Horrigan FT , Aldrich RW .

MH48108 NIMH NIH HHS, NS42901 NINDS NIH HHS , R01 NS042901 NINDS NIH HHS

	Figure 1. . Slo1 gating mechanisms. (A) The unliganded gating mechanism (Scheme I) involves an allosteric interaction between channel opening (C-O) and voltage sensor activation (R-A). L is the C-O equilibrium constant when all voltage sensors are in the resting (R) state. J is the R-A equilibrium constant when channels are closed. D is the allosteric interaction factor such that the C-O equilibrium constant increases D-fold for each voltage sensor activated, and the R-A equilibrium constant increases D-fold when the channel opens. (B) Scheme I specifies a 10-state gating scheme (Scheme I*) with the indicated equilibrium constants. Subscripts for closed and open states denote 0–4 activated voltage sensors. (C) A general allosteric gating mechanism (Scheme II) includes a Ca2+ binding transition (X-XCa) for each subunit with an equilibrium constant K = [Ca2+]/KD when channels are closed and voltage sensors are not activated. Allosteric interactions of Ca2+ binding with channel opening and voltage sensor activation are determined by allosteric factors C and E, respectively, as described in the text.
	Figure 2. . Mechanisms of interaction between voltage sensors and Ca2+-binding sites. (A1) If the binding of Ca2+ to a single subunit affects voltage sensors equally then voltage sensor equilibrium constants in all four subunits will increase E-fold to JE as indicated. (A2) In Scheme II, we assume Ca2+ binding only affects the voltage sensor in the same subunit. Consequently, the A2 mechanism predicts more states than the A1 mechanism. (B) For example, when a channel has two Ca2+-bound (open circles) and two voltage sensors activated (open squares), the A2 mechanism specifies three states depending on the relative location of Ca2+ and activated voltage sensors. That the states are functionally distinct can be seen by comparing the different Ca2+-binding equilibria for the unoccupied binding sites (K,K), (K,KE), and (KE,KE). Equilibrium constants for voltage sensor activation are also different. By contrast, the A1 mechanism specifies a single state with equilibrium constants KE2 for Ca2+ binding and JE2 for voltage sensor activation (not depicted).
	Figure 3. . Sub-Schemes derived from Scheme II. Under extreme conditions that limit Ca2+-binding, voltage sensor activation, or channel opening, the number of interactions that govern mSlo1 gating is reduced and Scheme II is reduced to the following subschemes. (A) unliganded, (B) Ca2+-saturated, (C) very negative voltages (voltage sensors resting), (D) very positive voltages (voltage sensors activated), (E) closed, and (F) open.
	Figure 4. . Effects of Ca2+ on IK. (A) Families of IK evoked by 20-ms depolarizations to different voltages (20 mV steps over the indicted range) are compared in 0 and 70 μM Ca2+ (different patches). (B) IK evoked by 10-ms pulses to 160 mV in 0 and 100 μM Ca2+ (same patch) are normalized to steady-state current during the pulse and superimposed together with exponential fits (dashed lines) to both activation and deactivation time courses. (C1) Normalized GK-V relationships (mean ± SEM) in 0 Ca2+(n = 51) and 70 μM Ca2+(n = 3) obtained from isochronal tail currents following 20-ms pulses. G-Vs were normalized by fitting with Boltzmann functions raised to a power n (solid lines)(0 Ca: z = 0.73 e, Vh = 144 mV, n = 2.93; 70 μM Ca2+: z = 1.22 e, Vh = 12.9 mV, n = 1.39). (D1) Mean time constants of IK relaxation (τ[IK]) are plotted on a log scale versus voltage for the same experiments as in C1. Dashed lines indicate similar exponential voltage dependencies of τ(IK) at negative voltages in the presence or absence of Ca2+. The shapes of the G-V and τ(IK)-V relationships from C1 and D1 are compared in C2 and D2, respectively, by shifting the 0 Ca2+ plot along the voltage-axis by 135 mV, which is sufficient to align the τ(IK)-V relationships at voltages less than the peak voltage. (E) The 10-state gating scheme (sub-Scheme IIb*) specified by Scheme II in saturating Ca2+.
