Zhang X et al. (2001), Allosteric regulation of BK channel gating by C...

XB-ART-8134

J Gen Physiol 2001 Nov 01;1185:607-36. doi: 10.1085/jgp.118.5.607.

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Allosteric regulation of BK channel gating by Ca(2+) and Mg(2+) through a nonselective, low affinity divalent cation site.

Zhang X , Solaro CR , Lingle CJ .

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The ability of membrane voltage to activate high conductance, calcium-activated (BK-type) K(+) channels is enhanced by cytosolic calcium (Ca(2+)). Activation is sensitive to a range of [Ca(2+)] that spans over four orders of magnitude. Here, we examine the activation of BK channels resulting from expression of cloned mouse Slo1 alpha subunits at [Ca(2+)] and [Mg(2+)] up to 100 mM. The half-activation voltage (V(0.5)) is steeply dependent on [Ca(2+)] in the micromolar range, but shows a tendency towards saturation over the range of 60-300 microM Ca(2+). As [Ca(2+)] is increased to millimolar levels, the V(0.5) is strongly shifted again to more negative potentials. When channels are activated by 300 microM Ca(2+), further addition of either mM Ca(2+) or mM Mg(2+) produces similar negative shifts in steady-state activation. Millimolar Mg(2+) also produces shifts of similar magnitude in the complete absence of Ca(2+). The ability of millimolar concentrations of divalent cations to shift activation is primarily correlated with a slowing of BK current deactivation. At voltages where millimolar elevations in [Ca(2+)] increase activation rates, addition of 10 mM Mg(2+) to 0 Ca(2+) produces little effect on activation time course, while markedly slowing deactivation. This suggests that Mg(2+) does not participate in Ca(2+)-dependent steps that influence current activation rate. We conclude that millimolar Mg(2+) and Ca(2+) concentrations interact with low affinity, relatively nonselective divalent cation binding sites that are distinct from higher affinity, Ca(2+)-selective binding sites that increase current activation rates. A symmetrical model with four independent higher affinity Ca(2+) binding steps, four voltage sensors, and four independent lower affinity Ca(2+)/Mg(2+) binding steps describes well the behavior of G-V curves over a range of Ca(2+) and Mg(2+). The ability of a broad range of [Ca(2+)] to produce shifts in activation of Slo1 conductance can, therefore, be accounted for by multiple types of divalent cation binding sites.

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Species referenced: Xenopus laevis
Genes referenced: kcnma1

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	Scheme S1.
	Scheme S2.
	Figure 1. Similar enhancement of Slo1 current activation by high concentrations of either Ca2+ and Mg2+. Each family of traces shows currents from the same inside-out patch from a Xenopus oocyte, expressing mSlo1 Î± subunits. Currents were activated by the voltage protocol shown on the top left with the indicated divalent cation concentrations applied to the cytosolic face of the patch. On the left, traces were obtained with 300 Î¼M Ca2+, 2 mM Ca2+, 10 mM Ca2+ and 50 mM Ca2+ from top to bottom. On the right, each family of traces was obtained with 300 Î¼M Ca2+ but with added 2, 10, and 50 mM Mg2+ from top to bottom. Tail currents were recorded at â140 mV. For solutions containing 10 and 50 mM divalent, the potential before the activation steps (â200 to +160 mV) was â180 mV, and â140 in other cases. Note the strong slowing of deactivation with either Ca2+ and Mg2+, the similar activation of current with additions of mM Ca2+ or Mg2+, and the strong block of current at positive activation potential at higher divalent concentrations.
