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Biophys J, October 1999, p. 1885-1904, Vol. 77, No. 4

Mechanisms of Cation Permeation in Cardiac Sodium Channel: Description by Dynamic Pore Model

Yasutaka Kurata,* Ryoichi Sato,# Ichiro Hisatome,§ and Sunao Imanishi*

 *Department of Physiology, Kanazawa Medical University, Ishikawa 920-0293, Japan,  #Department of Molecular Pharmacology and Biological Chemistry, Northwestern University Medical School, Chicago, Illinois 60611, and  §First Department of Internal Medicine, Tottori University School of Medicine, Yonago 683-0826, Japan.

    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The selective permeability to monovalent metal cations, as well as the relationship between cation permeation and gating kinetics, was investigated for native tetrodotoxin-insensitive Na-channels in guinea pig ventricular myocytes using the whole-cell patch clamp technique. By the measurement of inward unidirectional currents and biionic reversal potentials, we demonstrate that the cardiac Na-channel is substantially permeable to all of the group Ia and IIIa cations tested, with the selectivity sequence Na+ >=  Li+ > Tl+ > K+ > Rb+ > Cs+. Current kinetics was little affected by the permeant cation species and concentrations tested (<= 160 mM), suggesting that the permeation process is independent of the gating process in the Na-channel. The permeability ratios determined from biionic reversal potentials were concentration and orientation dependent: the selectivity to Na+ increased with increasing internal [K+] or external [Tl+]. The dynamic pore model describing the conformational transition of the Na-channel pore between different selectivity states could account for all the experimental data, whereas conventional static pore models failed to fit the concentration-dependent permeability ratio data. We conclude that the dynamic pore mechanism, independent of the gating machinery, may play an important physiological role in regulating the selective permeability of native Na-channels.

    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Cardiac tetrodotoxin (TTX)-insensitive Na-channels are structurally and pharmacologically distinct from TTX-sensitive ones in neurons or skeletal muscles (Doyle et al., 1993; Favre et al., 1995), and so are possibly different in permeability properties as well. There are many reports on the permeability of Na-channels to monovalent metal cations with little fundamental disagreement in the selectivity (Chandler and Meves, 1965; Hille, 1972, 1975; Cahalan and Begenisich, 1976; Ebert and Goldman, 1976; Begenisich and Cahalan, 1980a). However, most of the previous studies were not for cardiac TTX-insensitive but for TTX-sensitive isoforms; thus we have little information on the selective permeability of cardiac Na-channels. In the present study, therefore, we first investigated the permeability and selectivity of cardiac Na-channels to group Ia and IIIa cations. The inward unidirectional current (IUC), defined as the influx of external cations in the absence of internal permeant cations, as well as the biionic reversal potential (Vrev) from which the permeability ratio (PX/PNa) could be determined using the Goldman-Hodgkin-Katz (GHK) equation, was measured for Na-channels in guinea pig ventricular myocytes.

Single-channel analysis of the cation permeation in native (normally inactivating) Na-channels is technically difficult because of the very brief openings. For that reason, all the recent single-channel studies were not for native Na-channels, but for toxin-modified ones. However, the treatment with toxins such as batrachotoxin (BTX) has been shown to change the conductivity and selectivity of Na-channels (Huang et al., 1979; Khodorov, 1985), indicating that a study using the toxins to slow Na-channel inactivation may miss fundamental properties of the cation transfer in native (toxin-unmodified) Na-channels. Accordingly, we explored the selective permeability of native Na-channels in single heart cells, using the whole-cell current recording.

We also examined whether cation permeation could affect gating behavior by analyzing the activation and inactivation kinetics of IUCs recorded for various cation species and concentrations. It was reported for the neuronal TTX-sensitive Na-channel that the voltage dependence of current activation kinetics shifted to the positive potential by 8-10 mV on replacing Na+ with K+ in the external solution (Hille, 1972). This finding indicates that the rate of Na-channel activation depends on permeant cation species, and so the cation permeation possibly interacts with the gating machinery (also see Yamamoto et al., 1985; French et al., 1996). As suggested by Eisenman and Horn (1983), occupancy of channel pores by permeating cations may, in general, affect gating mechanisms (also see Chesnoy-Marchais, 1985; Matteson and Swenson, 1986; Shuba et al., 1991; Neyton and Pelleschi, 1991; Demo and Yellen, 1992; Gómez-Lagunas and Armstrong, 1994; Kiss and Korn, 1998). Thus, exploring effects of cation permeation on gating behavior may help us to understand more profoundly essential mechanisms of the selective ion permeation in Na-channels.

