The number of voltage-gated sodium (NaV) channels available to generate action potentials in muscles and nerves is adjusted over seconds to minutes by prior electrical activity, a process called slow inactivation (SI). The basis for SI is uncertain. NaV channels have four domains (DI–DIV), each with a voltage sensor that moves in response to depolarizing stimulation over milliseconds to activate the channels. Here, SI of the skeletal muscle channel NaV1.4 is induced by repetitive stimulation and is studied by recording of sodium currents, gating currents, and changes in the fluorescence of probes on each voltage sensor to assess their movements. The magnitude, voltage dependence, and time course of the onset and recovery of SI are observed to correlate with voltage-sensor movements 10,000-fold slower than those associated with activation. The behavior of each voltage sensor is unique. Development of SI over 1–160 s correlates best with slow immobilization of the sensors in DI and DII; DIII tracks the onset of SI with less fidelity. Showing linkage to the sodium conduction pathway, pore block by tetrodotoxin affects both SI and immobilization of all the sensors, with DI and DII significantly suppressed. Recovery from SI correlates best with slow restoration of mobility of the sensor in DIII. The findings suggest that voltage-sensor movements determine SI and thereby mediate NaV channel availability.

Sodium currents through voltage-gated sodium (NaV) channels activate and inactivate rapidly over several milliseconds. The molecular determinants of these rapid events have been studied extensively. The NaV channel corpus is a single large subunit with four homologous domains that fold to create a single central ion conduction pore with four nonidentical voltage-sensor domains, each carrying a positively charged S4 span (Fig. 1, A and B) (Catterall et al., 2005). On stimulatory depolarization, the S4 spans are propelled outward by the electric field: the pore opens, and sodium ions flow down the electrochemical gradient into the cell. Thereafter, a fast inactivation “lid” formed by the cytoplasmic linker between DIII and DIV occludes the pore (Fig. 1, C–E). The protein returns to its resting conformation on repolarization. Individual voltage sensors have unique roles in these rapid gating events. Using voltage-clamp fluorimetry (VCF) to detect motion of each S4 segment in NaV1.4 channels (Fig. 1, F and G), Bezanilla and colleagues demonstrated that movements of the sensors in DI, DII, and DIII correlate with activation, whereas DIII and DIV are coupled to fast inactivation and recovery (Cha et al., 1999; Chanda and Bezanilla, 2002; Chanda et al., 2004).

Upon prolonged depolarization, NaV channels progressively enter the slow inactivation (SI) state from which they are also slow to recover. Indicating that several conformation states are involved in SI gating, the kinetics of the development of SI show multiple time constants and the rate of recovery from SI slows with progressively longer depolarizing pulses (Toib et al., 1998; Vilin and Ruben, 2001). This complex response to long-lasting depolarization propagates from the cellular to organ level to mediate important aspects of physiology; thus, SI endows neuronal tissues with memory of previous excitation (Toib et al., 1998), prevents excitation of skeletal muscle by mild hyperkalemia (Bendahhou et al., 2002), and affects the conduction velocity and excitability of cardiac tissue (Shaw and Rudy, 1997).

Studies seeking to identify an SI gate in NaV channels have implicated sites throughout the channel, including the outer portion of the ion conduction pore, the inner pore region, and the voltage-sensor domains. Using VCF to assess changes in the environment of the four S4 segments in NaV1.4, we find that the magnitude, voltage dependence, and time course for SI development and recovery track slow immobilization and restoration of mobility of the voltage sensors in DI, DII, and DIII. Evidence for direct coupling of DI and DII immobilization and development of SI is provided by suppression of both by tetrodotoxin (TTX). In our companion paper in this issue (Silva and Goldstein), we evaluate NaV1.4 with a mutation that causes hyperkalemic periodic paralysis (L689I) (Bendahhou et al., 2002) and confirm coupling of voltage-sensor immobilization and SI, demonstrating correlated perturbations of sensor movements and changes in SI, corroborating the role of DIII in both onset and recovery, and offering a model that recapitulates the voltage dependence and kinetics of SI based on VCF-determined movements of the voltage sensors in DI, DII, and DIII in wild-type and L689I NaV1.4 channels.

