effect of voltage on estimates of the numbers of states.
Fig 5 plots representative examples of the effect of voltage on the time constants and areas of the longest and briefest duration exponential components (filled and open symbols, respectively) for both the open and closed dwell-time distributions for data obtained at 4.0, 20.3, and 1,024 µM Ca2+i. The time constant of the longest open component increased with depolarization (Fig 5 A), while the time constant of the longest closed component decreased with depolarization (B), and this was the case over the range of examined Ca2+i. In contrast, the time constants of the briefest open and closed components were little affected by depolarization for any given channel. For the low and intermediate levels of Ca2+i, depolarization shifted area from the briefest open intervals towards the longest open intervals and from the longest closed intervals towards the briefest closed intervals (Fig 5C and Fig D). (The effects of voltage on the intermediate components was more variable and will not be considered here.)
|
Voltage and Ca2+i Have Differential Effects on the Gating Kinetics
Data were presented in a previous section suggesting that the voltage dependence of the channel does not arise through voltage-induced alterations in the concentration of Ca2+i at binding sites located within the electric field of the membrane, consistent with previous studies (
The thick line in Fig 4 B plots the open dwell-time distribution obtained at +50 mV with 5.5 µM Ca2+i on the open distribution obtained at +30 mV with 12.3 µM Ca2+i. The Pos under these two sets of conditions were similar (0.22 vs. 0.20). Increasing Ca2+i and then decreasing depolarization to obtain the same Po shifted the open distribution to the left, with a decreased frequency of the longer open intervals and an increased frequency of the briefer open intervals. The thick line in Fig 4 F plots the closed dwell-time distribution obtained at +50 mV with 5.5 µM Ca2+i on the closed distribution obtained at +30 mV with 12.3 µM Ca2+i. For the closed distribution, increasing Ca2+i and then decreasing the depolarization to obtain the same Po greatly increased the frequency of the closed intervals with durations from 1 to 20 ms and slightly decreased the durations of the longer closed intervals. The differences in the open and closed distributions were not due to the small difference in Po, as shifting either voltage or Ca2+i sufficiently to change the Po 10% of its internal value had little effect on the distributions.
The marked changes in the dwell-time distributions in Fig 4 when changing voltage and Ca2+i to maintain the same Po indicates that depolarization does not have the same effects on single-channel kinetics as increasing Ca2+i. Similar shifts in the shapes of the distributions obtained at the same Po, but with different Ca2+i and voltage, were found in four additional comparisons from three additional channels for Pos ranging from 0.18 to 0.89, Ca2+i ranging from 5.5 to 1,024 µM, and voltage ranging from -20 to +50 mV. In all comparisons, increasing Ca2+i and decreasing depolarization to obtain the same Po decreased the observed mean durations of both the open and closed intervals. For example, in Fig 4B and Fig F, increasing Ca2+i from 5.5 to 12.3 µM and changing the voltage from +50 to +30 mV decreased the observed mean durations of both the open and closed interval durations 30%. As another example, in an experiment on a different patch, increasing Ca2+i from 20.3 to 132 µM and changing the voltage from +20 to -30 mV to maintain the Po at
0.19 decreased the observed mean open and closed interval durations
17%. The differential effects of voltage and Ca2+i on the single-channel kinetics at intermediate levels of Ca2+i shown in this section provides further evidence that voltage does not activate the channel solely through changes in the effective Ca2+i at the Ca2+-binding sites. Note that this conclusion applies to the limited case where voltage acts only by changing Ca2+i at its binding sites without changing any of the rate constants. Consequently, it does not exclude more complicated mechanisms in which voltage acts through both changes in Ca2+i at the binding sites and changes in rate constants.
Working Hypothesis for Voltage Dependent Gating
Any viable model for the gating of BK channels must account for the properties of the voltage dependence described above and also the properties of the Ca2+i dependence. We have recently suggested that the Ca2+ dependence of the gating is consistent with the 50-state model shown in Scheme 1, in which the top tier of states are closed and the bottom tier of states are open (
In the context of Scheme 1, the voltage dependence of activation could arise through voltage-dependent Ca2+-binding steps or voltage-dependent conformational changes not related to Ca2+ binding. The results in this (Fig 2 Fig 3 Fig 4) and previous (
For separate voltage- and Ca2+-dependent steps, the voltage activation would arise through one or more voltage-dependent conformational changes separate from the Ca2+-dependent transitions in Scheme 1. Thus, depolarization could activate the channel by driving the conformational change from the closed states on the upper tier to the open states on the lower tier (as indicated by the vertical arrow in Scheme 1), by driving the conformational changes of the individual subunits for transitions among states within each tier (as indicated by the oblique voltage arrow in Scheme 1), or by driving both of these types of conformational changes. To distinguish among these possibilities, the complex Scheme 1 was simplified by reducing the numbers of states to decrease the numbers of free parameters. If the simpler scheme could account for the single-channel data, then the more complex Scheme 1 should also be able to account for the data.
Based on our previous study of the Ca2+-dependent gating (
Note that Scheme 1 and Scheme 2 each consist of five parallel subschemes, with either 0, 1, 2, 3, or 4 Ca2+ bound to each state. For Scheme 1, each subscheme is comprised of five closed and five open states, and, for Scheme 2, each subscheme is comprised of three closed and two open states, as shown by Scheme 3.
Our general approach to testing Scheme 2 quantitatively was to estimate the most likely rate constants for this scheme, including their Ca2+i and voltage dependence, and then to determine whether Scheme 2, with the most likely rate constants, could account for the Ca2+i and voltage dependence of the single-channel data. To do this, we first examined which of the transitions in Scheme 2 were voltage dependent. This was done by examining the voltage dependence of the gating in the limiting cases of 0 Ca2+i and saturating Ca2+i, to confine the gating to subsets of states within Scheme 2 with either zero or four bound Ca2+, respectively.
Identifying the Voltage-dependent Transitions within the Subscheme of Unliganded States
The observation that V1/2 at very low Ca2+i (0.03 µM) is essentially independent of Ca2+ (Fig 2 D;
0.03 µM would reflect mainly the gating among the unliganded states, given by the left-most subscheme in Scheme 2. Since Scheme 3 is identical to the left-most subscheme in Scheme 2, identifying the voltage-dependent transitions for Scheme 3 under conditions where Ca2+i
0.03 µM should then identify the voltage-dependent transitions for the unliganded states in Scheme 2.
Five different forms of Scheme 3 were examined in which the voltage dependence of the various rate constants, indicated by q1q4, was constrained in different ways, as shown in Scheme 3 (AE). Rate constants without an associated q have no voltage dependence. Three estimates of the most likely rate constants and their voltage dependence were obtained for the unliganded channel for each form of Scheme 3. Each estimate was obtained by simultaneously fitting 2-D dwell-time distributions obtained at three different voltages (+30, +50, and +70 mV). One of the estimates was obtained from channel B15 for Ca2+i of 0.03 µM, and the other two were obtained from channel B14 for Ca2+i of 0.03 and 0.0003 µM. (The number of interval pairs fitted in each 2-D dwell-time distribution in these experiments ranged from 65 to 793.)
