Lingle CJ , Zeng XH , Ding JP , Xia XM .

DK46564 NIDDK NIH HHS , R01 DK046564 NIDDK NIH HHS

	Scheme S1.
	Scheme S2.
	Scheme S2a.
	Scheme S3.
	Figure 1. Ca2+ and voltage-dependent of activation of currents resulting from α + β3b coexpression. In A–D, each set of traces shows currents obtained from an inside-out patch from a Xenopus oocyte in which cRNAs encoding human β3b and mouse Slo α subunits were coinjected. Channels were activated by the indicated voltage-protocol with (from top to bottom) 0, 1, 10, and 300 μM Ca2+. Panels on the right show conductance measured from peak (⋄), steady-state (•), or tail currents (○; measured at 110 μs after the onset of the repolarizing voltage step). In all cases, maximal tail current at −120 mV greatly exceeds the steady-state level of current at +180 mV, indicative of a very rapid unblocking of channels. Also note the similarity in maximal tail current amplitude over all Ca2+. Fitted values of to the tail current G-V curves were as follows: for 0 μM, V0.5 = 120.8 mV and k = 15.22 mV; for 1 μM Ca2+, V0.5 = 104.6 mV and k = 14.32 mV; for 10 μM Ca2+, V0.5 = −19.6 mV and k = 15.75 mV; and for 300 μM Ca2+, V0.5 = −49.2 mV and k = 18.50 mV.
	Figure 2. α + β3b currents rapidly recover from inactivation. Currents through α + β3b channels were activated in the presence of 10 μM Ca2+ by the voltage protocol shown on the top. Scale bars apply to the expanded time base traces displayed on the right. In A, traces compare tail currents after repolarization to −80 mV at the end of either a 1- or 40-ms step to +160 mV. The left traces show the complete current record, whereas the right-hand traces show the tail currents on an expanded time base. Despite the fact that outward current at the end of the 1-ms step to +160 is more than twice that at the end of the 40-ms step to +160 mV, maximal tail current amplitude after repolarization is actually larger in the latter case. Furthermore, the current decay time is markedly slower. For currents activated with the brief steps to +160 mV, symbols plot every twentieth digitized point. In B, tail currents at −80 mV are compared after either a 2-ms or a 40-ms step to +160 mV. The tail current amplitude is similar in both cases despite the fact that outward current at +160 mV differs markedly.
	Figure 3. Slowing of deactivation as a function of activation step duration is not unique to α + β3b currents. In A1–D1, outward current was activated with 10 μM Ca2+ by a step to +100 mV from a holding potential of −120 mV. For each sweep, the step to +100 mV was varied from 0 to 9.5 ms in 0.5-ms increments, before a repolarizing step to −80 mV. Currents resulted from the following constructs: (A) α alone; (B) α + β3b-ΔN; (C) α + β3b; and (D) α + β3b-ΔC. For these constructs, a direct step to −80 mV from −120 mV results in minimal inward current activation. A2–D2 show the tail currents on an expanded time base. For α alone (A2) and for α + β3-ΔN (B2), tail currents become slower with command step duration, but the decay qualitatively appears to begin a single exponential time course immediately after the repolarizing step. For α + β3b (C) and α + β3b-ΔC (D), tail current decay also appears to slow with command step duration. However, in contrast to the noninactivating currents, as the command step is increased in duration there is an increase in a shoulder of tail current that precedes the onset of an exponentially decaying current. For all panels, a P/N leak subtraction procedure was used (see materials and methods).
	Figure 4. The dependence of tail current deactivation time constant on command step duration. The protocol shown in Fig. 3 was used to activate tail currents at different times after a step to +100 mV. In all cases, single exponential functions were fit to the decaying phase of the tail currents. In A, means and standard deviations of deactivation time constants measured with 10 μM Ca2+ are plotted as a function of activation step duration. Each construct exhibits a similar factional change in decay time as the command step is increased from 0.5 to 9.5 ms. In B, time constants and standard deviations were determined in 300 μM Ca2+. Prolongations are similar for each of the constructs. In both A and B, each point corresponds to a minimum of five patches. In C, a protocol similar to that used in Fig. 3 was simulated for a MWC 10-state activation model using rates similar to those given in Table derived from of Cox et al. 1997. In D, tail current time constants measured from C are plotted as a function of command step duration.