	Figure 2. High concentrations of Ca2+ and Mg2+ are similarly effective at shifting current activation. In A, G-V curves were generated from tail currents obtained with 300 Î¼M, 2 mM, 10 mM and 50 mM Ca2+ (patch in Fig. 1). Solid lines are fits of , with values for V0.5 of â21.5 Â± 1.0 mV (k = 17.1 mV), â57.1 Â± 0.7 mV (k = 14.6 mV), â87.5 Â± 0.7 mV (k = 14.4 mV) and â104.5 Â± 1.1 mV (k = 19.0 mV), for 300 Î¼Mâ50 mM Ca2+, respectively. In B, G-V curves from the same patch as in A are shown for currents obtained with 300 Î¼M Ca2+, and 300 Î¼M Ca2+ with either 2, 10, or 50 mM added Mg2+. Values for V0.5 for 2, 10, and 50 mM Mg2+ containing solutions were as follows:â48.7 Â± 1.0 mV (k = 14.8 mV), â75.5 Â± 0.8 mV (k = 14.5 mV), and â87.4 Â± 1.1 mV (k = 18.7 mV), respectively. In C, G-V curves are shown for 300 Î¼M Ca2+, 20 mM Ca2+, and 300 Î¼M Ca2+ + 20 mM Mg2+. In D, the mean conductance measured as a function of voltage is displayed for a set of patches over a range of Ca2+ concentrations from 0 to 100 mM. Solid lines are fits of . For 0 Ca2+ (â¢), V0.5 = 168.5 Â± 2.2 mV, k = 22.4 Â± 1.0 mV; for 1 Î¼M Ca2+ (â), V0.5 = 136.89 Â± 0.9 mV, k = 18.8 Â± 0.7 mV; for 4 Î¼M (â¦), V0.5 = 85.2 Â± 0.6 mV, k = 16.9 Â± 0.5 mV; for 10 Î¼M (â), V0.5 = 39.0 Â± 0.5 mV, k = 19.1 Â± 0.5 mV; for 30 Î¼M (âª), V0.5 = 22.4 Â± 0.5 mV, k = 17.9 Â± 0.4 mV; for 60 Î¼M (â¡), V0.5 = 5.8 Â± 0.8 mV, k = 19.3 Â± 0.5 mV; for 100 Î¼M (â´), V0.5 = â2.4 Â± 0.7 mV, k = 21.2 Â± 0.5 mV; for 300 Î¼M (âµ), V0.5 = â15.9 Â± 0.6 mV, k = 18.9 Â± 0.5 mV; for 1 mM (â¾), V0.5 = â42.4 Â± 0.6, k = 18.4 Â± 0.5 mV; for 2 mM (â¿), V0.5 = â60.5 Â± 0.6 mV, k = 15.6 Â± 0.5 mV; for 5 mM (â¸), V0.5 = â77.6 Â± 0.8 mV, k = 16.9 Â± 0.7 mV; for 10 mM (â¹), V0.5 = â85.2 Â± 0.8 mV, k = 16.5 Â± 0.7 mV; for 20 mM (â), V0.5 = â89.3 Â± 0.8 mV, k = 19.0 Â± 0.7 mV; for 50 mM (â), V0.5 = â97.9 + 1.1 mV, k = 22.2 Â± 0.9 mV; and for 100 mM (â), V0.5 = â93.5 Â± 0.9 mV, k = 22.5 Â± 0.8 mV. Each point represents the mean with SD of from 4 to 12 patches. In E, G-V curves were generated from a set of patches (mean and SD for 4â19 patches) with 300 Î¼M Ca2+ with various Mg2+ concentrations. Solid lines are fits of . For 300 Î¼M (â¢), V0.5 = â11.6 Â± 0.5 and k = 17.8 Â± 0.5 mV; with 1 mM Mg2+ (â), V0.5 = â28.5 Â± 0.7 mV, k = 17.4 Â± 0.6 mV; with 2 mM Mg2+ (â¦), V0.5 = â41.4 Â± 0.6 mV, k = 17.1 Â± 0.5 mV; with 5 mM Mg2+ (â), V0.5 = â58.4 Â± 0.6 mV, k = 16.9 Â± 0.6 mV; with 10 mM Mg2+ (âª), V0.5 = â67.1 Â± 0.7 mV, k = 16.5 Â± 0.6 mV; with 20 mM Mg2+ (â¡), V0.5 = â82.6 Â± 0.8 mV, k = 16.8 Â± 0.7 mV; with 50 mM Mg2+ (â´), V0.5 = â82.8 Â± 1.4 mV, k = 21.6 Â± 1.3 mV; and 100 mM Mg2+ (âµ), V0.5 = â79.6 Â± 1.3 mV, k = 21.3 Â± 1.1 mV. In F, V0.5 values measured in D and E are plotted as a function of the indicated divalent cation concentration for either solutions with Ca2+ alone (â¦) or for 300 Î¼M Ca2+ with added Mg2+ (â¡). The 5 mM EGTA, 0 Ca2+ solution was plotted as 10â9 M. Solid lines with small filled circles (Ca2+ alone) and small open squares (300 Î¼M Ca2+ plus Î[Mg2+]) represents expectations derived from a fit of Fig. 1 (values from Table , column D) to the G-V curves in Fig. 2 D.