Fitting sums of exponential components to the dwell-time distributions in these experiments indicated typically two significant open components and two to three significant closed components for unliganded gating. Similar experiments on mSlo analyzing greater numbers of intervals detected two to three open and three to five closed components in 0 Ca2+i (
0 Ca2+i.
Table 1 presents the normalized likelihood ratios for one interval pair, NLR1, to give a measure of how well the various models described the data. The NLR1 gives the ratio of the likelihood for fitting with the model to the likelihood for the theoretical best description of the data, normalized to one openclosed interval pair. [See METHODS and
|
The rankings of the schemes based on the Akaike criteria, which applies a penalty for additional free parameters (Equation 2), are also listed in Table 1. Scheme 3 A, with only the openclosed transitions being voltage dependent, gave the worst or next to worst descriptions of the data (lowest values for the log likelihood and NLR1) and also ranked the lowest (5th) or next to lowest (4th). Scheme 3 E, with voltage dependence in each rate constant, gave the best description of the data in each case (highest values for the NLR1) and ranked highest for two estimates and second highest for one estimate. Since all of the schemes are nested, the likelihood ratio test can be used to determine which of the rankings are significant (
The mean ± SEM of the estimated rate constants and their voltage dependence for Scheme 3 E are shown in Table 2. Although estimates of some of the rate constants were consistent among the three sets of data, others showed large variability from being poorly defined, due in part to the very limited amount of data that was obtained at the low Pos associated with the very low Ca2+i. For the well-defined rate constants, the transition from C5 to C4 was consistently slow at 2/s, generating the long closed intervals, and transitions such as O1C3O1 generated most of the brief closings (flickers) in the bursts due to the brief (
40 µs) lifetime of C3. Calculation of the equilibrium occupancies of the states for Scheme 3 E indicated that C5, the longest closed state, was occupied >98.6% of the time for the unliganded channel over the range of examined voltages of up to +70 mV.
|
To examine whether Scheme 3 E could describe the voltage dependence of the single-channel data for unliganded gating, predicted dwell-time distributions were obtained by simulating single-channel data with E for different voltages for comparison to the experimental distributions. The simulated single-channel currents were analyzed just like the experimental currents to obtain the predicted dwell-time distributions. Analyzing simulated single-channel data with filtering and noise equivalent to that in the experimental data automatically accounts for the effects of filtering (missed events) and noise on the predicted distributions.
The predicted distributions (thick lines) for the representative experiments in Fig 6 show that Scheme 3 E could approximate the observed shift in the open and closed dwell-time distributions with voltage for the unliganded channel. For the experiment in Fig 6AD, depolarizing from +30 to +70 mV with 0.0003 µM Ca2+i increased Po 33-fold (from 0.000036 to 0.0012) by shifting the open intervals towards longer durations and the longer closed intervals towards briefer durations (). A similar shift was seen for an experiment at 0.03 µM Ca2+i in Fig 6EH. The distributions predicted by Scheme 3 E (thick lines) captured the major aspects of the single-channel data as well as the voltage-dependent shifts in the distributions, with the predictions typically falling within the scatter in the data resulting from the limited number of intervals that could be collected at the low Pos. In spite of its relative success, Scheme 3 E underpredicted the intermediate duration (110 ms) closed intervals at +30 mV for the experiment in Fig 6AD. It is perhaps not surprising that Scheme 3 E with five states only approximated the data, as this scheme is simplified from the 10-state model expected for gating in zero Ca2+i described by the left-most subscheme of Scheme 1.
|
Identifying the Voltage-dependent Transitions within the Subscheme of Fully Liganded States
Having identified the possible voltage-dependent transitions among the unliganded states in Scheme 2, we next used the same approach to identify the voltage-dependent transitions among the fully liganded states (the right-most subscheme) in Scheme 2. We have previously shown for normal mode gating and Ca2+i 1,000 µM, that the channel would be expected to spend >99% of its time in the fully liganded states (
As with the data obtained at very low Ca2+i, the rate constants and their voltage dependence was estimated for Scheme 3, AE. Table 1 (right) presents the NLR1 and the rankings of the various schemes for three different channels studied at high Ca2+i in the fully liganded state. As was the case for the unliganded channel, Scheme 3 A, in which the voltage-dependent transitions were confined only to the opening and closing transitions, gave the worst descriptions of the data (lowest values of the log-likelihood and NLR1) and also ranked the lowest, while E, in which all the transitions were voltage dependent, gave the best descriptions of the data and also ranked first among the five models.
The mean ± SEM of the estimated rate constants and their voltage dependence for Scheme 3 E with all states fully liganded (1,024 µM Ca2+i) are shown in Table 2. As was the case for fitting the unliganded channel, a number of the rate constants were poorly defined, as reflected in the large SEM for those estimates.
The predicted distributions (thick lines) for the representative experiment in Fig 7 shows that Scheme 3 E could approximate the major effects of voltage on the open and closed dwell-time distributions for the fully liganded channel for voltages ranging from -80 to +30 mV, which increased the observed Po 37-fold, from 0.026 to 0.96. The predicted distributions described the pronounced depolarization-induced shifts in the open intervals to longer durations and in the closed intervals to briefer durations. The predicted increase in Po from 0.022 to 0.97 was similar to the observed increase. While Scheme 3 E captured the major features of the single-channel data over this large range of Po, it clearly had some deficiencies, as evident in the differences between the observed and predicted distributions and NLR1 values of 0.97 (Table 1), 3% less than the best possible description of 1.0.
|
As with the unliganded channel, it is perhaps not surprising that the five-state Scheme 3E only approximated the fully liganded gating, as this scheme is simplified from the minimal 10-state model expected for gating in the fully liganded states, as described by the right-most subscheme of Scheme 1. To determine how much improvement the 10-state model might provide, we also examined the ability of a 10-state model with q constrained similar to that in Scheme 3 E to describe the data. The description with the 10-state model was significantly improved over Scheme 3 E (P < 0.001), with an average NLR1 of 0.985 for the three data sets, indicating a 50% reduction in the error compared with the five-state model. While the 10-state model gave a better description of the data, so many of the large numbers of parameters were poorly defined that the focus in the present paper will be on the simpler models.
Comparison of Gating of the Unliganded and Fully Liganded Channel at +30 mV
Increasing Ca2+i from 0 to 1,024 µM increased Po
20,000-fold, from
0.00005 for the unliganded channel to 0.96 for the fully liganded channel (Fig 6 and Fig 7). In the context of Scheme 3 E, the Ca2+-induced changes in gating that give this phenomenal increase in Po can be seen in Table 2, which presents each rate constant and also the ratios of the forward to backward rate constants (F/B) for each of the transitions for both the unliganded and fully liganded channels. The binding of four Ca2+ altered the rate constants to have three major effects: (a) the duration of the long closed state C5 was greatly decreased, (b) the duration of the long open state O1 was increased, and (c) the ratios of the forward to backward rate constants were changed to drive the gating away from the long closed state and towards the long open state.
