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Department of Physiology, University of Pennsylvania School of Medicine Philadelphia, PA 19104

Correspondence to Frank T. Horrigan: horrigan{at}mail.med.upenn.edu

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
BK (Slo1) potassium channels are activated by millimolar intracellular Mg²⁺ as well as micromolar Ca²⁺ and membrane depolarization. Mg²⁺ and Ca²⁺ act in an approximately additive manner at different binding sites to shift the conductance–voltage (G_K-V) relation, suggesting that these ligands might work through functionally similar but independent mechanisms. However, we find that the mechanism of Mg²⁺ action is highly dependent on voltage sensor activation and therefore differs fundamentally from that of Ca²⁺. Evidence that Ca²⁺ acts independently of voltage sensor activation includes an ability to increase open probability (P_O) at extreme negative voltages where voltage sensors are in the resting state; 2 µM Ca²⁺ increases P_O more than 15-fold at –120 mV. However 10 mM Mg²⁺, which has an effect on the G_K-V relation similar to 2 µM Ca²⁺, has no detectable effect on P_O when voltage sensors are in the resting state. Gating currents are only slightly altered by Mg²⁺ when channels are closed, indicating that Mg²⁺ does not act merely to promote voltage sensor activation. Indeed, channel opening is facilitated in a voltage-independent manner by Mg²⁺ in a mutant (R210C) whose voltage sensors are constitutively activated. Thus, 10 mM Mg²⁺ increases P_O only when voltage sensors are activated, effectively strengthening the allosteric coupling of voltage sensor activation to channel opening. Increasing Mg²⁺ from 10 to 100 mM, to occupy very low affinity binding sites, has additional effects on gating that more closely resemble those of Ca²⁺. The effects of Mg²⁺ on steady-state activation and I_K kinetics are discussed in terms of an allosteric gating scheme and the state-dependent interactions between Mg²⁺ and voltage sensor that may underlie this mechanism.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The activity of BK-type Ca²⁺-activated K⁺ channels is important for the function of nerve, muscle, and secretory cells (Vergara et al., 1998). BK channels respond to two primary signals, membrane voltage and intracellular Ca²⁺, but are also sensitive to a variety of regulatory ligands, including intracellular Mg²⁺ (Shi and Cui, 2001; Zhang et al., 2001), heme (Tang et al., 2003), and protons (Avdonin et al., 2003), that can influence channel gating under physiological and/or pathophysiological conditions. Therefore, to understand how BK channel activity is regulated it is important to understand how these signaling and regulatory factors affect channel gating and interact with each other. Previous studies suggest that millimolar [Mg²⁺]_i and micromolar [Ca²⁺]_i activate BK channels through similar functional mechanisms (Shi and Cui, 2001; Zhang et al., 2001). Here we show that the action of Mg²⁺ differs from that of Ca²⁺ in its dependence on voltage sensor activation. The results highlight that multiple pathways of communication exist between the transmembrane and cytosolic domains of BK channels.

That Ca²⁺ and voltage act independently to regulate opening is evident from BK channel function and consistent with channel structure. BK channels can be fully activated by membrane depolarization in the absence of Ca²⁺ (Cui et al., 1997), and Ca²⁺ facilitates opening in a nearly voltage-independent manner, indicating that Ca²⁺ and voltage sensor activation have energetically additive effects on opening (Cui and Aldrich, 2000; Horrigan and Aldrich, 2002). The transmembrane domain of BK channels, like voltage-gated K⁺ (Kv) channels, includes an S5–S6 pore domain and a charged S1–S4 voltage sensor (Ma et al., 2006). Coupling between the voltage sensor and pore can occur presumably as in Kv channels, via interactions within the transmembrane domain (Fig. 1 A) (Lu et al., 2002; Long et al., 2005b). In addition, BK channels contain a large C-terminal cytosolic domain that interacts with intracellular ligands and is directly attached to the S6 activation gate. The cytosolic domain of each -subunit contains two putative RCK (regulator of K⁺ conductance) homology domains (RCK1, RCK2), like those in the prokaryotic channel MthK (Jiang et al., 2001). In MthK, RCK domains from different subunits assemble into a gating ring structure that expands upon Ca²⁺ binding to pull open the gate (Fig. 1 B) (Jiang et al., 2002; Ye et al., 2006), suggesting that Ca²⁺ opens BK channels by increasing tension on the RCK1–S6 linker (Niu et al., 2004). Thus models of BK channel structure support that voltage and Ca²⁺ sensors may act independently on the gate (Fig. 1 C) to exert additive effects on steady-state activation.

View larger version (35K): [in this window] [in a new window] [Download PPT slide]   Figure 1. Proposed pathways of sensor/gate interaction for different channels. (A) Kv1.2, where the charged S4 segment (light blue) in the voltage sensor is proposed to interact with the S6 activation gate (dark blue) in the pore via the S4–S5 linker (arrows). The outlines of the S1–S4 voltage sensor domain and S5–S6 pore domain for two subunits from the Kv1.2 crystal structure (Long et al., 2005a) are shown in dark and light gray, respectively, and are truncated at S1 (protein data bank code 2A79). (B) MthK, where Ca2+ binding to the cytosolic domain is proposed to cause a conformational change that pulls open the gate through short peptide linkers (dashed lines) that are unresolved in the crystal structure (Jiang et al., 2002) (protein data bank code 1LNQ). The attachment points of the linker on the cytosolic domain (in foreground and background) have been altered to better illustrate that linkers are pulled away from the pore axis. (C) A hypothetical BK channel structure formed by appending the Kv1.2 voltage sensors to MthK shows how Ca2+ and voltage may both interact with the gate to have independent effects on activation. The position of the voltage sensors was determined by superimposing the pore domains of Kv1.2 (residues 341–406) and MthK (residues 26–91) in PyMol (http://www.pymol.org). (D) The hypothetical BK channel structure also illustrates the possibility that the large cytosolic domain may interact directly with voltage sensors.