	Figure 3. Millimolar Mg2+ and Ca2+ produce similar shifts to more negative potentials in the relationship between open probability and voltage. In A, traces show currents from an inside-out patch containing two BK channels. Patches were held at â40 mV with repeated voltage steps to either +60 mV (A1 and A3), or â60 mV (A2 and A4). On the left (A1 and A2), channels were activated with 300 Î¼M Ca2+, whereas on the right (A3 and A4) channels were activated with 300 Î¼M Ca2+ plus 10 mM Mg2+. In each panel, the ensemble average expressed in units of probability of being open (Po) is plotted at the bottom. At +60 mV, the addition of Mg2+ has little effect on Po, but reduces the single-channel current amplitude. At â60 mV, Mg2+ produces a substantial increase in Po, with only a mild reduction in the single-channel amplitude. In B, Po estimates obtained from the ensemble averages are plotted as a function of command potential for the patch shown in A. Solid lines are fits of . At 300 Î¼M Ca2+, fitted values with 90% confidence limits were gmax = 0.89 Â± 0.02, V0.5 = â30.7 Â± 5.1 mV, and k = 19.2 Â± 4.4 mV; for 300 Î¼M Ca2+ plus 10 mM Mg2+, gmax = 0.91 Â± 0.01, V0.5 = â81.0 Â± 1.0 mV, and k = 17.9 Â± 1.0 mV. In C, Po versus voltage is plotted for a different patch showing that activation by 10 mM Ca2+ is similar to that produced by 10 mM Ca2+ plus 10 mM Mg2+. Fitted values were as follows: for 100 Î¼M Ca2+, gmax = 0.83 Â± 0.02, V0.5 = â16.5 Â± 4.9 mV, and k = 19.4 Â± 2.7 mV; for 100 Î¼M Ca2+ plus 10 mM Mg2+, gmax = 0.94 Â± 0.11, V0.5 = â66.2 Â± 8.9 mV, and k = 21.3 Â± 8.5 mV; for 10 mM Ca2+, gmax = 0.91 Â± 0.06, V0.5 = â89.2 Â± 5.4 mV, and k = 25 Â± 6.9 mV; and for 10 mM Ca2+ plus 10 mM Mg2+, gmax = 0.92 Â± 0.04, V0.5 = â87.7 Â± 3.2 mV, and k = 22.6 Â± 3.8 mV.
	Figure 4. Mg2+ also shifts current activation in lower Ca2+ or 0 Ca2+. In A, currents on the left were activated by the indicated protocol with a solution containing trace Ca2+ with 10 mM EGTA. On the right, currents were activated from the same patch with a solution containing 0 Ca2+, 5 mM EGTA but with 10 mM Mg2+. In 0 Ca2+, time constants of activation (Ïa) were 1.85, 1.50, 1.12 ms for +120, +140, and +160 mV, respectively. With 10 mM Mg2+, Ïa was 4.0, 2.72, and 2.22 ms at +120, +140, and +160 mV, respectively. In B, the normalized conductance is plotted as a function of command potential for 0 Ca2+ (eight patches), 10 mM Mg2+ (eight patches) and 50 mM Mg2+ (seven patches). Conductance values were normalized in each patch to the maximum value obtained with 50 mM Mg2+. Fits of (solid lines) yielded values for V0.5 of 170.7 Â± 2.6 mV (k = 23.6 mV) for 0 Î¼M Ca2+, 110.5 Â± 0.6 mV (k = 18.3 mV) for 10 mM Mg2+, and 78.0 Â± 0.5 mV (k = 18.3 mV) for 50 mM Mg2+. In C, currents activated at +140 mV were normalized to peak steady-state amplitude of a single exponential fit to the rising phase of currents activated either with 0 Ca2+ or with 0 Ca2+ + 10 mM Mg2+. The time constant of activation with 0 Ca2+ was 1.50 ms, whereas with 10 mM Mg2+ was 2.72 ms. The slowing of activation with Mg2+ was consistently observed at all activation voltages and argues that the additional activation by Mg2+ is not the result of an increase in trace Ca2+. In D, currents were activated by a voltage step to +80 mV with either 4 or 10 Î¼M Ca2+ without or with the addition of 10 mM Mg2+. Unbuffered divalent cation solutions were prepared as described in the materials and methods. Note the increased current amplitude and slower activation of current in the presence of Mg2+. In E, G-V curves were constructed from measurement of tail currents from a set of 4 patches studied as in D. Error bars represent the SEM of four patches. The V0.5 for each curve is 37.6 Â± 1.8 mV (10 Î¼M Ca2+), 11.6 Â± 2.5 (10 Î¼M Ca2+ + 10 mM Mg2+), 73.8 Â± 1.1 mV (4 Î¼M Ca2+), and 47.8 Â± 1.1 mV (4 Î¼M Ca2+ plus 10 mM Mg2+). Buffered Ca2+ solutions prepared at the same time and tested on the same patches yielded V0.5 values of 36.2 Â± 1.6 mV for 10 Î¼M Ca2+ and 71.2 Â± 1.2 mV for 4 Î¼M Ca2+. In F, ensemble averaged currents were generated from channels activated with the indicated solutions for a voltage-step to +40 mV from a patch containing two channels. The addition of Mg2+ increases the open probability towards maximal values but slows down the time constant of current activation. With 10 Î¼M Ca2+, the activation time constant was 1.4 Â± 0.3 ms, whereas with 10 Î¼M Ca2+ plus 10 mM Mg2+ the time constant was 11.1 Â± 0.5 ms.