The mean lifetime of the long closed state C5 at +30 mV was 530 ms for unliganded gating, compared with 1.6 ms for fully liganded gating, for a 330-fold increase in the rate of leaving C5 after binding four Ca2+ (P < 0.001, t test), and the mean lifetime of the long open state O1 at +30 mV was 210 µs in the unliganded state and 1.9 ms in the fully liganded state, for a ninefold decrease in the rate of leaving O1 after binding four Ca2+ (P < 0.05, t test). In addition, the binding of four Ca2+i decreased the transition rate from C4 to C5, from 7,000/s to 280/s (P < 0.001). This 25-fold decrease acts to increase the duration of the bursts in the fully liganded channel by slowing the return to the long closed state C5 that is the main contributor to the gaps between bursts. These Ca2+-induced changes in the transition rates between C5 and C4 biased the ratio of the forward to backward rate constants (F/B) between these states, from 0.0003 for the unliganded channel to 2.0 for the fully liganded channel, for a 6,600-fold increase in the ratio for transitions towards the long open state. As another example, the Ca2+-induced changes in the transition rates between O2 and O1 biased the ratio of the forward to backward rate constants between these states from 1 for the unliganded channel to 20 for the fully liganded channel, for a 20-fold increase in the ratio for transitions towards the long open state. Thus, the binding of Ca2+ to its allosteric sites on the BK channel acts to greatly decrease the stability of the long closed state while increasing the stability of the long open state.
In comparison with the orders of magnitude differences in some of the rate constants between the unliganded and fully liganded channels for Scheme 3 E, the estimates of the partial charges q1q4 that convey the voltage sensitivity to specific transitions (see Equation 3) were typically within a factor of two between the unliganded and fully liganded channel (Table 2), and none of the differences were significant (P > 0.20.5). The lack of significant effect of Ca2+i on estimates of the partial charge is consistent with the apparent lack of effect of Ca2+i on the apparent limiting slopes of the plots of Po versus membrane potential observed in Fig 2 B. Nevertheless, due to the variability in the estimates of partial charge among channels, a small effect of Ca2+ on partial charge cannot be excluded, as observed by
Scheme 2 Describes the Voltage and Ca2+i Dependence of the Gating
The results in the previous two sections identified the voltage-dependent steps in the gating of the unliganded and fully liganded channel as being consistent with Scheme 3 E. With this information, it was possible to examine whether Scheme 2 could account simultaneously for the voltage and Ca2+i dependence of the gating. In carrying out this test, it was assumed that the voltage-dependent steps for the partially liganded channel were also consistent with Scheme 3 E, and it was further assumed that the Ca2+-binding and -unbinding rate constants were independent of voltage, since there was no evidence to the contrary. With these assumptions, the rate constants for Scheme 2 were estimated by simultaneous fitting 2-D dwell-time distributions obtained over a range of voltages and Ca2+i. The data for the fitting were obtained at five to six different voltages and three to four different Ca2+i for each of three different channels, giving 610 2-D dwell-time distributions that were simultaneously fitted for each of the channels. For channel B13, the voltage ranged from -40 to +50 mV and the Ca2+i ranged from 5.5 to 20.3 µM. For channel B14, the voltage ranged from -40 to +70 mV and the Ca2+i ranged from 0.0003 to 1,024 µM and, for channel B16, the voltage ranged from -50 to +40 mV and the Ca2+i ranged from 20.3 to 1,024 µM. For channels B13 and B16, data were not obtained at 0 Ca2+i, so the rate constants for the transitions among the unliganded states were set to the mean values in Table 2 (left), determined from the separate fitting of data obtained at
0.03 µM Ca2+i. Setting the values of the rate constants of the unliganded states (vs. letting them be free parameters) had little effect on the estimates of the other rate constants in Scheme 2 for these channels. Although the constraints on the voltage-dependent steps were given by Scheme 3 E during the fitting, the specific partial charge estimates q1q4 were free parameters.
Estimates of the most likely rate constants for Scheme 2 for channel B13 are presented in Table 3, together with estimates of q1q4 for channels B13, B14, and B16. Also presented in Table 3 are the approximate ratios of the rate constants for the various transitions pathways between states for those transitions in which both rate constants were >0.1 s-1. These estimates were obtained from the means of the rate constants for channels B13, B14, and B16. F/B in Table 3 gives the ratio of the forward (towards O1) to the backward (towards C15) rate constants for those transition pathways independent of agonist binding or unbinding, and would be equivalent to the equilibrium constant for a model with only two states. In general, the ratios of the forward to backward rate constants (F/B) increase as the number of bound Ca2+ increase. B/F gives the ratios of the backward (towards C15) to the forward (towards O1) rate constants for the agonist-dependent transitions, and would be equivalent to the dissociation constant for a model with only two states. Since the forward agonist-dependent rate constants have units of µM-1 s-1, the ratio B/F has units of µM, corresponding to the concentration at which the individual forward rate constant is equal to its corresponding backward rate constant.
|
To examine whether Scheme 2 with the most likely rate constants could simultaneously describe the Ca2+ and voltage dependence of the single-channel data, predicted dwell-time distributions were obtained by simulating and then analyzing the simulated single-channel data. Results are shown in Fig 8 for channel B13, where the predicted distributions (thick lines) gave a reasonable description of the observed open and closed dwell-time distributions obtained over a 134-fold change in Po, from 0.0061 to 0.82, for voltages ranging from -40 to +50 mV, and for three Ca2+i of 5.5, 12.3, and 20.3 mM. The voltage- and Ca2+-dependent shifts in the distributions were predicted with a single set of parameters (Table 3). A similar agreement between experimental and predicted results was observed for the two other examined channels using seperately determined sets of rate constants for each channel.
|
The ability of Scheme 2 to give a reasonable description of the voltage and Ca2+ dependence of the single-channel kinetics in Fig 8 is reflected in an NLR1 value of 0.987, and the NLR1 values of 0.983 and 0.987 for the other two channels (B16 and B14, respectively) examined in this manner. Although these values are less than the theoretical best description of 1.0, they do indicate an average likelihood difference of only 1.4% per interval pair between the theoretical best description and that predicted by Scheme 2. A less than ideal description would be expected, since Scheme 2 is simplified from the more complete gating mechanism described by Scheme 1.