### Cut-open oocyte recording

The cRNA for the β subunit (NCBI Protein database accession no. AAH94523.1) of the rat skeletal muscle sodium channel and α-subunit NaV1.4 (NCBI Protein database accession no. CAA76659.1) was produced in pBSTA and injected at a 1:2 molar ratio (40 ng per cell total) into Xenopus laevis oocytes as reported previously (Chanda and Bezanilla 2002). Oocytes were incubated at 16.5°C for 2–5 d in solution with (mM) 96 NaCl, 4 KCl, 1.8 CaCl2, 1 MgCl2, 5 HEPES, and 0.1 EDTA, and 1% penicillin-streptomycin, pH 7.4. Recordings were performed using an amplifier (CA-1B; Dagan Corporation) coupled to an A/D converter (Digidata 1320; Molecular Devices) with Clampex and Clampfit software (v10; Molecular Devices) for acquisition and analysis. Temperature was maintained at 19°C with a controller (HCC-100A; Dagan Corporation). The internal solution was (mM): 113 NMG-Mes, 2 Na-Mes, 20 HEPES, and 2 EGTA, pH 7.4. The external solution was composed of (mM): 95 NMG-Mes, 20 Na-Mes, 20 HEPES, and 2 Ca-Mes2, pH 7.4. Capacitance and leak were subtracted manually. In ionic current studies, gating current was recorded with 2 µM TTX in the external solution and subtracted.

### Fluorescence measurements

Oocytes were labeled with 10 µM tetramethylrhodamine maleimide (TMRM; Invitrogen) in a depolarizing solution (mM: 110 KCl, 1.5 MgCl2, 0.8 CaCl2, and 10 HEPES, pH 7.4) on ice for 20 min. TMRM stock solution was 10 mM in DMSO and stored at −80°C. A tungsten halogen lamp with a 250-W filament powered by a 24-V linear power supply served as the light source. The lamp output was interrupted with a TTL-triggered shutter (Sutter Instrument) to minimize photobleaching of the probe. After collimation (Thorlabs Inc.), light was carried to the microscope via a liquid light guide (Sutter Instrument) and coupled to the microscope via a collimating adapter (EXFO). A 40× water-immersion objective with a numerical aperture of 1.0 and working distance of 2.1 mm (Plan Acrochromat; Zeiss) was used. Light measurements were made with a photodiode (PIN-040A; United Detector Technology) mounted on an XY axis manipulator (Thorlabs Inc.) at the microscope epifluorescence port. The photodiode was attached to the integrating headstage of a patch-clamp amplifier (Axopatch-200A; Molecular Devices) for low noise amplification of the photocurrent. A circuit with a 22.5-V battery and 6-GΩ resistance was used to remove integration spikes by offsetting current into the summing junction of the headstage. The fluorescence emission was focused onto the photodiode active area using an achromatic doublet (Thorlabs Inc.) with a focal distance of 25 mm.

### Data analysis

Parameters were determined by fits of the raw data: SI onset (Table 1) and SI recovery (Table 2). For each trace, three exponentials were fit to the raw data using the “lsqcurvefit” function in MATLAB (MathWorks), which implements a trust-region reflective optimization algorithm. Each of the three exponentials was allowed to range in a unique time scale: from 1 to 10 s, 10 to 100, and 100 to 1,000 s. Points logarithmically distributed in time were then plotted according to the fit. Later to compare traces quantitatively, it was useful to reduce the number of parameters and set the time constants to be invariant, while only the magnitudes were allowed to vary.

### Online supplemental material

Fig. S1 is provided to demonstrate the success of fitting SI traces by varying the magnitudes of three exponentials, while leaving the time constant for each unchanged. It is available at http://www.jgp.org/cgi/content/full/jgp.201210909/DC1.

### Sodium current: Onset of SI

SI develops with repetitive or prolonged activity, limiting the availability of channels that open on depolarization so that peak currents become progressively smaller. In this work, SI is induced using a triple-pulse protocol repeated 320 times (Fig. 2 A); each cycle includes a 5-ms step to +45 mV to measure peak current (phase a), an SI induction phase of 500 ms at various voltages (phase b), and a third phase (c) at the holding voltage of −100 mV lasting 30 ms, a duration sufficient to allow recovery from fast inactivation, but not SI, before the next pulse.

