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Figure 1. Single Slo3 channels exhibit complex open current level behavior. Slo3 channels were activated by repeated voltage steps to +100 (A), +140 (B), or +180 mV (C) from a holding potential of 0 mV. Example traces are shown at three different time bases. Horizontal bars under traces in A–C indicate segments of current displayed at a faster time-base below. Dotted lines on the expanded time-base segments indicate the 0 current level and the current level corresponding to a 110-pS single channel conductance. At the bottom of A–C, the average currents from sets of 40 sweeps are shown in each case, showing that a steady-state current level is rapidly achieved. Sample frequency, 100 kHz; filter, 10 kHz. pH 8.5. In D–F, histograms generated from all current values after the first 2 ms of each depolarizing step are shown. The time constant of macroscopic current activation at pH 8.5 over this voltage range is ∼1 ms (Zhang et al., 2006). D–F also display the best fit (dotted line) of a Gaussian to the baseline current values. At both +140 and +180 mV, two clear maxima are observed in the open current levels. Each histogram was generated from a set of forty 100-ms sweeps.
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Figure 2. Open current levels can be approximated by two or three Gaussian components. In A, total amplitude histograms for currents activated at either +140 mV (left) or +180 mV (right) were fit (blue line) with three Gaussian components (one baseline and two open level components). At +180 mV the two open level components do not adequately describe the data. In B, the total amplitude histograms from A were fit with four Gaussian components (red line, one baseline and three open level components) and the individual Gaussian components are displayed (filled squares, sum of baseline and smallest open level component; open diamonds, open level 1; open squares, open level 2). The insets to each panel illustrate the residuals associated with the best fit for either the three (blue line) or four (red line) Gaussian fit. Although the four Gaussian fit better describes the data, the residuals are still not symmetrical around 0, indicative that a sum of Gaussian components does not fully describe the nature of these distributions.
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Figure 3. Empirical description of Slo3 open current amplitudes. In A, the mean amplitudes for the two largest components in the total amplitude histograms are plotted as a function of voltage for a set of four patches. Lines are the best fit through each set of points of i = g*V, yielding conductance estimates of 108.5 ± 5.1 pS (O2) and 56.6 ± 1.7 pS (O1) for the two largest components of the histograms. In B, the total areas of components O1 and O2 was determined from histograms as in Fig. 2 and 100*O1/(O1 + O2) was calculated and plotted as a function of voltage. In C, average mean single channel current was determined from the areas and mean amplitude of O1 and O2, yielding an average single channel conductance of 77 ± 2 pS (mean ± 90% confidence limits). In D, an effective PO at each voltage was calculated based on the fraction of time channels were either in O1 or O2.
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Figure 4. Analysis of Slo3 current variance allows estimates of g and N. In A and B, the current variance is plotted against mean currents for sets of 100 activation steps to five different voltages at pH 8.5 (A) and three different voltages at pH 7.6 (B), all from one patch. Each color corresponds to individual σ2/I values at a different voltage as labeled on each panel. The activation step duration was 20 ms, sampled at 100 kHz, and filtered at 10 kHz. Lines are the best fit curves for Eq. 2 for each of the five voltages at pH 8.5. The fitted parameters were g = 68.2 ± 0.4 pS (mean ± 90% c.l.) and N = 2152.4 ± 51.9 channels. In C, the σ2/I relationships for both pH 7.6 (red) and pH 8.5 (black) for +280 mV show that pH has no effect on the average single channel current (i). Lines show expected σ2/I relationships for the indicated values of N with i = 19.1 pA. Values of N ∼20% smaller than the best value result in parabolic relationships that clearly deviate from the observed σ2/I values.