	Figure 9. . The Ca2+ dependence of PO. (A) NPO determined from the patch in Fig. 8 C is plotted on a semi-log scale vs. voltage for different [Ca2+] (in μM: 0 (•), 0.13 (○), 0.27 (▪), 0.58 (▵), 0.79 (▴), 3.8 (▾), 19 (♦), 68 (), 102 (), 313 (), 1030 ()). Dashed lines are exponential fits with z = 0.3 e. (B) PO-V relationships determined from normalized G-Vs at different [Ca2+](in μM: 0 (•), 0.27 (▪), 0.58 (▵), 0.81 (▴), 1.8 (▿), 3.8 (▾), 8.2 (⋄), 19 (♦), 68 (), 99 ()) are plotted on a semilog scale versus voltage (mean ± SEM). Data for PO < 10−2 were obtained from amplitude histograms as in A but were filtered at 5 kHz such that openings near the K+ reversal potential could be distinguished from noise based on a half-amplitude criterion (see materials and methods). The data were fit (solid lines) by Scheme I* (Fig 1 B) allowing all parameters (L0, zL, J0, zJ, D) to vary freely at each [Ca2+]. (C) A dose-response relationship for the effect of Ca2+on PO at negative voltages is obtained by plotting the log-ratio of NPO in the presence and absence of Ca2+ (log[Ro]) versus [Ca2+] for several experiments (symbols). NPO(V) was determined from exponential fits to the data with z = 0.3 e as in A. Log(RO) from A (•) spans the entire [Ca2+] range and is fit (dashed line) by Eq. 4 (C = 7.8, KD = 8.2 μM). (D) The mean log(RO)-[Ca2+] relationship is fit (solid line) by Eq. 4 (C = 7.4, KD = 9.3 μM) and compared with the half activation voltage (Vh) of PO (open symbols). Solid lines in C and D represent predictions of Scheme II for log(RO) and VH(PO), respectively, using the Fit B parameters in Table II (C = 8, KD = 11 μM; Table II, Fit B). The change in VH(PO) from 100–1,000 μM Ca2+ can be reproduced (dotted line) if Scheme II is modified to include an additional low affinity binding site in each subunit that interacts with the C-O transition through an allosteric mechanism analogous to that embodied by the C-factor in Scheme II. The parameters for the low affinity site (KDLow = 2.33 mM, CLow = 3.53) were taken from Zhang et al. (2001). However, this model predicts a marked increase of RO in 100–1,000 μM Ca2+ (dashed line) that is inconsistent with the data.
	Figure 5. . Effects of Ca2+ on gating currents (A) Gating currents evoked by 1-ms pulses to 160 mV in 0 and 70 μM Ca2+. Ig was recorded in the absence of K+ and the presence of 125 mM external TEA to eliminate ionic currents. (B) Families of Ig evoked by depolarizations to 160 mV of different duration (0.1–20 ms) in 0 and 70 μM Ca2+ from two different patches. Total OFF charge for each pulse (Qp) was determined by integrating IgOFF for 5 ms and is plotted against pulse duration in (C). Results were fit with double exponential functions (0 Ca2+: τ1 = 63 μs, A1 = 11.7 fC, τ2 = 4.2 ms, A2 = 8.7 fC; 70 Ca2+: τ1 = 68 μs, A1 = 14.6 fC, τ2 = 0.85 ms, A2 = 12.8 fC). (D) The derivative of the fits to QP (solid lines) are superimposed with IgON at 160 mV. Dashed lines represent the slow component of the fits.
	Figure 6. . Properties of gating charge movement in 70 μM Ca2+. (A) Families of Ig evoked by depolarizations of different duration to the indicated voltages in 70 μM Ca2+ (HP = −80 mV). (B) Plots of Qp versus pulse duration determined from A and fit with double exponential functions. The 160-mV trace (▾) was obtained from a different patch than the others (•) and was normalized to the 120 mV trace because the steady-state Q-V relationship is saturated for V ≥ 120 mV in 70 μM Ca2+ (see E). (C) τgSLOW-V relationships in 70 μM Ca2+ were determined at positive voltages from the slow component of Qp and at negative voltages from the slow component of QOFF (e.g., Fig. 13 C). Individual data points (Δ) and mean ± SEM (▴) are plotted. The mean τ(IK)-V relationship (○) was fit by exponential functions (solid lines) over voltage ranges corresponding to the τgSLOW data. These fits were then scaled (dashed lines) to match the τgSLOW-V relationships. (D) QP-V relationships determined following brief (0.25 ms) or prolonged (20 ms) pulses (from B) are compared with Qfast-V determined by integrating the fast component of IgON in the same patch (see Fig. 7 A). QP(20)-V and Qfast-V relationships are fit by Boltzmann functions (Qfast: z = 0.68, Vh = 123 mV, QP(20): z = 1.95, Vh = 40 mV). (E) Normalized steady-state Q-Vs (solid symbols) and G-Vs (open symbols) in 0 Ca2+ and 70 μM Ca2+. QSS was determined from 10–20-ms pulses and data from three experiments in each [Ca2+] are plotted. Individual Q-Vs were normalized based on fits to Boltzmann functions. Boltzmann fits to the cumulative data are shown (0 Ca2+: z = 0.59, Vh = 150 mV, 70 μM Ca2+: z = 1.19, Vh = 40 mV). G-Vs (mean ± SEM) were measured and fit as in Fig. 4 C.