Mg²⁺ has effects on BK channel gating that resemble those of Ca²⁺: increasing P_O, slowing I_K deactivation, and shifting the G_K-V relation to more negative voltages with little change in shape (Shi and Cui, 2001; Zhang et al., 2001). Effects of Mg²⁺ and Ca²⁺ on the half-activation voltage (V_0.5) are approximately additive and involve different binding sites (Shi et al., 2002; Xia et al., 2002). Consequently, Mg²⁺ has been proposed to act independently of Ca²⁺ but through a similar functional mechanism. Effects of Mg²⁺ on the G_K-V relation can be reproduced by gating schemes that assume Mg²⁺ acts, like Ca²⁺, to enhance channel opening independent of voltage sensor activation (Shi and Cui, 2001; Zhang et al., 2001; Hu et al., 2006). However, several lines of evidence suggest that Mg²⁺ and Ca²⁺ do not act through identical functional mechanisms. First, high concentrations of Ca²⁺ (>100 µM), which are known to occupy Mg²⁺ binding sites, have effects that differ qualitatively from those of low [Ca²⁺]_i. While 0–100 µM Ca²⁺ produces a nearly voltage-independent increase in log(P_O), 100–1,000 µM Ca²⁺ increases log(P_O) in a voltage-dependent manner (Horrigan and Aldrich, 2002). In addition, mutations in the voltage sensor, including R213Q in S4, disrupt Mg²⁺ sensitivity but not Ca²⁺ sensitivity, suggesting that the voltage sensor plays a critical role in Mg²⁺-dependent activation (Hu et al., 2003). Indeed, recent evidence indicates that Mg²⁺ bound to the cytosolic domain interacts electrostatically with R213 (Yang et al., 2007).

This study examines the functional interaction between Mg²⁺- and voltage-dependent activation of mSlo1 BK channels. Effects of 0–100 mM Mg²⁺ on the steady-state and kinetic properties of ionic and gating currents were examined over a wide voltage range in WT channels and channels where either the voltage sensor or a putative Mg²⁺-binding site in the RCK1 domain were mutated. The results show that Mg²⁺ at the RCK1 site acts primarily to strengthen the allosteric coupling of voltage sensor activation to channel opening. Only at high concentrations (>10 mM), involving an additional very low affinity binding site, does Mg²⁺ have direct effects on opening, like Ca²⁺. Our results together with the proposed electrostatic nature of Mg²⁺/voltage sensor interaction suggest that Mg²⁺ and the voltage sensor must interact in multiple states to account for the effects of Mg²⁺ on voltage sensor/gate coupling.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Channel Expression and Molecular Biology
Experiments were performed with the mbr5 clone of the mouse Slo1 gene (mSlo1) (Butler et al., 1993) expressed in Xenopus oocytes (for I_K) or HEK 293T cells (for gating current). The clone was propagated and cRNA transcribed as described previously (Cox et al., 1997). Oocytes were injected with 0.5–5 ng of cRNA, incubated at 18°C, and studied 3–7 d after injection. HEK cells were transfected with mSlo1 in an SR vector using Lipofectamine (GIBCO BRL/Life Technologies Inc.) 2–3 d before recording as described previously (Horrigan and Aldrich, 2002). Site-directed mutagenesis was performed with the QuikChange XL Site-Directed Mutagenesis Kit (Stratagene) and confirmed by sequencing.

Electrophysiology and Data Analysis
Currents were recorded using the patch-clamp technique in the inside-out configuration (Hamill et al., 1981) at 20 ± 1°C. For Ca²⁺ experiments, the external solution contained (in mM) 104 KMeSO₃, 6 KCl, 2 MgCl₂, 20 HEPES, and the internal solution contained 110 KMeSO₃, 6 HCl, 20 HEPES, and 2 EGTA (0 Ca²⁺) or 5 HEDTA (Ca²⁺ solution). Ca²⁺ was added as CaCl₂ and [Cl^–]_i was adjusted to 10 mM with HCl. Free [Ca²⁺] for the 2 µM Ca²⁺ solution was measured (1.8 µM) with a Ca²⁺ electrode (Orion Research Inc.). For Mg²⁺ experiments, the external solution contained (in mM) 225 KOH, 196 HCl, 2 MgCl₂, 10 HEPES, and internal solutions contained 225 KOH, 5 EGTA, 10 HEPES, plus MgCl₂ and HCl to obtain the desired [Mg²⁺] with [Cl^–]_i = 200 mM. 100 mM Mg²⁺ solution contained a total of 100 mM Mg²⁺ for an estimated free [Mg²⁺] of 96.1 mM. Total Mg²⁺ in other solutions was adjusted to obtain the indicated free [Mg²] (2, 5, 10, 21 mM) as calculated by MaxChelator (http://www.stanford.edu/cpatton/maxc.html) (Patton et al., 2004). Since free [Mg²⁺] was not measured, the purity of MgCl₂ and EGTA stocks were assayed by pH-metric titration (Tsien and Pozzan, 1989) against standardized solutions of EDTA and CaCl₂, respectively. For gating currents (I_g) the external solution contained 130 tetraethyl ammonium (TEA)-OH, 100 NMDG, 196 HCl, 2 MgCl₂, 10 HEPES, and internal solution contained 225 NMDG-MES, 10 HEPES, 5 EGTA, plus MgCl₂ and HCl as above. The pH of all solutions was adjusted to 7.2 with MeSO₃. Internal solutions contained 40 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA) to chelate contaminant Ba²⁺ (Diaz et al., 1996; Neyton, 1996).

Data were acquired with an Axopatch 200B amplifier (Molecular Devices Corp.) in patch mode with the Axopatch's filter set at 100 kHz. Currents were filtered by an 8-pole Bessel filter (Frequency Device, Inc.) at 50 kHz (I_K) or 20 kHz (I_g) and sampled at 200 kHz with an 18-bit A/D converter (Instrutech ITC-18). For gating currents, the voltage command was also filtered at 20 kHz. A p/4 protocol was used for leak subtraction (Armstrong and Bezanilla, 1974) with a holding potential of –80 mV. Electrodes were made from thick-walled 1010 glass (World Precision Instruments, Inc.) and their tips coated with wax (KERR Sticky Wax). The electrode's resistance in the bath solution (0.5–1.5 M) was used as an estimate of series of resistance (R_S) for correcting the voltage at which macroscopic I_K was recorded. Series resistance error was <15 mV for all data presented. A Macintosh-based computer system was used in combination with Pulse Control acquisition software (Herrington and Bookman, 1995) and Igor Pro for graphing and data analysis (WaveMetrics, Inc.). A Levenberg-Marquardt algorithm was used to perform nonlinear least-squared fits. Data are presented as mean ± SEM.

Open probability (P_O) was estimated by recording macroscopic I_K when P_O was high (0.005–0.05) and unitary currents in the same patch when P_O was low (0.01–0.1). Macroscopic conductance (G_K) was determined from tail currents at –80 mV following 50-ms voltage pulses, and was normalized by G_Kmax to estimate P_O. G_Kmax was measured in 5–100 mM Mg²⁺ (0 Ca²⁺) at V > 200 mV from tail currents and was estimated at [Mg²⁺] < 5 mM as G_Kmax (10 Mg²⁺) {_K([Mg²⁺])/_K(10 Mg²⁺)} where _K([Mg²⁺]) is the single channel conductance at –80 mV and is reduced slightly (5%) in 10 Mg²⁺ due to Mg²⁺ block. At more negative voltages, NP_O was determined from steady-state recordings of 1–60 s duration that were digitally filtered at 5 kHz. NP_O was determined from all-points amplitude histograms by measuring the fraction of time spent (P_K) at each open level (K) using a half-amplitude criteria and summing their contributions NP_o = kP_k. P_O was then determined by estimating N from G_Kmax (N = G_Kmax/_K, where _K is the single channel conductance at –80 mV). Mean activation charge displacement (q_a = kT d(ln(P_O)/dV) was measured from the slope of the ln(P_O)-V relation by linear regression over 60-mV intervals and plotted against mean voltage. Fits of the q_a-V relation were similarly determined by linear regression of simulated data (Ma et al., 2006).