SI depends on induction potential and cycle number; with greater depolarization, a larger fraction of the channels moves into SI states (Fig. 2 A). After 320 cycles to an induction potential of +45 mV, peak currents are decreased by 53 ± 3%. The decrease in current extends over a wide range of timescales (1, 10, and 100 s), requiring description in terms of multiple time constants. SI onset during 320 cycles (∼160 s) can be approximated by three exponential time constants (Fig. S1), τFast = 1.8 ± 0.2 s, τIntermediate = 13.1 ± 1.1 s, and τSlow = 195 ± 33 s, which have fractional magnitudes of 0.13 ± 0.01, 0.11 ± 0.01, and 0.51 ± 0.06, respectively, and a constant remainder (C) of 0.25 ± 0.05 (Table 1). τSlow and C reflect SI continuing in time scales beyond those well studied with 320 cycles and must, therefore, be considered with caution as suggestive; these transitions with τ > 100 s are often referred to as ultraslow (Sandtner et al., 2004; Szendroedi et al., 2007).

### Gating current: Onset of SI

NaV gating currents are generated by charges in the channel protein that move with changes in transmembrane potential and are primarily caused by arg and lys residues in the four S4 segments. Gating currents are recorded here by application of the pore blocker TTX at 2 µM to suppress all sodium ion permeation through the pore (Fig. 1 D). When the triple-pulse protocol is applied, the charge carried by the gating currents decreases with increasing potential and cycle number (Fig. 2 B). The magnitude, voltage dependence, and kinetics of gating charge suppression are observed to be quite different than for SI (Fig. 2 A). After 320 cycles to +45 mV, peak gating charge decreases by just 36 ± 1% and, of particular note, the log–log plot is flat in the 10-s time scale (Fig. 2 B), consistent with ∼70% reduction in the fractional magnitude of τintermediate (Table 1).

### Movement of S4 segments by VCF: Onset of SI

To examine movement of individual voltage sensors, rather than their aggregate manifestation in the gating current, we applied VCF to the same four NaV1.4 channels created by Bezanilla and colleagues to study fast gating events, DI-S216C, DII-S660C, DIII-L115C, and DIV-S1436C (provided by F. Bezanilla, University of Chicago, Chicago, IL; Cha et al., 1999; Chanda and Bezanilla, 2002; Chanda et al., 2004). Each channel bears a cys in place of a natural S4 span residue to permit modification by a fluorophore to monitor sensor movement. Bezanilla and colleagues studied these four mutant channels because they do not disrupt rapid gating. Similarly, we find that the mutations allow for the study of SI (Fig. 3).

Whereas activation of DI-S216C channels produces rapid voltage-dependent changes in fluorescence to a stable level (Fig. 1 F), repetitive activation cycles to induce SI decrease peak fluorescence (Fig. 4 A), indicating that the DI sensor slowly becomes immobile. Unexpectedly, the magnitude, voltage dependence, and kinetics of DI sensor immobilization (Fig. 4 B) resemble SI of ionic currents (Fig. 2 A) rather than gating currents (Fig. 2 B). Thus, SI and DI slow immobilization show voltage-dependent changes from −100 to +15 mV across the three time domains studied. Similarly, VCF with DII-S660C channels reveals slow immobilization of the DII sensor resembling SI of ionic currents rather than gating currents (Fig. 4 B). In contrast, immobilization of DIII bears some likeness to SI but develops at more hyperpolarized potentials (seen as clustering of the traces at potentials more positive than −45 mV). DIV immobilization is also more rapid to develop than SI and most closely resembles gating currents in small fractional amplitudes of τintermediate (Table 1).