In this study, we further developed a novel kinetic "dynamic pore" model, which satisfactorily accounts for all the experimental data, including the concentration-dependent biionic PX/PNa and the IUC-concentration relation. Biionic PX/PNa for Na-channels has been reported to depend on concentrations of internal K+, and other internal and external cations (Cahalan and Begenisich, 1976; Ebert and Goldman, 1976; Begenisich and Cahalan, 1980a; Yamamoto et al., 1985); thus the Na-channel selectivity may vary in response to changes in ionic composition. In the previous studies, the concentration-dependent selectivity was interpreted as reflecting the asymmetric energy profile and multiple occupancy of the static pore (Begenisich and Cahalan, 1980a; Eisenman and Horn, 1983; Pérez-Cornejo and Begenisich, 1994; Wells and Tanaka, 1997). Recently, however, the fluctuating-barrier and the conformational models, which allow structural transitions of channel pores between multiple conformations with different conductivity and selectivity properties, have been proposed for describing permeability properties of several ionic channels other than the Na-channel (Heinemann and Sigworth, 1990, 1991; Lux et al., 1990; Draber et al., 1991; Mironov, 1992; Hainsworth et al., 1994). These dynamic mechanisms may also account for the concentration-dependent changes in the Na-channel selectivity. This paper would be the first report to provide a quantitative basis for the hypothesis that Na-channel pores undergo the permeating cation (occupancy)-regulated transitions between two conformations with different selectivity properties.

    MATERIALS AND METHODS
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Cell preparation

Single ventricular myocytes were isolated by the enzymatic dissociation technique described by Mitra and Morad (1985). Briefly, hearts were excised from guinea pigs (300-600 g) under pentobarbital anesthesia (30-50 mg/kg, i.p.). Then, the coronary perfusion via the Langendorff apparatus was initiated with Tyrode's solution of the following composition (mM): NaCl, 140; KCl, 5.4; NaH2PO4, 0.33; MgCl2, 0.5; CaCl2, 1.8; D-glucose, 5.0; HEPES, 5.0 (pH = 7.4 with NaOH). After 5-10-min perfusion of the nominally Ca2+-free solution, the enzyme solution containing 50-100 units/ml collagenase (Yakult, Tokyo, Japan) was perfused for 10 min. The mechanically dispersed cells were stored in KB medium at 4°C, and studied within 8 hr. KB medium contained (mM) K-glutamate, 70; taurine, 20; KCl, 20; KH2PO4, 10; D-glucose, 10; HEPES, 10; EGTA, 0.5 (pH = 7.3 with KOH).

Electrophysiological recording

The whole cell configuration of the patch clamp technique was used for recording Na-channel currents. Pipette electrodes were made from 1.5 mm (o.d.) hematocrit glass capillary tubes with a vertical pipette puller (Narishige PP-83, Tokyo, Japan), having the resistance of 300-500 kOmega when filled with the internal solutions. Liquid junction potentials of the bath (external) solutions to the pipette (internal) solutions were +5 ± 3 mV.

Cell capacitance and series resistance calculated during the capacitive current cancellation ranged 60-180 pF and 0.6-1.5 MOmega , respectively. The series resistance was compensated by 50-70% of the originals. After the compensation, the voltage errors arising from the series resistance (200-800 kOmega ) were less than 2 mV; and capacitive transients were completed within 500 µs. Under our experimental conditions, recordings of Na-channel currents satisfied the criteria described by Colatsky and Tsien (1979), which permit the indirect determination of adequacy of space-clamp control.

The membrane potential was held at -80 mV, and depolarizing test pulses were preceded by 1.5-2.0-s hyperpolarization to -140 (or -150) mV for Na-channels to attain full recovery from inactivation. Cells were depolarized once each 2.0-2.5 s (at 0.4-0.5 Hz) for 10-80 ms. Currents were capacity- and leak-corrected by subtracting the currents in response to the test pulses after 1.5-2.0-s conditioning at -60 mV, where the steady-state availability of Na-channels was nearly zero. All experiments were performed at 8-10°C.

Currents were recorded with an EPC-9 amplifier (HEKA electronic, Lambrecht, Germany), and directly stored in a Macintosh Quadra 840AV computer (Apple Computer, Inc., Cupertino, CA) at 10 kHz. The capacity- and leak-corrected data were digitally filtered at 2 kHz, then analyzed with Pulse/Pulsefit (HEKA electronic) and IGOR (Wave Metrics Inc., Lake Oswego, OR) on the Macintosh computer. The curve fitting with the equations described later was performed using a nonlinear least-square algorithm available in the Pulse/Pulsefit program.

Solutions

Measurement of inward unidirectional currents

The composition of internal and external solutions used for the measurement of IUCs is shown in Table 1. To record IUCs, we used the internal (pipette) solution containing an impermeant cation, tetramethylammonium (TMA), as the only monovalent cation. The concentrations of Na+ and Li+ were limited to 10 mM, because the large currents yielded by Na+ or Li+ at >= 20 mM did not allow satisfactory voltage control. Ionic strength of the test solutions was held constant by adding TMA-salts to the total monovalent cation concentration of 160 mM. Because of the water insolubility of thallium halides, all the components used for Tl-solution (sol) (and for KNO3-sol) are nitrate salts (see Hille, 1972).


