Tang QY , Zeng XH , Lingle CJ .

GM 066215 NIGMS NIH HHS , R01 GM066215 NIGMS NIH HHS

	Figure 1. Steady-state block of BK currents by bbTBA. (A) BK currents were activated by steps to +180 mV with 0 Ca2+ (1), 4 µM Ca2+ (2), or 100 µM Ca2+ (3), along with 0, 1, 5, or 20 µM bbTBA. (B) GV curves generated from steady-state current levels were determined for each Ca2+ concentration (1, 0 µM; 2, 4 µM; 3, 100 µM) in the presence of various concentrations of bbTBA, and all curves were fit simultaneously with a strict open-channel blocking model (Eq. 12). Details of fitting are given in Materials and methods and Results. The optimal fit (red lines) for the open-channel block (OB) assumption yielded Kbo = 4.0 ± 0.32 µM with zb = 0.06 ± 0.01 e. (C) The same GV curves displayed in B were simultaneously fit to Eq. 13 with the constraint that Kbo = Kbc and zo = zc. In this case, Kbo = Kbc = 4.7 ± 0.3 µM with zb = 0.07 ± 0.1 e. Blue ovals highlight regions of the curves in which the fitted curves deviate markedly from the observed results, with the OB model doing poorly at low Ca2+, and the CB–OB model being inadequate at higher Ca2+.
	Figure 2. Current simulations with different blocking models. (A) Families of traces show control currents (no bbTBA) simulated with the indicated voltage protocol and either 4 µM Ca2+ (left) or 300 µM Ca2+ (right) using the 10-state activation model (Fig. S1 A). (B) Currents were simulated with classical open-state block in conjunction with the 10-state activation model (Scheme 1a). The slower onset of block in comparison to models with block of closed states reflects the coupling of inactivation to activation. (C) Traces show currents activated by the same conditions but with blockade defined by the full state–independent blocking model (Scheme 2a) with Kbo = Kbo and zo = zc. Note the prominent triphasic currents at 4 µM Ca2+. (D) Traces show currents simulated with Scheme 3a (block depends on activation of at least one voltage sensor) as well as prominent triphasic current relaxations at 4 µM.
	Figure 3. Models in which block is coupled to voltage sensor movement can account for differential ability of OB and CB–OB models to fit data at low and high Ca2+. (A) GV curves were generated with Scheme 1a, both with 4 µM Ca2+ (left) and 300 µM Ca2+ (middle). Simulations were done with nominal blocker concentrations of 0.14-, 0.57-, and 2.86-fold the effective Kb. Blue lines correspond to the best fit of a strictly open-channel block model (Eq. 8 with W = 100,000), and red lines correspond to the best fit of a completely state-independent CB–OB model (Eq. 8 with W = 1). On the right, the difference between OB–CB (Eq. 8 with W = 1) summed residuals measured for all [bbTBA] at each voltage and the OB summed residuals (W = 100,000) is plotted as a function of voltage. Points on the upper half of such plots indicate that the fit of the OB model (W = 100,000) yielded larger deviations than the W = 1 assumption. In this case, W = 1 yielded poorer fits both at 4 (filled circles) and 300 µM (open circles). (B) GV curves were generated from currents simulated using Scheme 2a (Kbo = Kbc and zo = zc). In this case, the W = 1 assumption fits the GV curves better at both 4 and 300 µM. (C) GV curves were generated with Scheme 2b (zc = 0 e) and fit as above. Again, the CB–OB equation provides a better fit both at 4 and 300 µM Ca2+. (D) GV curves were generated with Scheme 3a (Kbo = Kbc and zo = zc) and fit as above. The right-hand panel indicates that the GV curves at 4 µM were somewhat better fit with the CB–OB model, whereas at 300 µM, the standard OB model provided a better fit. Similar results were obtained with Scheme 3b (zc = 0 e).