### TTX inhibits SI onset and movement of sensors in DI and DII

The observed difference between gating and ion currents during SI is found to be caused in large part by the 2 µM TTX present in the bath during gating studies. Thus, the application of the pore blocker at low levels that inhibit only a portion of the ionic current is observed to suppress SI and, as TTX concentration increases, SI decreases (Fig. 5 A). Suppression of SI is significant in the intermediate time domain with the addition of just 0.2 µM TTX (Table 2). When VCF is performed with 2 µM TTX (the level added to study gating currents), significant suppression of slow immobilization of the DI and DII sensors in the intermediate time domain is observed (Fig. 5 B and Table 2). Potent suppression is apparent for DI and DII as well in the parameter C that reflects the summation of immobilization over the entire protocol (Fig. 5 B, insets, and Table 2). Although TTX-induced changes in SI of the DIII and DIV sensors did not reach significance, a trend was observed in the magnitude of τIntermediate for both domains and τSlow for DIV (P < 0.1) (Table 2). The impact of TTX on SI is perhaps not a surprise given that it shows use-dependent block (Lönnendonker, 1989) and indicates that gating current assessment can be confounded by the blocker, a concern supported by others (Capes et al., 2012).

Given that fluorescence changes are dependent on the movement of S4 sensors, we expect the summation of the traces in the presence of TTX to reflect gating charge immobilization, although correlation between gating currents and fluorescence will be imperfect because they report on different processes (Mannuzzu et al., 1996; Chanda and Bezanilla, 2002). To make the comparison, we estimate that each sensor carries 25% of gating charge (Sheets et al., 2000; Sokolov et al., 2008). A summation of the traces from Fig. 5 B in Fig. 5 C does resemble gating charge immobilization, particularly in the flattening of the curves in the 10-s region of the plot. In contrast, VCF shows inactivation at −75 mV (Fig. 5 C, double arrow) that is not observed in the gating charge perhaps because of movement of adjacent transmembrane segments that register differently in the two measures. Assigning up to 35% of the charge to any sensor at the expense of the others does not significantly affect the plot (not depicted).

### Recovery from SI

Channel availability is a balance between development of SI and recovery from SI. To study recovery, SI is induced by pulses to +45 mV that last 5, 40, or 160 s followed by two steps that are repeated 5,000 times: the first step allows for recovery for 20 ms at the holding voltage of −100 mV, and the second step measures recovery of peak current at +45 mV (Fig. 6 A). As reported by others (Hayward et al., 1997; Toib et al., 1998; Melamed-Frank and Marom, 1999), we observe recovery time constants to increase with longer induction pulses. In the time range studied here, recovery is adequately fit by three time constants (τFast = 0.6 ± 0.3 s, τIntermediate = 4.5 ± 1.1 s, and τSlow = 43.1 ± 4.8 s), with fractional magnitudes that shift to longer time scales with longer induction (Table 3). Thus, all recovery of ionic current occurs with τFast after inductions lasting 5 s. With 40-s inductions, recovery is spread equally across the three time constants, and with 160-s inductions, 90% of recovery occurs with τIntermediate and τSlow. Recovery time constants for gating currents vary less with induction time (Fig. 6 B and Table 3).

Like recovery of ionic currents, VCF shows that restoration of voltage-sensor mobility in all four domains shifts to longer time scales with longer inductions; that is, the amplitude of τS is greater after 160 s rather than after 40- or 5-s pulses (Fig. 7 and Table 3). This hallmark of recovery from SI is most prominent in DIII. Thus, 90% of DIII sensor recovery occurs with τFast after a 5-s induction. After a 40-s induction, recovery is spread evenly across the three time scales. With 160-s inductions, 93% of recovery occurs with τIntermediate and τSlow. In contrast, the sensors in DI, DII, and DIV recover more rapidly than DIII and show less induction time–dependent shift to τIntermediate and τSlow. Of note, the change in fluorescence with SI induced by steps to +45 mV (Fig. 4) is restored by recovery at −100 mV (Fig. 7), and this demonstrates that a potential confounding variable in these studies, bleaching of the reporter fluorophore (TMRM), did not prove to be a problem.

### Modeling voltage-sensor inactivation

To formalize correlations of voltage-sensor movements and SI quantitatively, we parameterized discrete-state Markov models to fit VCF recordings (Fig. 8). A model adequate to recapitulate SI across observed voltages and time scales has five sequential states: one closed, one active, and three inactive (C↔A↔I1↔I2↔I3). Accordingly, the fluorescence signal in the experiments correlates with the C to A transition in the model. As sensors move into the inactive states, the activating transition becomes unavailable and the magnitude of the fluorescence signal decreases. The presence of three inactivating transitions is expected given the success of fitting the experimental data with three independent exponentials (Tables 1 and 2).

