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Department of Molecular and Cellular Physiology, Stanford University, Stanford, CA 94305
Section of Neurobiology, University of Texas at Austin, Austin, TX 78705

Correspondence to Richard W. Aldrich: raldrich{at}mail.utexas.edu

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Intracellular blockade by quaternary ammonium (QA) molecules of many potassium channels is state dependent, where the requirement for channel opening is evidenced by a time-dependent component of block in the macroscopic record. Whether this is the case for Ca²⁺- and voltage-activated potassium (BK) channels, however, remains unclear. Previous work (Li, W., and R.W. Aldrich. 2004. J. Gen. Physiol. 124:43–57) tentatively proposed a state-dependent, trapping model, but left open the possibility of state-independent block. Here, we found BK channel blockade by a novel QA derivative, bbTBA, was time dependent, raising the possibility of state-dependent, open channel block. Alternatively, the observed voltage dependence of block could be sufficient to explain time-dependent block. We have used steady-state and kinetic measurements of bbTBA blockade in order to discriminate between these two possibilities. bbTBA did not significantly slow deactivation kinetics at potentials between –200 and –100 mV, suggesting that channels can close unhindered by bound bbTBA. We further find no evidence that bbTBA is trapped inside BK channels after closing. Measurements of steady state fractional block at +40 mV revealed a 1.3-fold change in apparent affinity for a 33-fold change in P_o, in striking contrast to the 31-fold change predicted by state-dependent block. Finally, the appearance of a third kinetic component of bbTBA blockade at high concentrations is incompatible with state-dependent block. Our results suggest that access of intracellular bbTBA to the BK channel cavity is not strictly gated by channel opening and closing, and imply that the permeation gate for BK channels may not be intracellular.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The mechanism of ion channel opening and closing is widely thought of in terms of a gate that permits or restricts access to the inner pore via a reversible conformational change. Much attention has been focused on locating the gate of K⁺ channels, as a first step toward understanding the conformational changes that underlie the gating process. Clay Armstrong's innovative use of intracellular organic blockers that could block K⁺ channels only when they were open (Armstrong, 1966, 1969, 1971) produced the first strong evidence for an intracellular activation gate. The classic features of state-dependent (open channel) block defined in this work (Armstrong, 1971) include (a) time-dependent block of macroscopic current, where steady-state block reaches equilibrium only after open probability is sufficiently high, (b) a "foot in the door" effect of blocker on channel closing, where internally bound quaternary ammonium (QA) ions of a sufficient size were found to delay closure of the activation gate, and (c) "trapping" of a blocker molecule inside the channel pore after closure of the activation gate. These observations strongly suggested that intracellular blockers required channel opening in order to access (and exit) the pore, and implied that the gating structure regulating access of the blocker to the pore must be located on the intracellular face of the channel. Numerous functional studies of K⁺ channels (Armstrong and Hille, 1972; MacKinnon and Miller, 1989; MacKinnon and Yellen, 1990; MacKinnon et al., 1990; Yellen et al., 1991; Heginbotham et al., 1992; Liu et al., 1997; Shin et al., 2001) and structural studies of bacterial (Doyle et al., 1998; Jiang et al., 2002a; Jiang et al., 2003; Kuo et al., 2003) and mammalian (Long et al., 2005) K⁺ channels have confirmed Armstrong's original hypothesis.

The structure of the mammalian voltage-gated K⁺ channel Kv 1.2 (Long et al., 2005) exemplifies the detailed organization of an archetypal K⁺ channel pore. The S5 and S6 transmembrane domains from each of four subunits define the central pore, a large water-filled cavity constrained at the extracellular end by the narrow selectivity filter, and at the intracellular end by the "bundle crossing," where the S6 helices come into close apposition. For the majority of K⁺ channels, permeation of K⁺ ions appears to be governed by constriction and enlargement of the S6 aperture. On the other hand, it is clear that some related ion channels employ a different gating mechanism. The case for cyclic nucleotide-gated (CNG) channels is particularly compelling, where Flynn and Zagotta (2001) found that although access of internally applied MTSET to pore residues depends upon the state of the channel, those residues are equally accessible to internal Ag⁺ (roughly equivalent to a K⁺ ion in size) in the open or closed state. The authors propose that although the larger MTS reagent is gated by conformational changes of the S6 bundle crossing, permeant ions may be gated at the selectivity filter for CNG channels. Similarly, small-conductance Ca²⁺-activated K⁺ (SK) channels (Bruening-Wright et al., 2002), ATP-sensitive inward rectifier K⁺ (K_ATP) channels (Proks et al., 2003), and KcsA K⁺ channels (Cordero-Morales et al., 2006) may also be gated at the selectivity filter.

For BK Ca²⁺- and voltage-activated K⁺ channels, the location of the permeation gate remains an open question. Although the structure of a bacterial Ca²⁺-gated K⁺ channel (MthK) is known (Jiang et al., 2002a), and functional evidence from BK channels is consistent with motion of the intracellular S6 domains during gating (Niu et al., 2004), the mechanism of BK channel gating is far from fully understood. In some ways, intracellular block of BK channels appears similar to classical open channel block. Most notably, block of BK channels by intracellular Shaker ball peptide is state dependent; the peptide blocks only open channels and must exit before channels can close (unpublished data). Several other observations could also be consistent with an intracellular gate for BK channels: mutations in S6 disrupt activation gating (Piskorowski, 2005), BK channels can close when the selectivity filter is occupied by either Na⁺ or Ba²⁺ (Miller et al., 1987; Neyton and Pelleschi, 1991), and high concentrations of external K⁺ have no obvious slowing effect on deactivation of BK channels (Neyton and Pelleschi, 1991; Demo and Yellen, 1992).