	Figure 4. Coupling block of closed and open states to voltage sensor movement improves fit of GV curves at both 4 and 300 µM Ca2+. (A) GV curves were generated from steady-state currents in a set of patches in which the blocking effects of 0, 1, 5, and 20 µM bbTBA were examined at both 4 and 300 µM. The full set of GV curves was then fit to Eq. 13, corresponding to a block with a completely state-independent blocking scheme (2a) for channels activated in accordance with a full allosteric activation scheme (Horrigan and Aldrich, 2002). Scheme 2a provides a poor fit (SSQ = 0.0417/pt) to the GV curves, particularly at 20 µM bbTBA and 300 µM Ca2+ (blue circle). Kbc = Kbo = 7.48 ± 0.43 µM (zc = zo = 0.17 ± 0.02 e). (B) GV curves were fit with the open-channel block model (Eq. 12; Scheme 1a). Kbo = 5.94 ± 0.39 µM (zo = 0.13 ± 0.02 e); SSQ/pt = 0.0525. Deviations between the data and the fit are particularly apparent at 20 µM bbTBA and 4 µM Ca2+ (blue circle). (C) The GV curves were fit with Eq. 14 for Scheme 3a, in which block depends on movement of at least one voltage sensor. Kbo = Kbc = 6.36 ± 0.27 µM (zo = zc = 0.14 ± 0.01 e), with SSQ/pt = 0.0219. For D–I, fitted curves correspond to schemes in which Kbo ≠ Kbc. In D and E, both zo and zc varied independently, whereas in F and G, zc = 0.0 e. (D) For Scheme 2′, the best fit to the GV curves yielded Kbo = 6.00 ± 0.3 µM, zo = 0.095 ± 0.02 e, Kbc = 45.8 ± 35.9 µM, and zc = 0.81 ± 0.21 e, with SSQ = 0.0140/pt. (E) For Scheme 3′, Kbo = 6.01 ± 0.27 µM, zo = 0.10 ± 0.02 e, Kbc = 8.1 ± 6.7 µM, and zc = 0.44 ± 0.23 e, with SSQ = 0.0131/pt. (F) For Scheme 2b′, with zc constrained to 0 e, Kbo = 6.36 ± 0.45 µM, zo = 0.15 ± 0.02 e, and Kbc = 21.4 ± 12.2, with SSQ = 0.0453/pt. The blue circles highlight the poorly fit region. (G) For Scheme 3b′, zc = 0 e, Kbo = 6.48 ± 0.29 µM, zo = 0.13 ± 0.01 e, and Kbc = 2.34 ± 0.38, with SSQ = 0.0192/pt.
	Figure 5. Differences in fractional unblock of BK channels by bbTBA between 4 and 300 µM Ca2+ are not supportive of fully state-independent block. (A) From measurements of macroscopic conductance (Fig. 1), the fractional unblock (=G(bbTBA/G(control)) with 5 µM bbTBA was determined over the full range of voltages for both 300 µM Ca2+ (red circles) or 4 µM Ca2+ (blue circles) and compared with GVs for current activation. Over the range of +20 to +60 mV, the fractional unblock at 4 µM Ca2+ is larger than that for 300 µM Ca2+, whereas fractional unblock with 300 µM Ca2+ approaches 1.0 at the most negative activation voltages. (B) Predictions for simple open-channel block (Scheme 1a) are illustrated. GV curves at 4 (open circle) and 300 (closed circle) µM Ca2+ are plotted along with GV curves in the presence of bbTBA (blue with 4 µM Ca2+ and red with 300 µM Ca2+). Fractional unblock is also plotted for 4 µM (blue circle) and 300 µM (red circle) at each voltage. (C) Similar plots for currents generated with Scheme 2a show that fractional unblock is identical for both 4 and 300 µM Ca2+ at each voltage. (D) The relationships for Scheme 2b, in which closed-channel block is voltage independent, are shown. The limiting fractional unblock at negative voltages reflects the voltage independence of closed-channel block. (E) Block and fractional unblock were determined from currents simulated using blocking constants derived from simultaneous fitting of GV curves to Scheme 2b (Fig. 4 G, with Kbc of ∼3 Kbo). (F) Predictions derived from currents simulated with Scheme 3a are plotted. (G) Predictions based on Scheme 3b (zc = 0.0 e) are plotted. (H) Predicted block and fractional unblock are shown based on currents simulated with blocking constants from simultaneous fitting of GV curves to Scheme 3b (Fig. 4 H, with Kbo = 3 Kbc).