                              
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  		TABLE 1   Composition of solutions for recording inward unidirectional currents

Measurement of biionic reversal potentials

The external and internal solutions used for the biionic Vrev measurement are listed in Table 2. The internal concentration of Tl+ was limited to 10 mM for stable Vrev measurement. For blocking the passage of K+ or Tl+ through K-channels and minimizing accumulation of these cations at the intracellular space, 10 mM Cs+ was added to the external K- and Tl-sols. Adding 10 mM Cs+ to the external Na-sol produced no significant change in Vrev.


                              
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  		TABLE 2   Composition of solutions for measurement of biionic reversal potentials

Activity coefficients for monovalent metal cations

Thermodynamic activities (not concentrations) of the test cations in solution should be used to determine the biionic PX/PNa from the GHK equation, and to compute the amplitude of currents carried in model pores. According to the Debye-Hückel theory, the activity coefficients for Li+, Na+, K+, Rb+, Cs+, and Tl+ in 0.16 M salt solutions were assumed to be 0.77, 0.72, 0.71, 0.70, 0.70, and 0.70, respectively. The activity coefficient for Tl+ was set equal to 0.55, because TlNO3 was estimated to be only 78% dissociated in the test solutions (see Hille, 1972).

Experimental procedures

Measurement of inward unidirectional currents

Cells were internally perfused with the TMA-sol containing no permeant cations, and then exposed to a series of the external test solutions with different permeant cation species or different concentrations of a given cation species. The perfusion of the cell interior with the internal TMA-sol was determined to be complete when time-dependent outward currents were almost entirely abolished in the external TMA-sol. For precluding contamination by previously administered cations, the TMA-sol was perfused until inward currents almost completely disappeared before the subsequent test perfusion. In the experiments with various concentrations of a test cation species, external solutions were perfused in the order of increasing concentration, and then the solution of the lowest concentration was readministered to check the reproducibility. Because time-dependent currents could be quickly and almost completely abolished by perfusing the external TMA-sol during repeated applications of the test cations, multiple concentrations and multiple cation species could be studied in the same cell.

With the TMA-sol inside, time-independent leakage and residual K-channel currents were usually very small. When the linear leak resistance between -100 and 0 mV was less than 500 MOmega , the data were discarded. In some experiments, 50 µM TTX was added to provide evidence that time-dependent currents recorded in a test solution were carried in the Na-channel.

Measurement of biionic reversal potentials

Under biionic conditions with one reference species inside and the other test species outside, currents were recorded during 10-20-ms step depolarizations at 5-mV intervals. A value of Vrev was determined for each current family by interpolating peak currents to the zero current axis of the current-voltage (I-V) plot. The reference (control) Vrev was also determined with the reference cation at symmetrical concentrations on both sides of the membrane. When the difference between the reference Vrev values measured before the first and after the final test recording was >2.0 mV, the data were discarded.

Analysis of selective permeability

Current-concentration relationship

Concentration dependence of the peak amplitude of IUCs was approximated with a Michaelis-Menten equation,
I=I<SUB><UP>max</UP></SUB>/[1+(K<SUB><UP>m</UP></SUB>/C)], (1)
where I represents the amplitude of peak currents at a concentration of C. Imax and Km are the maximum current and the apparent dissociation constant, respectively.

Biionic permeability ratio

Selectivity to the monovalent metal cations was quantified as the permeability ratio PX/PNa, which was determined from biionic Vrev using the GHK equation. The permeability ratio PB/PA is given by a biionic form of the GHK equation,
P<SUB><UP>B</UP></SUB>/P<SUB><UP>A</UP></SUB>=([<UP>A<SUP>+</SUP></UP>]<SUB><UP>o</UP></SUB>/[<UP>B<SUP>+</SUP></UP>]<SUB><UP>o</UP></SUB>) · <UP>exp</UP>(&Dgr;V<SUB><UP>rev</UP></SUB> · F/RT), (2)
where Delta Vrev represents the change in Vrev on replacing the reference cation A+ with the test cation B+ in the bath. The constants F, R, and T have their conventional thermodynamic meanings (F/RT = 0.041 mV-1 at 10°C).

Analysis of gating kinetics

Steady-state availability

Voltage-dependent steady-state availability was fitted by a Boltzmann distribution,
I/I<SUB><UP>max</UP></SUB>=1/[1+<UP>exp</UP>{(V<SUB><UP>C</UP></SUB>−V<SUB><UP>H</UP></SUB>)/s}]. (3)
Here, the peak current (I) in the test depolarization to -20 mV after conditioning at various voltages (VC) is expressed relative to the maximum peak current (Imax). Parameters estimated by the fit were the voltage of the half-point (VH) and the slope factor (s), both expressed in mV.

Activation kinetics (time to peak current)

To quantify the shift in voltage dependence of the time to peak current (TP), we used the equation,
T<SUB><UP>P</UP></SUB>(V<SUB><UP>t</UP></SUB>)=T<SUB><UP>C</UP></SUB>+T<SUB><UP>I</UP></SUB> · <UP>exp</UP>{<UP>−</UP>S · (V<SUB><UP>t</UP></SUB>+40)}. (4)
Following Hanck and Sheets (1992b), we constrained TC and S to the values required to fit the control data (for Na+). Then, a shift of the TP-voltage relation for cation X+ relative to that for Na+ (Delta VP) is given by
&Dgr;V<SUB><UP>P</UP></SUB>=<UP>−</UP>(1/S) · <UP>ln</UP>(T<SUB><UP>INa</UP></SUB>/T<SUB><UP>IX</UP></SUB>), (5)
where the TI values for Na+ and X+ are denoted TINa and TIX, respectively.