The first model transition (C↔A) is orders of magnitude faster (<1 ms) than the rest of the transitions that occur over seconds and is assumed to be in equilibrium so that the steady-state probability that a sensor is in the activated conformation can be used for calculations; steady-state values are derived by fitting F-V curves (Fig. 1) with two saturating Boltzmann functions. In each case, only one Boltzmann function accounted for voltage dependence of a sensor greater than −100 mV, and the second reflected movement at hyperpolarized potentials (Table 4). Rate constants for inactivating transitions are independent of voltage with the exception of recovery for DI and DII, suggesting that voltage acts primarily on the closed to active transition (Table 5).

This work shows that the voltage sensors in all four NaV channel domains slowly immobilize with the development of SI. All four sensors are also restored to mobility with recovery from SI. The sensors do not, however, track these transitions equally well over the times studied (1–160 s). Immobilization of the voltage sensors tracks the onset of SI with a rank order of DI, DII > DIII >> DIV. Consistent with a causal link, TTX significantly reduces both SI in the intermediate (10-s) time domain and slow immobilization of the sensors in DI and DII. Recovery from SI takes longer when induction pulses are extended, and remobilization of voltage sensors tracks this prolonged recovery time course. DIII is notable for resisting remobilization compared with the other sensors and manifests a time course that correlates with recovery, suggesting that it has a role in the transition to restored mobility. A model is where sensors are trapped in an inactive state after activation recapitulates SI and suggests that the voltage dependence of slow sensor immobilization arises from the closed to active transition.

Our findings show that sensor immobilization with SI is different than gating charge immobilization that develops much more rapidly with fast inactivation. In the latter state, NaV sensor immobilization follows occlusion of the inner pore by residues on the DIII–DIV linker, and mobility is restored by repolarization in <20 ms. This does not preclude direct transition between the two immobilized states; indeed, mutations in the inner pore can modify the onset of both (McNulty et al., 2006). However, mutating the “lid” to eliminate fast inactivation allows SI to develop more quickly and completely (Featherstone et al., 1996), and this suggests that SI does not require prior entry in the fast inactive state. Although the inner portion of the NaV channel pore has been implicated in SI by mutations that cause hyperkalemic periodic paralysis (Cummins et al., 1993; Hayward et al., 1999; Bendahhou et al., 2002; Webb and Cannon, 2008), this may be an allosteric effect on sensor movement, as shown here for TTX in the outer pore.

Our demonstration that increasing the concentration of TTX progressively inhibits SI supports the notion that conformational changes in the NaV channel pore cause SI and are suppressed by the toxin. Studies of mutations (Balser et al., 1996; Vilin et al., 1999; Vilin and Ruben, 2001; Xiong et al., 2003, 2006) and alkali ions that stabilize the open state (Townsend and Horn, 1997) have previously argued for a link between the outer pore and SI. Although NaV channel SI has been compared with C-type inactivation of voltage-gated potassium (KV) channels, a process dependent on outer pore collapse, the latter is well described by a single-exponential process and does not change its kinetics of recovery with inducing pulse duration (Toib et al., 1998). These differences may be caused by the coupling of SI and processes in the voltage sensors unique to NaV channels. For example, voltage sensors in NaV channels are sensitive to movement of adjacent sensors (Chanda et al., 2004) and, unlike those in KV channels formed of homotetramers, individual NaV sensors move over different time scales (Gagnon and Bezanilla, 2010). Thus, it may be different kinetic profiles for individual voltage sensors and their interaction that endow a sensor-linked process like SI with greater kinetic complexity in NaV channels.

Unlike the sensors in DI, DII, and DIII, we observe immobilization and restored mobility of the DIV sensor to be poorly correlated with the kinetics of both SI development and recovery in the 1–160-s time range. Nonetheless, a role for DIV in SI at times faster than 1 s seems plausible given its demonstrated function in both activation and fast inactivation (Horn et al., 2000). Although 2 µM TTX shows a nonsignificant trend toward impeding slower components of DIV immobilization (Table 2), this may result from a conformational change in DI with SI that is reflected in DIV as a result of strong cooperativity between the two domains (Chanda et al., 2004).

