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# Gating properties conferred on BK channels by the beta3b auxiliary subunit in the absence of its NH(2)- and COOH termini.

### Author information

^{1}Department of Anesthesiology, Washington University School of Medicine, St. Louis, Missouri 63110, USA.

### Abstract

^{2}+ binding equilibria where K

_{c}, K

_{x}, and K

_{o}correspond to Ca

^{2}+ dissociation constants for channels either when closed (K

_{c}), following a voltage-dependent conformational change preceding channel opening (K

_{x}) or following channel opening (K

_{o}), where V(0) corresponds to the zero voltage equilibrium between C

_{1}and C

_{1}* at 0 Ca

^{2}+ and L(0) corresponds to the zero voltage equilibrium between C

_{1}* and O at 0 Ca

^{2}+. This model results in the following expression for steady-state open probability: 6 where D = [(1 + Ca/K

_{x})/(1 + Ca/K

_{o})]

^{4}and B = [(1 + Ca/K

_{c})/(1 + Ca/K

_{o})]

^{4}

_{.}Q

_{1}and Q

_{2}are the net charge associated with movement from C

_{1}to C

_{1}* and C

_{1}* to O

_{1}, respectively. Although can be viewed as a subset of a general 50-state model, it differs from the specific 50-state model evaluated by in that Ca

^{2}+ binding affinity is allowed to change as a consequence of voltage-sensor movement.

^{2}+ (•, tail; ○, peak) or 300 μM Ca

^{2}+ (♦, tail; ⋄, peak) for a representative patch expressing α alone. In each panel, the solid lines over the tail current G-Vs are the best fit of (see materials and methods), while lines over peak or steady-state current G-Vs simply connect the points. At 10 μM, V

_{0.5}= 48.3 mV, with

*k*= 17.7 mV; at 300 μM, V

_{0.5}= −31.4 mV, with

*k*= 17.2 mV. In B, both peak current and tail current G-V curves (symbols as in A) are plotted for α + β3b currents, along with the steady-state conductance (▴, 300 μM; ▵, 10 μM) determined at the end of each activation step. For tail current G-V curves, at 10 μM, V

_{0.5}= −18.6 mV, with

*k*= 15.9 mV; at 300 μM, V

_{0.5}= −49.3 mV, with

*k*= 18.1 mV. In C, peak, tail, and steady-state G-V curves (symbols as in A and B) are plotted as in B but for α + β3b-ΔC currents. At 10 μM, V

_{0.5}= −4.9.1 mV, with

*k*= 12.8 mV; at 300 μM, V

_{0.5}= −50.6 mV, with

*k*= 14.7 mV. In D, peak and tail current G-V curves (symbols as in A) are plotted for α + β3b-ΔN currents. For tail currents, a fit of yielded, at 10 μM, V

_{0.5}= 52.3 mV, with

*k*= 21.4 mV; and, at 300 μM, V

_{0.5}= −19.3 mV, with

*k*= 25.2 mV. A function with two Boltzmann terms () better fit the tail current G-V curves. For 10 μM, V1

_{0.5}= 42.0 mV (k

_{1}= 15.7 mV) and V2

_{0.5}= 108.0 (k

_{2}= 27.0 mV) with G

_{max1}contributing 72.8%. For 300 μM, V1

_{0.5}= −34.9 mV (k

_{1}= 14.6 nmV) and V2

_{0.5}= 50.4 (k

_{2}= 34.2 mV) with G

_{max1}contributing 67.4%.

_{2}- and COOH termini. In A, traces show currents obtained from an inside-out patch from a

*Xenopus*oocyte injected with cRNA encoding the mouse

*Slo*α subunit alone. Channels were activated by voltage steps from −100 to +180 mV after 20 ms at −140 mV; from left to right, panels show currents activated with 0, 1, 10, or 300 μM Ca

^{2}+. The voltage protocol is shown on the top. In B, traces show currents resulting from coexpression of α + β3b under conditions identical to those in A. In C, traces show currents resulting from α + β3b-ΔC coexpression, whereas, in D, currents reflect α + β3b-ΔN coexpression.