Patch-to-patch variation in V_0.5 of the G-V and Q-V relationships are observed for Slo1 channels (Stefani et al., 1997; Horrigan et al., 1999). To compensate for the effect of such variation on mean P_o-V and Q_C-V relations, V_0.5 was determined for each patch and individual relations were shifted along the voltage axis by V_0.5 = (<V_0.5> – V_0.5) before averaging, where <V_0.5> is the mean for all experiments at the same [Mg²⁺]. Patch to patch variation in P_O at extreme negative voltages is also observed (Horrigan et al., 1999). Therefore, mean log(P_O)-V and _K-V relations for 0, 10, and 100 mM Mg²⁺ were constructed using only experiments in which both Mg²⁺ data and matching 0 Mg²⁺ controls exist. In this way, mean relations accurately reflect effects of Mg²⁺ that were observed in individual experiments.

Gating capacitance (C_g) was measured using admittance analysis as previously described (Horrigan and Aldrich, 1999). In brief, gating currents were recorded in response to 0.5-s voltage ramps upon which a sinusoidal voltage command (781 hz, 60 mV peak to peak) was superimposed. Admittance was calculated for each cycle of the sinewave, and capacitance was determined after correcting for phase shifts due to instrumentation.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Mg²⁺ and Ca²⁺ Act through Different Mechanisms
The effects of millimolar [Mg²⁺]_i and micromolar [Ca²⁺]_i on steady-state activation are compared in Fig. 2. In addition to increasing open probability, intracellular Mg²⁺ rapidly blocks the pore in a voltage-dependent manner that effectively reduces single channel conductance at depolarized voltages (Ferguson, 1991). Both of these effects are evident by comparing macroscopic potassium currents (I_K) in the presence and absence of 10 mM Mg²⁺ (Fig. 2 A). I_K was evoked by 50-ms pulses to different voltages in inside-out patches from Xenopus oocytes expressing mSlo1 BK channels. Mg²⁺ decreases outward current at the most positive voltages owing to pore block, but increases tail currents at –80 mV, indicating that P_O is increased. Normalized G_K-V relations, determined from tail currents exhibit a –67.2 ± 4.9 mV shift in half-activation voltage (V_0.5) in response to 10 mM Mg²⁺, with little change in shape, similar to the effect of 2 µM Ca²⁺ (Fig. 2 B).

View larger version (40K): [in this window] [in a new window] [Download PPT slide]   Figure 2. Effects of Mg2+ on steady-state activation. (A) Effect of 10 mM Mg2+ on macroscopic IK evoked from mSlo1 channels in response to 50-ms pulses to different voltages in 0 Ca2+ from a holding potential of –80 mV. Mg2+ decreases outward current at high voltages owing to rapid pore block. However tail currents indicate an increase in PO and slowing of channel deactivation. (B) Mean normalized GK-V relations (Po = GK/GKmax) determined from tail currents in 10 mM Mg2+(O), 2 µM Ca2+() or the absence of divalent cations (control, •). (C) Mean log(PO)-V relations corresponding to B achieve a weakly voltage-dependent limiting slope at extreme negative voltages, indicating that voltage sensors are in the resting state. Dotted lines are exponential fits to control and Ca2+ data with partial charge zL = 0.3e (Ma et al., 2006). (D) Voltage sensor mutations R207Q (, ) and R167E (, ) shift both the voltage dependence of activation and Mg2+ sensitivity (0 Mg: filled symbols; 10 mM Mg2+: open symbols) relative to the WT (O, •), implying that Mg2+ action depends on voltage sensor activation and is not intrinsically voltage dependent. (E) Voltage-gating mechanism (Scheme 1). Channels undergo a closed–open (C-O) conformational change that is allosterically regulated by four independent and identical voltage sensors that can undergo a resting-activated (R-A) transition. L and J are voltage-dependent equilibrium constants (L = L0exp(zLV/kT), J = J0exp(zJV/kT) = exp(zJ[V – VhC]/kT)) and D is an allosteric factor. (F) Scheme 2 includes a ligand-binding transition (X-X·M2+) in each subunit that allosterically regulates channel opening and voltage sensor activation as described by factors C and E, respectively. Solid curves in B and C represent a fit of this model to Ca2+-dependent activation in 0–100 µM Ca2+ (Horrigan and Aldrich, 2002) (VhC = 156 mV, zJ = 0.58e, L0 = 1.06 x 10–6, zL = 0.3e, KD(Ca2+) = 11 µM, C = 8, D = 24.4, E = 2.4). The same model with identical values of VhC, zJ, L0, zL, D, and E can fit the Mg2+ data (dotted curves) if Mg2+ binding is assumed to be voltage dependent (i.e., KD(Mg2+) = KD(0)exp(–V2e/kT)) (KD(0) = 9.35 mM, = 0.2, C = 1.66) (G) Scheme 3 assumes that ligand binding allosterically regulates voltage/sensor gate coupling and voltage sensor activation as described by allosteric factors F and E, respectively.

Why Is the Effect of Mg²⁺ Voltage Dependent?
Two different mechanisms could potentially account for the voltage dependence of Mg²⁺ action; the effect of Mg²⁺ could depend on the activation state of the voltage sensor, or Mg²⁺ binding could be intrinsically voltage dependent. Voltage-dependent binding must be considered because if Mg²⁺ interacts with the voltage sensor it could also lie within the membrane electric field; and a model assuming that Mg²⁺ traverses a fraction of the electric field ( = 0.2) to reach its binding site can reproduce the effect of 10 mM Mg²⁺ (Fig. 2, B and C, dotted curves, see legend for details). However, the effects of Mg²⁺ on two voltage sensor mutants (R207Q, R167E) in Fig. 2 D indicate that voltage sensor activation is critical to the effect of Mg²⁺ and probably sufficient to account for the voltage dependence of Mg²⁺ action.

