Ma Z , Lou XJ , Horrigan FT .

NS42901 NINDS NIH HHS , R01 NS042901 NINDS NIH HHS

	Figure 1. Charged residues in the transmembrane segments of BK and KV channels. (A) The membrane topology of Slo1 and Shaker potassium channel subunits. Both contain a core domain including S1–S4 voltage sensor and S5–S6 pore. Slo1 contains an additional NH2-terminal transmembrane segment (S0) and large COOH-terminal tail. Conserved basic (+) and acidic (−) amino acids in the S1–S4 segments are indicated. (B) Multiple sequence alignment of voltage sensor domain from mouse and Drosophila homologues of Slo1 (mSlo1, dSlo1) and KV channels (KVAP2.1, KVAP, Shaker, KV1.2) based on Jiang et al. (2003). Putative transmembrane segments are denoted by solid lines based on hydropathy analysis of Slo1 (Wallner et al., 1996) and dashed lines based on the structure of KVAP (Jiang et al., 2003). Charged residues that are highly conserved in Slo1 or in KV channels are bold. Positions that were mutated in mSlo1 are numbered and indicated by boxes. Potential voltage-sensing residues in Shaker are indicated by stars, with double stars indicating those where mutation has the greatest impact on gating charge (Aggarwal and MacKinnon, 1996; Seoh et al., 1996).
	Figure 2. Mutation of charged residues in voltage sensor domain alter mSlo1 gating. Families of IK evoked from (A) WT (B) R207Q, and (C) R213C channels in response to pulses to different voltages at 20-mV intervals from a holding potential of −80 mV. Currents in 0 Ca2+ and 50 μM Ca2+ for each channel were recorded from the same patch. Dashed lines indicate the zero current level. (D) GK-V relations (mean ± SEM) for WT and mutant channels are normalized by GKmax determined in 50 μM Ca2+ and are fit by Boltzmann functions (lines). WT (•), R113Q (○), D133Q (□), D153K (▪), D153C (▵), Y163E (▴), R167E (▿), R167A (▾), E180A (), D186A (), R201Q (), R207E (), R207Q (), R210C (), R210E (), R210N (), R213C (), R213E (), E219Q ().
	Figure 3. Data analysis and modeling. (A) Po-V relation for WT mSlo1 channels in 0 Ca2+ (mean ± SEM) is plotted on a semilog scale and fit by the HCA model (solid line, see be-low). The limiting slope at negative voltages is indicated by a dashed line representing the partial charge associated with channel opening (zL = 0.3 e). (B) qa-V relation determined from the logarithmic slope of mean PO (see MATERIALS AND METHODS). (C) HCA gating mechanism asserts that equilibration of the channel gate between closed and open (C–O) is influenced allosterically by four independent and identical voltage sensors that each can be in a resting or activated state (R–A). The equilibrium constants for channel opening L and voltage sensor activation J are voltage dependent with partial charges zL and zJ, respectively (\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{L}}={\mathrm{L}}_{0}e^{{\mathrm{z}}_{{\mathrm{L}}}{\mathrm{V/kT}}},\hspace{.167em}{\mathrm{J}}={\mathrm{J}}_{0}e^{{\mathrm{z}}_{{\mathrm{J}}}{\mathrm{V/kT}}}\end{equation*}\end{document}). The activation of each voltage sensor increases the C–O equilibrium constant by an allosteric coupling factor D. (D) Gating scheme shows the closed and open states (Ci, Oi, where i = number of activated voltage sensors) and equilibrium constants specified by the HCA mechanism. Horizontal transitions represent voltage sensor activation, and vertical transitions represent channel opening. Solid lines in A and B represent best fits to the HCA model (zJ = 0.59 e, zL = 0.3 e, J0 = 0.017, Lo = 1.4 × 10−6, D = 23.1) determined by a semi-automated method (see MATERIALS AND METHODS). Dashed lines in B indicate the charge distribution for open channels (QO, Eq. 5) and the difference between charge distributions for open and closed channels Qo − Qc, Eq. 6), defined by the fit parameters. (E–H) Predicted effects of changing various parameters in the HCA model. (E) Changes in peak qa, expressed as a fraction of the control value (fqaMAX), produced by changing gating charge (zJ, zL) are directly proportional to the fractional change in total gating charge (fzT, where zT = zL + 4zJ). Dashed line indicates unity slope (b = 1). Solid lines indicate effects of proportional changes in both zL and zJ (b = 0.99) or changing zJ alone (b = 0.94). (F) Effects on fqaMAX of fractional changes in L0, J0, or D. (G) Effects on PO-V relation of changing zJ(0.35 e), D(5.1), J0(1.7), or L0(1.4 × 10−4) and leaving other parameters the same as the WT (solid line). (H) The decreases in zJ or D both decrease qaMAX relative to the WT (solid line) but have distinct effects on the qa-V relations. In particular, the steepness of the foot of the curve is reduced together with zJ but is not altered by changing D.