Recent work by others supports our conclusion that there is conformational coupling of the pore and voltage sensors in NaV1.4 (Capes et al., 2012). They find that neutralizing three charges in the S4 span of DIV creates a new pathway that allows omega currents to pass through the sensor domain, and that TTX in the ion conduction pore alters both omega currents and off-gating currents carried by the remaining DIV charges; these effects were not observed in domains I, II, or III. Although apparently discrepant with our findings, Capes et al. (2012) did not monitor the kinetic development of TTX effects, suggesting that the results can be reconciled if the events they monitor occur on a time scale <1 s.

The structural basis for slow immobilization is not known. Supporting the notion that voltage sensors in KV channels can reside stably in an inactive conformation, the crystal structure of the KV1.2 KV channel (Long et al., 2007) appears to show inactivated sensors (Lewis et al., 2008; Villalba-Galea et al., 2008). The dependence of NaV1.4 SI on time and voltage suggests that slow immobilization of the four nonidentical sensors involves many conformations. For our simulations >1–160 s, linear five-state, four-transition models have proven adequate. However, continuous-time semi-Markovian modeling has also been used, rather than multi-exponential fits, to elegantly describe SI (Marom, 2009; Soudry and Meir, 2010), and a power law with a continuum shift of the time constant value may represent more accurately both the experimental observations and the structural basis for slow voltage-sensor transitions.

Here, we demonstrate correlation of voltage-sensor immobilization and SI, highlighting the close relationship of DI and DII with development of SI and DIII with recovery from SI. DIII appears to reflect the onset of SI but tracks it with less fidelity than DI and DII. We hypothesize that these associations are causal. In our companion paper (Silva and Goldstein 2013), we present further evidence for direct linkage of slow changes in the mobility of these voltage sensors and the onset of SI and the recovery from SI through study of a point mutation in NaV1.4 that is linked to hyperkalemic periodic paralysis and impedes SI.

The authors are grateful to F. Bezanilla, A. Correa, D. Hanck, R. Goldstein, and S. Marom for materials and intellectual gifts during the performance of this work.

This work is supported by the National Institutes of Health (grants 5T32HL007237 and RO1NS058505 to S.A.N. Goldstein) and a Burroughs Wellcome Fund Career Award at the Scientific Interface (to J.R. Silva).

Kenton J. Swartz served as editor.