Inactivation kinetics

The decay phase of Na-channel currents over the voltage range from -60 to +20 mV was fitted by a double exponential function,
I(t)=a<SUB><UP>F</UP></SUB> · <UP>exp</UP>(<UP>−</UP>t/&tgr;<SUB><UP>F</UP></SUB>)+a<SUB><UP>S</UP></SUB> · <UP>exp</UP>(<UP>−</UP>t/&tgr;<SUB><UP>S</UP></SUB>), (6)
where I(t) represents the amplitude of currents at time t, with tau  being the time constant of fast (tau F) or slow (tau S) inactivation. The initial values extrapolated to time zero for the fast and slow components are denoted aF and aS, respectively. According to Hanck and Sheets (1992b), the tau F-voltage relation was fitted to an exponential function,
&tgr;<SUB><UP>F</UP></SUB>(V<SUB><UP>t</UP></SUB>)=&tgr;<SUB><UP>C</UP></SUB>+&tgr;<SUB><UP>I</UP></SUB> · <UP>exp</UP>{<UP>−</UP>S · (V<SUB><UP>t</UP></SUB>+40)}. (7)
A shift of the tau F-voltage relation for cation X+ relative to that for Na+ (Delta VI) is given by
&Dgr;V<SUB><UP>I</UP></SUB>=<UP>−</UP>(1/S) · <UP>ln</UP>(&tgr;<SUB><UP>INa</UP></SUB>/&tgr;<SUB><UP>IX</UP></SUB>), (8)
where tau INa and tau IX represent the tau I values for Na+ and X+, respectively.

Vestibule surface potential and surface charge effects

Na-channels are known to carry fixed negative charges arising from an excess of acidic amino acid residues located in the channel vestibules (Green et al., 1987; Cai and Jordan, 1990). These permanent charges, creating the vestibule surface potential (VS), would affect cation permeation, selectivity, and gating kinetics (Dani, 1986; Cai and Jordan, 1990; Dani and Fox, 1991; Correa et al., 1991; Hanck and Sheets, 1992b; Naranjo and Latorre, 1993). Therefore, we considered the effects of VS and the charge screening or binding by permeant cations in analyzing the Na-channel permeability as well as the gating property.

We approximated VS according to the Gouy-Chapman-Stern (GCS) double layer theory (see Dani, 1986; Hanck and Sheets, 1992b; Naranjo and Latorre, 1993). The relation of VS (mV) to the density of cation-free surface charge sites to be screened (denoted sigma F in sites/nm2) is described by the Grahame equation,
&sfgr;<SUB><UP>F</UP></SUB>=(1/G)[C<SUB>1</SUB> · <UP>exp</UP>(<UP>−</UP>V<SUB><UP>S</UP></SUB>F/RT) (9)

−C<SUB>1</SUB>+C<SUB>2</SUB> · <UP>exp</UP>(<UP>−</UP>2V<SUB><UP>S</UP></SUB>F/RT)−C<SUB>2</SUB>]<SUP>1/2</SUP>,
where the bulk concentrations of monovalent and divalent cations are denoted C1 and C2 (both in M), respectively. The constant G can be set equal to 2.71 at 10°C.

In addition to the screening effect, some cations also reduce VS by binding to the surface charges. According to Hanck and Sheets (1992b), sigma F can be expressed as
&sfgr;<SUB><UP>F</UP></SUB>=&sfgr;<SUB><UP>T</UP></SUB>/<FENCE>1+<LIM><OP>∑</OP></LIM>[C<SUB><UP>i</UP></SUB> · <UP>exp</UP>(<UP>−</UP>V<SUB><UP>S</UP></SUB>z<SUB><UP>i</UP></SUB>F/RT)/K<SUB><UP>Di</UP></SUB>]</FENCE>, (10)
where sigma T is the total density of surface charge sites, being set equal to 0.72 sites/nm2. The dissociation constant for binding the ith cation species is denoted KDi (in M), with Ci being the bulk concentration (in M) and zi the valency. We calculated VS by simultaneously solving Eqs. 9 and 10 with the preselected KD values (0.05 M through infinity for the monovalent metal cations, and 1.2 M for Ca2+).

Kinetic modeling of cation permeation

We examined how well the permeability properties of the Na-channel observed in this study (e.g., I-V and IUC-concentration relations, biionic PX/PNa) can be described by the two types of model pore: 1) static pore of a rigid structure, and 2) "dynamic pore," which undergoes the cation-regulated transition between two conformations with different selectivity properties. State diagrams and mathematical procedures for the dynamic pore model are shown in the Results and in the Appendix; those for the static pore model are essentially the same as described previously (Hille and Schwarz, 1978; Begenisich and Cahalan, 1980a).