R207Q in S4 and R167E in S2 shift voltage sensor activation to more negative and positive voltages, respectively (Ma et al., 2006), such that log(P_O)-V relations for these mutants are shifted along the voltage axis relative to the WT in 0 Mg²⁺ (Fig. 2 D, filled symbols). R207Q also shifts the Q-V relation by more than –250 mV, based on gating current measurements, such that even at –200 mV a significant fraction (0.2) of voltage sensors are activated (Ma et al., 2006). Both R207Q and R167E are readily activated by 10 mM Mg²⁺ at depolarized voltages (Fig. 2 D), suggesting these mutations do not disrupt Mg²⁺ binding nor interactions of Mg²⁺ with the voltage sensor (Hu et al., 2003; Yang et al., 2007). However the voltage dependence of Mg²⁺-dependent activation for the mutants is greatly altered relative to the WT, suggesting that Mg²⁺ action depends on the activation state of the voltage sensor. In the case of R167E, Mg²⁺ has no effect on P_O at voltages up to +60 mV where the WT is strongly activated by Mg²⁺. Conversely, R207Q exhibits a robust 30-fold increase in P_O at negative voltages (–120 to –200 mV) where the WT appears insensitive to Mg²⁺. The response of R207Q indicates that Mg²⁺ is capable of occupying its binding site even at extreme negative voltages. Thus, it is unlikely that Mg²⁺ binding is intrinsically voltage dependent; and the inability of the WT to be activated at negative voltages likely reflects that Mg²⁺ is incapable of increasing P_O when voltage sensors are in the resting state. This hypothesis is supported by comparison of the WT and R167E data that show that channels are Mg²⁺ insensitive when P_O is weakly voltage dependent.

Understanding the Action of Mg²⁺ in Terms of Allosteric Mechanisms
To determine how Mg²⁺ and voltage sensors interact mechanistically we interpreted our results in terms of a well-established allosteric gating scheme that accounts for the effects voltage on steady-state activation of BK channels (Fig. 2 E, Scheme 1) (Horrigan and Aldrich, 1999; Horrigan et al., 1999). Scheme 1 asserts that the opening of the gate can be described as a concerted, weakly voltage-dependent transition between an open and closed conformation (C-O) with zero-voltage equilibrium constant L₀ and partial charge z_L. In addition, voltage sensors in each of four independent and identical subunits can undergo a transition between a resting and activated conformation (R-A) characterized by equilibrium constant J₀ and partial charge z_J. The coupling between voltage sensor and gate is described by an allosteric factor D, such that the C-O equilibrium constant increases D-fold for each voltage sensor activated and the voltage sensor equilibrium increases D-fold when the channel opens.

Based on Scheme 1 there are four distinct mechanisms by which a ligand might alter P_o. Ligand binding could (a) influence the intrinsic stability of the gate (L₀), (b) perturb the voltage sensor equilibrium (J₀), (c) alter voltage sensor/gate coupling (D-factor), or (d) alter the gating charge associated with voltage sensor activation (z_J) or channel opening (z_L). The action of Ca²⁺ is mainly accounted for by an effect on the gate (L₀) with a minor impact on voltage sensor activation (J₀). This mechanism can be represented by an allosteric model (Fig. 2 F, Scheme 2) that successfully reproduces the effects of Ca²⁺ (Fig. 2, B and C, solid lines) in terms of a ligand-binding equilibrium (X-X·M²⁺) and allosteric factors C and E that describe the coupling of Ca²⁺ sensors to the gate and to voltage sensors, respectively (Horrigan and Aldrich, 2002). Direct coupling between Ca²⁺ sensors and gate is evident from the ability of Ca²⁺ to increase P_O whether or not voltage sensors are activated. Thus the insensitivity of P_O to 10 mM Mg²⁺ when voltage sensors are in the resting state rules out a similar interaction between Mg²⁺ sensors and gate and indicates that L₀ is unchanged, but leaves open the possibility that Mg²⁺ affects voltage sensor activation or coupling (Fig. 2 G, Scheme 3) or charge.

Mg²⁺ Has Little Effect on Voltage Sensor Activation when Channels Are Closed
To characterize effects of Mg²⁺ on the voltage sensor we recorded gating current from WT and mutant channels (Fig. 3). The results indicate that Mg²⁺ has little effect on the voltage sensor equilibrium (J₀) or gating charge (z_J).

View larger version (19K): [in this window] [in a new window] [Download PPT slide]   Figure 3. Effects of Mg2+ on gating current were measured in the absence of permeant ions and presence of extracellular tetraethyl ammonium (TEA) to block the pore. (A) Ig evoked by 0.5-ms pulses to +200 mV in the presence (dotted traces) or absence (solid traces) of Mg2+, from two different patches testing the effects 10 or 100 mM Mg2+. (B) Mean QC-V relations in 0 (•), 10 (), and 100 () mM Mg2+ are fit by Boltzmann functions with identical equivalent charge (zJ = 0.58e) (Horrigan and Aldrich, 2002) and were normalized by the fit amplitude (QcMax). QC represents the charge distribution for closed channels, determined by fitting the initial 50–100-µs decay of IgON with an exponential function with time constant gFast and integrating the area under the rising phase and fit (Horrigan and Aldrich, 1999). (C) gFast-V relations for the patch in A are shifted by –21 mV in 10 mM Mg2+. Relations are fit by functions of the form gFast = [(V) + β(V)]–1 where and β are forward and backward rate constants for voltage sensor activation (0 Mg: (0) = 58600 s–1, β(0) = 1930 s–1; 10 Mg: (0) = 45400 s–1, β(0) = 2350 s–1) (z = 0.3 e, zβ = –0.2e). Representative Cg-V relations obtained with admittance analysis for (D) WT or (E) E374A/E399N channels in the presence (black curves) and absence (gray curves) of 10 or 100 mM Mg2+ are fit by the derivative of a Boltzmann function with respect to voltage (dotted curves) with identical amplitude and charge (zJ = 0.58e). Shifts along the voltage axis indicate the change in VhC (VhC). Arrows indicate the upper voltage limit of the fit that was determined over a range where most channels are closed (Po < 0.1). (F) VhC = [VhC(Mg2+) – VhC(0 Mg2+)] for WT (, n = 6) and E374A/E399N (, n = 4) determined from Cg-V relations.

To better quantify small changes in V_hC (V_hC) by Mg²⁺ we examined gating capacitance (C_g) (Fig. 3, D–F). C_g is the voltage-dependent component of membrane capacitance and reflects the derivative of gating charge with respect to voltage. The C_g-V relation was determined from admittance analysis by measuring I_g evoked by a sinusoidal voltage command superimposed on a 500-ms voltage ramp from –200 to +200 mV (see Materials and methods) (Horrigan and Aldrich, 1999, 2002). At voltages where steady-state P_O is low (<0.1), the C_g-V relation approximates the derivative of Q_C-V (Horrigan and Aldrich, 1999). Thus V_hC can be determined directly from shifts in the foot of C_g-V relation (Fig. 3 D). Because C_g-V is determined rapidly and with high voltage resolution, small V_hC shifts are detectable, the effects of applying and washing out Mg²⁺ can be assessed rapidly, and errors in V_hC due to slow changes in V_hC from channel oxidation or electrode potential drift are minimized. C_g-V analysis for the WT (Fig. 3 D) yielded V_hC values (10 Mg: 17.2 ± 1.5 mV [n = 6], 100 Mg: 36.1 ± 1.6 mV [n = 6]) similar to those determined from Q_C-V relations.