To examine whether Scheme 2 could describe the effects of Ca2+i on Po, V1/2, and qeff over an even wider range of Ca2+i, Scheme 2 with the most likely parameters for each of three channels was used to predict Po versus voltage curves for values of Ca2+i ranging from 0.0003 to 1,024 µM. The Po versus voltage curves were also used to estimate the values of V1/2 and qeff over a range of Ca2+i for the three channels. The predicted values of Po, V1/2, and qeff were plotted in Fig 2 AD as continuous (channel B13), dashed (channel B14), and dotted (channel B16) thin lines. The points on these figures are a composite of data from a number of different channels so an exact fit would not be expected. Nonetheless, the results show that Scheme 2 approximated both the Po vs. voltage curves and the effective gating charge for the three channels (Fig 2, AC), and also the general shape of the Ca2+-dependent and -independent regions of the V1/2 versus Ca2+i relation for two of the three channels (Fig 2 D). Scheme 2 also approximated the general effects of voltage on the mean open and closed interval durations (Fig 3A and Fig B, thin lines) and also the effect of voltage on the apparent mean opening and closing rates (Fig 3 D, thin lines).
Scheme 2 predicted single-channel current records that were essentially indistinguishable from the experimental data over wide ranges of Ca2+i and voltage, after allowing for stochastic variation and a slightly more stable baseline in the simulated data. Examples of simulated current records can be found in the online supplement to this paper for comparison with the experimental data in Fig 1.
The partial charges q1q4 in Table 3 show that, in terms of Scheme 2, the gating steps with the most voltage dependence were the transitions between the closed states (closedclosed) and between the open states (openopen) in each of the five parallel subschemes (as described by Scheme 3 E) that form Scheme 2. For all three channels, depolarization facilitated the forward steps (mean q1 = +1.05 eo) and slowed the backwards steps (mean q 2 = -0.36 eo). The closedopen transitions (mean q3 = -0.05) and the openclosed transitions (mean q4 = -0.06) were much less voltage sensitive, with the variability in the estimates exceeding the mean values.
Although there was reasonable consistency among the partial charge estimates for the three different channels, for many of the rate constants there was considerable variability among estimates for the three different channels, as many of the rate constants were poorly defined. Consequently, the rate constants in Table 3 must be viewed as an example of a set of most likely rate constants that, when used with Scheme 2, can describe the gating of the channel without placing too much emphasis on the specific values. The most likely rate constants for the various channels were sufficient to show that Scheme 2 could describe the gating, even though they do not necessarily represent unique values of the rate constants.
Partial Charge Estimates
In the above sections, estimates of the partial charge movement associated with specific gating steps for Scheme 2 were obtained separately under the three conditions of 0 Ca2+i, saturating Ca2+i, and for simultaneously fitting data over a wide range of Ca2+i. The mean ± SEM of these estimates are presented in Table 4. The partial charge estimates for the forward (q1 = +0.57 eo) and backward (q2 = -0.43 eo) steps for the C-C and O-O transitions in Scheme 3 E were significantly different from zero (P < 0.05, signs test). The estimates for the C-O transitions (q3 = +0.030) were not significantly different from zero (P > 0.4), and the estimates for the O-C transitions (q4 = -0.18) were significantly different from zero (P < 0.05). These mean global estimates suggest that the voltage dependence of the gating arises primarily from the C-C and O-O transitions in each subscheme (Scheme 3 E), with less voltage dependence arising from the opening C-O and closing O-C transitions. These findings, obtained from the simultaneous analysis of single-channel data recorded over a range of both voltage and Ca2+i, are consistent with findings obtained from analysis of macroscopic ionic and gating currents obtained over a wide range of voltage at
0 Ca2+i (
|
Voltage-induced Shifts in the Gating
We have previously described, in terms of a two-tiered model such as Scheme 2, how increased Ca2+ shifted the gating from the closed states in the top left of the scheme to the open states in the bottom right (Figure 14 in
|
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Two-Tiered Gating Mechanisms Can Describe the Gating of BK Channels Over Wide Ranges of Voltage, Ca2+, and Po
This study used single-channel analysis to examine the mechanism of the voltage- and Ca2+-dependent gating of native BK channels from cultured rat skeletal muscle. It was found that the simplified two-tiered model, Scheme 2, could describe the major effects of voltage and Ca2+i and their interaction on the single-channel kinetics during normal activity over wide ranges of voltage (-80 to +80 mV), Ca2+I (0 to 1 mM), and Po (
10-4 to 0.96), as shown in Fig 2 and Fig 6 Fig 7 Fig 8. Since Scheme 2 is simplified from Scheme 1, it would be expected that the full two-tiered model described by Scheme 1 would give even better descriptions of the data, since Scheme 1 reflects more completely the subunit structure of the channel. In Scheme 1, the top and bottom tiers contain the closed and open states of the channel, respectively. The 25 states on each tier arise because each of the four subunits can bind Ca2+ (indicated by shading) and also make voltage-dependent transitions between two conformations (indicated by squares and circles).
The two-tiered gating mechanism of Scheme 1 can be functionally divided into five parallel (two-tiered) subschemes, each having five closed and five open states. The subschemes differ only in the numbers of Ca2+ bound to each, with zero, one, two, three, or four bound Ca2+. The binding and unbinding of Ca2+ shifts the channel laterally between the parallel subschemes, while voltage shifts the gating among the 10 states within each of the subschemes, including between the upper and lower tiers. Both Ca2+ binding and depolarization increase Po by increasing the stability of the open states. The Ca2+-induced increase in stability is illustrated in
Depolarization increases Po by increasing the rate of the (forward) conformational changes of the subunits and decreasing the rate of the backward conformational changes of the subunits (Scheme 1, oblique arrow), and this is the case for both the closedclosed transitions on the top tier and the openopen transitions on the bottom tier (Scheme 3 E and Tables IIIV). Depolarization also alters the transition rates between the two tiers to stabilize the open states (vertical arrow). These effects of voltage obtained from 0 to saturating Ca2+i in our study are consistent with those of
0 Ca2+i.
MWC- and Eigen-type Models Are Subsets of Scheme 1
Before considering Scheme 1 as a working hypothesis, it is necessary to establish that simpler models do not describe all of the experimental observations. Most previous studies of the gating of BK channels have been based on either 0 Ca2+i (
0 and saturating Ca2+i, in contrast to the correlations that are observed (
Nevertheless, MWC- and Eigen-type models can describe many features of the gating over restricted conditions. The reason for this is that these models are contained within the two-tiered 50-state model, where both Ca2+ and voltage are separate allosteric activators. Restricting the experimental conditions can effectively reduce the 50-state model to one of the simpler models, so that under restricted conditions, the gating can be well approximated by these simpler models. Thus, the two-tiered 50-state model is a unifying model, as it includes and expands upon the previous models for the gating of BK channels.