	Figure 6. The dependence of fractional unblock on Po may not discriminate among various state-dependent blocking models. Fractional unblock was determined based on generation of families of Po versus voltage curves over a range of Ca2+ assuming various blocking schemes. (A) Dotted and solid lines correspond, respectively, to dependence of fractional unblock on Po for +60 and +100 mV, based on the open-channel block model given by Scheme 1a. Filled and open circles correspond to predictions based on Scheme 2a at +100 and +60 mV, respectively. (B) For Scheme 2b, fractional unblock exhibits a slight dependence on Po. (C) For Scheme 2b′, based on values derived from the fit of GV curves (Fig. 4 G), fractional unblock exhibits a strong dependence on Po. (D) Fractional unblock is plotted as a function of Po for Scheme 3a. (E) Fractional unblock is plotted as a function of Po for Scheme 3b. (F) Fractional unblock is plotted as a function of Po based on fitted values for Scheme 3b′ (Fig. 4 H), exhibiting largely Po-independent fractional unblock.
	Figure 7. 100 µM bbTBA has no inhibitory effect on NPo at voltages over which voltage sensor activation is minimal. (A) Po-V curves are plotted based on a full Horrigan-Aldrich activation scheme for 30 µM Ca2+ (black line) along with predictions for block in the presence of 100 µM bbTBA for either Scheme 1a (open-channel block; dotted line), Scheme 2a (state-independent block; blue line), or Scheme 3a (block dependent on voltage sensor movement; red line). The state-independent Scheme 2a predicts the same percent block at positive potentials and at potentials where voltage sensors are inactive, whereas Schemes 1a and 3a predict no change in NPo when voltage sensors are inactive. (B) Channel openings were monitored with 30 µM Ca2+ at −150 mV before a step to +20 mV either in the absence (black) or presence (red) of 100 µM bbTBA. 100 µM bbTBA produces >90% block of BK current at +20 mV, with minimal obvious effect at −150 mV. (C) Expanded time base records from the traces in B are shown during the periods at −150 mV. (D) Histograms of the current amplitudes of all digitized time points during the recording at −150 mV in the absence (black) and presence (red) of 100 µM bbTBA are plotted, with the bottom panel showing the same data on a different scale. bbTBA results in an increase in NPo in this patch.
	Figure 8. Block by bbTBA results in complex multicomponent relaxations. (A) Currents were activated with the indicated voltage protocol (top), with 10 µM Ca2+ in the presence of 75 µM bbTBA. Each trace is the average of 30 individual runs. Dotted red lines indicate the average current level at the end of each voltage step to highlight the marked undershoot that can occur after the initial rapid onset of block. (B) In a different patch, the same voltage protocol was used to activate BK currents either with 4 (top) or 300 µM Ca2+ (bottom), in both cases with 75 µM bbTBA. At 4 µM, dotted lines indicate steady-state current levels to highlight the undershoot after initial rapid block. With 300 µM Ca2+, no undershoot is observed.