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Figure 5. Binned σ2/I data also indicate that Slo3 unitary current varies in an ohmic fashion. A–F display the average variance for sets of mean current values grouped into bins of identical width. Error bars indicate the standard deviation for the variance estimates in a given bin. For voltages from +120 through +280 mV, σ2/I relationships are shown for both pH 8.5 (black) and pH 7.6 (red). The lack of effect of pH on the initial slope of the σ2/I relationship indicates that pH has no direct effect on the average single channel current. Fitting Eq. 2 simultaneously to all the σ2/I values (six voltages and two values of pH) yielded g = 77.1 ± 2.1 pS and N = 2349.5 ± 302.8 channels, resulting in the solid lines in each panel. In A, solid lines are also shown for N = 2000, N = 1500, and N = 800, indicating that smaller estimates of N (larger effective Po) result in clear deviation from the observed data.
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Figure 6. The dependence of Slo3 unitary current amplitude on voltage. Estimates of the unitary current amplitude from σ2/I analysis are plotted as a function of voltage for both pH 8.5 and pH 7.6. Individual estimates at each voltage were obtained as described in the text. For comparison, red symbols correspond to average unitary current estimates from single channel measurements. Lines correspond to the best fit of i(V) = g*V – b.
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Figure 7. The pH and voltage dependence of Slo3 Po. In A, values of N obtained from fitting families of σ2/I relationships were used to define the estimated Po at different pH and voltage. Po was defined for eight patches at pH 8.5 (filled diamonds), for which N was defined from simultaneous fit of at least five different σ2/I relationships. For five of those patches, Po was also determined for four voltages at pH 7.6 (filled circles). Error bars correspond to SD. For comparison estimates of Po at pH 8.5 based on single channel current measurements are included (red circles). In B, the macroscopic G-V curves for Slo3 activation at pH 8.5 (red circles) and 7.6 (red diamonds) were normalized to the unitary current Po estimates in A (blue symbols) by setting the macroscopic conductance estimate at pH 8.5 and +280 mV identical to the unitary current estimate at the same condition. In C, following the procedure used in B, all macroscopic conductance values at pH of 6.0, 7.0, 7.4, 7.6, 7.8, 8.0, 8.5, and 9.0 (Zhang et al., 2006) were normalized to absolute Po estimates. Blue symbols represent estimates from σ2/I analysis as in A.
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Figure 8. Nonohmic behavior of tail current amplitude at negative potentials is associated with nonohmic reductions in apparent average single channel current amplitude. In A, binned σ2/I relationships for four sets of 100 steps to +240 mV are displayed along with the best fit of Eq. 1 with i = 21.15 pA; N = 1146. In B, the tail currents (10 kHz filtering) after repolarization to −60 (black), −100 (red), −140 (blue), and −180 (green) mV from the initial step to +240 mV are shown on a logarithmic time base to emphasize the two exponential nature of the tail current decay. The peak of the tail current is essentially unchanged between −100 and −180 mV. In C, the binned σ2/I relationships for each of the tail currents shown in B are shown. N was constrained to the value obtained in B (N = 1146) and i obtained from the fit of Eq. 1. Apparent single channel current amplitude does not increase at potentials more negative than −100 mV, despite the increase in driving force. In D, the estimated i from examples like that in C are plotted as a function of voltage (red symbols), along with the estimates of i obtained from σ2/I analysis at positive potentials. Blue symbols correspond to records filtered at 50 kHz and red symbols to those filtered at 10 kHz.
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Figure 9. Filtering accounts for apparent reductions in single channel current amplitude, but does not compromise estimates of net current flux. In A, tail currents decaying with deactivation time constants (τd) of either 10 (left) or 50 μs were simulated and digitally filtered with 10, 20, or 50 kHz 8-pole Bessel filter settings. In the bottom panel, peak tail current amplitude as a function of τd is plotted at different filter settings. In B, the theoretical reduction of peak tail current determined from simulations as in A based on measured Slo3 τd values (blue line, 50 kHz Bessel; red line, 10 kHz Bessel) are compared with the single channel estimates from σ2/I analysis (10 kHz, red circles; 50 kHz, blue circles; Fig. 8 D). Tail current amplitude estimates were normalized to the single channel current amplitude at +240 mV. Solid black line shows a strictly ohmic relationship. In C, the impact of filtering (10 kHz) on idealized single channel closures (top traces) after repolarization is illustrated. After the time of repolarization, examples show channels closing at times ranging from 5 to 100 μs. With 10 kHz filtering, channels closing in <20 μs would be barely detectable based on half-amplitude detection. In D, the effect of filtering on detection of average current is shown. On the top, idealized single channel openings are shown either without or with (red line) 5 kHz filtering. On the bottom, the total charge passing through channels in the two cases is compared showing that filtering does not reduce the total current arising from any individual channel opening.