	Figure 7. . Ca2+ has little effect on fast gating charge movement. The fast components of IgON evoked at 160 mV in 0 Ca2+ (A) and 70 μM Ca2+ (B) are determined by fitting the first 100 μs of the decay with exponential functions (dashed lines; 0 Ca: τgfast = 69.7 μs, 70 μM Ca: τgfast = 73.6 μs). Fast charge movement (Qfast) was estimated by integrating under the exponential fits (shaded areas in A and B). Qfast-V relationships (mean ± SEM) are plotted on linear (C) and semilog (D) scales for 0 Ca2+ (solid symbols, n = 10) and 70 μM Ca2+ (open symbol, n = 7). To determine mean Qfast, normalized Qfast-V relationships from individual experiments were shifted along the voltage-axis by ΔVh = <Vh>-Vh to align their half-activation voltages (Vh) to the mean (0 Ca2+: <Vh> = 155 mV; 70 μM Ca: <Vh> = 135 mV). Then the shifted data were averaged in 25 mV bins (see materials and methods). The mean Qfast-Vs are fit by Boltzmann functions (lines) where the valence z = 0.58 e was constrained to the mean voltage sensor charge determined from fits to individual Qfast-Vs in 0 Ca2+ and 70 μM Ca2+. (E) Mean τgfast-V relationships were determined in 60 mV bins after individual τgfast-V relationships were normalized to peak τgfast and shifted by ΔVh (as determined from Qfast-V relationships in C). The curves are fit with functions of the form τgfast = [α0e−zα/kT + β0e−zβ/kT]−1 where zα= 0.33 e, zβ = −0.22 e and 0 Ca: α0 = 1,020 s−1, β0 = 32,500 s−1; 70 Ca: α0 = 1,220 s−1, β0 = 25,500 s−1. (F) Cg-V relationships measured with admittance analysis in 0 and 70 μM Ca2+ for a single patch indicate a Ca2+-dependent shift in the voltage dependence of fast charge movement. The membrane was clamped with a sinusoidal voltage command (868 Hz, 60 mV peak to peak) superimposed on a 1-s voltage-ramp from −200 to 160 mV. Cg was determined for each cycle of the sin wave. The Cg-V relationships were fit with the derivative of Boltzmann functions: Cg = A*z((1 + e−z(V − Vh)/kT)/(kTez(V − Vh)/kT))2 over voltage intervals where most channels are closed (0 Ca, −160 to 100 mV; 70 Ca, −160 to −10 mV). The 0 Ca2+ data were fit first (A = 1,390, z = 0.61 e, Vh = 108 mV) and the 70 Ca2+ data were fit with identical amplitude and charge (A, z) while Vh was reduced to 75 mV.
	Figure 13. . IgOFF components. (A) OFF gating currents recorded at −80 mV in 70 μM Ca2+ following pulses of different duration (0.11–20 ms) to 120 mV decay more slowly as pulse duration increases. IgOFF traces were integrated to obtain QOFF time courses in B. QOFF saturates for pulses of 5 ms or greater duration. (C) OFF kinetics following brief (0.11 ms) or prolonged (5–20 ms) pulses are compared by plotting the quantity QOFF(t)-QOFFSS on a log scale versus time where QOFFSS is the mean value of QOFF(t) for t = 4–5 ms. The 5–20 ms trace is the average of 5, 7, 10, and 20 ms records and is fit by a double exponential function (solid line, qMED = 14.1 fC, τMED = 200 μs, qSLOW = 7.4 fC, τSLOW = 810 μs) with dashed lines representing the two components. The 0.11-ms trace is fit by a triple exponential function (solid line, qFAST = 4.9; fC, τFAST = 25 μs, qMED = 0.6 fC, τMED = 200 μs, qSLOW = 0.4 fC, τSLOW = 810 μs) with a dashed line indicating the fast component. (D) The Ca2+-saturated gating scheme (sub-Scheme IIB*) indicates the origin of the three OFF components which are determined by voltage sensor deactivation when channels are closed (Fast) or open (Medium), or by channel closing (Slow). (E) OFF kinetics for all pulse durations are plotted as in C using the data in B. Dashed lines are triple exponential fits (τFast = 25 μs, τMED = 200 μs, τSLOW = 810 μs). (F) The amplitude of the three OFF components are plotted versus pulse duration and fit by exponential functions with 1.4-ms time constants representing the time course of channel opening.