^{2}+ dependence of tail current conductance for different β3b constructs. In A, tail current G-V curves are plotted for 0 (⋄), 0.5 (♦), 1 (□), 4 (▪), 10 (○), 60 (•), and 300 μM Ca

^{2}+ (▵) for currents arising from α subunit alone. Each point shows the mean and SEM for a set of five patches. Values for V

_{0.5}are 167.1, 153.7, 143.1, 85.4, 43.2, −7.7, and −30.3 mV, while values for

*k*are 17.1, 18.5, 18.6, 19.2, 17.2, 17.6, and 18.0 mV for 0 through 300 μM, respectively. In B, tail current G-V curves are plotted as in A but for α + β3b currents for the same Ca

^{2}+ concentrations. Values for V

_{0.5}were 122.1, 95.6, 57.6, 37.1, −21.6, −35.0, and −53.3 mV, while values for

*k*were 16.4, 21.9, 18.4, 14.8, 15.3, 16.2, and 16.5 mV for 0 through 300 μM respectively. In C, tail current G-Vs are plotted for α + β3b-ΔC with values of V

_{0.5}of 115.1, 90.4, 68.3, 22.0, −29.7, −40.6, and −60.5 mV, and values of k of 15.7, 17.5, 14.9, 15.0, 14.2, 15.0, and 14.7 mV for 0 through 300 μM, respectively. In D, tail current G-V curves are plotted for α + β3b-ΔN. Solid lines show fits of for points at 0, 0.5, and 1 μM, and fits of for 4, 10, 60 and 300 μM. For fits of , values of V

_{0.5}were 178.7, 156.6, 124.6, 67.4, 41.4, 17.5, and −26.3 mV, and values for

*k*were 19.2, 17.2, 16.7, 16.5, 18.0, 33.0, and 25.4 mV, for 0 through 300 μM, respectively. For fits of , at 4 μM, with G

_{max1}contributing 42.5%, V

_{0.5}(1) = 66.1 mV (

*k*= 14.0 mV) and V

_{0.5}(2) = 110.1 mV (

*k*= 21.7 mV); at 10 μM, with G

_{max1}= 57.4%, V

_{0.5}(1) = 25.0 mV (

*k*= 15.1 mV) and V

_{0.5}(2) = 77.1 mV (

*k*= 27.8 mV); at 60 μM, with G

_{max1}= 68.9%, V

_{0.5}(1) = −23.1 mV (

*k*= 15.3 mV) and V

_{0.5}(2) = 56.7 mV (

*k*= 36.1 mV); and at 300 μM, with G

_{max1}= 66.2%, V

_{0.5}(1) = −45.8 mV (

*k*= 14.9 mV) and V

_{0.5}(2) = 37.9 mV (

*k*= 41.9 mV) In E, the mean values for the V

_{0.5}for activation for each construct (α, •; α + β3b, ○; α + β3b-ΔC, ♦; and α + β3b-ΔN, ⋄) are plotted as a function of Ca

^{2}+. Values for α + β3b-ΔN were taken either from the V

_{0.5}for a fit of a single Boltzmann or, at 10, 60, and 300 μM, from the more negative V

_{0.5}of the two Boltzmann components. Error bars indicate SD for each set of values with at least five determinations in each case. In F, the mean values for

*k*, the parameter for voltage dependence of activation, is plotted as a function of Ca

^{2}+ for α alone (•), α + β3b (○), and α + β3b-ΔC (♦).

_{2}terminus. In A, traces on the left show currents resulting from α alone, activated by a voltage-step to +160 mV in the presence of 300 μM Ca

^{2}+, followed by repolarization to potentials between +150 mV and –180 mV. Measurement of current levels 100 μs after the nominal imposition of the repolarizing voltage step resulted in the plot on the right, in which current amplitudes were normalized to the amplitude measured at +100 mV. In B, traces are currents resulting from expression of α + β3b subunits. Here, the instantaneous I-V is largely linear over the entire range, (but see , in this issue). In C, traces show currents resulting from α + β3b-ΔC subunits. The instantaneous I-V shows a small outward rectification. We attribute the differences in the examples in B and C primarily to patch-to-patch variability in the relative rates of activation and inactivation at a given set of activation conditions. In D, traces show currents resulting from α + β3b-ΔN. The instantaneous I-V curve exhibits marked outward rectification with the conductance at +100 mV being at least twofold greater than at −100 mV.