	Figure 5. Inactivation is associated with the appearance of a rapid unblocking component in the tail current. In A, a protocol similar to that used in Fig. 2 was used to examine tail currents at repolarization potentials of −40, −80, −120, and −160 mV with 10 μM Ca2+. In the right-hand traces of A, points show every twentieth digitized value for currents resulting from a 40-ms activation step. In B, normalized tail currents after the 2-ms activation step (from A) are shown for the indicated repolarization potentials. Only every fifth digitized value (50 μs) is displayed. At the most positive repolarization potential (−40 mV), there is a pronounced lag before the tail current begins to decay in an exponential fashion. At more negative potentials, after a brief capacitative current, the current begins an exponential decay fairly rapidly. Lines correspond to a fitted two exponential function, A1 · exp(−t/τu) + A2 · exp(−t/τd) + offset, where τu corresponds to an unblocking relaxation, and τd corresponds to the deactivation time course. At −160 mV, τu = 0.087 ms and τd = 0.44 ms; at −120 mV, τu = 0.113 ms and τd = 0.98 ms; at −80 mV, τu = 0.172 and τd = 1.50 ms; and at −40 mV, τu = 0.134 and τd = 2.16 ms. In C, normalized tail currents activated after a 40-ms activation step are shown over the same range of repolarization potentials. At both −40 and −80 mV, there is a distinct increase in tail current after the capacitative transient. At both −120 and −160 mV, the shoulder of current before the onset of exponential decay is more pronounced than in B. Open symbols again show every fifth digitized data value, whereas solid lines correspond to a two exponential fit to the decay time course. Fitted values were as follows: at −160 mV, τu = 0.128 ms and τd = 0.57 ms; at −120 mV, τu = 0.173 ms and τd = 1.42 ms; at −80 mV, τu = 0.232 ms and τd = 2.415 ms; and at −80 mV, τu = 0.183 and τd = 5.64 ms.
	Figure 6. Effects of trypsin on α + β3b currents. In A, currents in an inside-out patch expressing α + β3b channels were activated by the indicated voltage protocol with 10 μM Ca2+. In B, the tail currents at potentials from 0 mV to −180 mV are displayed at higher magnification. In C, trypsin was briefly applied to the same patch shown in A resulting in removal of inactivation, whereas D shows the tail currents after trypsin at higher magnification. After trypsin, peak outward current at +160 mV appears to activate more slowly and is markedly larger. In contrast, tail current amplitudes exhibit a more modest increase after trypsin. The calibration bar in A also applies to C, while B and D share a calibration bar. Tail current amplitude at more positive repolarization potentials exhibits a larger increase following trypsin than those at more negative potentials. After trypsin application, the tail current decay follows a relatively simple exponential time course, whereas, before trypsin, there is a brief rising phase. In E, time constants of deactivation (τd) are plotted for α + β3b currents before (•) and after (○) trypsin and compared with τd for currents arising from α alone (□). Tail currents for intact α + β3b were fit with a two exponential function to approximate the fast unblocking shoulder of current and then the deactivation of current. Points show means and standard deviations for at least four patches.