In spite of these observations, however, there is equally compelling evidence suggesting that the BK channel gate may lie elsewhere. First, QA molecules, which have been shown functionally to promote C-type inactivation (a form of selectivity filter gating in Kv channels; Choi et al., 1991) and are proposed to induce constriction of the Kcsa selectivity filter in structural studies (Lenaeus et al., 2005), also speed closing of BK channels (Li and Aldrich, 2004), raising the possibility that BK channels gate at the selectivity filter via a C-type collapse mechanism. Also, permeant thallium favors Kcsa selectivity filter collapse (Zhou and MacKinnon, 2003) and speeds BK channel deactivation (Piskorowski and Aldrich, 2006). Second, although binding of the N-terminal inactivation peptide to the intracellular mouth of the pore of many K⁺ channels follows predictions of open channel block (Demo and Yellen, 1991), the case for BK channels is far more complex and intriguing. Most importantly, binding and unbinding of the BK inactivation particle (provided by the ß subunit) does not require channels to visit the fully conducting open state (Benzinger et al., 2006). Third, no evidence has been obtained thus far for trapping of large intracellular blocker molecules like leupeptin, curare, QX-314, and chlorisondamine (Solaro et al., 1997). Fourth, external Rb⁺ has been shown to destabilize the closed state, presumably due to occupancy of the selectivity filter (slowing deactivation and speeding channel opening; Demo and Yellen, 1992). Finally, a novel conotoxin, K-BtX, appears to stabilize the open state of BK channels from the external side (Fan et al., 2003). It is thus not unreasonable to consider the possibility that BK channels are gated at the selectivity filter, particularly in light of the fact that three other channels activated by intracellular ligands, the CNG, K_ATP, and SK channels, appear to use selectivity filter gates (Flynn and Zagotta, 2001; Bruening-Wright et al., 2002; Proks et al., 2003).

The classic QA blocker experiments that have worked so well for other K⁺ channels have been less informative for BK channels because of the relatively large size of the BK channel intracellular cavity. In order for a time-dependent component of block to be visible, the kinetics of block must be slow with respect to the intrinsic rate of channel opening, and the kinetics of block by even the largest molecule tested thus far, decyltriethylammonium (C10), have been too fast to resolve (Li and Aldrich, 2004). We sought to find a QA blocker with sufficiently slow kinetics to allow resolution of time-dependent block and to discern whether intracellular block of BK channels requires channel opening. Here we provide evidence that the QA ion bbTBA (N-(4-[benzoyl]benyl)-N,N,N-tributylammonium bromide) can block both closed and open channels. We conclude that access of bbTBA to the BK channel pore does not appear to be strictly regulated by an intracellular gating structure, and speculate that permeant K⁺ ions may be gated in the selectivity filter itself.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Channel Expression
All experiments were conducted using the mSlo gene encoding the mouse BK channel (Butler et al., 1993). Freshly isolated Xenopus oocytes were injected with 5 ng or 0.05 ng cRNA for macroscopic or microscopic experiments, respectively. Patch clamp recordings were made 1–4 d after injection.

Electrophysiology
All recordings were made from oocyte macropatches using the inside-out patch configuration (Hamill et al., 1981). Pipettes were pulled from borosilicate glass (VWR Scientific) to yield resistances of 1–3 M, and coated with sticky wax (Kerr Corporation). All experiments were performed at 22°C. Data were acquired with an Axopatch 1B or Axopatch 200A amplifier (Axon Instruments, Inc.), low pass filtered at 10 kHz, and digitized using an ITC-16 converter (Instrutech). Sampling interval was set at 10 or 20 µs using Pulse software (HEKA Electronik) and a Macintosh G3 computer. Data were leak subtracted using a –P/4 protocol stepping from leak holding potential of –120 mV. Macroscopic ionic currents were usually averaged from three or more consecutive sweeps. Idealization of microscopic recordings was accomplished using the TAC software suite (Bruxton Corporation); all further analysis of macrosopic and microscopic data was performed with Igor (WaveMetrics, Inc.).

Analysis and Curve Fitting
Dose–response data were fitted with the Hill equation:

(1)

where I_bbTBA and I_control = current with and without bbTBA, respectively, K_d = apparent dissociation constant for bbTBA, and n = Hill coefficient. The voltage dependence of k_OFF, k_ON, or K_d was determined by fitting with the Woodhull equation (Woodhull, 1973):

(2)

where V = test potential, k(0) = the rate at 0 mV, z = valence of bbTBA (+1), and = effective electrical distance; together, z roughly approximates the voltage dependence of blockade. Voltage dependence of block was also measured by fitting fractional unblock as a function of voltage with a Woodhull equation of the form

(3)

Conductance–voltage relationships were calculated from isochronal tail current measurements at –80 mV after variable test steps, and normalized to maximal tail current amplitude. This procedure avoids complications induced by fast Ca²⁺ block of steady-state currents, and thus accurately reflects relative macroscopic open probability (P_o) as a function of voltage (Cox, Cui and Aldrich, 1997). The data were fitted with a Boltzman function:

(4)

where G = conductance, V_1/2 = potential for half-maximal activation, and z = apparent equivalent gating charge. Current traces depicted in the figures were zero subtracted for display purposes. In general, the SEM is given with averaged values, while the 95% confidence interval is provided for fitted parameters.

Predictions of Percent Block (Fig. 3 C)
Competitive Block.
The apparent K_ds (K_app) for bbTBA or tetrabutylammonium (TBA) were estimated from the average fractional block (F) observed for each blocker alone using F^QA = [QA]/[QA] + K_app^QA. This yielded K_app^bbTBA = 5.9 µM and K_app^TBA = 0.628 mM. The K_app^bbTBA in the presence of TBA was then calculated: K_app^bbTBA/TBA = K_app^bbTBA(1 + [TBA]/K_app^TBA = 15.3 µM; the fraction of current blocked by bbTBA in the presence of TBA is thus F^bbTBA/TBA = [bbTBA]/[bbTBA]+K_app^bbTBA/TBA = 0.25. Similarly, the K_app^TBA/bbTBA = 1.16 mM, and the F^TBA/bbTBA = 0.46. Together, both blockers block 0.25 + 0.46 = 71% of total current.