^{2}+, whereas at −40, −80, and −100 mV, the patch was bathed with 10 μM Ca

^{2}+. The dotted lines indicate the current level characteristic of α subunits alone, ∼250 pS. Even at +100 mV, α + β3b-ΔNΔC channels exhibit a flickery behavior, suggestive that a rapid blocking process is still present. For any individual channel burst, definition of an open level is unclear.

^{2}+. The top current trace shows the average current from 75 sweeps

**,**while the bottom trace shows the variance of all current values around the mean. In B, the current variance was plotted as a function of mean current at +60 mV (♦) and during repolarization to −60 mV (○). The initial slope of the variance versus mean relationship is steeper at +60 mV, indicative of a larger single-channel current amplitude. The solid lines are fits of in the materials and methods, where

*N*and

*i*are the fitted values for number of channels and single-channel current, respectively. At +60 mV,

*N*= 100.1 and

*i*= 6.1 pA, whereas at −60 mV,

*N*= 99.7 and

*i*= 4.0 pA. In C, mean current and variance determined for 90 sweeps are shown for the same patch with currents activated by a step to +140 mV with 10 μM Ca

^{2}+. In D, at +140 mV (♦),

*N*= 106.9 and

*i*= 17.1, whereas, at −60 mV (○),

*N*= 91.2 with

*i*= 4.2 pA. Currents were sampled at 5 μs per point at a bandwidth of 10 kHz. At +140 mV, the ensemble variance analysis would suggest that average open probability for these channels at 10 μM Ca

^{2}+ was 0.85, whereas at +60 mV, the average open probability was 0.79. These values are generally consistent with the near maximal activation of conductance observed in D for the α + β3b-ΔN currents at +60 mV. In E, estimates of average open channel current obtained by different methods are plotted as a function of voltage. Open symbols correspond to individual ensemble variance analysis estimates. Values were obtained from α + β3b-ΔNΔC (○), α + β3b (⋄), and α + β3b-ΔN (□) currents, with no obvious differences among constructs. Mean values (•, and SD) for all variance analysis estimates for the three constructs were also determined at each potential. Mean values were calculated based on 2–16 estimates at each potential. The plot also includes estimates (▴) of single-channel current amplitude from the amplitude histograms shown in . The solid line is an instantaneous I-V curve for the α + β3b-ΔN currents (see A in , in this issue) with the values normalized to the single-channel current value at +100 mV. The line with diamonds corresponds to the function: I(

*V*) = V · G/(1 + K(0)exp

^{−zFV/RT}), with G = 173 pS, K(0) = 0.7 and z = 0.2, suggesting a limiting single-channel conductance of 173 pS.

^{2}+. Error bars are SEM for seven patches. Lines with small dotted circles represent fits of to each G-V curve, whereas a solid line shows the fit of , and 300 μM Ca

^{2}+. In B, G-V curves obtained from α + β3b-ΔNΔC tail (B1) and peak (B2) currents (4 patches) are plotted along with the fits of and . In C, normalized peak (open symbols) and tail current G-V curves for α + β3b-ΔN are compared for 0 (♦, ⋄), 1 (▪, □), 10 (•, ○), and 300 μM Ca

^{2}+ (▴, ▵). For each patch, the maximum tail current conductance was normalized to the maximum conductance estimated from the peak current. Error bars for the tail current estimates are larger here than in A because of additional variability in the relative amount of maximal tail to peak current conductance among patches. Fits of and to the peak current G-V curves are shown for 10 and 300 μM Ca

^{2}+ to emphasize that fails to describe the G-V curves at higher Ca

^{2}+. In D, relative amplitude of peak and tail current G-Vs are compared for α + β3b-ΔNΔC currents with symbols as in C. In E, the normalized peak (solid symbols) and tail current G-V curves for α + β3b-ΔN currents obtained at 10 and 300 μM Ca

^{2}+ are overlaid to emphasize the difference in shape between peak and tail G-V curves that is particularly pronounced at higher Ca

^{2}+. In F, a corrected tail current conductance (•, 10 μM Ca

^{2}+; ▪, 300 μM Ca

^{2}+) at each potential based on the measured tail current conductance and the nonlinearity of the instantaneous I-V curves ( E) was determined for α + β3b-ΔN currents. At each potential, tail current conductances (as in E) were scaled by a factor defined by the idealized instantaneous I-V curve in , with the instantaneous conductance at −100 mV set to 1. Actual peak conductance values are also plotted (○, 10 μM; □, 300 μM).