	Figure 7. Trypsin removes the unblocking relaxation observed in α + β3b tail currents. In A, panels from top to bottom compare tail currents at the four indicated repolarization potentials, before and after (line with points) trypsin application. Despite the extensive unblocking that occurs during repolarization, the ability of trypsin to increase the tail current amplitude suggests that even at negative potentials some voltage-dependent block of channels persists. At −120 mV, tail current amplitudes before trypsin are ∼70% of those after trypsin application. For the traces after trypsin application, the points correspond to every fifth digitized value. The horizontal bars overlaid on the rising phase of the tail currents indicate the calculated level of tail current expected at the repolarization potential assuming an instantaneous ohmic step from the residual level of current at +160 mV. A small segment of the steady-state–inactivated current at +160 mV is shown for the traces before trypsin application. Filter, 10-kHz bandwidth; sampling period, 10 μs. In B, each pair of traces was normalized to the same peak amplitude. For the trace obtained before trypsin application, the deactivation time course was fit with the following two exponential function: A1 · exp(−t/τu) + A2 · exp(−t/τd) + offset. At −120, −100, −80, and −60 mV, the unblocking relaxations were 0.18, 0.13, 0.20, and 0.24 ms, respectively, whereas the subsequent deactivation time constants were 0.40, 0.57, 0.71, and 0.98 ms, respectively. After trypsin, a fit of A1 · exp(−t/τd) + C yielded time constants of 0.42, 0.52, 0.74, and 1.06 ms.
	Figure 8. Properties of instantaneous current-voltage (I-V) curves following repolarization from a steady-state–inactivated condition. In A, currents were activated by the indicated voltage protocol at various Ca2+ (0, 1, 4, and 10 μM Ca2+). For all Ca2+, there is a large, immediate nonohmic increase in tail current indicative of rapid unblocking from inactivation. In B, the current was measured 100 μs after the nominal time of the repolarizing voltage step and normalized to the current measured with the step to −100 mV. The shape of the I-V curve is identical for all Ca2+. In C, the mean and standard deviation for the instantaneous I-V curve from five patches at 10 μM Ca2+ are plotted, along with the best fit of . For the fit with solid circles all values were unconstrained yielding Gmax = 30.5 ± 24.0; K2(0) = 51.7 ± 49.44 and Q2 = 0.154e ± 0.020e. For the fit with diamonds, Gmax was constrained to 2.0 with K2(0) = 2.27 ± 0.045 and Q2 = 0.209e ± 0.005e. For the open circles, Gmax was constrained to 1.0 with K2(0) = 0.504 ± 0.07 and Q2 = 0.341e ± 0.03e.
	Figure 9. Despite fast unblocking, α + β3b tail currents exhibit a residual voltage-dependent blockade at negative potentials. In A, the instantaneous I-V curve obtained with 10 μM Ca2+ (○) is replotted (from Fig. 8 C) along with the fit for the case where Gmax was constrained to 2.0 (•). Predictions based on the values given in Table and used for the simulations in Fig. 15 are also shown (□; also see Online Supplemental Materials available at http://www.jgp.org/cgi/content/full/117/6/583/DC1). In B, based on the values for K2(V) obtained from the fit shown in A, fractional occupancy in O*n (○) and In (•) was calculated and plotted as a function of the potential at which the tail current was measured. In C, tail current amplitudes (normalized to −100 mV) were measured for three patches before (•) and after (○) removal of inactivation with trypsin. In D, the ratio (○) of tail current amplitude at 100 μs before trypsin application to that after removal of inactivation is plotted as a function of repolarization potential. Note the correspondence of these values to those for O*n in panel B. The solid line is a fit of the following equation:fV=fmax1+K0exp−zFVRT,where fmax = 0.613, K(0) = 3.32 and z = −0.503.
	Figure 10. Paired pulse recovery protocols reveal a slow recovery from inactivation despite nearly complete recovery from block in the peak tail current. Recovery from inactivation was assessed using the indicated voltage-protocol. The duration of the initial inactivating step to +160 mV was 40 ms. Recovery steps were varied from 50 μs to 40 ms, although not all are displayed. In A and B, currents were activated with 10 μM Ca2+, and the recovery potential was either −80 mV (A) or −120 mV (B). In C and D, selected traces from A and B are shown on a faster time base. For faster time records, traces correspond to recovery intervals of 0, 0.05, 0.25, 0.5, 1.0, 2.0, and 5.0 ms. Triangles draw attention to the amount of outward current present immediately after completion of the capacitative transient associated with the second test step to +160 mV. For brief recovery intervals, this instantaneous level of current is identical to the steady-state level of current at +160 mV. With longer recovery intervals, the amplitude of the instantaneous current indicated by the triangles increases even as the tail current at −80 or −120 mV is beginning to decrease. The dotted line indicates the zero current level. In C, the percent recovery measured from the paired pulse protocol is plotted as a function of the recovery duration at each of three recovery potentials with 10 μM Ca2+. The solid lines represent single exponential fits to the recovery time course. At −80 mV, a two exponential fit gave a somewhat better description of the recovery time course, but, at more negative potentials, a two exponential time course did not substantially improve the quality of the fit. At −160 mV, τr = 0.5 ms; at −120 mV, τr = 0.61 ms; and at −80 mV, τr = 0.67 ms. In D, the time course of recovery in the paired pulse protocol is shown for 300 μM from the traces in Fig. 11 B. At −160 mV, τr = 0.84 ms; at −120 mV, τr = 1.00 ms; and at −80 mV, τr = 1.04 ms.