The effect of Mg²⁺ on V_hC is comparable to that of micromolar Ca²⁺ (Horrigan and Aldrich, 2002), consistent with a weak interaction between Mg²⁺ binding and voltage sensor activation in closed channels that increases the voltage sensor equilibrium constant J₀ (e.g., E-factor in Schemes 2 and 3, Fig. 2, F and G). However, millimolar Mg²⁺ may also shift voltage-dependent parameters by nonspecific mechanisms such as screening of membrane surface charge (Hu et al., 2006). Therefore, to assess the impact of the RCK1 Mg²⁺ site on J₀ we compared effects of Mg²⁺ on the WT channel to those of a mutant (E374A/E399N) whose RCK1 site is disrupted (Shi et al., 2002; Hu et al., 2006). This mutation of putative Mg²⁺-coordinating residues, which reduces the G_K-V shift in 10 mM Mg²⁺ by 80% to –14.0 ± 2.0 mV, also reduces effects of 10 or 100 mM Mg²⁺ on the C_g-V relation (Fig. 3, E and F). The difference in V_hC between the WT and mutant (V_hC = V_hC(E374A/E399N) – V_hC(WT)) was –9.5 ± 2.8 mV and –11.6 ± 2.8 mV for 10 and 100 Mg²⁺, respectively, likely representing the effect of RCK1 site occupancy on J₀. The similar impact of mutation in 10 and 100 mM Mg²⁺ is consistent with the expectation that the RCK1 site is nearly saturated in 10 mM Mg²⁺(Hu et al., 2006).

The small effect of Mg²⁺ on gating current suggests that Mg²⁺ enhances voltage sensor/gate coupling (D). The –17.2 mV V_hC by 10 mM Mg²⁺ (Fig. 3 F) can account for a similar G_K-V shift but is much too small to explain the observed –67-mV shift (Fig. 2 B). By contrast, an increase in the coupling factor D can shift V_0.5 without affecting V_hC. In addition, enhanced coupling should facilitate channel opening when voltage sensors are fully activated and facilitate voltage sensor activation when channels are open. These predictions are confirmed below by results in Figs. 4 and 5.

View larger version (13K): [in this window] [in a new window] [Download PPT slide]   Figure 4. Mg2+ facilitates opening in a voltage-independent manner when voltage sensors are constitutively activated. (A) Mean log(PO)-V relations for WT (•), R207Q (), and R210C () in 0 Mg2+. Arrows indicate the voltage range where voltage sensors of WT, R207Q, and R210C are fully activated (see text). Dotted curve represents a Boltzmann fit to R210C with partial charge z = 0.46e that describes the weak voltage dependence of channel opening in both mutants when voltage sensors are fully activated (Ma et al., 2006). (B) Mean log(PO)-V relations for R207Q show that 10 mM Mg2+ () increases PO even when voltage sensors are fully activated. Dotted Boltzmann fits from –20 to +240 mV have identical charge (0.46e) but V0.5 is shifted by –91.6 mV in Mg2+, consistent with a 8.2-fold increase in the C-O equilibrium constant. (C) Mean log(PO)-V relations for R210C show that 10 mM Mg2+() increases the C-O equilibrium constant in a voltage-independent manner when voltage sensors are constitutively activated. Boltzmann fits have identical charge (0.46e) but V0.5 is shifted by –122 mV in Mg2+, consistent with a 16.6-fold increase in the C-O equilibrium constant and a twofold increase in the allosteric coupling factor D.

View larger version (33K): [in this window] [in a new window] [Download PPT slide]   Figure 5. Effects of Mg2+ on different binding sites were determined by measuring PO for WT and mutant channels in 0–100 mM Mg2+ (0, blue circle; 2, ; 5, ; 10, blue triangle; 21, ; 100, blue diamond, mM Mg2+). (A) Normalized mean GK-V relations for the WT in 0–100 mM Mg2+. (B) Mean log(PO)-V relations for WT in 0, 10, and 100 mM Mg2+ reveal that 100 Mg2+ increases PO at extreme negative voltages. These plots represent the same data as in A but were averaged in 20 mV rather than 10-mV bins to match the voltage interval for low PO measurements. Dotted lines are exponential fits to PO at extreme negative voltages in 0 and 100 Mg2+ with partial charge zL = 0.3e. (C) Mean log(PO)-V relations in 0, 10, and 100 mM Mg2+ for E374A/E399N show that mutation of the putative Mg2+ site in RCK1 almost abolishes effects of 10 mM Mg2+ but leaves the PO increase by 100 Mg2+ (dotted lines) intact. (D) Mean log(PO)-V relations in 0, 10, and 100 mM Mg2+ for R167E achieve a limiting slope at more positive voltages than the WT, confirming that PO is increased by 100 Mg2+ when voltage sensors are in the resting state (dotted lines). Inset graph plots the ratio of NPO in the presence and absence of Mg2+ at –80 mV from a larger set of experiments. (E) Mean qa-V relations for the WT in 0, 10, and 100 mM Mg2+ were derived from the slope of log(PO)-V in B (see text). Solid curves are estimates of the QO-V relation determined by fitting the foot of the qa-V relation (to 80% of peak qa) with a function qa = zL + 4zJ [1 + exp([VhO – V]zJ/kT)]–1 where zL = 0.3e, zJ = 0.58e, and VhO = 26.5 ± 2.1, –33.6 ± 2.4, –65.6 ± 3.7 mV in 0, 10, and 100 mM Mg2+, respectively. (F) Plot of VCO = VhC – VhO for 10 and 100 mM Mg2+ in WT (blue circle) and E374A/E399N (red square) channels where VhO = [VhO(Mg2+) – VhO(0 Mg2+)] was estimated from the qa-V relation as in E and VhC was determined from gating current (Fig. 3 F). Nonzero values of VCO indicate that Mg2+ alters voltage sensor/gate coupling in the WT. However, effects on coupling are abolished by the E374A/E399N mutation. (G) Alternative representation of Scheme 2 (Fig. 2 F) shows the four states defined by the voltage sensor and gate conformation in each subunit and the equilibrium constants defined by Scheme 1 (Fig. 2 E). Boxes denote the states stabilized by ligand binding, as defined by allosteric factors C and E. (H) In Scheme 3, the allosteric factor F defines a stabilization of the OA state that alters voltage sensor/gate coupling (allosteric factor D). Dotted curves in A–E represent simultaneous fits to the Po-V, log(PO)-V, and qa-V relations in 0, 10, and 100 mM Mg2+ using Scheme 1 (Fig. 2 E) (Table I parameters WTA, E374A/E399N). Solid black curves in A and B represent an alternative fit to the WT data (WTB parameters). Red curves in A represent fits to a two-site model (Eq. 2) that assumes each subunit in the WT contains a very low affinity and an RCK1 binding site described by Schemes 2 and 3, respectively (Table II parameters).