Additional Evidence for Two-Tiered Gating Mechanisms
Scheme 1 indicates that up to four Ca2+ can be bound. Evidence for three to four bound Ca2+ for maximal activation comes from Hill coefficients typically approaching three to four for plots of Po vs. Ca2+i (
Scheme 1 indicates that the channel can gate among as many as five open and five closed states in both 0 Ca2+i (left-most subscheme) and saturating Ca2+i (right-most subscheme). The gating at 0 Ca2+i is consistent with the left-most subscheme in Scheme 1 with no bound Ca2+ (
Scheme 1 has a tier of closed states and a tier of open states because there is an additional conformational change associated with the openingclosing transitions that is separate from the conformational changes of the four voltage-sensing subunits. Evidence for this additional conformational change in BK channels at 0 Ca2+i has been obtained with voltage-jump studies of ionic and gating currents (
Scheme 1 has five open states connected to five closed states, giving five separate pathways in each subscheme between the open and closed states in the two tiers. Thus, at least five separate transition pathways between the open and closed states are available over the entire range of Ca2+i. Support for gating with multiple separate transition pathways over the entire range of Ca2+i comes from observations of correlation between adjacent open and closed intervals for single-channel data obtained from 0 to saturating Ca2+i (
0 Ca2+i,
In Scheme 1, the voltage-dependent steps are separate from the Ca2+-dependent steps. Support for separate steps comes from the observations that voltage still activates the channel in 0 Ca2+ and that changes in Ca2+i at very low Ca2+i have little effect on the gating (Fig 1, Fig 2, and Fig 6;
0 to 1 mM in our experiments (Fig 2B and Fig C), although we cannot rule out that there is some effect (
Scheme 1 predicts that gating charge movement can occur after the channel opens its pore through transitions among the open states on the bottom tier. Support for this prediction comes from the observations of charge movement after the channel opens (
Thus, support for Scheme 1 comes from both its ability to describe the single-channel kinetics over wide ranges of voltage, Ca2+i, and Po, and also from the additional experimental observations discussed in this section that lend support to the underlying assumptions embodied in Scheme 1.
Gating Charge and the Voltage-dependent Steps
The effective gating charge for activation of the BK channels by voltage, estimated from the maximum limiting slope of plots of Po vs. voltage, was 2.3 ± 0.6 eo (Fig 2), and this effective gating charge was predicted by Scheme 2 (Fig 2 C). Our estimate of effective gating charge compares favorably with estimates of 1.11.8 eo obtained from mSlo by 0 Ca2+i. Calculations with Scheme 2 using the rate constants in Table 3 indicated an approximately twofold decrease in limiting slope for Pos < 10-4 and Ca2+i < 1 µM (not shown). Thus, the two-tiered scheme can predict the mean effective gating charge and also a decrease in limiting slope at very low Po.
In the context of Scheme 1 and Scheme 2, the effective gating charge arises from voltage-dependent conformational changes. Our mean estimates of partial charge movement associated with the forward (q1) and backward (q 2) steps for both C-C and O-O transitions in Scheme 3 E were +0.57 eo for q1 and -0.43 eo for q 2 (Table 4). These estimates can be compared with those of +0.27 eo and -0.27 eo obtained by 0 Ca2+i for a model given by the left-most subscheme in Scheme 1, where no Ca2+ are bound. There is reasonable agreement between our estimates and those of
The Rate Constants for Scheme 2 Represent Combined Rate Constants from Scheme 1
Because of the large numbers of rate constants in Scheme 1, we have used the simplified Scheme 2, drawn from Scheme 1, to assess Scheme 1. To reduce further the numbers of rate constants, we have limited the number of transition pathways between the parallel subschemes in the simplified Scheme 2. Since, based on subunit structure, the channel would be expected to gate like the more complex Scheme 1 rather than the simplified Scheme 2, the individual rate constants for the simplified scheme necessarily reflect combined rate constants from the more complex scheme. Consequently, while the rate constants for the simplified Scheme 2 are adequate to evaluate and rank models and to predict single-channel gating kinetics, they to not necessarily reflect a single transition rate, and should be interpreted with caution. Furthermore, even with reduced numbers of rate constants for Scheme 2, many of the rate constants were not unique, being poorly defined.
In spite of these limitations, the general Ca2+- and voltage-dependent shifts in the equilibrium occupancies, mean lifetimes, and frequency of entry into the various states give information about the underlying mechanism, as it is these shifts that describe the experimental data. These shifts are illustrated in Fig 9 for the voltage dependence of the gating, and in Figure 14 in
Where Do the Flickers Come From?
A characteristic kinetic feature of the gating of BK channels is the large number of brief closed intervals (flickers) entered during normal activity (
0 Ca2+ using a model described by the left-most subscheme in Scheme 1, with the assumption that the rate constants for the voltage-dependent conformational changes of each of the four subunits were identical and independent of the conformational states of the other subunits. To test whether the rate constants they found could describe the steady state single channel data in
0 Ca2+, we simulated single-channel currents using the rate constants in Table 1, Case A of
Since the state structure of the model of
Scheme 1 Itself Is a Simplification
Scheme 1 and Scheme 2 assume that the properties of each state are determined by both the number of bound Ca2+ and the number of subunits that have undergone a conformational change, without regard to which specific subunits have bound Ca2+ and which have undergone conformational changes. If Ca2+ has different effects depending on whether or not it binds to subunits that have undergone a conformational change, then there would be 35 possible combinations (
While Scheme 2 can serve as a starting point to quantitatively define the interactions between the voltage- and Ca2+-dependent activation of BK channels, the determined sets of rate constants for Scheme 2 are limited to the specific physiological state of the channel used to estimate the rate constants. The reason for this is that so many other factors alter BK channel activity, such as phosphorylation (
Are BK Channels Voltage or Calcium Activated?
In terms of Scheme 1, the channel gates in 0 Ca2+i as a purely voltage-activated channel among the five closed and five open unliganded states (left-most subscheme). Ca2+i-dependent steps are not required for full activation in 0 Ca2+i, as depolarizing voltage steps to +300 mV with
0 Ca2+i can fully activate the channel (
0.150 µM then modulates the gating by moving the voltage towards hyperpolarized potentials for half maximal activation, by changing the intrinsic closedopen equilibrium, with little effect on the voltage sensitivity (Fig 2). The shift in equilibrium results because each additional bound Ca2+ leads to increases in the ratios of the forward to backward rate constants, driving the equilibrium further towards the long open state (Table 2 and Table 3). Consistent with a voltage-activated and Ca2+-modulated channel, it has been suggested that BK channels may have evolved from an ancestral voltage-sensitive K+ channel, with the later addition of the extended COOH-terminal tail as a Ca2+-dependent modulatory domain (
If the BK channel is, from a mechanistic viewpoint, voltage activated and Ca2+ modulated, should the "calcium activated" name of the channel be changed to reflect the underlying mechanism? We think not. Under physiological conditions, Ca2+i is usually the limiting factor controlling activation, not voltage, since voltage changes within the physiological range will not activate the channel unless Ca2+i is elevated above the typical resting level in cells. Furthermore, the voltage dependence of BK channels (1115 mV/e-fold change in Po; effective charge movement of
2 eo) is considerably less than the voltage dependence of other K+ channels (
2 mV/e-fold change; effective charge movement of
13 eo;
Conclusions
This study presents a comprehensive kinetic gating mechanism for BK channels that can describe the major features of both Ca2+ and voltage dependence of the single-channel kinetics over the entire range of 0 to saturating Ca2+i. The two-tiered 50-state working hypothesis both expands upon and unifies many of the previous models, which are nested within the 50-state scheme. Nevertheless, as with previously proposed mechanisms, it will undoubtedly be necessary to expand upon this mechanism to account for all details of the gating.