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Figure 10. Openings of Slo3 channels at positive and negative potentials. Channels were activated by voltage steps to potentials of +100 (A), −100 (B), +200 (C), and −200 (D) mV from a holding potential of 0 mV. Dotted lines correspond to the expected current level for the maximal open level component for one (110 pS; Figs. 2 and 3) or two open (220 pS) channels. Brief, small amplitude openings are observed at −100 and −200 mV. 10 kHz filtering. Horizontal lines above or below traces in panels A–D define segments shown at expanded time base in E. C, O1, and O2 correspond to the closed current level and the 110 pS level for one (O1) or two open channels (O2).
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Figure 11. Comparison of total amplitude histograms at positive and negative potentials reveals that Slo3 conductance at pH 8.5 is appreciable at negative potentials. In A–D, total amplitude histograms for traces from the patch in Fig. 9 were generated for each of four voltages and fit with some number of Gaussian components. In E and F, histograms for currents at −100 and −200 mV were rescaled to emphasize the open channel activity. In G, the average current during all sweeps at a given voltage were converted into a conductance normalized to the value at +200 mV (black circles). For comparison, normalized macroscopic conductance (blue circles) and Po estimated from σ2/I measurements (red circles) are overlaid. In H, log(G) is plotted as a function of voltage. Lines represent limiting slope fits of G(V) = G(0)*exp(zFV/RT) for the two most negative voltages (−200 and −100 mV, zL ∼ 0.075 e) and the three most positive voltages (−100–200 mV, zJ ∼ 0.354 e).
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Figure 12. Tails of Slo3 channel openings after repolarization. Slo3 openings at pH 8.5 in a single channel patch were activated by 10-ms depolarizations to +240 mV from a holding potential of 0 mV, with a subsequent repolarizing step to −80 mV. Sweeps either immediately preceding or following a sweep with an opening at the end of the 10-ms step were used for subtraction of uncompensated Cm and leak. Traces on the right show the tail openings for the traces on the left at a faster time base. Sample traces were selected to emphasize the openings and closures after repolarization, except in the case of the third trace from the top. On average, tail openings were not observed in over half of those sweeps in which a Slo3 channel was active at the end of the depolarization.
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Figure A1. σ2 estimates of single channel properties for channels with two conductance levels. In A, predicted σ2/I relationships for a population of 1,000 channels in which each channel can occupy a main conductance level (i1) of 20 units and a second level, i2, as indicated. Fractional occupancy in each level is 0.5. In each case, a parabolic relationship is expected, but the maximal possible value of I when all channels are open depends on the relative amplitudes of i1 and i2. The curve in red approximates the expectation based on the single channel properties of Slo3. In B, the values of i (solid circles) and Po (diamonds) based on applying Eq. 1 to the parabolas in A are given for different values of i2. For estimates of i, the estimated value is given as a percentage of the nominal value of i1, while, for Po, the value given is the percentage by which the apparent Po defined from application of Eq. 1 will underestimate the true Po. For comparison, the weighted-mean estimate of single channel current based on the relative amplitudes and fractional occupancy in each of two open states based on amplitude histograms is given (open circles). For the case applicable to Slo3 (red symbols), i estimated using Eq. 1 will be within 10% of the weighted-mean estimate of average single channel current, while the Po estimate will underestimate the true Po by ∼10%. In C, the impact of changing the relative occupancy, k, in i2 and i1 is considered, while in D, the impact of k on parameter estimates using Eq. 1 are shown.
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