	Figure 4. Effects of voltage sensor mutations on gating charge and allosteric coupling. (A) qaMAX for each voltage sensor mutant was determined from the mean PO-V relation in 0 Ca2+ (see MATERIALS AND METHODS) and normalized to that of the WT (1.89 e). qaMAX for R210C could not be determined for reasons discussed in the text. (B) The total gating charge (zT = zL + 4zJ) and (C) allosteric coupling factor D were estimated from fits of PO-V and qa-V relations to the allosteric models and normalized to those for the WT (zT = 2.62 e, D = 23.9). Shaded bars were determined by semi-automated fitting of the HCA model to 0 Ca2+ data (see MATERIALS AND METHODS). Solid bars represent fits to data in all [Ca2+] using the HA model (Table I) with parameters adjusted manually. (D and E) Confidence limits for manual fits were estimated for zT or D by adjusting zJ (panel D) or D (panel E) respectively from the best fit values (solid line) to exceed the error range of PO as indicated by dashed lines.
	Figure 5. Effect of potential voltage-sensing residue mutations on PO. Mean log(PO)-V relations for (A) WT, (B) R213C, (C) D153K, (D) R167A, and (E) D186A in 0–50 μM Ca2+. Solid lines are the fits to the HA model (Table I parameters). Dashed lines represent the WT fit. (F) Log(PO)-V relations in 0 Ca2+ for WT (○), D153C(▵), D153K (▴), R213C (▿), R213E (▾), R167A (□), R167E (▪), D186A(•), and R113Q () are superimposed to show that mutations reduce voltage dependence at the foot of the curve, consistent with a change in gating charge. Mutant curves were shifted along both axes as described below to match the WT at −90 mV. According to analysis presented in the text, the qa-V relation can be approximated by QO (Eq. 5) at extreme negative voltages. Therefore ln(PO) can be approximated as the sum of a linear and exponential function: ln(PO) = [ln(L0/(1 + L0))+(zL/kT)V] + [4DJ0exp(zJV/kT)]. Curves were shifted along the voltage axis such that the exponential component of this equation for all curves equaled 0.1 log unit at −90 mV, representing the transition between a linear and nonlinear function (i.e., the foot of the curve). Thus, the voltage shift for mutants was ΔV = V0.1(WT) − V0.1(mutant) where V0.1= (kT/zJ)ln[0.1/(4DJ0log(e))], and the parameters zJ, D, and J0 were taken from Table I.
	Figure 6. Effect of potential voltage-sensing residue mutations on qa. Mean qa-V relations for (A) WT, (B) R213C, (C) D153K, (D) R167A, and (E) D186A in 0 Ca2+ and 50 μM Ca2+. Solid lines are the fits to the HA model (Table I parameters). Dashed lines represent the WT fit. (F) Foot of the qa-V relations in 50 Ca2+ for WT (•), Y163E (▾), R213C (□), D153K(○), and R167A (▿) are superimposed to show that the limiting value of qa (i.e., zL) is reduced by voltage sensor mutation. Dashed line represents zL for the WT (0.30 e).