Kinetics of ion translocation in the channel pore was described by the discrete energy barrier models based on the Eyring absolute reaction rate theory. We used the two-barrier single-site (2B1S), three-barrier two-site (3B2S) single-occupancy, and 3B2S double-occupancy models. For simplicity, the dynamic pore was assumed to have the 2B1S energy profile, whereas all the energy models were tested for the static pore. (General Gibbs free energy profiles for the 2B1S and 3B2S models are depicted in Fig. A1 in the Appendix.) Rate constants of ion translocation were calculated from the rate theory formulas expressed as functions of total free energies at peaks, wells, and vestibules. Mathematical expressions for the total free energies and transition rate constants are given in the Appendix.

The pore models actually have far more free parameters than can be determined from the experiments, so that it is not possible to optimize all the model parameters. Therefore, the electrical distances in the energy profiles for ion translocation were preselected and held constant while adjusting the parameters (see the Appendix). The first step of the fitting procedure was to systematically compute I-V and IUC-concentration curves from the models, thereby searching a set of the parameters (e.g., energy peak heights, well depths, rate constants of conformational transitions) to give satisfactory fit for the experimental observations. The most promising set of the parameters was then selected and refined for each model to fit the biionic PX/PNa data. The theoretical PX/PNa, as defined by Eq. 2, was determined from the Vrev in I-V relation predicted by the models.

Programming for mathematical analyses and numeric calculations with matrix equations were performed on a Power Macintosh 7600/200 computer (Apple Computer, Inc., Cupertino, CA) using MATLAB, a numeric computation and visualization software for the sciences, from MathWorks, Inc. (Natick, MA).

    RESULTS
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Inward unidirectional currents carried by monovalent metal cations

Figure 1 shows an example of the families of IUCs recorded from a guinea pig ventricular cell bathed in the external solutions containing either TMA alone, one of the group Ia cations (Li+, Na+, K+, Rb+, Cs+), or the group IIIa cation Tl+ (see Table 1). Voltage- and time-dependent IUCs were measurable for all the monovalent metal cations tested. The current families were very similar in the kinetics of current activation and inactivation, and all the time-dependent currents were completely abolished by 50 µM TTX. The currents evoked in the external TMA-sol were very small (<1 pA/pF) but clearly appreciable as compared with the records after TTX perfusion, being possibly carried by Ca2+. According to the previous report by Hille (1972), Tl+ was so toxic to the nerve membrane that the perfusion of Tl+ solutions caused the rundown of Na+ currents as well as the very low membrane resistance. In this study, however, most of the cells tested were tolerant of Tl+: the Na+ currents recorded before and after the exposure to Tl-sols were nearly identical.



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  		FIGURE 1   Families of IUCs carried by the monovalent metal cations during 40-msec step depolarizations to the test potentials ranging from -100 to +40 mV in 10-mV increments. All currents were recorded in the same cell. The order of perfusion of the external test solutions was TMA-, Cs-, Rb-, KCl-, Li-, Na-, KNO3-, Tl-sol (currents in KNO3-sol were not shown). TMA-sol was perfused for 5 min before each application of the test solutions containing the metal cations. The numbers above the current families represent the extracellular cation concentrations in mM.

Influence of cation permeation on gating kinetics

Gating kinetics does not depend on permeant cation species

Figure 2 shows the effects of permeant cation species on the kinetics of Na-channel currents such as the peak IUC-voltage relation, steady-state availability, time to peak current (TP), and fast inactivation (tau F). The availability curve (half-point VH), as well as the peak IUC-voltage relation, shifted toward the negative potentials in accordance with the order of perfusion of all the test solutions except Tl-sol in which the small depolarizing shifts occurred. Coincident with the shifts in the availability and I-V curves, there were significant changes in both TP- and tau F-voltage relation, which were parallel to those in the availability curve (Fig. 2 F). This finding indicates that all the voltage shifts in the kinetic parameters are chiefly due to the time-dependent spontaneous negative shift (see Kimitsuki et al., 1990; Hanck and Sheets, 1992a) or surface charge effects. The rates of the hyperpolarizing shifts during a series of recordings were <10 mV/h, being less than those reported for canine Purkinje cells (>20 mV/h, Hanck and Sheets, 1992a).



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  		FIGURE 2   Voltage-dependent kinetics of the currents carried by the test cations. (A, B) Peak IUC-voltage relationships. Currents in response to step depolarizations from a holding potential of -140 (or -150) mV were recorded, and the peak amplitude of capacity-corrected currents was measured after subtractions of time-independent leak currents. (C) Steady-state availability curves. As shown in the inset, currents were evoked by the step depolarization to -20 mV after 2-s conditioning pulses ranging from -150 to -50 mV in 10-mV increments. Peak currents were normalized to the maximal current at -150 (or -140) mV, then graphed as a function of the conditioning potentials. The solid lines are the best fits with Eq. 3. (D, E) Voltage dependence of TP (D) and tau F (E) determined for the identical current records from the same cell as for (C). (F) Relationships between the voltage shifts in the kinetic parameters. The shift (Delta V) of the TP- or tau F-voltage relation for each test cation relative to that for Na+ was plotted against the half-point (VH) of the availability curve. Means of the data sets from three cells are shown. The solid line represents a parallel shift in two parameters. The order of perfusion of the test solutions is the same as that in Fig. 1. Changing the external anion from Cl- to NO3- yielded the hyperpolarizing shifts of about 10 mV in the kinetic parameters.