	Figure 5. The ability of mM concentrations of Ca2+ and Mg2+ to shift G-V curves is similar. In A, the V0.5 for activation is plotted as a function of Mg2+ for G-V curves obtained in two separate sets of patches each activated by 300 Î¼M Ca2+ plus the indicated Mg2+. The predictions for the shift in V0.5 as a function of Mg2+ based on two sets of fitted values for Fig. 1 (Table , columns A [â¦] and D [âª]) are also displayed. In B, the ability of Mg2+ to shift V0.5 at different Ca2+ is displayed. Triangles show V0.5 values from macroscopic currents without (â´) or with (âµ) 10 mM Mg2+. Circles ([â¢] no Mg2+; [â]: + 10 mM Mg2+) are means and SD for V0.5 determined from Po measurements from four patches with either one or two channels as in Fig. 3. Diamonds ([â¦] no Mg2+;[â] +10 mM Mg2+) are values obtained with unbuffered Ca2+ solutions. Predictions from the fitted values for Fig. 1 (Table , column D) are also shown for Ca2+ alone (âª) and with 10 mM Mg2+ (â¡). In C, the change in V0.5 (ÎV0.5) produced by 10 mM Mg2+ at different [Ca2+] is displayed for macroscopic current measurements (â) and single-channel estimates (âª). Estimates of predicted ÎV0.5 based on a fit of Fig. 1 to G-V curves with or without Mg2+ are also shown for two cases: first, Mg2+ inhibition of the high affinity site is allowed (â¢; Table , column D) and no inhibition by Mg2+ occurs (â¦; Table II; column F). In D, values of V0.5 obtained as a function of Ca2+ (â¡) are replotted along with estimates of the V0.5 corrected at Ca2+ of 1 mM and above by the additional shift produced by Mg2+ shown in A obtained with 300 Î¼M Ca2+. These values (â) provide an indication of the ability of the higher affinity, Ca2+ selective site to shift activation of BK channels, in the absence of the low affinity effect, assuming that the high and low affinity effects are independent and additive. Predicted values for V0.5 based on a fit of Fig. 1 are also shown for the case of both low and high affinity Ca2+ binding sites (âª; Table II; column D), and also for Ca2+ action alone in the absence of a high affinity site (â¦). The latter values were also corrected for the approximately â17-mV shift that 300 Î¼M Ca2+ should produce by acting at the low affinity sites (â¢). The discrepancy between the Mg2+ corrected data and the prediction from Fig. 1 arises from the fact that the Mg2+ correction was obtained with solutions with 300 Î¼M Ca2+ such that the effect of 300 Î¼M Ca2+ on the low affinity site is not taken into account.