Noncompetitive Block.
Percent block was calculated by summing the fraction of current blocked by TBA, F^TBA = 0.62, and the fraction of current remaining in the presence of TBA that is blocked by bbTBA, F^bbTBA/TBA = (1 – F^TBA)F^bbTBA = 0.18, yielding 80% block.

Final Model for bbTBA Blockade
A final model for state-independent blockade of BK channels by bbTBA was constructed (Scheme 1), which accurately reproduced steady-state and kinetic features of block (see Figs. 1, 3, 5, 8, 10, and 11).

(SCHEME 1)

This model, based on the simulation protocol developed by Horrigan et al. (1999), consisted of four connected states, with parameters taken from our average macroscopic and microscopic data (see Table I ). The final z value of 0.15 was calculated from the average values of z derived from six different measurements, and closely matches that observed for C10 and TBA (0.16 and 0.21; Li and Aldrich 2004). K_d(0 mV) was allowed to vary somewhat (8–10 µM) in order to compensate for the observed shift in K_d over time and variability in individual patches. Because microscopic measurements were made earlier in time, the average on and off rates are biased toward the lower K_d(0) observed at that time (5 µM; Table I). Assuming that the decline in apparent affinity of bbTBA over time is the result of a degradative process, we expect that the increased K_d reflects a decrease in k_ON, with relatively little change in k_OFF. Thus, in order for our final model to accommodate measurements made later in time, we constrained the model to the macroscopic steady-state parameters K_d(0) = 8–10 µM and z = 0.15, and also required that k_OFF (0) = 562 s^–1, while k_ON(0) was scaled to match the K_d (k_ON = 0.625 x 10⁸ M^–1s^–1). Microscopic measurements of the voltage dependence of k_ON(0.05) and k_OFF(0.7) were assumed to be accurate, and k_OFF was adjusted slightly (to 0.1) to yield z_total = 0.15. Note that without these adjustments, the kinetic features of block, including the triphasic time dependence observed at high concentrations, were still reproducible. Our final model makes two assumptions: (1) bbTBA binding does not alter the intrinsic rates of channel activation and deactivation (e.g., the same values for and ß were used for the closed/open transition for both unblocked and blocked channels), and (2) intrinsic affinity of bbTBA for the open and closed states is equal (which our data suggest is not entirely accurate; see Figs. 8–10).

N-(4-[benzoyl]benyl)-N,N,N-tributylammonium bromide (bbTBA) was acquired from Spectra Group Limited, Inc. All experiments were performed using dilutions of an initial 50 mM stock prepared from newly obtained salt, which was stored frozen in small aliquots at –20°C. We did notice a slow decline in efficacy of block over a period of 9 mo. This apparent degradation of bbTBA was independent of storage in solution (50 mM stocks frozen at –20°C) or as a salt, based on comparison of K_d at +100 mV of (a) the original stock solution, 3.2 µM, (b) the same stock solution 9 mo later, 4.4 µM, and (c) a freshly made solution prepared from 9-mo-old salt, 4.4 µM. The latter measurements (b and c) were made from Hill fits of dose–response data obtained from single patches, n = 3 patches. The absorption spectra (measured after 9 mo) for the latter two solutions were also comparable (A_max = 0.20 or 0.18, respectively); no measurement had been made for the original stock solution 9 mo prior. This slow decline in efficacy of block adds some variability to our averages, but will otherwise not affect the conclusions of this work, as the fractional block experiments were all performed in an 3-mo period, and all comparisons were made to control experiments performed concurrently. Tetrabutylammonium (TBA) was purchased from Alfa Aesar. All other chemicals were purchased from Sigma-Aldrich.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Macroscopic bbTBA Blockade of BK Channels Is Time Dependent
To characterize blockade of BK channels by bbTBA, we first performed dose–response experiments, where macroscopic K⁺ currents were elicited from inside-out macropatches using a series of voltage steps in the absence and presence of varying concentrations of bbTBA (Fig. 1 ). Fig. 1 A illustrates blockade of BK currents measured at +140 mV. bbTBA block was dose dependent and fully reversible (see Figs. 3 and 9). In Fig. 1 B, average fractional block, calculated from steady-state ionic currents in the presence and absence of bbTBA, was plotted as a function of bbTBA concentration for each of six test voltages in order to determine the dosage for half-maximal block (K_d). Hill fits of these data yielded K_d values in the low micromolar range, with Hill coefficients near 1. The resulting K_d values were then plotted as a function of test voltage, for voltages +40 mV (Fig. 1 C), where open probability (P_o) in 100 µM Ca²⁺ is expected to saturate. As expected for a charged molecule (see structure in Fig. 1 B), block was modestly voltage dependent, with a K_d at 0 mV of 9.5 µM, and a total voltage dependence z of 0.15, similar to other QA blockers in BK channels (Li and Aldrich, 2004). The lesser degree of voltage dependence compared with QA block of Kv channels (z 0.4) may reflect the larger diameter, and presumed lower resistance, of the vestibule in BK channels. Fig. 1 demonstrates that bbTBA behaves as a typical QA blocker, where dose-dependent blockade results from binding of bbTBA to a single voltage-dependent binding site.

View larger version (8K): [in this window] [in a new window]   Figure 1. Macroscopic bbTBA blockade is dose and voltage dependent. (A) Representative family of steps from a holding potential of –80 mV to +140 mV (100 µM internal Ca2+) in the absence and presence of the indicated concentrations of bbTBA. Traces shown are averages of three consecutive sweeps. (B) Macroscopic fractional block (1 – IbbTBA/Icontrol) was measured from ionic currents, averaged across patches at six different voltages (+40 to +140 mV), and plotted against bbTBA concentration. Smooth curves are Hill fits to the average data (mean ± SEM; n = 6 patches). The structure of bbTBA is indicated in the inset; bbTBA carries a charge of +1. (C) Macroscopic Kds from Hill fits were plotted as a function of test voltage; error bars represent the standard deviation of the Hill fits in B. Parameters (±95% confidence interval) of bbTBA blockade derived from fitting of the data to Eq. 2 were (dashed line) Kd(0 mV) = 9.53 ± 3.32 µM, z = 0.148 ± 0.024.