^{2}+ binding affinity can account for the unusual shape of the α + β3b-ΔN G-V curves. In A1, points show G-V curves arising from α alone while the lines show the best fit with the 50-state model () in which voltage sensor movement does not affect Ca

^{2}+ affinity. Best fit values are given in . In A2, defined by the 15-state model () was used to fit the α alone G-V curves. With all parameters not constrained, the value for K

_{x}was indeterminate. Fixing K

_{x}near the value for K

_{c}yielded the fit shown by the solid line. In an alternative fit (dotted line), it was assumed that the charge moved during voltage-sensor movement (Q

_{1}) and that during the closed-to-open transition (Q

_{2}) were identical to that revealed by the fit to G-V curves arising from α + β3b-ΔN. In this case, the value for K

_{x}converged to a value near that for K

_{c}. Best fit values are given in . The fit corresponding to the line with open circles resulted when all parameters except K

_{c}and K

_{x}were constrained to values that resulted from fitting the α + β3b-ΔN curves in B2. In B1, G-V curves resulting from α + β3b-ΔN were fit with (50-state model). Two fits are shown: one in which the peak conductance was constrained to be 100%, and the other with all parameters unconstrained. In B2, G-V curves resulting from α + β3b-ΔN were fit with (15-state model), with all values unconstrained. In comparison to the best fit for α alone, values for K

_{x}approach that for K

_{o}. In C1, mean G-V values for α + β3b-ΔNΔC were fit with with all values unconstrained. In C2, G-V values for α + β3b-ΔNΔC were fit with , in one case with all values unconstrained (dotted line) and the other (solid line) with values for V(0) and L(0) constrained to those obtained in the fit to the α + β3b-ΔN data.

^{2}+ for each β3b construct. In A, on the left, currents resulting from expression of α alone in an inside-out patch were activated at 10 μM with the indicated voltage-protocol. Each current was fit with a single exponential function, and the currents were then normalized to the maximal current activated at each command potential. On the right, currents were activated at +100 mV with 1, 4, 10, 60, and 300 μM Ca

^{2}+. Currents were again normalized to the maximal current amplitude activated at the command potential. In B, similar normalized currents are shown for α + β3b. In C, normalized currents are shown for α + β3b-ΔC. These appear essentially identical to those for α + β3b. In D, normalized currents are shown for α + β3b-ΔN. Even at the strongest activation conditions (+180, 10 μM Ca

^{2}+ on the left and +100 mV, 300 μM Ca

^{2}+ on the right), the α + β3b-ΔN currents activate more slowly than any of the other constructs.

_{a}, for currents arising from expression of the α subunit alone is plotted as a function of command potentials for 1 (♦), 4 (⋄), 10 (•), 60 (○), and 300 (▪) μM Ca

^{2}+ for 5–7 patches at each [Ca

^{2}+]. Error bars indicate standard deviation. In B, τ

_{a}is plotted for α + β3b currents. Note the apparent faster time constant for α + β3b currents relative to α alone. Symbols in B–D are identical to those in A. In C, τ

_{a}is plotted for α + β3b-ΔC currents, showing the similarity with α + β3b currents. In D, τ

_{a}is plotted for α + β3b-ΔN currents. At all potentials and Ca

^{2}+, α + β3b-ΔN currents appear to activate more slowly than those arising from α alone. In E, apparent activation rates at +60 mV were calculated and plotted as a function of Ca

^{2}+ for each of the four sets of currents (α, ○; α + β3b, ▵; α + β3b-ΔC, ▴; and α + β3b-ΔN, •). Solid lines represent a fit of

*k*(Ca) =

*k*(0) 1

*k*

_{max}/(1 + ([Ca

^{2}+]/

*K*)