Fig. 4 A compares the log(P_O)-V relations for WT, R207Q, and R210C channels in 0 Mg²⁺. R207Q shifts Q_C-V, as noted above, such that this relation is saturated and voltage sensors are fully activated at V –20 mV (Ma et al., 2006) (Fig. 4 A, labeled arrow). Over this voltage range, P_O is weakly voltage dependent and well described by a Boltzmann function (dotted curve) as expected for channels with fully activated voltage sensors undergoing a two-state C-O transition with equilibrium constant L₀D⁴ (Horrigan and Aldrich, 2002). Importantly, the weak voltage dependence of L₀ reduces P_O to nonsaturating levels at potentials where the mutant voltage sensors are still fully activated (e.g., P_O = 0.04 at –20 mV). The P_O-V relation for R210C is indistinguishable from that of R207Q at V –20 but extends the weakly voltage-dependent phase of P_O to less than –200 mV, suggesting that R210C voltage sensors are constitutively activated (Ma et al., 2006). The difference between WT and R207Q in Fig. 4 A is consistent with a 100-fold change in the voltage sensor equilibrium constant J₀ (Horrigan and Aldrich, 1999; Ma et al., 2006) and illustrates qualitatively the effect expected if Mg²⁺ acts merely to promote voltage sensor activation. That is, an increase in J₀ can shift the steepest part of the log(P_O)-V relation to more negative voltages but cannot increase P_O above the limiting relation defined by L₀D⁴ (Fig. 4 A, dotted curve). By contrast, 10 mM Mg²⁺ markedly increases P_O for R207Q (Fig. 4 B) and R210C channels (Fig. 4 C) when voltage sensors are fully activated, indicating that L₀D⁴ is increased. This increase presumably reflects enhanced voltage sensor/gate coupling (increased D) because L₀, although it cannot be measured directly for R207Q or R210C channels, is insensitive to 10 mM Mg²⁺ in WT and R167E (Fig. 2 D).

Analysis of the mutant data indicate that 10 mM Mg²⁺ produces an approximate twofold increase in the coupling factor D. Fig. 4 C shows that R210C channels are activated by 10 mM Mg²⁺ in a voltage-independent manner, consistent with the assumption that voltage sensors are constitutively activated. Mean log(P₀)-V relations in the presence and absence of Mg²⁺ were fit by Boltzmann functions with identical charge (Fig. 4 C, dotted curves), as expected if Mg²⁺ increases the C-O equilibrium constant by a voltage-independent factor (D⁴) and Mg²⁺ binding is not voltage dependent. A similar response is observed for R207Q at V –20 mV (Fig. 4 B, dotted curves). The fits to R207Q and R210C yield D⁴ values of 8.2 and 16.6, respectively, implying a 1.7–2.0-fold increase in D. A more direct estimate of D⁴ is obtained from the Mg²⁺-dependent increase in P_O for R210C at extreme negative voltage. Over a range of voltages (–200 to –140 mV) where P_O is small (<0.1) and therefore approximates the C-O equilibrium constant, Mg²⁺ increases P_O by an average of 21.6 ± 6.0-fold (D⁴), indicating a 2.16 ± 0.13-fold increase in D, consistent with the Boltzmann fits.

Different Mg²⁺ Sites Have Distinct Effects on Gating
To further characterize the action of Mg²⁺ at both RCK1 and very low affinity binding sites we examined the effects on P_O of different [Mg²⁺]_i, up to 100 mM, in WT and mutant channels (Fig. 5). The RCK1 site with an estimated K_D of 2.2–5.5 mM should be nearly saturated at 10 mM Mg²⁺, whereas a putative very low affinity site (K_D: 40–136 mM) is not significantly affected until concentrations >10 mM (Hu et al., 2006). The effects of high and low concentrations of Mg²⁺ appear similar in that G_K-V relations are progressively shifted to more negative voltages with little change in shape (Fig. 5 A) (Shi and Cui, 2001; Zhang et al., 2001; Hu et al., 2006). Increasing Mg²⁺ from 10 to 100 mM shifted the G-V by an additional –34 mV (Fig. 5 A). However, log(P_O)-V relations reveal that 100 mM Mg²⁺ also increases P_O significantly at extreme negative voltages (Fig. 5 B). Thus it appears that occupancy of very low affinity Mg²⁺ sites, unlike the RCK1 site, influence the gate (L₀) to increase P_O when voltage sensors are not activated.

The log(P_O)-V relation in 100 mM Mg²⁺ appears to achieve a limiting slope between –160 and –140 mV, where P_O is increased 2.9-fold relative to the control (Fig. 5 B, dotted lines), implying a 2.9-fold increase in L₀. However measurements below –140 mV were difficult to obtain. Therefore, to confirm that 100 mM Mg²⁺ increases L₀ we also compared log(P_O)-V relations in 0, 10, and 100 mM Mg²⁺ for two mutant channels (Fig. 5, C and D).

Mutation of the RCK1 site (E374A/E399N) largely eliminates the response to 10 mM Mg²⁺ but leaves the P_O increase by 100 mM Mg²⁺ intact (Fig. 5 C). The mutation reduces the G_K-V shift (V_0.5) by 10 and 100 Mg²⁺ to –14.0 ± 2.0 mV and –34.6 ± 1.8 mV, respectively, similar to previous reports (Shi and Cui, 2001; Hu et al., 2006). The reduced shift allows log(P_O)-V to achieve a limiting slope at more positive voltages than the WT (Fig. 5 C, dotted lines), indicating a 2.9-fold increase in L₀ with 100 mM Mg²⁺, like the WT.

The response of E374A/E399N is important not only in verifying that L₀ is increased by 100 mM Mg²⁺ but also in ruling out that Mg²⁺ occupancy of either the RCK1 site or Ca²⁺-binding sites contribute to L₀. The insensitivity of L₀ to 10 mM Mg²⁺ in the WT could conceivably reflect an ability of Mg²⁺ at the RCK1 site to decrease L₀ that is masked by the action of Mg²⁺ at other sites. However, this possibility is unlikely since L₀ is also insensitive to 10 mM Mg²⁺ in E374A/E399N. In addition this result indicates that high affinity Ca²⁺-binding sites, which are known to bind Mg²⁺ at millimolar concentrations, are not responsible for the L₀ increase in 100 mM Mg²⁺ because such sites should already be nearly saturated in 10 mM Mg²⁺ (Shi and Cui, 2001; Zhang et al., 2001; Hu et al., 2006). Thus the E374A/E399N results confirm that occupancy of a very low affinity Mg²⁺ site is required to increase L₀.