	Figure 9. Triphasic relaxations arise from closed-channel block, but do not clearly distinguish among different models of closed-channel block. (A) These traces replot Fig. 8 A to allow comparison to simulated currents. Red traces correspond to +240 mV. (B) Currents were simulated using Scheme 2a with activation rates given in Table I, with the effective [blocker] = 5.71 * Kdo, with zo = zc = 0.2 e. Top traces correspond to 4 µM Ca2+ and the bottom traces to 300 µM. When zo = zc = 0.1 e, the triphasic relaxations were not as obvious. (C) Currents were simulated with Scheme 2b with zc = 0.0. No triphasic relaxations are observed. (D) Currents were simulated with Scheme 2b′ but with a ratio of Kdo/Kbc based on fitted values from Fig. 4 F. Again, no triphasic relaxation is observed. (E) Currents were simulated with Scheme 3a with zo = zc = 0.1 e. (F) Currents were simulated with Scheme 3b (zo = 0.1 e and zc = 0.0 e). (G) Currents were stimulated with values corresponding to the fitted values of Scheme 3b′ from Fig. 4 G.
	Figure 10. Fractional availability of current in the presence of bbTBA exhibits voltage independence at negative potentials. (A) Slo1 currents from excised inside-out patches were activated by the indicated voltage protocol (top; prepulse voltages from −300 to +100 mV with 40-mV increments) with 4 µM of internal Ca2+ and 20 µM bbTBA. The peak amplitude of the rapidly decaying current exhibits little change until prepulse voltages of 0 mV or more positive. Red trace corresponds to a −300-mV prepulse and blue to a +60-mV prepulse. (B) In the same patch, currents were activated with 4 µM Ca2+ along with 75 µM bbTBA. Red trace, −300-mV prepulse; blue trace, −20-mV prepulse. (C) The peak current amplitudes are plotted as a function of prepulse potential for both 20 µM (open circles) and 75 µM (filled circles) bbTBA. Red lines correspond to fits of a Boltzmann function with Vh = 64.9 ± 54.4 mV (z = 0.62 ± 0.33 e) and 22.9 ± 34.9 mV (z = 0.46 ± 0.13 e) for 20 and 75 µM bbTBA, respectively. (D) Normalized fractional availability was determined based on the fit of the Boltzmann function in C, better illustrating the leftward shift in availability with the increase in bbTBA. (E) The same protocol was used to activate currents in 100 µM Ca2+ (a different patch) with 20 µM bbTBA. The peak current at −100 mV (blue trace) shows some reduction compared with −300 mV (red trace). (F) The same patch was exposed to 75 µM bbTBA, producing more rapid and complete block. (G) The peak current is plotted as a function of prepulse potential either with 20 µM bbTBA (Vh = −39.4 ± 3.3 mV and z = 0.73 ± 0.06 e) or 75 µM bbTBA (Vh = −72.7 ± 4.5 mV and z = 0.72 ± 0.09 e). (H) The normalized fractional availability curves for the data in G are replotted.
	Figure 11. Dependence of BK fractional availability during bbTBA block on [Ca2+] and [bbTBA]. (A) Currents were activated with 4 µM of internal Ca2+. Control GV curves in the absence of bbTBA were generated from tail currents (open circles), and then fractional availability was determined either with 20 µM (filled circles) or 75 µM (diamonds) bbTBA using the protocol shown in Fig. 9. For 20 µM bbTBA, Vh = 67.1 ± 3.6 mV with z = 0.76 ± 0.02 e, whereas for 75 µM bbTBA, Vh = 5.1 ± 3.9 mV with z = 0.59 ± 0.01 e. The activation GV yielded Vh = 97.7 ± 0.7 mV (q = 1.32 ± 0.07 e). (B) Fractional availability and activation were defined in patches bathed with 100 µM of internal Ca2+. With 20 µM bbTBA (filled squares), Vh = −32.6 ± 1.33 mV (z = 0.88 ± 0.03 e) and, for 75 µM bbTBA (filled triangles), Vh = −58.4 ± 1.4 mV (z = 0.80 ± 0.02 e). The activation GV (open squares) yielded Vh = 22.7 ± 1.15 mV (q = 0.98 ± 0.04 e). For each condition, five to six patches were used. (C) Curves from A and B are replotted to show the shift in fractional availability with 20 µM bbTBA as [Ca2+] is increased from 4 to 100 µM. (D) Curves from A and B are replotted to show the shift in fractional availability with 75 µM bbTBA with increases in [Ca2+] from 4 to 100 µM.