	Figure 6. The current activation rate increases substantially as Ca2+ is raised from 1 Î¼M to 100 Î¼M. In A, currents were activated by a voltage step to +40 mV with Ca2+ concentrations of 0, 1, 4, 10, 30, 60, and 100 Î¼M as indicated. In B, currents were activated in the same patch by a voltage-step to +80 mV with the same Ca2+ concentrations. In C, currents activated by the step to +40 mV were normalized to their maximal amplitude and fit with single exponentials. The activation time constants (Ïa) were 5.45, 3.38, 1.21, 1.05, and 0.80 ms, for 4, 10, 30, 60, and 100 Î¼M, respectively. In D, the normalized current activation time course for the voltage-steps to +80 mV are shown. Ïa's were 7.08, 3.77, 1.23, 0.53, 0.46, and 0.39, for 1, 4, 10, 30, 60, and 100 Î¼M Ca2+, respectively. In E and F, the same normalized traces shown in C and D are plotted on a logarithmic time base to show the shift in activation time course with Ca2+. An increase in Ca2+ from 1 to 10 Î¼M produces a similar three to fourfold change in activation rate as the increase from 10 to 100 Î¼M. At +40 mV, the trace in response to 4 Î¼M Ca2+ is plotted since at 1 Î¼M there is almost no detectable current activation.
	Figure 7. Increases of Ca2+ from 300 Î¼M to 10 mM produce smaller increases in current activation time rate. In A and B, currents were activated by 300 Î¼M, 1 mM, and 10 mM Ca2+ at either +40 mV (panel A) or +80 mV (panel B). In C and D, each trace in A and B was normalized to the maximal current amplitude to compare the activation time course. Points show every fourth digitized current value. Solid lines are the best fit of a single exponential function to the activation time course. At +40 mV, the activation time constant (Ïa) was 0.73, 0.52, and 0.33 ms for 300 Î¼M, 1 mM, and 10 mM Ca2+, respectively. At +80 mV, Ïa was 0.38, 0.28, and 0.19 ms for 300 Î¼M, 1 mM, and 10 mM Ca2+, respectively. In E and F, the normalized current activation time course is plotted on a logarithmic time base to allow better comparison of the relatively small concentration dependence of the activation rate for this 30-fold change in concentration compared with that shown in Fig. 6.
	Figure 8. Addition of Mg2+ concentrations which markedly shift G-V curves does not increase the limiting rate of Slo1 current activation. In A and B, traces were elicited in each panel with 300 Î¼M Ca2+ alone, and with 300 Î¼M Ca2+ with either 1 mM or 10 mM Mg2+. Traces on the left were activated by a voltage step to +40 mV and, on the right, to +80 mV. In C and D, the normalized current activation time course is plotted on a linear time base (every fourth digitized value is plotted), while, in E and F, the same traces are shown on a logarithmic time base. Solid lines are fits of a single exponential function to the activation time course. At +40 mV, Ïa was 0.75, 0.64, and 0.59 ms for 300 Î¼M Ca2+, 300 Î¼M Ca2+ + 1 mM Mg2+, and 300 Î¼M Ca2+ + 10 mM Mg2+, respectively. At +80 mV, Ïa was 0.38, 0.36, and 0.33 ms for each solution. Raising Mg2+ up to 10 mM results in little effect on the time course of current activated in the presence of 300 Î¼M Ca2+.
	Figure 9. Millimolar concentrations of either Ca2+ or Mg2+ are similar in their effects on current activation rates. In A, the time constant of activation (Ïa) is plotted as a function of command potential for Ca2+ concentrations of 1 Î¼M (â¢), 4 Î¼M (â), 10 Î¼M (â¦), 30 Î¼M (â), 60 Î¼M (â´), 100 Î¼M (âµ), and 300 Î¼M (âª). Error bars in A and B are SEM for 4-13 patches. In B, Ïa is plotted as a function of command potential for Ca2+ concentrations of 300 Î¼M (â¢), 1 mM (â), 2 mM (â¦), 5 mM (â), 10 mM (âª), 20 mM (â¡), 50 mM (â´), and 100 mM (âµ). In C, Ïa is plotted as a function of command potential for solutions containing 300 Î¼M with added Mg2+ of 0 mM (â¢), 1 mM (â), 2 mM (â¦), 5 mM (â), 10 mM (âª), 20 mM (â¡), 50 mM (â´), and 100 mM (âµ). Each point shows the mean and SEM of 4-11 patches. In D, the mean rate of current activation for Slo1 currents is plotted as a function of Ca2+ for command potentials of +20 (â¢), +60 (â), +100 (â¦), and +140 (â) mV. Error bars are SEM. Solid lines are fits of . At +20 mV, kmax was 2.4, Kd = 0.87 Â± 0.30 Î¼M, and n = 0.88 Â± 0.28. At +60 mV, kmax was 4.1, Kd = 398 Â± 160 Î¼M, and n = 0.77 Â± 0.20; at +100 mV, kmax = 6.0, Kd = 181 Â± 59 Î¼M, and n = 0.72 Â± 0.14; at +140 mV, kmax = 7.7, Kd = 59 Â± 25 Î¼M, and n = 0.92 Â± 0.32. Note the anomalous slowing of current activation rate at 1 Î¼M Ca2+ relative to 0 Î¼M at +140 mV. This point was not included in the fit. In E, current activation rate is plotted as a function of total divalent in the solution at +140 mV for solutions with no added Mg2+ (â¢) and solutions with Mg2+ added to 300 Î¼M Ca2+ (â), showing that Mg2+ has little effect on the limiting rate of current activation, although additional depolarization will produce an increase in current activation rate. Note the inhibition of activation rate at the highest [Mg2+]. Current activation with 0 Ca2+ and various [Mg2+] is also plotted (â¡), showing the relative lack of effect of Mg2+ in comparison to Ca2+.