The R167E mutant was used to better quantify the effects of Mg²⁺ on L₀ (Fig. 5, D and E). R167E is activated strongly by 100 mM Mg²⁺ but achieves a limiting slope at voltages 100 mV more positive than the WT (Fig. 5 D, dotted lines). Thus L₀ can be determined at voltages that are sufficiently negative to achieve a limiting slope but not too extreme to prevent steady-state recording. The effects on L₀ of 10 and 100 mM Mg²⁺ were determined from the change in NP_O at –80 mV in patches where Mg²⁺ was repeatedly applied and washed out. The results confirm that 10 mM Mg²⁺ has little or no effect on L₀ (1.06 ± 0.05-fold change, n = 10), whereas 100 mM Mg²⁺ increased L₀ by a factor of 2.24 ± 0.23 (n = 5)(Fig. 5 D, inset).

Mg²⁺ Enhances Voltage Sensor Activation when Channels Are Open
The voltage dependence of P_O in the WT channel provides further evidence that Mg²⁺ enhances voltage sensor/gate coupling. According to Scheme 1, the equilibrium constant for voltage sensor activation when channels are open (J₀D) is directly proportional to D. Therefore the charge–voltage relation for open channels (Q_o-V), should be shifted to more negative voltages by Mg²⁺ if coupling is enhanced. Although BK channel voltage sensors can move when channels are open, determination of Q_o from gating currents is difficult because channels close rapidly (Horrigan and Aldrich, 1999). However, Q_o can be assessed in a model-independent fashion from the logarithmic slope of the P_o-V relation (Horrigan and Aldrich, 2002). The mean activation charge displacement (q_a = kTd(ln[P_o])/dV) exhibits a bell-shaped dependence on voltage that is plotted in Fig. 5 E for 0, 10, and 100 mM Mg²⁺. q_a is expected to approximate Q_o at voltages where both P_O and Q_c are small (Horrigan and Aldrich, 2002; Ma et al., 2006). Thus the Q_o-V relation is approximated by the foot of the q_a-V relation at negative voltages, and is markedly left-shifted by Mg²⁺, indicating that voltage sensor activation is enhanced when channels are open.

To estimate the increase in voltage sensor/gate coupling by Mg²⁺ we fit the foot of the mean q_a-V relations with a function predicted by Scheme 1 to describe Q_o: Q_o = z_l + 4z_JB(V), where B(V) is a Boltzmann function with charge z_J and half activation voltage V_hO (Fig. 5 E, solid curves). The fits indicate that V_hO is shifted by –60 ± 3 mV and –92 ± 4 mV in 10 Mg²⁺ and 100 Mg²⁺, respectively. Changes in the coupling factor D can be determined by comparing the shift in Q_O (V_hO) to that in Q_C (V_hC). Q_O depends on both D and J₀, whereas Q_C depends only on J₀. Therefore the quantity V_CO = [V_hC – V_hO], plotted in Fig. 5 F for WT and E374A/E399N channels, should depend only on D (i.e., D = exp(z_JV_CO/kT), based on Scheme 1). Fig. 5 F indicates V_CO = 43 ± 3 mV in 10 mM Mg²⁺, corresponding to a 2.7-fold increase in D. 100 mM Mg²⁺ produces a larger V_CO (56 ± 4 mV), corresponding to a 3.6-fold increase in D, that probably represents the effect of saturating the RCK1 site. V_CO for the E374A/E399N mutant is not significantly different from 0 (P < 0.05, t test) in 10 or 100 Mg²⁺ (Fig. 5 F), implying that all changes in voltage sensor/gate coupling can be attributed to the RCK1 site.

Modeling the Effects of Mg²⁺ on Steady-State Activation
The above results suggest that 10 mM Mg²⁺ acts primarily at the RCK1 binding site to enhance voltage sensor/gate coupling (D) with a minor effect on the voltage equilibrium (J₀), and that 100 mM Mg²⁺ causes additional increases in D, J₀, and L₀ that reflect action at both RCK1 and very low affinity binding sites. To confirm that these parameter changes are sufficient to describe the effects of Mg²⁺ on steady-state activation and to better quantify the changes in D we fit simultaneously the log(P_O)-V, q_a-V, and P_O-V relations for 0, 10, and 100 mM Mg²⁺ using Scheme 1, as defined by Eq. 1:

(1)

The 0 Mg²⁺ data were fit by setting charge parameters to values determined previously (z_J = 0.58 e, z_L = 0.3 e) (Horrigan and Aldrich, 2002) and allowing all other parameters (J₀, L₀, D) to vary, yielding results (Table I, WT 0 Mg²⁺) similar to previous reports (Horrigan and Aldrich, 2002; Ma et al., 2006). To fit the Mg²⁺ data, the change in J₀ relative to 0 Mg²⁺ was set by gating current measurements (V_hC, Fig. 3 F), while L₀ and D were allowed to vary. Excellent fits to the log(P_O)-V and q_a-V relations were obtained in this way (Fig. 5, B and E, dotted curves), with 10 Mg²⁺ increasing D by a factor of 2.14, and 100 Mg²⁺ causing a greater increase in D (2.83-fold) together with a 2.43-fold increase in L₀ (Table I, WT_A parameters). A similar procedure was used to fit the E374A/E399N data (Fig. 5 C, dotted curves), yielding values of D (Table I, E374A/E399N parameters) that vary by <15% relative to the control, which is within the resolution of our measurement (Ma et al., 2006). Thus, shifts in V_hc determined from gating currents together with an increase in L₀ in 100 Mg²⁺ appear sufficient to account for the changes in log(P_O)-V when the RCK1 site is disrupted.