View larger version (10K): [in this window] [in a new window]   Figure 2. bbTBA blockade is time dependent. (A) Representative current families (averages of three consecutive sweeps) measured in 100 µM internal Ca2+ in the absence and (B) presence of 5 µM bbTBA. Test voltages ranged from +20 to +120 mV (in increments of 20 mV). Holding potential was –80 mV. In saturating Ca2+, the time-dependent component of block first becomes obvious at +80 mV. (C) Average currents at +180 mV in the absence and presence of the indicated concentrations of bbTBA, on an expanded time scale. The time-dependent component of blockade is visible at bbTBA concentrations between 1 and 100 µM. The time constants of current relaxation in the presence of bbTBA measured from single exponential fits (dashed lines) were 3.71 ms (1 µM), 1.43 ms (5 µM), and 526 µs (20 µM). Note that the time constant of current relaxation decreases in rough proportion to the concentration of blocker applied, consistent with expectations of a two-state blocking reaction.

(SCHEME 2)

The approximately twofold change in fractional block (estimated from the peak and steady-state levels of current in bbTBA) during the time-dependent component is well within the range that could be explained by voltage-dependent, state-independent block (Scheme 3 ) alone (assuming z 0.15, which predicts an approximately threefold change in block for the 260-mV step shown in Fig. 2 C), without a need to invoke state-dependent block.

(SCHEME 3)

View larger version (17K): [in this window] [in a new window]   Figure 3. bbTBA behaves as a traditional pore blocker. (A) Ionic currents were sampled for 30 ms at +120 mV (from a holding potential of –80 mV) five times in each condition (100 µM internal Ca2+ or in the presence of 5 µM bbTBA, 1 mM TBA, or both blockers together) in the order shown in the time course. (B) Each set of five sweeps was averaged to yield the average traces for this experiment in the absence and presence of the indicated blocker solutions. Percent block in each case was then calculated from these average sweeps (for this experiment: bbTBA, 51%; TBA, 65%; both, 72%). Smooth lines represent modeling of ionic current under each condition. For modeling, channel opening ( = 2254 s–1) and closing (ß = 46 s–1) rates were determined from a single exponential fit to the control data and assuming Po 0.98, using 1/ = + ß and Po = /( + ß). Kinetics of TBA block were estimated from Li and Aldrich (2004): Kd(0 mV) = 1 mM and z = 0.2. bbTBA block was modeled using parameters for the final model (Kd(0) = 9.9 µM and z = 0.15). Currents in individual blockers were modeled with Scheme 3. Block by bbTBA + TBA was modeled using either a noncompetitive (Scheme 4, dashed line) or competitive (Scheme 5, solid line) model. Time dependence was drastically slowed in both cases, but the observed steady-state level of block is compatible only with a competitive model of block. (C) The average (±SEM) percent block observed in three patches for bbTBA alone (46%), TBA alone (62%), or both blockers together (71%) follows exactly the predictions of a competitive model of blockade (71%). A noncompetitive model predicts both blockers will block 80% of total current. Predictions of percent block were calculated as described in Materials and methods. The ability of bbTBA to compete for the binding site of a known pore blocker of BK channels strongly suggests that the bbTBA binding site is located in the pore cavity.

(SCHEME 4)

The data in Fig. 3 B were compared with the predictions of our final model (described in Materials and methods and Table I) to assess its adequacy in describing steady-state and kinetic properties of bbTBA blockade, and to illustrate the predictions made in Fig. 3 C. Blockade of ionic current by bbTBA was well described by our final model, as were currents in TBA (using estimates of block kinetics from Li and Aldrich [2004]; solid lines). The degree of blockade observed in the presence of both blockers matched predictions of the competitive model (Scheme 5, solid line), but was not compatible with noncompetitive block (Scheme 4, dashed line). Note that the virtual absence of time dependence can be accounted for by both models. These data, along with the bimolecular kinetics and voltage dependence, provide good evidence that bbTBA is a pore blocker, as expected.

(SCHEME 5)

Microscopic Blockade
To evaluate more carefully the kinetics and voltage dependence of bbTBA blockade, we performed microscopic experiments (Fig. 4 ). Fig. 4 A illustrates representative single channel records from inside-out patches at +100 mV in 100 µM Ca²⁺ internal solution, in the absence and presence of either 1 or 3 µM bbTBA. While the BK channel activity is characterized by high open probability (P_o) and short flickery closings, P_o decreases and open times become progressively shorter as the concentration of bbTBA is increased. Dwell time histograms constructed from idealized records were fitted with single exponential functions in order to yield the mean open and shut dwell times (Fig. 4 B). Block rates calculated from these mean dwell times were then plotted as a function of bbTBA concentration in order to yield the second order k_ON at +100 mV, the average k_OFF, and the resultant K_d (Fig. 4 C). As an alternative to the kinetic measurements, we also determined the microscopic K_d using steady-state measurements of open probability in various bbTBA concentrations (Fig. 4 D). The results from Hill fits to normalized P_o plotted as a function of bbTBA concentration were roughly similar to those of the kinetic measurements in Fig. 4 C.