	Figure 8. . The Ca2+ dependence of PO. (A) Scheme II predicts Ca2+ binding may affect the C-O transition directly (solid arrow) or indirectly (dashed arrow) by altering voltage sensor activation. (B) At low voltages Scheme II specifies an MWC-type gating scheme (Sub-Scheme IIc*) that is independent of voltage sensor activation. (C) Inward potassium currents recorded at −120 mV and filtered at 20 kHz from a macro patch in the indicated [Ca2+] demonstrate that PO increases in a Ca2+-dependent manner when voltage sensors are not activated. The corresponding all-point amplitude histograms are plotted in (D) on a semi-log scale and were constructed from 10-s recordings. (E) Similar histograms from another experiment at −160 mV over a wider [Ca2+] range (0, 0.8, 8.2, 102, 1,030 μM) reveal saturation of PO near 100 μM Ca2+.
	Figure 10. . Fitting steady-state data with Scheme II. (A) Mean PO-V relationships in different [Ca2+](in μM: 0 (•), 0.27 (▪), 0.58 (▵), 0.81 (▴), 1.8 (▿), 3.8 (▾), 8.2 (⋄), 19 (♦), 68 (), 99 ()) were fit by Scheme II by holding L0, zL constant and allowing the other parameters to vary (Fit A, Table II). (B) Mean log(RO)-[Ca2+] relationship (symbols) is compared with predictions of Scheme II based on different fits to the PO data (Table II, Fits A, B, and C). (C) Mean PO (C1) and log(PO) (C2) are plotted versus voltage for different [Ca2+] (symbols) and are fit by Scheme II (Table II, Fit B). The linear and log transformed data were fit simultaneously using a weighting function to compensate for the greater amplitude range of log(PO). (D) Scheme II reproduces (lines) the observed change in relationship between mean steady-state Q-V and PO-V relationships (Table II, Fit B parameters). (E) Gating schemes for unliganded and Ca2+-saturated channels illustrate the changes in equilibria induced by Ca2+ binding. By increasing the C-O equilibrium constants Ca2+ has the effect of changing the primary activation pathway, accounting in part for the altered relationship between Q-V and G-V.
	Figure 12. . Estimating QO from the limiting voltage dependence of PO. (A) <qa>-V relationships representing the derivative with respect to voltage of mean log(PO) (Eq. 7) are plotted for 0 and 70 μM Ca2+. Dashed lines are smoothing functions determined from fits to mean log(PO) in Fig. 9 B. QO-V relationships (solid lines) were estimated by fitting the smoothing functions with Eq. 12 at voltages where QC and PO are small (0 Ca2+: V ≤ 0 mV; 70 μM Ca2+: V ≤ −50 mV). (B) QO is estimated as in A for all Ca2+ (0 to 100 μM). <qa> was determined from mean log(PO) in Fig. 9 B after excluding some data points that represent single measurements at the most positive or negative voltages. (C) Parameters for the QO-V fits are plotted versus [Ca2+]. Dashed lines indicate mean values. (D) The ratio of the valence (z) and amplitude (q1) of the voltage-dependent component of QO is plotted versus [Ca2+] and fit by a Hill equation (n = 1.6, K1/2 = 8.1 μM). (E) Peak <qa> determined from smoothing functions in (B) (symbols) is reproduced by Scheme II (solid line; Table II, Fit B parameters). Peak <qa> decreases with increasing [Ca2+] and underestimates total gating charge assigned to Scheme II (QT, dashed line).
	Figure 11. . Charge distribution of open and closed channels. Normalized plots of QC, QO, PO, and QSS versus voltage predicted by Scheme II (Table II, Fit B parameters) are compared in (A) 0 Ca2+ and (B) 70 μM Ca2+. (C) A double pulse experiment in 70 μM Ca2+ shows that peak Ig evoked by the second pulse (P2) is larger than that evoked by the first pulse (P1) when the interpulse interval is brief. This behavior is consistent with the predicted difference between QC and QO as illustrated by the numbered arrows in (D) corresponding to the pulse intervals in C. Arrows 1 and 4 represent the amount of charge that should move in response to a step from −80 to 120 mV if channels are closed or open, respectively.