Thallous ion apparently affects gating kinetics via surface charge binding effect

Voltage-dependent kinetics of K+ and Tl+ currents was further determined at various concentrations. As shown in Fig. 3, A-D, the increase in external [Tl+] led to the positive shift in the availability curve as well as in the peak I-V relation, whereas the voltage dependence of K+ current kinetics little changed with increasing external [K+]. When Tl-sols containing 5-100 mM Tl+ were consecutively perfused over the same cell, the VH of availability curves positively shifted with the linear concentration dependence (Fig. 3 E). Assuming that the voltage shifts in availability curves entirely reflect the changes in VS, the KD value for Tl+ binding to a negative surface charge was approximated to be 6.0 M from the GCS analysis, being fivefold higher than that reported for Ca2+ (1.2 M, Hanck and Sheets, 1992b). Similarly, both TP- and tau F-voltage curves shifted toward the depolarizing direction as external [Tl+] was raised; the shifts were parallel to those in the availability curve (Fig. 3 F).



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  		FIGURE 3   Voltage-dependent kinetics of K+ and Tl+ currents at various concentrations. (A, B) Peak IUC-voltage and (C, D) steady-state availability curves for K+ (left) and Tl+ (right) at 20-80 mM. Cells were consecutively perfused with 20, 40, and 80 mM KNO3-sols, then with 20, 40, and 80 mM Tl-sols. (E) Half-points of steady-state availability curves determined for Tl+ at 5-100 mM (closed circles) and for K+ at 20-80 mM (open circles). The data for Tl+ and K+ were obtained from different cells. The solid line is a theoretical prediction of VH for Tl+ currents. The changes in the external VS were calculated by the GCS analysis, and added to the control VH value at 10 mM. Thallous ion was estimated to have the surface charge binding effect with KD = 6.0 M. (F) Relationships between the voltage shifts in Tl+ current kinetics. The shift (Delta V) of the TP- or tau F-voltage relation was plotted against the VH of the availability curve. The means of three determinations are plotted. The solid line represents a parallel shift in two parameters. Pulse protocols and procedures for data analyses are the same as those for Fig. 2.

Selective permeability to monovalent metal cations

Concentration dependence of inward unidirectional currents

Figure 4 shows the concentration dependence of peak IUCs carried by the test cations at -20 mV. Within the concentration range tested (<= 160 mM), the peak IUC-concentration relation followed a simple Michaelis-Menten formalism (Eq. 1). As listed in Table 3, the best-fit Km values for K+, Rb+, Cs+, and Tl+ were close to those reported for the TTX-sensitive isoform (Hille, 1975). For estimating the relative permeability to the test cations, the IUC ratio, defined as the amplitude of peak IUCs relative to the Na+ current at the same concentration of C mM (abbreviated by [IX/INa]C), was determined for each test cation at a low concentration of 5 mM (Present study 1 in Table 3). Thallous ion exhibited the apparently high affinity (Km = 21.8 mM) and high conductivity at low concentrations ([ITl/INa]5 = 0.82) for the cardiac TTX-insensitive Na-channel.



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  		FIGURE 4   Peak IUC-concentration relationships for the monovalent metal cations. First, current recordings were performed with the control test solutions (160 mM Cs-, 160 mM Rb-, 40 mM KCl-, 5 mM Li-, 5 mM Na-, and 10 mM Tl-sol) in the same cell. Peak currents were normalized to the Na+ current at 5 mM. Next, currents carried by each test cation at various concentrations were recorded in other cells, and then a peak current at each concentration was normalized to the current at the control concentration as given above for each test cation (e.g., 160 mM for Cs+). The relative amplitude of current peaks at -20 mV was finally calculated as a ratio to the Na+ current at 5 mM. The averaged values for individual test cations (n = 3-4) are plotted. The smooth curves are the best fits with Eq. 1.


                              
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  		TABLE 3   Apparent dissociation constants and permeability ratios for monovalent metal cations

Determination of biionic reversal potential and permeability ratio

The selective permeability to the monovalent metal cations was also examined by a conventional method, that is, the biionic Vrev measurement (Fig. 5). The values of Vrev measured under various biionic conditions and PX/PNa computed using Eq. 2 are shown in Fig. 6, as well as in Table 3 with the previously reported data for comparison. The permeability ratios determined by the two distinct methods (i.e., [IX/INa]5 from IUC data and PX/PNa from biionic Vrev data) for each test cation were very close, consistent with the notion that biionic PX/PNa is directly comparable to the conductance ratio in the limit of low ionic concentrations (i.e., at low occupancy of binding-sites) where the conductance is proportional to the permeant ion concentration (Eisenman and Horn, 1983). The selectivity sequence for group Ia cations was Na+ >=  Li+ > K+ > Rb+ > Cs+ (Eisenman sequence X), being qualitatively the same as for TTX-sensitive isoforms. As shown in Table 3, the relative permeability to K+, Rb+, and Tl+ of the native cardiac Na-channel was greater than that of the native TTX-sensitive one (Hille, 1972), but less than that of the BTX-modified one (Huang et al., 1979).