To account explicitly for the effects of Mg²⁺ binding on the parameters in Scheme 1 we modeled the effects of very low affinity and RCK1 binding sites in terms of Schemes 2 and 3, respectively (Fig. 2, F and G). These allosteric mechanisms assume that Mg²⁺ can bind to any state of the channel defined by Scheme 1 and that effects of Mg²⁺ on the relative stability of different states therefore reflect the relative affinity of Mg²⁺ for these states. This principal is illustrated in Fig. 5 (G and H) by alternative representations of Schemes 2 and 3 that include the four states (CR, OR, CA, OA) and equilibrium constants defined by Scheme 1 for a single subunit, where boxes and associated allosteric factors indicate the states that are stabilized relative to the CR state by ligand binding. In Scheme 2, the action of Mg²⁺ is defined by its dissociation constant for the CR state (K_D) and two allosteric factors (C and E). C defines the increase in affinity associated with channel opening, such that K_D is reduced C-fold for the OR and OA states (Fig. 5 G, labeled box). Likewise, E defines the change in K_D associated with voltage sensor activation (Fig. 5 G, CA and OA states). These changes in affinity can account for effects of Mg²⁺ on the equilibria for channel opening (L₀) and voltage sensor activation (J₀). However, voltage sensor/gate coupling (D) is unchanged in Scheme 2 because the effects of C and E are independent and neither alters binding in a manner that depends on the state of both the voltage sensor and gate. By contrast, in Scheme 3, D is increased F-fold upon ligand binding by assuming that the affinity of the open-activated state (OA) is increased relative to all other states by an allosteric factor F. Scheme 3 also includes an independent effect of voltage sensor activation on Mg²⁺ affinity (E-factor) as in Scheme 2, to account for effects on J₀.

The data in Fig. 5 (A and B) were fit (red curves, Table II parameters) by a two-site model that assumes the channel contains a single RCK1 (site 1, Scheme 3) and a very low affinity (site 2, Scheme 2) binding site in each of four identical subunits, yielding Eq. 2 (see below), where L, J, and D are defined as in Eq. 1; E₁, F₁ and C₂, E₂ are allosteric factors for sites 1 and 2, respectively; and K_i = [Mg²⁺]/K_Di (i = 1,2), where K_Di is dissociation constant for each binding site in the CR state.

(2)

Effects of Mg²⁺ on I_g Kinetics and the Deactivation Pathway
Although gating current is relatively insensitive to Mg²⁺ when channels are closed (Fig. 3), the ability of Mg²⁺ to shift the Q_o-V relation implies that I_g kinetics must be altered when channels are open. Such an effect is evident from OFF gating currents (I_gOFF) following pulses of different duration (0.05–20 ms, +200 mV) in 0 and 10 mM Mg²⁺ (Fig. 6 A). Normalized I_gOFF traces (Fig. 6 B) show that OFF kinetics following brief pulses (0.1 ms, red traces), that are comparable to the delay in I_K activation (Horrigan et al., 1999) and open few channels, are similar in 0 or 10 Mg²⁺. However, as pulse duration increases and channels open, voltage sensor deactivation is slowed, reflecting that Q_o-V is shifted to more negative voltages than Q_c-V (Horrigan and Aldrich, 1999). The slowing of I_gOFF occurs in 0 Mg²⁺ but is more prominent in 10 Mg²⁺ (Fig. 6 B) because Mg²⁺ increases the difference between Q_O and Q_C (Fig. 5 F) and the fraction of channels that open at +200 mV (Fig. 2 B).

View larger version (32K): [in this window] [in a new window] [Download PPT slide]   Figure 6. Mg2+ affects voltage sensor deactivation when channels are open. (A) Ig evoked by pulses to +200 mV of different duration (0.05–20 ms) in 0 and 10 mM Mg2+. (B) Normalized OFF currents from A decay more slowly as pulse duration increases, especially in the presence of Mg2+. Red traces represent 0.05 and 0.1-ms pulses. (C) OFF kinetics at –80 mV following brief (closed) or prolonged (open) pulses are compared by plotting the quantity Q = QOFF(t) – QOFFSS on a log scale vs. time where QOFF is the integral of IgOFF and QOFFSS is the steady-state value of QOFF(t). The "closed" traces, representing the average of 0.05 and 0.1-ms records, have an exponential time course with almost identical kinetics (Fast) in 0 Mg2+ (15.5 µs) or 10 mM Mg2+ (16.3 µs). The "open" traces, representing the average of 10, 15, and 20-ms records, were fit by triple exponential functions (0 Mg2+: qFast = 6.2 fC, Fast = 15.5 µs, qMED = 24.9 fC, MED= 54.1 µs, qSLOW = 11.2 fC, SLOW = 500 µs; 10 Mg2+: qFast = 2.6 fC, Fast = 16.3 µs, qMED = 10.6 fC, MED = 127 µs, qSLOW = 39.1 fC, SLOW = 756 µs). The Med and Slow components of the fits are shown as dotted and solid lines respectively. (D) Scheme 1* depicts the five closed (Ci) and open (Oi) states defined by Scheme 1, where i represents the number of activated voltage sensors (i = 0–4). i and i are forward and reverse rate constants for channel opening while and β are rates for voltage sensor activation when channels are closed, and f = . Colored arrows represent different pathways of deactivation and QOFF components for open channels in 0 Mg2+ (top) or 10 mM Mg2+ (bottom) at –80 mV. In 10 mM Mg2+, channels can close from open states other than O0 because Mg2+ allows voltage sensors in open channels to remain activated at –80 mV (QO, Fig. 5 E). The figure illustrates one possible pathway, through the O2 state. After channels close, voltage sensors can completely deactivate in 10 mM Mg2+ (QC, Fig. 3 B). This charge movement is limited by the closing rate and therefore contributes to the Slow component of QOFF. (E) The amplitude of the three OFF components (Fast, ; Med, light blue square; Slow, pink circle) for the experiment in A are plotted vs. pulse duration and fit by exponential functions (0 Mg2+, = 2.8 ms; 10 Mg2+, = 2.6 ms).

Further insight into the mechanism of Mg²⁺ action is provided by plotting the amplitude of the three OFF components (Q_Fast, Q_Med, Q_Slow) versus pulse duration (Fig. 6 E). As pulse duration increases, Q_Fast is reduced while Q_Med and Q_Slow increase, following the exponential time course of channel opening (solid curves Fig. 6 E) (Horrigan and Aldrich, 1999, 2002). These kinetics are similar in the presence and absence of Mg²⁺ because 10 mM Mg²⁺ has little effect on activation kinetics (Shi and Cui, 2001; Zhang et al., 2001). However the relative amplitudes of Q_Med and Q_Slow are reversed by Mg²⁺. The change in relative amplitude of Q_Med and Q_Slow by Mg²⁺ is qualitatively similar to the effect of recording I_gOFF at a more positive voltage in 0 Mg²⁺ (Horrigan and Aldrich, 1999), supporting that Mg²⁺ shifts Q_o to more negative voltages. In the absence of Mg²⁺, Q_Med is greater than Q_Slow because voltage sensors can completely deactivate at –80 before channels close (Fig. 6 D, 0 Mg²⁺ light blue arrow). That is, the Q_o-V relation in 0 Mg²⁺ indicates that voltage sensors equilibrate to the resting state at –80 mV (Fig. 5 E). By contrast, in 10 Mg²⁺ more than 25% of voltage sensors should remain activated at –80 mV wh