	Figure 14. . IK kinetics. (A) Mean τ(IK)-V relationships for different [Ca2+] (in μM: 0 (•), 0.27 (▪), 0.58 (▵), 0.81 (▴), 1.8 (▿), 3.8 (▾), 8.2 (⋄), 19 (♦), 68 (), 99 (). Dashed lines are fits to exponential functions at extreme positive voltages (V ≥ 200 mV in 0 Ca2+ or for V ≥ 140 mV in high Ca2+ (68 and 99 μM)). (B) Comparison of τ(IK)-V (mean ± SEM) in 0, 0.81, and 68 μM. Dashed lines are fits to exponential functions between −300 and −150 mV, indicating that the voltage dependence of τ(IK) at extreme negative voltages is not appreciably Ca2+ sensitive. However, the voltages where τ(IK) begins to deviate from these fits in 0 and 68 μM Ca2+ differ by approximately −150 mV (arrows). (C) The partial charges determined from exponential fits to τ(IK) at extreme positive (zP) and negative (zN) voltages as in A and B, respectively, are plotted against [Ca2+] and fit by lines (zP = 0.203–0.0044 log[Ca2+], zN = −0.161–0.0042 log[Ca2+]). Individual data points (open symbols) and mean ± SEM (solid symbols) are shown. The fits in A and B were constrained to the mean values of zP and zN respectively for each [Ca2+].
	Figure 15. . The Ca2+ and voltage dependence of C-O rate constants. (A) Mean τ(IK)-V relationships in 0 and 68 μM Ca2+ are fit by Scheme I* (unliganded, Fig. 1 B) and sub-Scheme IIb* (Ca2+ saturated, Fig. 4 E), respectively, with the assumption the voltage sensors are equilibrated (Eq. 13). Each model contains five C-O transitions whose equilibrium constants are defined by the steady-state parameters (Table II, Fit B), increasing D-fold (25-fold) for each voltage sensor activated. (B) The backward rate constants for the C-O transitions (γij) determined from the fits are plotted (symbols) versus the number of activated voltage sensors (i). The forward rate constants (δij) are specified by γij and the equilibrium constants. Dashed lines in A and open symbols B represent fits where γij was allowed to vary freely. Similar fits (solid lines [A] and closed symbols [B]) were obtained when γij was constrained to decrease by at most D−1-fold when a voltage sensor activates such that δij increases monotonically. (C) Mean τ(IK)-V at all [Ca2+] (0–100 μM) are fit by Scheme II using the steady-state parameters in Table II (Fit B) and a two-barrier transition state model to describe the C-O rate constants (dashed lines, Eq. 20; solid lines, Eq. 21). The corresponding values of γij are plotted in B (lines). (D) τ(IK)-V relationships (mean ± SEM) in 0, 0.81, and 68 μM Ca2+ are compared with fits (Eq. 21). (E) Transition state diagrams illustrate how a model with two transition states (T1, T2) can account for a complex relationship between Ca2+, voltage, and closing rates. Free energy (ΔG) relative to the open state is plotted against the C-O reaction coordinate for the unliganded (E1) and Ca2+-saturated (E2) case. Solid lines represent the transition when voltage sensors are not activated (i = 0). Dashed lines indicate the additive perturbations produced by activation of 1–4 voltage sensors. The relative energies of C versus O and T1 versus T2 and the perturbations to each of these states produced by Ca2+ binding and voltage sensor activation were determined from the fits in (C) using Eq. 21. The ΔG between the open and transition states is not determined by the data and was adjusted arbitrarily. (E1) In the unliganded state when voltage sensors are not activated (solid line) the transition rate is dominated by a single barrier (T1). Voltage sensor activation produces a small perturbation to T1 (\documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}{\mathrm{{\Psi}}}_{V}^{1}\end{equation*}\end{document} = 0.041) such that γij is not sensitive to voltage sensor activation for i = 1–3. However, T2 is strongly perturbed (\documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}{\mathrm{{\Psi}}}_{V}^{2}\end{equation*}\end{document} = 1) such that it becomes rate-determining when i = 4 (starred barrier). (E2) Ca2+ binding also perturbs T2 more than T1 (\documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}{\mathrm{{\Psi}}}_{Ca}^{2}\end{equation*}\end{document} = 0.7; \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}{\mathrm{{\Psi}}}_{Ca}^{1}\end{equation*}\end{document} = 0.089) such that when the channel is Ca2+ saturated (thick solid line) T2 becomes rate determining when i = 2–4 (starred traces).

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