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  		FIGURE 5   Measurement of biionic Vrev with 40 (top) or 160 (bottom) mM internal K+ and 5-40 mM external Na+. The traces show the capacity- and leak-corrected currents in response to test pulses separated by 5 mV near the reversal potential. Biionic conditions are indicated above each current family. The numbers for individual currents are the test potentials corrected for the liquid junction potentials (in mV). As shown on the extreme right, Vrev was determined by interpolating the peak I-V plots, which exhibited almost linear relation.



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  		FIGURE 6   Biionic Vrev and PX/PNa determined under various biionic conditions. (A, B, D, E). The values of Vrev measured with fixed internal and varied external cation concentrations. Only the mean Vrev values (n = 3-4) are shown, because all the SEMs are within the size of the symbols. The solid lines have a slope of 17.9 mV per twofold change in the external cation concentration, designating the Vrev for the constant (concentration-independent) PX/PNa in Eq. 2; the arrows indicate the reference conditions to predict the Vrev values. (C, F) Concentration dependence of biionic PX/PNa. The values of PX/PNa for individual biionic conditions were computed with Eq. 2 and plotted against the concentrations of the external test cations.

Dependence of biionic permeability ratio on ionic composition

According to the GHK equation (Eq. 2), the concentration-independent biionic PX/PNa requires the identical Vrev for a constant [X+]/[Na+]. However, Fig. 5 clearly shows that the Vrev values measured with a fixed ratio of internal [K+] and external [Na+] are not the same; therefore, biionic PK/PNa is concentration dependent. The concentration dependence of PX/PNa became more manifest when Vrev was measured for various biionic concentrations (Fig. 6). If PX/PNa remains constant as the concentration of a test cation varies on the inside or outside, there should be a shift in Vrev of 17.9 mV (at 10°C) for a twofold change in cation concentration (activity). When internal [K+] or external [Tl+] was varied, however, the Vrev values determined by the experiments were not in accord with the predictions by Eq. 2 for the constant PX/PNa: the shifts were substantially less than 17.9 mV per twofold concentration change (Fig. 6, B and D).

The raise in internal [K+] led to the reduction in PK/PNa: PK/PNa = 0.08 for 160 mM internal K+, and PK/PNa = 0.15-0.16 for a lower internal [K+] of 40 mM (Fig. 6 C). Similarly, PTl/PNa substantially decreased as external [Tl+] increased (Fig. 6 F). The PTl/PNa measured with external Tl+ and internal Na+ both at 80 mM (0.29) was far less than that measured at 10 mM (0.61), indicating that the concentration-dependent manner of PTl/PNa is preserved even when internal [Na+] and external [Tl+] are symmetrically varied. For Rb+ and Cs+, the permeability ratio as determined from the biionic Vrev at 160 mM was less than the IUC ratio at 5 mM ([IX/INa]5) inferred from the IUC-concentration curve (see Table 3). This possibly reflects that PRb/PNa and PCs/PNa are decreasing functions of increasing external [Rb+] and [Cs+], respectively. In contrast, the PK/PNa measured with the fixed internal [Na+] was apparently invariant with changing external [K+]. Thus, the concentration-dependent nature of the cardiac Na-channel selectivity was asymmetric with respect to both ion type and membrane surface.

Kinetic modeling of selective ion permeation in cardiac Na-channel

Development of dynamic pore model

A salient point in the experimental findings is that the biionic PX/PNa depends on concentrations of the permeant cations. Conventional static pore models ascribed the concentration-dependent PX/PNa to the asymmetric energy profile and multiple occupancy. However, we can propose an alternative hypothesis: permeant cations possibly induce a conformational transition of the Na-channel pore associated with a change in selectivity when they occupy a site in the permeation path, thereby causing the occupancy-dependent selectivity change. This mechanism would also yield the low Km in IUC-concentration curves as for Tl+, if the cation-induced conformational transition involves the increase in energy barriers for permeation of the cation on its own.

Based on these notions, we developed the dynamic pore model, assuming that the selectivity filter region of Na-channel pores exists in two conformational states, and examined how well the dynamic pore model accounts for the experimental findings as compared with the static pore model. As illustrated in Fig. 7, the dynamic pore mechanism involves the permeating cation (occupancy)-regulated transition between two conformations with different permeability properties, which are characterized by different energy profiles for each cation. According to this novel mechanism, the decrease in PX/PNa with increasing internal [K+] or external [Tl+], as well as the low Km for Tl+, is attributable to the cation concentration (occupancy)-dependent transition of Na-channel pores from one conformation with low Na+ selectivity (high Tl+ permeability) to the other with high Na+ selectivity (low Tl+ permeability).