	Figure 11. α + β3b channels pass through different open states during recovery from inactivation. Currents displayed in A–C were evoked with the portion of the voltage protocol shown above C. An example of the full current waveform (for α + β3b) is shown above B1. Steady-state current activation was achieved at +140 mV, and the patch was stepped to −120 mV for either 100 μs (top traces) or 500 μs (bottom traces) before a subsequent depolarization to potentials between −120 and +140 mV. In A1, traces show currents resulting from only α subunits activated with 300 μM Ca2+. The current amplitude was measured at a time point 80 μs after the nominal time of the final voltage step. In A2, instantaneous current amplitudes were normalized for five patches to current amplitudes elicited at +100 mV with 300 μM. At 300 μM Ca2+, current has decayed ∼25% more at 500 μs than at 100 μs. Similar normalized I-V curves were obtained with 10 μM Ca2+. In all cases, the instantaneous I-V curve is essentially linear from −100 through +100 mV. In B1, similar tests were performed on α + β3b currents with 300 μM Ca2+. Note the larger amplitude of instantaneous current at positive voltages after 500 μs at −120 mV. In B2, instantaneous current amplitudes were normalized as in A2 for five patches with 300 μM Ca2+. Instantaneous currents activated at 100 μs are inwardly rectifying, whereas those activated at 500 μs approach linearity. In C1, a similar experiment was done on patches expressing α + β3b-ΔN. In C2, the instantaneous I-V curves obtained with 300 μM are similar for both 100- and 500-μs recovery steps.
	Figure 12. Instantaneous I-V curves for α + β3b currents change as a function of duration of the activation step. In A, α + β3b currents were activated with 10 μM Ca2+ with the voltage protocol shown on the top, except the command step duration was varied as indicated on the figure. Traces on the right are faster time base records of the traces on the left focusing on the properties of currents after repolarization. The vertical bars show the time points at 0 and 80 μs relative to the nominal time of the voltage-step. For the 200-μs activation step, note that currents after repolarization to voltages negative to zero are more closely spaced than those positive to zero, indicative of the intrinsic outward rectification. Sampling period, 10 μs; filter, 10 kHz. In B, current amplitudes were measured at the 80-μs time point after repolarization for each voltage, normalized to the trace at −100 mV, and plotted as a function of repolarization potential.
	Figure 13. Kinetic characterization of α + β3b currents. In A, inactivation time constants (τi) were measured over a range of voltages for currents activated with either 10 (•) or 300 μM (○) Ca2+. Each point represents values for 11–14 patches with error bars showing the standard deviation. Diamonds indicate τi measured from the simulated currents (see Supplemental Materials, Figure S3 available at http://www.jgp.org/cgi/content/full/117/6/583/DC1) for 10 μM (♦) and 300 μM (⋄) Ca2+. The dotted line was calculated from with values from Table . In B, the fast unblocking component observed in tail currents was measured from fits of A1 · exp(−t/τ1) + A2 · exp(−t/τ2) + B to the α + β3b tail currents as in Fig. 5 and Fig. 7. The fast unblocking time constants plotted here were from measurements made at either 10 μM (•) and 300 (○) μM Ca2+ (error bars are the standard deviation). The dotted line corresponds to the expectations for the fast unblocking time constant from values in Table assuming that describes τu. Triangles are fitted τu values from simulated currents (see Fig. 15) for 10 μM (▵) and 300 μM (▴) Ca2+. In C, time constants for recovery in outward current amplitude measured from the paired pulse protocol of Fig. 10 are plotted as a function of recovery potential for 10 μM (•, five patches) and 300 μM (○: three patches) Ca2+. For comparison, values for current deactivation of α + β3b currents at 10; ♦, seven patches) and 300 μM Ca2+ (⋄, six patches) are also shown. Error bars indicate SD. The similarity of deactivation time constants and the recovery in amplitude from the paired pulse protocol suggests that similar rate-limiting transitions are involved for each.