![]() |
Footnotes |
---|
Dr. Rothberg's present address is Department of Neurobiology, Harvard Medical School, Boston, MA 02115.
Portions of this work were previously published in abstract form (Rothberg, B.S., and K.L. Magleby. 1996. Soc. Neurosci. Abstr. 22:1443. Rothberg, B.S., and K.L. Magleby. 1999. Biophys. J. 76:A333. Rothberg, B.S., and K.L. Magleby. 2000. Biophys. J. 78:92A).
The online version of this article contains supplemental material.
1 Abbreviations used in this paper: BK channel, large conductance calcium-activated K+ channel; MWC, Monod-Wyman-Changeux; NLR1, normalized likelihood ratio per interval pair.
![]() |
Acknowledgements |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
This work was supported in part by grants from the National Institutes of Health (NS007044 and AR32805) and the Muscular Dystrophy Association.
Submitted: 20 December 1999
Revised: 18 May 2000
Accepted: 22 May 2000
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Akaike, H. 1974. A new look at the statistical model identification. IEEE Trans. Auto. Control. 19:716-723.
Almers, W. 1978. Gating currents and charge movements in excitable membranes. Rev. Physiol. Biochem. Pharmacol. 82:96-190[Medline].
Andersen, O.S. 1999. Editorial: graphic representation of the results of kinetic analyses. J. Gen. Physiol 114:589-590
Atkinson, N.S., Robertson, G.A., and Ganetzky, B. 1991. A component of calcium-activated potassium channels encoded by the Drosophila slo locus. Science. 253:551-555[Medline].
Barrett, J.N., Magleby, K.L., and Pallotta, B.S. 1982. Properties of single calcium-activated potassium channels in cultured rat muscle. J. Physiol. 331:211-230[Medline].
Bello, R.A., and Magleby, K.L. 1998. Time-irreversible subconductance gating coupled to permeation of Ba2+ through large-conductance Ca2+-activated K+ channels. J. Gen. Physiol. 111:343-362
Bielefeldt, K., and Jackson, M.B. 1994. Phosphorylation and dephosphorylation modulate a Ca2+-activated K+ channel in rat peptidergic nerve terminals. J. Physiol. 475:241-254[Abstract].
Brenner, R., Jeglas, T.J., Wickenden, A., Liu, Y., and Aldrich, R.W. 2000. Cloning and functional characterization of novel large conductance calcium-activated potassium channel ß subunits, hKCNMB3 and hKCNMB4. J. Biol. Chem 275:6453-6461
Butler, A., Tsunoda, S., McCobb, D.P., Wei, A., and Salkoff, L. 1993. mSlo, a complex mouse gene encoding "maxi" calcium-activated potassium channels. Science. 261:221-224[Medline].
Changeux, J.-P., and Edelstein, S.J. 1998. Allosteric receptors after 30 years. Neuron 21:959-980[Medline].
Colquhoun, D., and Hawkes, A.G. 1995a. The principles of the stochastic interpretation of ion-channel mechanisms. In Sakmann B., Neher E., eds. Single-Channel Recording. New York, NY, Plenum Publishing Corp, 397-482.
Colquhoun, D., and Hawkes, A.G. 1995b. A Q-matrix cookbook. In Sakmann B., Neher E., eds. Single-Channel Recording. New York, NY, Plenum Publishing Corp, 589-633.
Colquhoun, D., and Sigworth, F.J. 1995. Fitting and statistical analysis of single-channel records. In Sakmann B., Neher E., eds. Single-Channel Recording. New York, NY, Plenum Publishing Corp, 483-587.
Conley, E.C. 1996. The ion channel facts book II. Intracellular ligand-gated channels. New York, NY, Academic Press, Inc, pp. 607720.
Cox, D.H., Cui, J., and Aldrich, R.W. 1997. Allosteric gating of a large conductance Ca-activated K+ channel. J. Gen. Physiol. 110:257-281
Crouzy, S.C., and Sigworth, F.J. 1990. Yet another approach to the dwell-time omission problem of single-channel analysis. Biophys. J. 58:731-743[Abstract].
Cui, J., Cox, D.H., and Aldrich, R.W. 1997. Intrinsic voltage dependence and Ca2+ regulation of mslo large conductance Ca-activated K+ channels. J. Gen. Physiol. 109:647-673
Diaz, L., Meera, P., Amigo, J., Stefani, E., Alvarez, O., Toro, L., and Latorre, R. 1998. Role of the S4 segment in a voltage-dependent calcium-sensitive potassium (hSlo) channel. J. Biol. Chem. 273:32430-32436
DiChiara, T.J., and Reinhart, P.H. 1995. Distinct effects of Ca2+ and voltage on the activation and deactivation of cloned Ca2+-activated K+ channels. J. Physiol. 489:403-418[Abstract].
DiChiara, T.J., and Reinhart, P.H. 1997. Redox modulation of hslo Ca2+-activated K+ channels. J. Neurosci. 17:4942-4955
Eigen, M. 1968. New looks and outlooks on physical enzymology. Q. Rev. Biophys. 1:3-33[Medline].
Eisenberg, R.S. 1990. Channels as enzymes. J. Membr. Biol. 115:1-12[Medline].
Ferguson, W.B., McManus, O.B., and Magleby, K.L. 1993. Opening and closing transitions for BK channels often occur in two steps via sojourns through a brief lifetime subconductance state. Biophys. J. 65:702-714[Abstract].
Fersht, A. 1985. Enzyme structure and mechanism. San Francisco, CA, W.H. Freeman Co, pp. 263278.
Fredkin, D.R., Montal, M., and Rice, J.A. 1985. Identification of aggregated Markovian models: application to the nicotinic acetylcholine receptor. In LeCam L.M., Olshen R.A., eds. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer. Belmont, CA, Wadsworth Publishing Co, 269-289.
Hamill, O.P., Marty, A., Neher, E., Sakmann, B., and Sigworth, F.J. 1981. Improved patch clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflügers Arch. 391:85-100[Medline].
Hodgkin, A.L., and Huxley, A.F. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:500-544[Medline].
Horn, R. 1987. Statistical methods for model discrimination: application to gating kinetics and permeation of the acetylcholine receptor channel. Biophys. J. 51:255-263[Abstract].
Horrigan, F.T., and Aldrich, R.W. 1999. Allosteric voltage gating of potassium channels II. mSlo channel gating charge movement in the absence of Ca2+. J. Gen. Physiol 114:305-336
Horrigan, F.T., Cui, J., and Aldrich, R.W. 1999. Allosteric voltage gating of potassium channels I. mSlo ionic currents in the absence of Ca2+. J. Gen. Physiol 114:277-304
Islas, L.D., and Sigworth, F.J. 1999. Voltage sensitivity and gating charge in Shaker and Shab family potassium channels. J. Gen. Physiol. 114:723-741
Jan, L.Y., and Jan, Y.N. 1997. Cloned potassium channels from eukaryotes and prokaryotes. Annu. Rev. Neurosci. 20:91-123[Medline].