	Figure 7. Voltage sensor mutations reduce the voltage dependence of channel closing. (A) Mean time constants of macroscopic IK (τ(IK)) for WT mSlo1 in 0 Ca2+(○) and 50 μM Ca2+(▴) are plotted on a log scale versus voltage. The limiting exponential voltage dependence is indicated by a solid line that has a slope representing the partial charge zN for channel closing (0 Ca2+, 0.122 ± 0.002 e; 50 Ca2+, 0.130 ± 0.002 e). (B) τ(IK)-V relations in 50 μM Ca2+, normalized at −360 mV, for WT (○), D153K (□), R167A (▾), R213C (▵), and E219Q (). Lines are exponential fits. (C) zN for WT and mutants in 50 μM Ca2+ (▪) is compared with the limiting slope of Po (qaLim) (○). Starred symbols indicate values of zN that are significantly different from the WT (P < 0.0001, Student's t test).
	Figure 8. Effects of S4 mutation on the equilibrium for voltage sensor activation. (A) Mean log(PO)-V relations in 0 Ca2+ for WT(○), R207Q (▵), R207E (▴), and R210C (□). Mutant curves are shifted to more negative voltages, consistent with an increase in the equilibrium constant for voltage sensor activation (J0) in the HA model (lines, Table I parameters). (B) Normalized Q-V relations for WT and R207Q in 0 Ca2+ measured with admittance analysis from single experiments (see MATERIALS AND METHODS). Curves are fit with Boltzmann functions (WT: z = 0.59 e, Vh = 132 mV; R207Q: z = 0.65 e, Vh = −146 mV). (C) Po-V relations and fits from A are plotted on a linear scale to show that mutants have a similar PO and voltage dependence when voltage sensors are fully activated (i.e., V > 0). (D) qa-V relations for WT and R210C in 0 Ca2+ together with HA model fits showing that the voltage dependence of R210C is consistent with a gating charge similar to the WT. (E) Log(PO)-V relations for R210 mutants in 0 Ca2+ (R210C [□], R210N [], R210E []). R210E was best fit at positive voltages by a Boltzmann function with a partial charge of 0.47 e (solid line). Dashed lines are Boltzmann functions with charge of 0.3 e, representing the value of zL for the WT. (F) τ(IK)-V relations for WT, R207Q, and R210C. Mutant curves are fit (lines) with a bell-shaped function τ(IK) = [δ4 + γ4]−1 at potentials where voltage sensors are fully activated. δ4 and γ4 represent forward and backward rates for the C4–O4 transition in the HCA model (Fig. 3 D) and are exponentially dependent on voltage with partial charges z(δ4) and z(γ4), respectively.
	Figure 9. Effects of voltage sensor mutations on coupling. (A) Mean log(PO)-V relations for WT (○), E180A(▪), and R210E (▵) in 0 Ca2+ are superimposed as in Fig. 5 F to show that mutations reduce the magnitude of the voltage-dependent PO increase without altering the voltage sensitivity of PO at negative voltages. (B) Mean log(PO)-V relations for R210E in 0–50 μM Ca2+. Solid lines are the fits to the HA model (Table I parameters) with the coupling factor D reduced sevenfold relative to the WT (dashed lines). (C) qa-v relations for R210E (•) and WT (○) in 0 Ca2+ with HA model fits. The similar voltage dependence of the foot of these curves show that gating charge (zJ, zL) is unchanged.