Balser
J.R.
,
Nuss
H.B.
,
Chiamvimonvat
N.
,
Pérez-García
M.T.
,
Marban
E.
,
Tomaselli
G.F.
.
1996
.
External pore residue mediates slow inactivation in mu 1 rat skeletal muscle sodium channels
.
J. Physiol.
494
:
431
442
.
Bendahhou
S.
,
Cummins
T.R.
,
Kula
R.W.
,
Fu
Y.H.
,
Ptácek
L.J.
.
2002
.
Impairment of slow inactivation as a common mechanism for periodic paralysis in DIIS4-S5
.
Neurology.
58
:
1266
1272
.
Capes
D.L.
,
Arcisio-Miranda
M.
,
Jarecki
B.W.
,
French
R.J.
,
Chanda
B.
.
2012
.
Gating transitions in the selectivity filter region of a sodium channel are coupled to the domain IV voltage sensor
.
Proc. Natl. Acad. Sci. USA.
109
:
2648
2653
.
Catterall
W.A.
,
Goldin
A.L.
,
Waxman
S.G.
.
2005
.
International Union of Pharmacology. XLVII. Nomenclature and structure-function relationships of voltage-gated sodium channels
.
Pharmacol. Rev.
57
:
397
409
.
Cha
A.
,
Ruben
P.C.
,
George
A.L.
Jr
,
Fujimoto
E.
,
Bezanilla
F.
.
1999
.
Voltage sensors in domains III and IV, but not I and II, are immobilized by Na+ channel fast inactivation
.
Neuron.
22
:
73
87
.
Chanda
B.
,
Bezanilla
F.
.
2002
.
Tracking voltage-dependent conformational changes in skeletal muscle sodium channel during activation
.
J. Gen. Physiol.
120
:
629
645
.
Chanda
B.
,
Asamoah
O.K.
,
Bezanilla
F.
.
2004
.
Coupling interactions between voltage sensors of the sodium channel as revealed by site-specific measurements
.
J. Gen. Physiol.
123
:
217
230
.
Cummins
T.R.
,
Zhou
J.
,
Sigworth
F.J.
,
C.
,
Stephan
M.
,
Ptácek
L.J.
,
Agnew
W.S.
.
1993
.
Functional consequences of a Na+ channel mutation causing hyperkalemic periodic paralysis
.
Neuron.
10
:
667
678
.
Featherstone
D.E.
,
Richmond
J.E.
,
Ruben
P.C.
.
1996
.
Interaction between fast and slow inactivation in Skm1 sodium channels
.
Biophys. J.
71
:
3098
3109
.
Gagnon
D.G.
,
Bezanilla
F.
.
2010
.
The contribution of individual subunits to the coupling of the voltage sensor to pore opening in Shaker K channels: Effect of ILT mutations in heterotetramers
.
J. Gen. Physiol.
136
:
555
568
.
Hayward
L.J.
,
Brown
R.H.
Jr
,
Cannon
S.C.
.
1997
.
Slow inactivation differs among mutant Na channels associated with myotonia and periodic paralysis
.
Biophys. J.
72
:
1204
1219
.
Hayward
L.J.
,
Sandoval
G.M.
,
Cannon
S.C.
.
1999
.
Defective slow inactivation of sodium channels contributes to familial periodic paralysis
.
Neurology.
52
:
1447
1453
.
Horn
R.
,
Ding
S.
,
Gruber
H.J.
.
2000
.
Immobilizing the moving parts of voltage-gated ion channels
.
J. Gen. Physiol.
116
:
461
476
.
Lewis
A.
,
Jogini
V.
,
Blachowicz
L.
,
Lainé
M.
,
Roux
B.
.
2008
.
Atomic constraints between the voltage sensor and the pore domain in a voltage-gated K+ channel of known structure
.
J. Gen. Physiol.
131
:
549
561
.
Long
S.B.
,
Tao
X.
,
Campbell
E.B.
,
MacKinnon
R.
.
2007
.
Atomic structure of a voltage-dependent K+ channel in a lipid membrane-like environment
.
Nature.
450
:
376
382
.
Lönnendonker
U.
1989
.
Use-dependent block of sodium channels in frog myelinated nerve by tetrodotoxin and saxitoxin at negative holding potentials
.
Biochim. Biophys. Acta.
985
:
153
160
.
Mannuzzu
L.M.
,
Moronne
M.M.
,
Isacoff
E.Y.
.
1996
.
Direct physical measure of conformational rearrangement underlying potassium channel gating
.
Science.
271
:
213
216
.
Marom
S.
2009
.
Adaptive transition rates in excitable membranes
.
Front Comput Neurosci.
3
:
2
.
McNulty
M.M.
,
Kyle
J.W.
,
Lipkind
G.M.
,
Hanck
D.A.
.
2006
.
An inner pore residue (Asn406) in the Nav1.5 channel controls slow inactivation and enhances mibefradil block to T-type Ca2+ channel levels
.
Mol. Pharmacol.
70
:
1514
1523
.
Melamed-Frank
M.
,
Marom
S.
.
1999