Jones, E.M., Gray-Keller, M., and Fettiplace, R. 1999. The role of Ca2+-activated K+ channel spliced variants in the tonotopic organization of the turtle cochlea. J. Physiol. 518:653-665
Jones, S.W. 1999. Commentary: a plausible model. J. Gen. Physiol. 114:271-275
Kaczorowski, G.J., Knaus, H.G., Leonard, R.J., McManus, O.B., and Garcia, M.L. 1996. High-conductance calcium-activated potassium channels: structure, pharmacology, and function. J. Bioenerg. Biomembr. 28:255-267[Medline].
Kleinbaum, D.G, Kupper, L.L., and Muller, K.E. 1988. Applied regression analysis and other multivariable methods. Belmont, CA, Duxbury Press, pp. 8889.
Lagrutta, A., Shen, K.R.A., North, R.A., and Adelman, J.P. 1994. Functional differences among alternatively spliced variants of slowpoke, a Drosophila calcium-activated potassium channel. J. Biol. Chem. 269:20347-203511
Latorre, R., Vergara, C., and Hidalgo, C. 1982. Reconstitution in planar lipid bilayers of a Ca2+-dependent K+-channel from transverse tubule membranes isolated from rabbit skeletal muscle. Proc. Natl. Acad. Sci. USA. 79:805-809[Abstract].
Latorre, R. 1994. Molecular workings of large conductance (maxi) Ca2+ -activated K+ channels. In Peracchia C., ed. Handbook of Membrane Channels: Molecular and Cellular Physiology. New York, NY, Academic Press, Inc., 79-102.
Levitan, I.B. 1994. Modulation of ion channels by protein phosphorylation and dephosphorylation. Annu. Rev. Physiol. 56:193-212[Medline].
Liu, D.T., Tibbs, G.R., and Siegelbaum, S.A. 1996. Subunit stoichiometry of cyclic nucleotide-gated channels and effects of subunit order on channel function. Neuron 16:983-990[Medline].
Magleby, K.L. 1992. Preventing artifacts and reducing errors in single-channel analysis. Methods Enzymol. 207:763-791[Medline].
Magleby, K.L., and Pallotta, B.S. 1983. Calcium-dependence of open and shut interval distributions from calcium-activated potassium channels in cultured rat muscle. J. Physiol. 344:585-604[Abstract].
Magleby, K.L., and Song, L. 1992. Dependency plots suggest the kinetic structure of ion channels. Proc. R. Soc. Lond. B Biol. Sci. 249:133-142[Medline].
Magleby, K.L., and Weiss, D.S. 1990. Identifying kinetic gating mechanisms for ion channels by using two-dimensional distributions of simulated dwell times. Proc. R. Soc. Lond. B Biol. Sci. 241:220-228[Medline].
Marks, T.N., and Jones, S.W. 1992. Calcium currents in the A7r5 smooth musclederived cell line: an allosteric model for calcium channel activation and dihydropyridine agonist action. J. Gen. Physiol 99:367-390[Abstract].
Marty, A. 1981. Ca-dependent K channels with large unitary conductance in chromaffin cell membranes. Nature. 291:497-500[Medline].
McCormack, K., Joiner, W.J., and Heinemann, S.H. 1994. A characterization of the activation structural rearrangements in voltage-dependent Shaker K+ channels. Neuron 12:301-315[Medline].
McManus, O.B., Blatz, A.L., and Magleby, K.L. 1985. Inverse relationship of the durations of adjacent open and shut intervals for Cl and K channels. Nature. 317:625-628[Medline].
McManus, O.B., Blatz, A.L., and Magleby, K.L. 1987. Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise. Pflügers Arch. 410:530-553.
McManus, O.B., Helms, L.M.H., Pallanck, L., Ganetzky, B., Swanson, R., and Leonard, R.J. 1995. Functional role of the beta subunit of high-conductance calcium-activated potassium channels. Neuron. 14:645-650[Medline].
McManus, O.B., and Magleby, K.L. 1988. Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle. J. Physiol. 402:79-120[Abstract].
McManus, O.B., and Magleby, K.L. 1989. Kinetic time constants independent of previous single-channel activity suggest Markov gating for a large-conductance Ca-activated K channel. J. Gen. Physiol. 94:1037-1070[Abstract].
McManus, O.B., and Magleby, K.L. 1991. Accounting for the Ca2+-dependent kinetics of single large-conductance Ca2+-activated K+ channels in rat skeletal muscle. J. Physiol. 443:739-777[Abstract].
Meera, P., Wallner, M., Jiang, Z., and Toro, L. 1996. A calcium switch for the functional coupling between (hslo) and ß subunits (Kv, Cab) of maxi K channels. FEBS Lett. 382:84-88[Medline].
Methfessel, C., and Boheim, G. 1982. The gating of single calcium-dependent potassium channels is described by an activation/blockade mechanism. Biophys. Struct. Mech. 9:35-60[Medline].
Moczydlowski, E., and Latorre, R. 1983. Gating kinetics of Ca2+-activated K+ channels from rat muscle incorporated into planar lipid bilayers: evidence for two voltage-dependent Ca2+ binding reactions. J. Gen. Physiol. 82:511-542[Abstract].
Monod, J., Wyman, J., and Changeux, J.-P. 1965. On the nature of allosteric transitions: a plausible model. J. Mol. Biol. 12:88-118[Medline].
Nimigean, C.M., and Magleby, K.L. 1999. The ß subunit increases the Ca2+-sensitivity of large conductance Ca2+-activated channels by retaining the gating in the bursting states. J. Gen. Physiol. 113:425-439
Nimigean, C.M., Moss, B.L., and Magleby, K.L. 1999. Single-channel gating kinetics of BK channels in 0 µM Ca2+ are inconsistent with gating models based on the Monod-Wyman-Changeux (MWC) model for tetrameric allosteric proteins. Soc. Neurosci. Abst r. 25:985.
Nimigean, C.M., and Magleby, K.L. 2000. Gating in the absence of Ca2+i reveals Ca2+i-independent coupling of the ß1 subunit to large conductance Ca2+-activated K+ (BK) channels: increased Ca2+ sensitivity from a Ca2+-independent mechanism. J. Gen. Physiol. 115:719-734
Pallanck, L., and Ganetzky, B. 1994. Cloning and characterization of human and mouse homologs of the Drosophila calcium-activated potassium channel gene, slowpoke. Hum. Mol. Genet. 3:1239-1243[Abstract].
Pallotta, B.S., Magleby, K.L., and Barrett, J.N. 1981. Single channel recordings of Ca2+-activated K+ curtrents in rat muscle cell culture. Nature. 293:471-474[Medline].
Pallotta, B.S. 1985. N-Bromoacetamide removes a calcium-dependent component of channel opening from calcium-activated potassium channels in rat skeletal muscle. J. Gen. Physiol. 86:601-611[Abstract].