	Figure 10. (A) Changes in the free energy of voltage sensor activation produced by different mutations (\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*}{\Delta}{\Delta}{\mathrm{G}}_{{\mathrm{V}}}=-{\mathrm{kTln}}({\mathrm{J}}_{0}^{{\mathrm{M}}}/{\mathrm{J}}_{0}^{{\mathrm{WT}}})\end{equation*}\end{document}), where the equilibrium constant J0 is from Table I. (B) Free energy diagram for voltage sensor activation illustrates how mutation of a positively charged (+) residue representing R207 or R210 to a neutral or negatively charged residue (M) may enhance voltage sensor activation by disrupting a salt bridge interaction that normally occurs only in the resting state (R). Solid and dashed curves represent the WT and mutant, respectively. Mutation destabilizes the resting but not the activated state. (C) Scheme I represents the HCA model (Fig. 3 D) modified such that zL increases when voltage sensors are activated . The charges for each transition are shown and the equilibrium constants are as in Fig. 3 D. \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{z}}_{{\mathrm{L}}}^{i}\end{equation*}\end{document} represents the C–O charge where i is the number of activated voltage sensors and \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{z}}_{{\mathrm{L}}}^{i}={\mathrm{z}}_{{\mathrm{L}}}^{0}+i{\Delta}{\mathrm{z}}\end{equation*}\end{document}. To satisfy detailed balance the charge associated with voltage sensor activation must also be increased when channels are open (\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{z}}_{{\mathrm{J}}}^{{\mathrm{O}}}={\mathrm{z}}_{{\mathrm{J}}}^{{\mathrm{C}}}+{\Delta}{\mathrm{z}}\end{equation*}\end{document}). (D) Mean log(PO)-V relation for R210E in 0 Ca2+ is fit (solid curve) by Scheme I (zJ = 0.59 e, \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{z}}_{{\mathrm{L}}}^{0}\end{equation*}\end{document} = 0.3 e, J0 = 1.73, Lo = 8.7 × 10−5, D = 3.1, Δz = 0.04 e). \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{z}}_{{\mathrm{L}}}^{0}\end{equation*}\end{document} was set to the WT value of zL determined at negative voltages (0.3 e, Table I); and the fit indicates that that zL increases to \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{z}}_{{\mathrm{L}}}^{4}\end{equation*}\end{document} = 0.46 e when all four voltage sensors are activated. Solid and dashed lines are exponential functions with partial charges of 0.3 e and 0.46 e, respectively, to show the difference between \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{z}}_{{\mathrm{L}}}^{0}\end{equation*}\end{document} and \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{z}}_{{\mathrm{L}}}^{4}\end{equation*}\end{document}.
	Figure 11. Mechanisms of voltage sensor activation. (A) Cartoon illustrates how voltage sensors may contribute to the gating charge associated with channel opening (zL). The pore and voltage sensor domains for two subunits in a channel are depicted in different combinations of O/C and R/A states respectively. When all voltage sensors are in the resting state, channel opening (RC to RO) displaces peripherally associated voltage sensors through the membrane electric field, thereby moving gating charge (red arrow, \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{z}}_{{\mathrm{L}}}^{{\mathrm{O}}}\end{equation*}\end{document}). For illustration purposes, the voltage sensor is represented by a positively charged rod that translates along its axis when activated (e.g., RC to AC, blue arrow). Activation alters the charge distribution; in this case, moving one of the voltage sensor charges into the electric field. This redistribution allows more gating charge to move upon channel opening (double red arrows) such that zL is increased when voltage sensors are activated (i.e., \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{z}}_{{\mathrm{L}}}^{4}>{\mathrm{z}}_{{\mathrm{L}}}^{0}\end{equation*}\end{document}). (B) Transporter-type mechanism of voltage sensor activation illustrates how positively and negatively charged voltages sensing residues in S2, S3, and S4 may both contribute to gating charge in mSlo1. All charged residues in S2–S4 are shown. Mutation of potential voltage-sensing residues (circled) reduce gating charge, implying that positive and negative charges must move in opposite directions through the electric field during activation. In the resting state, these positive and negative charges are shown as exposed to the internal (yellow) and external (red) solutions, through aqueous crevices, and therefore lie outside of the electric field. Upon activation, the packing of S2–S4 segments is altered such that charges are buried in the electric field, effectively moving positive charges outward and negative charge inward. Colors indicate the exposure of each residues (red, out; yellow, in; gray, buried). Non–voltage-sensing residues and positions (Y163) are shown as remaining in a constant environment.

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