	Figure 10. Millimolar concentrations of Mg2+ and Ca2+ have similar effects on current deactivation. In A, the deactivation time constants are plotted as a function of command potential for [Ca2+] spanning over six orders of magnitude, 1 Î¼Mâ100 mM. Points and error bars are means and SEM of 5â15 patches. In B, the deactivation time constants are plotted as a function of command potential for tail currents obtained with 300 Î¼M Ca2+ and 300 Î¼M Ca2+ plus 1, 10, and 100 mM added Mg2+. Points show means and SEM for 4â8 patches. In C, the deactivation time constant measured at â100 mV is plotted as a function of total [divalent] for solutions with only Ca2+ (â¢) and for solutions with 300 Î¼M Ca2+ with added Mg2+ (â). The slowing of deactivation with either elevated Ca2+ or Mg2+ exhibits saturation, although at somewhat different concentrations.
	Figure 11. Comparison of effects of Ca2+ and Mg2+ on primary time constant of Slo1 current relaxations. In A, activation and deactivation time constants obtained at 0, 10, and 300 Î¼M Ca2+ are plotted as a function of potential. In B, the shift in relaxation time constant with 1 and 4 Î¼M are compared with 0 Î¼M Ca2+. Note the unusual slowing of activation with 1 Î¼M Ca2+. In C, the effects of 10 and 50 mM Ca2+ are compared with 0 Ca2+, whereas, in D, the effects of 10 and 50 mM Mg2+ are compared with 0 Ca2+. In E, the effects of 10 and 50 mM Ca2+ are compared with 300 Î¼M Ca2+, whereas, in F, the effects of 10 and 50 mM Mg2+ plus 300 Î¼M Ca2+ are compared with 300 Î¼M Ca2+.
	Figure 12. The behavior of Kd and Hill coefficient over all [Ca2+]. In A, conductances given in Fig. 2 D were replotted to show the Ca2+ dependence of conductance at a given voltage. Each point is the mean and SEM for the estimate. Solid lines are fits of the modified Hill equation given in the text. Symbols correspond to potentials of â200 (â¢), â180 (â), â160 (â¦), â140 (â), â120 (âª), â100 (â¡), â80 (â´), â60 (âµ), â40 (â¾), â20 (â¿), 0 (â¸), +20 (â¹), +40 (â), +60 (â), +80 (â), +100 (â), +120 (closed six-pointed star), and +140 (open six-pointed star) mV. In B, conductance values predicted from Fig. 1 (see Fig. 14) based on values given in Table (column D) were plotted as a function of [Ca2+] and fit with the modified Hill equation (solid lines). Symbols are as in A. In C, estimated values for the Kd for apparent Ca2+ affinity (â¢) obtained from fitting the data in Fig. 12 A are plotted as a function of command potential. The solid line with small filled circles corresponds to values for Kd predicted from Fig. 1 as shown in Fig. 12B. The line with small open circles corresponds to Kd values assuming no Mg2+ inhibition of the high affinity site. In D, the Hill coefficients determined from Fig. 12 A (â¢) are plotted as a function of voltage. Error bars represent the 90% confidence limit on the estimate of the Hill coefficient. The dotted lines show the predictions from Fig. 1 as determined from values in Table , column D (Fig. 12 B, small closed circles) or from Table , column F (small open circles, no Mg2+ inhibition).