View larger version (18K): [in this window] [in a new window]   Figure 4. Kinetic and steady-state measurements of microscopic block at +100 mV are consistent with a bimolecular blocking reaction. (A) Representative single channel recordings (200 ms) measured at +100 mV in 100 µM internal Ca2+ in the absence or presence of the indicated concentration of bbTBA. The effective filtering frequency used for display purposes only was 1.96 kHz (for analysis of dwell times, records were sampled at 100 kHz and filtered at 10 kHz). Openings are upward. (B) Shut (left) or open (right) dwell time histograms were prepared from idealized records of control (top), 1 µM bbTBA (middle), or 3 µM bbTBA (bottom) data. Records were idealized with half amplitude threshold analysis using TAC software. Each histogram was constructed from 30–70 s of data, containing 1722–5081 events. Dwell times shorter than twice the filter dead time 2Td (76 µs) were excluded. Histogram data (gray) plotted as square root of counts vs. log of dwell times were fitted with single exponential functions (solid lines) in order to determine mean dwell times for each condition. (C) Average rates of block at +100 mV were calculated from the dwell time histograms and plotted as a function of bbTBA concentration. The off rate (kOFF, triangles) at each concentration of bbTBA was taken to be the reciprocal of the mean shut dwell time in blocker, assuming that excursions to the open level in the record largely reflect unblocking events. The first order on rate (kON, squares) was calculated at each concentration by subtracting the native closing rate, 1/ß (the reciprocal of the control mean open time), from the reciprocal of the mean open time in bbTBA to prevent contamination of the calculated on rate by the intrinsic rate of channel closing. Data from three patches at +100 mV were averaged (±SEM) and fitted with linear equations to yield the second order association rate (±95% confidence interval) kON = 1.16 x 108 ± 0.258 x 108 M–1s–1. The dissociation rate (average of all values ± SEM) was kOFF = 435 ± 28 s–1, and the Kd (the intersection where kON = kOFF) was Kd = 3.9 µM. (D) Microscopic Kd was also obtained from steady-state measurements of open probability in various blocker concentrations. Open probabilities calculated from raw amplitude histograms were normalized, averaged, and plotted as a function of bbTBA concentration (n = 4 patches, ±SEM). The average data were fitted with the Hill equation, which yielded parameters (±95% confidence interval) Kd at +100 mV = 2.9 ± 5.5 µM and Hill coefficient of 1.0 ± 2.5. The linear increase in kON as a function of bbTBA concentration and the independence of kOFF are consistent with a bimolecular blocking reaction where a single bbTBA molecule binds at a single site.

View larger version (8K): [in this window] [in a new window]   Figure 5. Average microscopic parameters of bbTBA blockade. (A) Average second order on rates calculated from kinetic measurements at each voltage as in Fig. 4 were fitted to Eq. 2 either by Igor (dashed line) to yield (parameters ± 95% confidence interval) kON(0) = 1.108 ± 0.3 x 108 M–1s–1 and zON = 0.012 ± 0.093, or with the final model (solid line) with parameters: kON(0) = 1.0 x 108 M–1s–1 and zON = 0.05. Data were averaged from six patches; error bars represent the standard deviation of fits of kON vs. [bbTBA] as in Fig. 4 C. (B) Average off rates (±SEM; n = 6 patches) were plotted as a function of voltage and fitted to Eq. 2 (dashed line), yielding parameters (±95% confidence interval) kOFF(0) = 562 ± 27 s–1 and zOFF = 0.07 ± 0.015. (C) Average microscopic Kd measured from steady-state open probability (filled squares) or kinetics (open squares) were plotted as a function of voltage and fitted with Eq. 2 either by Igor (dashed lines) with parameters (±95% confidence interval): steady-state, Kd = 4.8 ± 1.1 µM and z = 0.14 ± 0.08; kinetic, Kd = 5.5 ± 1.1 µM and z = 0.11 ± 0.07, or the final model (solid lines) with parameters: steady-state, Kd = 5 µM and z = 0.15; kinetic, Kd = 6 µM and z = 0.15. (In this particular instance, the Kd in the final model was not constrained to the 8–10 µM range, in order to account for microscopic measurements made earlier in time; see Materials and methods). Error bars represent the standard deviation from fits of the Po vs. [bbTBA] curves as in Fig. 4 D. The Kd for the kinetic measurements was taken to be the intersection where kON = kOFF. Data were averaged from six or four patches for kinetic and steady-state measurements, respectively.

View larger version (14K): [in this window] [in a new window]   Figure 6. bbTBA does not interfere with closure of the activation gate. (A) An instantaneous IV protocol was used to measure rates of channel deactivation in the absence and presence of 5 µM bbTBA. Channels were maximally activated by a step from –80 to +120 mV, and then returned to a series of repolarization potentials ranging from –200 to –30 mV. Representative tail currents elicited by repolarization to –100 mV in the absence (black) and presence (gray) of 5 µM bbTBA are illustrated. Tail currents were fitted with single exponential functions (dashed lines) in order to obtain deactivation time constants. (B) Deactivation time constants from 14 patches in the absence (black) or presence (gray) of 5 µM bbTBA were averaged (±SEM) and plotted as a function of repolarization voltage. (C) Deactivation time constants from a single patch comparing control (circles) with 5 µM bbTBA (triangles), 1 mM TBA (squares), or both blockers together (bowties) illustrate the speeding effect of TBA on deactivation, which persists in the presence of both blockers. The mild slowing of deactivation kinetics at positive potentials can be explained by the tendency of channels at these potentials to close via the same two-step pathway that state-dependent models would require.