	Figure 12. Fractional availability predictions for various models favor the idea that block of closed channels depends on voltage sensor movement. (A) Currents were simulated (10-state activation model) with the indicated voltage protocol (top left) for nominal 4 µM Ca2+ in the absence of blocker. Conditioning voltages were stepped in 20-mV increments, although for display purposes, only 40-mV increments are shown. (B) Currents were simulated with Scheme 1a, the open-channel block model. Red highlights traces (and voltage in red) in which the available fraction of current is ∼0.5. Half-availability occurs near +80 mV, and at voltages negative to +40 mV, there is no additional increase in current availability. (C) Currents were simulated for Scheme 2a. No saturation in fractional availability is observed down through −300 mV. (D) Currents simulated with Scheme 2b exhibit saturation in fractional availability with half-availability around 60–80 mV. (E) Currents simulated with Scheme 3a showed half-availability near +20 mV with clear saturation. (F) Currents simulated with Scheme 3b showed half-availability near +40 mV with clear saturation. (G) The activation GV for 4 µM Ca2+ (filled black circles) is plotted along with normalized fractional availability curves for the peak transient currents for different schemes, as labeled. The voltage dependency of availability for Schemes 1a (red squares) and 2b (blue circles) yield values comparable in magnitude to that of activation (z of ∼0.9 e). For Scheme 2a (red circles), the voltage dependence mirrors that of channel block (z of ∼0.2 e). For Schemes 3a (red diamonds) and 3b (blue diamonds), the magnitude of the voltage dependence is less than that predicted for open-channel block, characteristic of bbTBA of Slo1 current.
	Figure 13. bbTBA causes slight tail current prolongation at higher Ca2+, but not at 4 µM Ca2+. (A) BK currents were activated by steps to +180 mV from a −100-mV holding potential with 4 µM of internal Ca2+. Both 5 (black) and 20 µM (red) cause appreciable reduction both in outward current at +180 mV and tail current at −150 mV. (B) Tail currents in A were normalized to the peak tail current amplitude showing no difference in time course. (C) Deactivation time constants are plotted as a function of tail current potential for control and 5- and 20-µM bbTBA conditions. (D) Currents were activated by steps to +100 mV with 300 µM of internal Ca2+, with tail current at −150 mV. (E) Tail currents in D were normalized to the peak current amplitude and the baseline for an exponential fitted to the decay phase, showing the slowing of deactivation and a slight hook of unblock in the current before deactivation. (F) The time constant of deactivation is plotted for the same three conditions as shown in C. The time constants in 5 and 20 µM bbTBA were indistinguishable from each other, but clearly were slowed relative to control time constants.
	Figure 14. Absence of slowing of tail current deactivation is not strongly diagnostic among different versions of closed-channel block models. (A) Simulated tail currents were generated with Scheme 1a at −200 mV in the absence of blocker and then with effective 1×, 2×, and 10× increments of [blocker] (50, 100, and 500 kf) for both 4 µM Ca2+ (1) and 300 µM Ca2+ (2). At each concentration, sets of simulated traces show net current for 1,000 channels (left) and normalized tail currents (right). The trace in red highlights the normalized tail current in the absence of blocker. (B) Simulated tail currents are shown for Scheme 2a under the same conditions as in A. Note that for the highest [blocker] producing an almost 90% reduction in tail current amplitude, there is a noticeable unblocking hook, although changes in the time constant of deactivation are minimal. (C) Simulated tail currents are shown for Scheme 2b (zc = 0 e). There is minimal tail current prolongation and any unblocking hook is reduced compared with Scheme 2a. (D) Tail currents were simulated for a Scheme 2b′ model with parameters based on Fig. 4 F. (E) Tail currents were simulated with Scheme 3a. (F) Tail currents were generated with Scheme 3b. (G) Tail currents were simulated with Scheme 3b′ with parameters from the fit of the GV curve in Fig. 4 G.

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