Reinhart, P.H., Chung, S., Martin, B.L., Brautigan, D.L., and Levitan, I.B. 1991. Modulation of calcium-activated potassium channels from rat brain by protein kinase A and phosphatase 2A. J. Neurosci. 11:1627-1635[Abstract].
Ríos, E., Karhanek, M., Ma, J., and Gonzalez, A. 1993. An allosteric model of the molecular interactions of excitationcontraction coupling in skeletal muscle. J. Gen. Physiol. 102:449-481[Abstract].
Rothberg, B.S., Bello, R.A., Song, L., and Magleby, K.L. 1996. High Ca2+ concentrations induce a low activity mode and reveal Ca2+-independent long shut intervals in BK channels from rat muscle. J. Physiol. 493:673-689[Abstract].
Rothberg, B.S., and Magleby, K.L. 1996. Gating of BK channels can be independent of calcium or voltage. Soc. Neurosci. Abstr 22:1443.
Rothberg, B.S., and Magleby, K.L. 1998. Kinetic structure of large-conductance Ca2+-activated K+ channels suggests that the gating includes transitions through intermediate or secondary states: a mechanism for flickers. J. Gen. Physiol. 111:751-780
Rothberg, B.S., and Magleby, K.L. 1999. Gating kinetics of single-large-conductance Ca2+-activated K+ channels in high Ca2+ suggest a two-tiered allosteric gating mechanism. J. Gen. Physiol. 114:95-124.
Roux, M.J., Olcese, R., Toro, L., Bezanilla, F., and Stefani, E. 1998. Fast inactivation in Shaker K+ channels. Properties of ionic and gating currents. J. Gen. Physiol 111:625-638
Schoppa, N.E., McCormack, K., Tanouye, M.A., and Sigworth, F.J. 1992. The size of gating charge in wild-type and mutant Shaker potassium channels. Science. 255:1712-1715[Medline].
Schoppa, N.E., and Sigworth, F.J. 1998. Activation of Shaker potassium channels. III. An activation gating model for wild-type and V2 mutant channels. J. Gen. Physiol. 111:313-342
Schreiber, M., and Salkoff, L. 1997. A novel calcium-sensing domain in the BK channel. Biophys. J. 73:1355-1363[Abstract].
Schreiber, M., Yuan, A., and Salkoff, L. 1999. Transplantable sites confer calcium sensitivity to BK channels. Nat. Neurosci. 2:416-421[Medline].
Shen, K.-Z., Lagrutta, A., Davies, N.W., Standen, N.B., Adelman, J.P., and North, R.A. 1994. Tetraethylammonium block of slowpoke calcium-activated potassium channels expressed in Xenopus oocytes: evidence for tetrameric channel formation. Pflügers Arch. 426:440-445.
Sigg, D., and Bezanilla, F. 1997. Total charge movement per channel: the relation between gating charge displacement and the voltage-sensitivity of activation. J. Gen. Physiol. 109:27-39
Sigg, D., Qian, J., and Bezanilla, F. 1999. Kramers' diffusion theory applied to gating kinetics of voltage-dependent ion channels. Biophys. J. 76:782-803
Sigworth, F.J. 1994. Voltage gating of ion channels. Q. Rev. Biophys. 27:1-40[Medline].
Smith, M.A., and Ashford, M.L.J. 1998. Mode switching characterizes the activity of large conductance potassium channels recorded from rat cortical fused nerve terminals. J. Physiol. 513:733-747
Song, L., and Magleby, K.L. 1994. Testing for microscopic reversibility in the gating of maxi K+ channels using two-dimensional dwell-time distributions. Biophys. J. 67:91-104[Abstract].
Stefani, E., Ottolia, M., Noceti, F., Olcese, R., Wallner, M., Latorre, R., and Toro, L. 1997. Voltage-controlled gating in a large conductance Ca2+-sensitive K+ channel (hslo). Proc. Natl. Acad. Sci. USA. 94:5427-5431
Stevens, C.F. 1978. Interactions between intrinsic membrane protein and electric field: an approach to studying nerve excitability. Biophys. J. 22:295-306[Abstract].
Talukder, G., and Aldrich, R.W. 2000. Complex voltage-dependent behavior of single unliganded calcium-sensitive potassium channels. Biophys. J. 78:761-772
Tanaka, Y., Meera, P., Song, M., Knaus, H.-G., and Toro, L. 1997. Molecular constituents of maxi Kca channels in human coronary smooth muscle: predominant + ß subunit complexes. J. Physiol. 502:545-557[Abstract].
Thuringer, D., and Findlay, I. 1997. Contrasting effects of intracellular redox couples on the regulation of maxi-K channels in isolated myocytes from rabbit pulmonary artery. J. Physiol. 500:583-592[Abstract].
Toro, L., Wallner, M., Meera, P., and Tanaka, Y. 1998. Maxi-KCa, a unique member of the voltage-gated K channel superfamily. News Physiol. Sci 13:112-117
Tseng-Crank, J., Foster, C.D., Krause, J.D., Mertz, R., Godinot, N., DiChiara, T.J., and Reinhart, P.H. 1994. Cloning, expression, and distribution of functionally distinct Ca2+-activated K+ channel isoforms from human brain. Neuron. 13:1315-1330[Medline].
Wallner, M., Meera, P., and Toro, L. 1999. Molecular basis of fast inactivation in voltage and Ca2+-activated K+ channels: a transmembrane beta-subunit homolog. Proc. Natl. Acad. Sci USA. 96:4137-4142
Wei, A., Solaro, C., Lingle, C., and Salkoff, L. 1994. Calcium sensitivity of BK-type KCa channels determined by a separable domain. Neuron. 13:671-680[Medline].
Weiss, D.S., and Magleby, K.L. 1992. Voltage-dependent gating mechanism for single fast chloride channels from rat skeletal muscle. J. Physiol. 453:279-306[Abstract].
Wong, B.S., Lecar, H., and Adler, M. 1982. Single calcium-dependent potassium channels in clonal anterior pituitary cells. Biophys. J. 39:313-317[Abstract].
Wu, Y.-C., Art, J.J., Goodman, M.B., and Fettiplace, R. 1995. A kinetic description of the calcium-activated potassium channel and its application to electrical tuning of hair cells. Prog. Biophys. Mol. Biol 63:131-158[Medline].
Xia, X.M., Ding, J.P., and Lingle, C.J. 1999. Molecular basis for the inactivation of Ca2+- and voltage-dependent BK channels in adrenal chromaffin cells and rat insulinoma tumor cells. J. Neurosci 19:5255-5264
Zagotta, W.N., Hoshi, T., and Aldrich, R.W. 1994. Shaker potassium channel gating. III: evaluation of kinetic models for activation. J. Gen. Physiol. 103:321-362[Abstract].
Zheng, J., and Sigworth, F.J. 1998. Intermediate conductances during deactivation of heteromultimeric Shaker potassium channels. J. Gen. Physiol. 112:457-474