^{n}) where

*k(*0

*)*is the activation rate at 0 Ca

^{2}+,

*k*

_{max}is the maximal Ca

^{2}+-dependent increase in activation rate,

*K*is the concentration of half effect, and n is the Hill coefficient. For α, α + β3b, α + β3b-ΔC, and α + β3b-ΔN, respectively, the maximal

*k(*Ca

*)*was 3.24, 2.34, 2.18, and 0.96 ms

^{−1},

*K*was 54.7, 6.7, 7.8, and 37.8 μM, and

*n*was 1.4, 6.3, 4.5, and 1.01. Confidence limits on estimates of

*K*and

*n*were large, but at +60 mV the steeper Ca

^{2}+ dependence of the apparent activation rate for α + β3b and α + β3b-ΔC currents is clear. In F, apparent activation rates are plotted as in E but for currents measured at +120 mV. For α, α + β3b, α + β3b-ΔC, and α + β3b-ΔN, the maximal

*k(*Ca

*)*was 6.6, 4.9, 4.6, and 1.8 ms

^{−1}, respectively,

*K*was 29.1, 5.5, 5.6, and 15.6, respectively, and n was 0.99, 1.33, 1.39, and 0.99, respectively. At +120 mV, the relatively faster intrinsic rate of activation of the β3b and β3b-ΔC constructs compared with +60 mV reduces the effect of inactivation on the apparent activation rate. Note that at both +60 and +120 mV, the limiting maximal

*k(*Ca

*)*for α + β3b-ΔN currents is less than that for any of the other constructs.

_{2}- and COOH-terminals. In A, normalized tail currents are shown for the α subunit alone. On the left, traces show tail currents evoked with 300 μM Ca

^{2}+ at potentials from −180 to −30 mV (voltage protocol on the top). On the right, traces show tail currents evoked at −100 mV with 0, 1, 4, 10, 60, and 300 μM Ca

^{2}+. Points show every second or fourth digitized data value, while lines are single exponential fits to the current decay. For −180, −150, −120, −90, −60, and −30, the fitted τ

_{d}was 0.16, 0.21, 0.26, 0.38, 0.56, and 1.01 ms, respectively. For 0, 1, 4, 10, 60, and 300 μM, τ

_{d}was 0.12, 0.21, 0.30, 0.30, 0.52, and 0.85 ms, respectively. In B, traces show normalized tail currents for α + β3b currents. Note the delay before the exponential decay of the tail current observed at more positive deactivation potentials and higher Ca

^{2}+. For −180, −150, −120, −90, −60, and −30, τ

_{d}was 0.41, 0.58, 0.70, 1.33, 2.16, and 4.8 ms, respectively. For 0, 1, 4, 10, 60, and 300 μM, τ

_{d}was 0.25, 0.34, 0.53, 0.46, 0.88, and 1.24 ms, respectively. In C, normalized tail currents are shown for α + β3b-ΔC. Again note the delay in current decay before the onset of exponentiality. For −180, −150, −120, −90, −60, and −30, the fitted τ

_{d}was 0.39, 0.48, 0.71, 1.2, 2.32, and 2.74 ms, respectively. For 0, 1, 4, 10, 60, and 300 μM, τ

_{d}was 0.25, 0.39, 0.60, 0.93, 1.76, and 1.96 ms, respectively. In D, normalized tail currents are shown for α + β3b-ΔN. Note the absence of the delay before exponentiality. For −180, −150, −120, −90, −60, and −30, the fitted τ

_{d}was 0.29, 0.37, 0.47, 0.67, 0.96, and 1.51 ms, respectively. For 0, 1, 4, 10, 60, and 300 μM, τ

_{d}was 0.30, 0.47, 0.58, 0.60, 1.21, and 1.56 ms, respectively.