Some channels are capable of trapping small molecules inside the pore cavity after closure of the activation gate (Armstrong, 1971; Strichartz, 1973; Neely and Lingle, 1986; Holmgren, Smith and Yellen, 1997). This would be represented by extension of the state- dependent model (Scheme 2) into C-O-OB-CB. Modeling confirms that this trapping model could also explain the mild slowing of deactivation by bbTBA and still assume that block is state dependent. Indeed, there is evidence that the internal cavity of BK channels is larger than that of most K⁺ channels (Li and Aldrich, 2004), and thus may be large enough to accommodate bbTBA with a closed (cytoplasmic) gate. If BK channels can trap bbTBA, then one would expect that a substantial fraction of open channels that are blocked during the test pulse will remain blocked immediately after rapid closure and reopening, and current will simply rise to steady-state block levels with minimal or no time dependence. However, we found no evidence for trapping of bbTBA inside BK channels (Fig. 7 ). Fig. 7 A shows a trapping experiment performed in 20 µM internal Ca²⁺, where three control pulses to +150 mV were followed by three pulses in the presence of 5 µM bbTBA. The interpulse interval was set to 5 ms at –200 mV, in order to close channels rapidly and minimize the possibility of bbTBA escaping from open channels, either before closing or during rare reopening events (P_o at –200 mV 0.0001; Horrigan and Aldrich, 2002). Fig. 7 A shows that time-dependent block remained intact for each test pulse. In the context of a state-dependent model of block, the persistence of the time dependence would suggest that channels do not remain blocked during the interpulse interval, i.e., channels cannot trap bbTBA and have to wait for blocker to exit before closing (in which case one would expect to see slowing of deactivation). Obviously, this interpretation is difficult to reconcile with Fig. 6. Alternatively, a state-independent model of block posits that time dependence simply reflects equilibration of channels to the change in test potential; one would not expect this to change for three identical test pulses.

View larger version (14K): [in this window] [in a new window]   Figure 7. BK channels show no evidence of trapping bbTBA inside the cavity after closure. (A) To test for trapping, channels were stepped from a holding potential of –200 mV to a test potential of +150 mV three times, separated by a 5-ms interpulse interval at –200 mV, first in a control solution containing 20 µM internal Ca2+ (black traces), and then in 5 µM bbTBA (gray traces). Traces were then superimposed (one control sweep, average of three sweeps in blocker) for comparison. (B) The trapping experiment was repeated in 4 µM internal Ca2+, where open probability at –200 mV was roughly an order of magnitude lower (0.00001; Horrigan and Aldrich, 2002), in order to minimize the possibility of escape of blocker from channels reopening during the 5-ms repolarization to –200 mV. In this experiment, the test potential was +200 mV, and the traces shown are averages of three (control) or four (bbTBA) sweeps. This experiment in 4 µM Ca2+ was repeated in eight different patches. (C) Fractional unblock (1 – IbbTBA/Icontrol) was measured in 100 µM internal Ca2+ either from steady-state currents (black triangles; n = 19 patches ± SEM) or peak tail currents (gray squares; n = 4 patches ± SEM) and plotted as a function of test voltage. The steady-state data are the high Po measurements displayed in Fig. 8 C. Steady-state data were fit with Eq. 3 either by Igor (dashed line; parameters ± 95% confidence interval were Kd(0) = 8.3 ± 1.2 µM and z = 0.14 ± 0.03) or by our final model (thick black line, Kd(0) = 8.5 µM and z = 0.15). The final model fit was then extrapolated to negative potentials. Fractional unblock computed from tail currents was also fitted (thin gray line) with parameters (±95% confidence interval): Kd(0) = 2.9 ± 1.8 µM and z = 0.12 ± 0.016. The observed level of block at negative potentials is much greater than steady-state predictions, indicating that bbTBA has not dissociated from channels at the time of closing. The persistence of time-dependent block after closure and reopening of blocked channels suggests that bbTBA is able to dissociate from closed channels during the 5-ms repolarization.

bbTBA Blockade Does Not Depend Strongly upon Open Probability
One can directly assay the state dependence of channel blockade by comparing the efficacy of block under conditions where P_o is high and low, while voltage is kept constant. The BK channel is particularly amenable to such experiments by virtue of its activation by both voltage and Ca²⁺. Thus, one can measure ionic current (and blockade) at a single test potential while activating channels to different levels of open probability with Ca²⁺. If bbTBA block requires channel opening, steady-state block should be maximal at high P_o and minimal at low P_o where only a few channels have reached the open state. Conversely, block that is independent of channel conformation should be equally effective at all levels of P_o. To discriminate between these possibilities, macroscopic steady-state fractional block was measured at several test potentials under a variety of different Ca²⁺ conditions representing a wide range of open probabilities (Fig. 8). Fig. 8 A illustrates two representative measurements of ionic current blockade at +90 mV from the same patch exposed to either 100 or 1 µM internal Ca²⁺, ±5 µM bbTBA. The relative P_o vs. voltage relationships for this patch (Fig. 8 B) show that open probability at this voltage is 1 or 0.25 under these conditions, respectively. It is apparent in Fig. 8 A that despite the large difference in open probability, fractional block appears roughly equivalent (although block at low P_o is 5% less effective). When fractional unblock is plotted as a function of test potential together with relative P_o for both Ca²⁺ conditions (Fig. 8 B), it is evident that fractional block changes modestly with test voltage, in accordance with a Woodhull model of voltage-dependent block, even between +90 and +180 mV where P_o changes dramatically. The voltage dependence of blockade is characterized further in Fig. 8 C.