.
A global defect in scaling relationship between electrical activity and availability of muscle sodium channels in hyperkalemic periodic paralysis
.
Pflugers Arch.
438
:
213
217
.
Sandtner
W.
,
Szendroedi
J.
,
Zarrabi
T.
,
Zebedin
E.
,
Hilber
K.
,
Glaaser
I.
,
Fozzard
H.A.
,
Dudley
S.C.
,
Todt
H.
.
2004
.
Lidocaine: a foot in the door of the inner vestibule prevents ultra-slow inactivation of a voltage-gated sodium channel
.
Mol. Pharmacol.
66
:
648
657
.
Shaw
R.M.
,
Rudy
Y.
.
1997
.
Ionic mechanisms of propagation in cardiac tissue. Roles of the sodium and L-type calcium currents during reduced excitability and decreased gap junction coupling
.
Circ. Res.
81
:
727
741
.
Sheets
M.F.
,
Kyle
J.W.
,
Hanck
D.A.
.
2000
.
The role of the putative inactivation lid in sodium channel gating current immobilization
.
J. Gen. Physiol.
115
:
609
620
.
Silva
J.R.
,
Goldstein
S.A.N.
.
2013
.
Voltage-sensor movements describe slow inactivation of voltage-gated sodium channels II: A periodic paralysis mutation in NaV1.4 (L689I)
.
J. Gen. Physiol.
141
:
323
334
.
Sokolov
S.
,
Kraus
R.L.
,
Scheuer
T.
,
Catterall
W.A.
.
2008
.
Inhibition of sodium channel gating by trapping the domain II voltage sensor with protoxin II
.
Mol. Pharmacol.
73
:
1020
1028
.
Soudry
D.
,
Meir
R.
.
2010
.
History-dependent dynamics in a generic model of ion channels—an analytic study
.
Front Comput Neurosci.
4
:
12
.
Stefani
E.
,
Toro
L.
,
Perozo
E.
,
Bezanilla
F.
.
1994
.
Gating of Shaker K+ channels: I. Ionic and gating currents
.
Biophys. J.
66
:
996
1010
.
Szendroedi
J.
,
Sandtner
W.
,
Zarrabi
T.
,
Zebedin
E.
,
Hilber
K.
,
Dudley
S.C.
Jr
,
Fozzard
H.A.
,
Todt
H.
.
2007
.
Speeding the recovery from ultraslow inactivation of voltage-gated Na+ channels by metal ion binding to the selectivity filter: a foot-on-the-door?
Biophys. J.
93
:
4209
4224
.
Toib
A.
,
Lyakhov
V.
,
Marom
S.
.
1998
.
Interaction between duration of activity and time course of recovery from slow inactivation in mammalian brain Na+ channels
.
J. Neurosci.
18
:
1893
1903
.
Townsend
C.
,
Horn
R.
.
1997
.
Effect of alkali metal cations on slow inactivation of cardiac Na+ channels
.
J. Gen. Physiol.
110
:
23
33
.
Vilin
Y.Y.
,
Ruben
P.C.
.
2001
.
Slow inactivation in voltage-gated sodium channels: molecular substrates and contributions to channelopathies
.
Cell Biochem. Biophys.
35
:
171
190
.
Vilin
Y.Y.
,
Makita
N.
,
George
A.L.
Jr
,
Ruben
P.C.
.
1999
.
Structural determinants of slow inactivation in human cardiac and skeletal muscle sodium channels
.
Biophys. J.
77
:
1384
1393
.
Villalba-Galea
C.A.
,
Sandtner
W.
,
Starace
D.M.
,
Bezanilla
F.
.
2008
.
S4-based voltage sensors have three major conformations
.
Proc. Natl. Acad. Sci. USA.
105
:
17600
17607
.
Webb
J.
,
Cannon
S.C.
.
2008
.
Cold-induced defects of sodium channel gating in atypical periodic paralysis plus myotonia
.
Neurology.
70
:
755
761
.
Xiong
W.
,
Li
R.A.
,
Tian
Y.
,
Tomaselli
G.F.
.
2003
.
Molecular motions of the outer ring of charge of the sodium channel: Do they couple to slow inactivation?
J. Gen. Physiol.
122
:
323
332
.
Xiong
W.
,
Farukhi
Y.Z.
,
Tian
Y.
,
Disilvestre
D.
,
Li
R.A.
,
Tomaselli
G.F.
.
2006
.
A conserved ring of charge in mammalian Na+ channels: a molecular regulator of the outer pore conformation during slow inactivation
.
J. Physiol.
576
:
739
754
.

Abbreviations used in this paper:
KV

voltage-gated potassium

NaV

voltage-gated sodium

SI

slow inactivation

TMRM

tetramethylrhodamine maleimide

TTX

tetrodotoxin

VCF

voltage-clamp fluorimetry

## Author notes

J.R. Silva’s present address is Dept. of Biomedical Engineering, Washington University, St. Louis, MO 63130.