_{d}) obtained from single exponential fits to the tail current time course () are plotted as a function of repolarization potential for currents from α subunit alone for 0 (⋄), 1 (♦), 4 (□), 10 (▪), 60 (○), and 300 (•) μM. In B, τ

_{d}is plotted as a function of voltage for α + β3b currents with symbols as in A. In C, τ

_{d}is plotted as a function of voltage for α + β3b-ΔC currents. In D, τ

_{d}is plotted as a function of voltage for α + β3b-ΔN currents. In E, the deactivation rate measured at −80 mV is plotted as a function of Ca

^{2}+ for each construct (α, ⋄; α + β3b, ♦; α + β3b-ΔC, ○; and α + β3b-ΔN, •). In F, the deactivation rate measured at −160 mV is plotted as a function of Ca

^{2}+ with symbols as in E. Current deactivation for α alone is ∼1.5–2-fold faster than for currents resulting from any β3b construct.

_{0.5}for activation at low Ca

^{2}+ to higher values and results in a weaker apparent voltage dependence of activation. In A, traces show α + β3b currents activated with the indicated voltage-protocol before (left column) and after (right column) removal of inactivation by brief trypsin application to the cytosolic face of the inside-out patch. Concentrations were 0, 1, and 10 μM Ca

^{2}+ as indicated. In B, normalized tail current G-V curves are plotted for a different set of five α + β3b patches before (open symbols) and after (solid symbols) trypsin application for 0 (•, ○), 1 (▪, □), 10 (♦, ⋄), and 300 (▴, ▵) μM Ca

^{2}+. Solid lines are fits of . Before trypsin, values for V

_{0.5}were 132.3, 108.9, 21.1, and −51.2 mV for 0, 1, 10, and 300 μM Ca

^{2}+, respectively. After trypsin, V

_{0.5}values were 170.2, 148.0, 50.1, and −41.3 mV for 0, 1, 10, and 300 μM, respectively. Average value of

*k*before trypsin for this set of patches was 16.5 ± 1.3 mV (mean ± SD) and, after trypsin, 23.9 ± 2.6 mV. The solid line with smaller circles was the fit of to currents obtained at 10 and 300 μM Ca

^{2}+. For 10 μM Ca

^{2}+, G

_{max1}= 60.0, k

_{1}= 14.8 mV, V1

_{0.5}= 34.3 mV, G

_{max2}= 40.0, k

_{2}= 26.6 mV, and V2

_{0.5}= 89.3 mV. For 300 μM, G

_{max1}= 70.2, k

_{1}= 17.7 mV, V1

_{0.5}= −54.9 mV, G

_{max2}= 29.8, k

_{2}= 47.1 mV, and V2

_{0.5}= 53.2 mV. In C, mean values for V

_{0.5}obtained from fits of at four different [Ca

^{2}+] are plotted as a function of [Ca

^{2}+] for the five patches with α + β3b currents shown in B both before (•) and after (○) trypsin was applied to remove inactivation. Error bars are SD. The V

_{0.5}for four patches (♦) expressing only α alone was also determined from the same batch of oocytes.

^{2}+ by a step to +40 mV before and after trypsin application. At +40 mV with 10 μM Ca

^{2}+, there is no detectable time-dependent inactivation but just current rectification. On the right, the normalized currents are overlaid to show the faster apparent activation before trypsin-mediated removal of inactivation. In B, traces on the left show currents activated with 1 μM Ca

^{2}+ at +100 mV. The normalized currents on the right show a markedly faster time-to-peak of currents before trypsin application. In C, time constants of current activation were plotted as a function of command voltage for currents activated with either 1 or 10 μM Ca

^{2}+ either before (○, 1 μM; ⋄, 10 μM) or after (•, 1 μM; ♦, 10 μM) trypsin-mediated removal of inactivation. With inactivation intact, there is a faster apparent rate of current activation at low and moderate [Ca

^{2}+]. Points are mean and SD for three patches.

### Publication Types, MeSH Terms, Substances, Grant Support

#### Publication Types

#### MeSH Terms

- Animals
- Electrophysiology
- Ion Channel Gating/physiology*
- Kinetics
- Large-Conductance Calcium-Activated Potassium Channels
- Oocytes
- Patch-Clamp Techniques
- Potassium Channels/physiology*
- Potassium Channels, Calcium-Activated*
- Xenopus

#### Substances

- Large-Conductance Calcium-Activated Potassium Channels
- Potassium Channels
- Potassium Channels, Calcium-Activated

## PubMed Commons