	Figure 14. Families of G-V curves obtained from both steady-state and tail current measurements do not distinguish between Fig. 1 and Fig. 2. Tail current amplitudes and steady-state current amplitudes were measured in one patch at 0, 0.5, 1, 4, 10, and 300 μM Ca2+. The normalized conductance is plotted as a function of command potential with tail current measurements in the left column (A1 and B1) and steady-state current estimates (A2 and B2) on the right. In A, both panels were fit simultaneously with the expanded MWC version of Fig. 2 defined by and . KC = 10.11 ± 0.75; K0 = 0.66 ± 0.05; L(0) = 1775.74 ± 1280; Q = 1.26e ± 0.13; K1(0) = 0.31 ± 0.10; Q1 = 0.44e ± 0.14e; K2(0) = 2.17 ± 3.6; Q2 = 0.19e ± 0.21. In B, both panels were fit simultaneously with similar equations defined by Fig. 1, assuming essentially instantaneous recovery from I to O at the tail current potential. KC = 11.20 ± 0.17; K0 = 0.75 ± 0.04; L(0)=1096.3 ± 243; Q = 1.41e ± 0.045; K1(0) = 0.71 ± 0.14; Q1 = 0.342e ± 0.04.
	Figure 15. Fig. 2 predicts currents that exhibit properties similar to those observed for α + β3b currents. In A, Fig. 2 (with parameters in Table ), assuming 10 μM Ca2+, was used to simulate currents with the indicated protocol (as in Fig. 2). Tail currents were compared at either −80 mV (A1) or −160 mV (A2), after either a short (1 ms) or longer (10 ms) activation step. Single exponential fits to the decay phases yielded time constants of 1.23 and 1.24 ms, for the shorter and longer activation steps, respectively. In A2, tail current was elicited at −160 mV. Time constants of deactivation were 0.227 ms (longer step) and 0.221 ms. In B, a paired-pulse protocol (as in Fig. 10) was used to model the recovery from inactivation with Fig. 2 (values from Table ; 10 μM Ca2+). Points show each simulated value (10 μs). The tail current exhibits the rapid nonohmic unblocking, followed by a slower unblocking. After the shorter recovery steps (500 μs), a subsequent depolarization to +160 mV results in rapid reblock with only a small excess of current over the previous steady-state level of block. Longer recovery steps result in an increase in the initial amount of current observed during the step to +160 mV, even as the tail current at −80 mV decreases. For the transition rates between O* and I in Table , at short recovery times the step to +160 mV also results in a 10–20-μs rapid spike of current associated with the rapid reblocking of channels from O* to I. Currents were simulated at 10 μs per point, and the spike of current lasted 1–2 points. In C, the indicated protocol (as in Fig. 11) was used to simulate currents assuming 10 μM Ca2+. In the middle panel, a 100-μs recovery step to −120 mV preceded a subsequent step to potentials between −120 and +180 mV. In the bottom panel, a 500-μs step to −120 mV was used to produce recovery from inactivation. In D, the instantaneous I-V from the traces in C were determined by measuring current values 30 μs after the nominal end of the recovery steps. Values were normalized to current amplitudes at −100 mV. At 30 μs, the spike of reblocking observed in the simulated currents is complete. The I-V curve becomes more linear after the 500-μs recovery step (•), which is indicative of greater occupancy of On. Simulation frequency: 100 kHz.

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