Wilkens CM , Aldrich RW .

	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, zδ = 0.148 ± 0.024.
	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.
	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 (α = 2254 s−1) and closing (β = 46 s−1) rates were determined from a single exponential fit to the control data and assuming Po ∼ 0.98, using 1/τ = α + β and Po = α/(α + β). Kinetics of TBA block were estimated from Li and Aldrich (2004): Kd(0 mV) = 1 mM and zδ = 0.2. bbTBA block was modeled using parameters for the final model (Kd(0) = 9.9 μM and zδ = 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.
	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/β (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 × 108 ± 0.258 × 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.
	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 × 108 M−1s−1 and zδON = 0.012 ± 0.093, or with the final model (solid line) with parameters: kON(0) = 1.0 × 108 M−1s−1 and zδON = 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 zδOFF = 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 zδ = 0.14 ± 0.08; kinetic, Kd = 5.5 ± 1.1 μM and zδ = 0.11 ± 0.07, or the final model (solid lines) with parameters: steady-state, Kd = 5 μM and zδ = 0.15; kinetic, Kd = 6 μM and zδ = 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.
	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.
	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 zδ = 0.14 ± 0.03) or by our final model (thick black line, Kd(0) = 8.5 μM and zδ = 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 zδ = 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.
	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 zδ = 0.13 ± 0.03; 1 μM Ca2+, Kd(0) = 9.1 ± 3.6 μM and zδ = 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 zδ = 0.17 ± 0.13; medium Po, Kd(0) = 8.1 ± 2.8 μM and zδ = 0.16 ± 0.09; high Po, Kd(0) = 8.3 ± 1.2 μM and zδ = 0.14 ± 0.03. A fit to the final model of bbTBA block (Kd(0) = 8.9 μM and zδ = 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.
	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.
	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.
	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 α = 2330 s−1 and β = 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/τ = α + β and Po = α/(α + β)), Kd(0) = 9 μM, zδ = 0.15, and 50% channels initially in CB. Minor adjustment of these model parameters (Kd(0) = 11 μM, zδ = 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, zδ = 0.15, 35% CB, α = 1500 s−1, β = 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.

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