	Figure 13. The apparent Hill coefficient for activation of conductance by Ca2+ is increased by Mg2+. In A, each point is the estimate of conductance activated at a given Ca2+ and voltage obtained from normalized G-V curves. Solid lines are fits of the modified Hill equation given in the text. Fitted values for apparent Kd and Hill coefficient are plotted in C and D, respectively. Values used in this figure were from a different set of patches than shown in Fig. 2 or Fig. 12. In B, conductance estimates obtained in the presence of 10 mM Mg2+ are plotted as a function of Ca2+ for a range of voltages. At comparable voltages, the Hill coefficient for activation is higher in the presence of Mg2+. In C, the apparent Kd (in Î¼M) for activation of conductance by Ca2+ either in the absence (â¢) or presence (â) of 10 mM Mg2+ is plotted as a function of activation potential. The apparent Ca2+ affinity is increased at a given potential in the presence of Mg2+. The error bars are 90% confidence limits from the estimates of K0.5 obtained in A and B. Predictions from Fig. 1 (Table , column D) for solutions without Mg2+ (âª) or with Mg2+ (â¡) are also shown. In D, the Hill coefficient and confidence limits for the activation of conductance by Ca2+ either in the absence (â¢) or presence (â) of Mg2+ are plotted as a function of command potential, along with estimates (no Mg2+ [â¦], +10 mM Mg2+ [â]) from Fig. 1 based on estimates of Mg2+ affinities from column B of Table . Both for experimental data and the theoretical predictions, there is a trend for increased Hill coefficient at more positive potentials and, at any given potential, Mg2+ increases the apparent Hill coefficient. In E, the Kd for Ca2+ effect predicted from Fig. 1 is plotted over a wider range of potentials. Both with (â) and without (â¢) 10 mM Mg2+, at the most negative potentials a limit in the Kd is observed, while affinity increases dramatically with depolarization. In F, the behavior of Hill coefficient as a function of command potential predicted by Fig. 1 is displayed over a wider range of potentials. Predictions from Fig. 1 assuming Mg2+ inhibition of the high affinity site (Table , column D) are shown both without (â¢) and with (â) 10 mM Mg2+. Predictions from Fig. 1 with no Mg2+ inhibition (Table , column F) are also shown without (â¦) and with (â) 10 mM Mg2+.
	Figure 14. The dependence of Slo1 conductance on Ca2+, Mg2+ and voltage can be described by a 250 state allosteric model involving the independent action of Ca2+, Mg2+ and voltage-sensor movement. In A, G-V curves obtained at different [Ca2+] given in Fig. 2 D (data set 1) were fit with with the solid lines resulting from the values given in column A, Table . L(0) was constrained to 500000. In B, G-V curves obtained with 0 Ca2+ (â¢) plus 0.5 (â), 1 (â¦), 2 (â), 5 (âª), 10 (â¡), 20 (â´), 50 (âµ), and 100 (5) mM Mg2+ (data set 2) were also fit with , with parameters given in Table , column B. In C, G-V curves obtained with 300 Î¼M Ca2+ with [Mg2+] from 0 to 100 mM (data set 3; symbols are as in B, but with no 0.5-Î¼M points) were fit with . The solid lines correspond to the fit resulting from the values given in column C, Table . Comparison of the values in columns A, B, and C indicate that quite similar values yield a good general description of G-V curves over all [Ca2+], all [Mg2+], and all voltages, except that the multiple Mg2+ binding affinities defined by are not well-described in the fit to data set 3. In D1âD3, G-V curves shown in A-C were simultaneously fit with , yielding the values given in Table (column D). Again, the general features of the shift in curves as a function of Ca2+ and Mg2+ is reasonably well-described. In E, G-V curves obtained over all [Ca2+] were fit with , which assumes that Mg2+ influences the voltage-sensor equilibrium. Fitted curves correspond to values given in Table (column A). In F, G-V curves at 0 Ca2+ were also fit with . When values obtained from fitting G-V curves at higher Ca2+ were used, it was not possible to obtain estimates for Km and E that resulted in adequate descriptions of the data. The curves with open circles were generated from values in column C, Table . L(0) was set to a value in which currents in 0 Ca2+ were well-described. However, the G-V curves at 10 and 50 mM Mg2+ could not be captured. However, when more parameters were left unconstrained, could yield a fit that captured the G-V curves in 0 Ca2+ (smaller closed circles), but these values (column D, Table ) totally failed to describe the behavior of G-V curves at higher Ca2+.

References [+] :

Barrett, Properties of single calcium-activated potassium channels in cultured rat muscle. 1982, Pubmed