View larger version (24K): [in this window] [in a new window]   Figure 8. Efficacy of macroscopic bbTBA blockade appears largely independent of open probability. (A) Representative BK currents measured from a single patch at +90 mV from a holding potential of –80 mV, ±5 µM bbTBA in either 100 µM internal Ca2+ (Po 1) or 1 µM internal Ca2+ (Po 0.25); fractional block computed from the steady-state currents was 50.1% or 44.7%, respectively. (B) Relative Po was estimated from normalized conductance voltage relationships obtained in the absence (filled symbols) and presence (open symbols) of 5 µM bbTBA, for both 1 µM internal Ca2+ (circles) or 100 µM internal Ca2+ (triangles) solutions. Relative conductance was calculated from tail current amplitudes measured at –80 mV, and then normalized and plotted as a function of test potential. Resulting Po-V curves were fit with a Boltzmann equation (Eq. 4) to yield parameters (±95% confidence interval): 100 µM Ca2+ (control/ +bbTBA), V1/2 = –40 ± 1.5 mV/–42 ± 2.0 mV and z = 1.7 ± 0.15/2.1 ± 0.32; 1 µM Ca2+ (control/+bbTBA), V1/2 = +113 ± 1.2 mV/+107 ± 2.6 mV, z = 1.5 ± 0.9/1.4 ± 0.18. Fractional unblock (IbbTBA/Icontrol) was computed from steady-state currents ± 5 µM bbTBA exposed to 1 µM internal Ca2+ (circles) or 100 µM internal Ca2+ (triangles), plotted as a function of voltage and fitted with Eq. 3, yielding the parameters (±95% confidence interval): 100 µM Ca2+, Kd(0) = 8.9 ± 0.6 µM and z = 0.13 ± 0.03; 1 µM Ca2+, Kd(0) = 9.1 ± 3.6 µM and z = 0.09 ± 0.08. Measurements in A and B were all made in the same patch. (C) Relative Po and fractional unblock (Iblock/Icontrol) were measured over a range of test potentials from each of 24 patches in solutions ranging from 0 to 100 µM Ca2+, and measurements of fractional unblock at each voltage were binned into Po categories of "low" (0 < Po < 0.2; crosses), "medium" (0.4 < Po < 0.6; circles), and "high" (0.8 < Po < 1.0; triangles). Within each Po category, fractional unblock was averaged at each test potential, plotted ± SEM as a function of voltage, and fitted with Eq. 3 (dashed lines) to yield parameters (±95% confidence intervals): low Po, Kd(0) = 10.1 ± 5.6 µM and z = 0.17 ± 0.13; medium Po, Kd(0) = 8.1 ± 2.8 µM and z = 0.16 ± 0.09; high Po, Kd(0) = 8.3 ± 1.2 µM and z = 0.14 ± 0.03. A fit to the final model of bbTBA block (Kd(0) = 8.9 µM and z = 0.15) is also illustrated with a solid line. (D) The same fractional unblock data were then binned into three separate test voltages: +60 mV (circles), +100 mV (triangles), and +150 mV (bowties), and each data point plotted individually versus relative Po estimated from the Po -V curve for that patch. Data points within each voltage category were then fitted with a linear equation. Macroscopic fractional unblock does not depend strongly upon open probability, although block may be slightly less effective at low Po.

Because the macroscopic measurements shown in Fig. 8 are subject to limitations such as voltage-dependent Ba²⁺ block (Cox et al., 1997) and difficulty in measuring small current amplitudes at low P_o, as well as potential errors in estimating open probability from macroscopic P_o-V curves, we performed similar experiments using microscopic measurements of fractional block (Fig. 9 ). The time course of a typical experiment is shown in Fig. 9 A. 10-s sweeps at +40 mV were recorded from an excised patch perfused with 2 µM internal Ca²⁺, which was alternated with 5 µM bbTBA several times before repeating the process with 4, 10, and 100 µM Ca²⁺ solutions ± 5 µM bbTBA. This procedure allowed us to monitor directly the stability of P_o over the duration of the experiment and ensure accurate measurement of P_o changes induced by blocker. The first two sweeps in the absence and presence of bbTBA for 2 µM Ca²⁺ (sweeps 1 and 2 in Fig. 9 A) are illustrated in Fig. 9 B. As shown in the top left panel of Fig. 9 B, P_o in 2 µM Ca²⁺ was 0.09; 100 ms of this record shown on an expanded time scale below illustrates that channel activity mainly consisted of short openings punctuated by flickery closing events. When 5 µM bbTBA was applied, P_o was reduced to 0.05, primarily due to a reduction in mean open time (Fig. 9 B, right). Fractional block at P_o 0.09 computed from the raw amplitude histograms in Fig. 9 C was 45%.

View larger version (26K): [in this window] [in a new window]   Figure 9. Microscopic steady-state block decreases slightly at low Po. (A) A typical experiment where block was evaluated at several different Ca2+ concentrations is illustrated. Each experiment consisted of several "trials," where block was measured at a particular Ca2+ concentration, beginning with the lowest value (2 µM). Within each trial, a control solution (open circles) was alternated with the corresponding blocker solution (+5 µM bbTBA, filled circles) several times while channel activity was monitored with 10-s sweeps to +40 mV. Po was calculated from each individual sweep by integrating Gaussian fits to raw amplitude histograms (Po = Po/Po + Pc). The illustrated time course allowed us to directly monitor Po during the course of an experiment. Trials consisting of acceptably stable sweeps were identified using the following selection criteria. For Po 0.15, each control record was required to be ±0.01 Po units of the preceeding control. For Po > 0.15, control Po values that were within 0.1Po unit were accepted (e.g., ±0.05). Thus, for any particular Ca2+ concentration, episodes of block were only accepted when sandwiched by stable control activity. After identifying stable records, raw amplitude histograms were constructed from all acceptable control records and blocker records within a trial (10–40 s total for each) and fitted with Gaussian functions in order to yield the average Po values. Fractional block at that Ca2+ concentration was calculated as 1 – PobbTBA/Pocontrol. Fractional block for a few experiments was also computed from bursts of activity ± bbTBA, such as those illustrated in B and D on an expanded time scale; percent block from these analyses was within 5% of that calculated from the complete dataset. Long closures were occasionally omitted from records. (B) Representative sweeps illustrating block at low Po (sweeps number 1 and 2 in A). The top row illustrates 4 s of recording in 2 µM internal Ca2+ (sweep 1) and 2 µM Ca2+ + 5 µM bbTBA (sweep 2). Average Po under these conditions for this experiment was 0.09 or 0.05, respectively. 100-ms sections (indicated by brackets) are shown on an expanded time scale below each trace. All sweeps in this figure were filtered at 2 kHz for illustration purposes. (C) Fractional block was calculated from the average raw amplitude histograms for the control (solid line) and 5 µM bbTBA (dashed line) data. For this experiment, at Po = 0.09, fractional block was 44.5%. (D) Block at high Po is illustrated by 500 ms of recording in 100 µM internal Ca2+ (sweep 3) or 100 µM Ca2+ + 5 µM bbTBA (sweep 4), where Po was 0.89 or 0.44, respectively. 100-ms sections (indicated by brackets) are shown below each trace on the same expanded time scale as in B in order to facilitate comparison with the traces in 2 µM Ca2+. (E) Fractional block computed from the raw amplitude histograms for this experiment at Po = 0.9 was 51.2%. The efficacy of microscopic block appears to decrease by 6% at low Po.

View larger version (8K): [in this window] [in a new window]   Figure 10. bbTBA blockade of BK channels closely matches predictions of a state-independent model of block. Experiments of type illustrated in Fig. 9 were repeated in 12 patches, and fractional block at +40 mV was plotted versus Po calculated directly from the raw amplitude histograms. Data from each experiment are indicated by a separate filled symbol. Open symbols represent measurements of block at two different Ca2+ concentrations with no washout to confirm stable Po. Crosses represent measurements of block made at only one Ca2+ concentration (stable Po confirmed with washout in two of three cases). Dashed lines represent predictions of fractional block as a function of Po made using parameters from our kinetic measurements of block at +40 mV in 100 µM internal Ca2+ (kON = 1.108 M–1s–1, kOFF = 498 s–1; Fig. 5, A and B) and Schemes 1 (final state independent) and 2 (state dependent). The solid line is a best fit of the data to the linear equation: Fractional Block = (0.073*Po) + 0.45. The 1.3-fold change in apparent affinity of block over a range of Po spanning nearly two orders of magnitude is not compatible with state-dependent block.

The mechanistic picture of bbTBA blockade that emerges from Figs. 8–10 is one where binding of bbTBA is enhanced to a small degree in the open state, but not gated in an absolute fashion by channel conformation. The difference in apparent affinity between the open and closed conformations results in a modest 7% change in the fraction of blocked channels over a range of P_o encompassing nearly two orders of magnitude. The final piece of evidence that we present against open channel block comes from returning again to the initial observation that bbTBA blockade is time dependent.

At high concentrations of bbTBA (75–100 µM), a third component of time-dependent block becomes apparent in the macroscopic record. Fig. 11 A illustrates the three kinetic phases of time-dependent block for currents at +90 or +150 mV in the presence of 75 µM bbTBA; current initially increases to a maximum, and then rapidly declines, and finally increases again to steady state. These complex kinetics are predicted by our final model of state-independent block, and, importantly, are not compatible with state-dependent block (Fig. 11 B). The data at +90 mV were roughly approximated by our final model (dashed black line). Only minor adjustment of those parameters was required to fit the steady-state level of blockade in this patch; we also added the assumption that bbTBA slows activation in order to more accurately describe the kinetics (solid red line). (It is important to note that, while we have no evidence to justify this particular adjustment, this slowing of activation was not required in order to reproduce the triphasic kinetics of block.) The data require that some fraction of channels start in the closed, blocked state, consistent with expectations of voltage-dependent, state-independent block. The smaller fraction of closed, blocked channels required to fit our data (35–50%, compared with predictions of 80%) may be due to the preference of bbTBA for the open state. Finally, the state-dependent version of our final adjusted model is grossly incompatible with the observed data, predicting a much larger change in fractional block during the time-dependent component, and biphasic kinetics (solid blue line).

View larger version (11K): [in this window] [in a new window]   Figure 11. Blockade at high concentrations of bbTBA has three kinetic components. (A) Ionic currents (average of 10 sweeps) in the presence of 75 µM bbTBA at +90 or +150 mV. Holding potential was –80 mV. Triphasic block kinetics become more obvious at higher potentials; current rises during the first phase, then falls during the second phase, and finally rises again to steady-state levels during the third phase. (B) The current trace at +90 mV (+75 µM bbTBA) is shown on an expanded time scale. Smooth lines represent model predictions. The final state-independent model of bbTBA blockade (illustrated in C) was able to reproduce general kinetic and steady-state features of block (black dashed line). Model parameters were = 2330 s–1 and ß = 24 s–1 for channel opening and closing, respectively (using single exponential fits to activation of control current at +90 mV and Po = 0.99, 1/ = + ß and Po = /( + ß)), Kd(0) = 9 µM, z = 0.15, and 50% channels initially in CB. Minor adjustment of these model parameters (Kd(0) = 11 µM, z = 0.15, 35% channels initially in CB) and adding the assumption that bbTBA slows activation (from 2,330 to 1,500 s–1) produced a better fit (solid red line). This adjusted state-independent model fits only when some fraction of channels are blocked at rest (compare with dashed red line where 100% channels start in C). Using the same adjusted parameters (Kd(0) = 11 µM, z = 0.15, 35% CB, = 1500 s–1, ß = 24 s–1), the state-dependent model (e.g., Scheme 2) is clearly incompatible with the observed kinetics of block (solid blue line). Importantly, the state-dependent model was never able to reproduce triphasic block kinetics, even with extensive alteration of parameters (including starting up to 100% of channels in the blocked state). (C) Occupancy of the closed (C, blue), open (O, red), open blocked (OB, black), and closed blocked (CB, green) states over time illustrates the origin of triphasic block kinetics. Initial conditions for this occupancy plot modeling block by 75 µM bbTBA at +90 mV were 50% C + 50% CB; the same rate constants that were used for modeling the solid red line in B were used, as illustrated in the inset. Triphasic time-dependent block is a direct result of rapid population of blocked states prior to equilibration of the open state, in direct contrast to state-dependent models that require that the slow C to O transition be rate limiting for block. The triphasic kinetics of block observed at high concentrations of bbTBA strongly suggest that blockade is not state dependent.