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  		FIGURE 7   Minimal dynamic pore schemes for the cardiac Na-channel. (Top) Schematic diagrams of the dynamic pore existing in two conformational states, A and B, with the 2B1S energy profiles for ion passage. The rate constants for the conformational transition are denoted alpha  and beta . (Bottom) State diagrams describing the states of occupancy and possible transitions between the states for three distinct dynamic pore mechanisms, enzymatic transition (Model 1), fluctuation-mode switch (Model 2), and allosteric interaction (Model 3). In the presence of only one permeant cation species, the four allowed states are assigned for the cation-pore interaction. The subscripts O and X represent the empty pore and the pore occupied by the permeant cation X+, respectively.

We tested three subclasses of the dynamic pore model: 1) Model 1 (enzymatic transition), in which the conformational transition of the pore is strictly coupled with occupancy of the site by permeating cations, and so essentially deterministic (irreversible); 2) Model 2 (fluctuation-mode switch) involving random (reversible) fluctuations between two conformational states of the pore, the equilibrium of which shifts toward the Na+-selective structure when a cation occupies the site within the pore; and 3) Model 3 (allosteric interaction), which requires an allosteric regulatory site located out of the restricted pore (e.g., in the vestibule). Basic state diagrams for these distinct model subtypes are depicted at the bottom of Fig. 7.

A set of the model parameters for Na+, K+, and Tl+ was searched for each model subtype to reproduce all the experimental observations satisfactorily. For simplicity, we assumed the conformational transitions to be voltage independent, displacement of the binding site during the conformational transitions to be negligible (see Läuger, 1985), and occupancy of the site by 2 mM Ca2+ to be negligible at >= -20 mV.

Energy profiles for pore models to fit inward unidirectional current data

We first fitted the static and dynamic pore models to the IUC-concentration relationships and to I-V curves. In this study, we could not directly determine the energy profile for Na+ as a reference cation because of the restriction of external [Na+] to 10 mM. Therefore, the energy parameters for Na+ translocation were somewhat arbitrarily set, according to the previous reports for cardiac Na-channels (Sheets et al., 1987; Nilius, 1988). As the initial step, the model parameters were adjusted for each test cation (K+, Rb+, Cs+, Tl+) by reconciling the theoretically computed Km and [IX/INa]5 with the experimentally determined ones. A parameter set that provides the most reasonable fit to the biionic PX/PNa data and to I-V curves was then selected for each model. The best-fit parameters for K+ and Tl+ (and Na+) permeation in the 3B2S static and the dynamic pores are shown in Fig. 8. Also, the energy profiles of the symmetrical static pores to fit the IUC data for all the test cations (except Li+) are listed in Table 4 for reference.



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  		FIGURE 8   Best-fit parameters for the dynamic pores (Models 1 and 3) and for the 3B2S static pore. The parameter values were determined for each model to mimic the kinetic properties of the Na-channel including the biionic PX/PNa and I-V relation. The energy profiles for Na+, K+, and Tl+ (at 0 mV) are shown by the numbers in RT units on individual energy diagrams. The rate constants for the transition from A to B in Model 1 are given as activation energy in RT units (i.e., Delta Galpha in Eq. A21), and the time constants (1/alpha in ns) are also shown in the parentheses. The time constant for the backward transition from B to A (1/beta ) was adjusted to 1000 ns (Delta Gbeta  = 15.6 RT). The dissociation constants (beta /alpha ) for binding K+ and Tl+ (in mM) are shown for Model 3.


                              
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  		TABLE 4   Best-fit energy parameters for static pore models

With the 3B2S static pore model, the energy profiles optimized for single- and double-occupancy pores were very similar, and the location of the rate-limiting barrier for Na+ permeation little affected the determination of energy parameters for other test cations. The well depths for Tl+ binding predicted by the static pore models were <= -4.3 RT, being lower than those previously determined for the binding of divalent metal cations such as Ca2+ (>= -3.5 RT: see Yamamoto et al., 1984; Sheets et al., 1987), whereas the dynamic pore could have shallower wells.

Discrimination of pore models by biionic permeability ratio data

Figure 9 shows how well the biionic PX/PNa data fit the theoretical predictions by the two classes of pore model, the parameters of which were determined from the IUC data. We calculated the theoretical PX/PNa using the 3B2S static and the dynamic pore models with the parameter values selected for providing reasonable fit to the PX/PNa data, especially to the internal [K+]- and external [Tl+]-dependent decreases in PX/PNa (Fig. 8). The comparisons clearly support the choice of the dynamic pore model over the static pore model.



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  		FIGURE 9   Prediction of biionic PX/PNa by the 3B2S static pore and the dynamic pore models. Theoretical Vrev for various biionic conditions was determined by calculating I-V relations for the model pores with the best-fit parameters, then PX/PNa was derived from Eq. 2. The continuous lines show the theoretical PX/PNa predicted by the 3B2S static (single- and double-occupancy) pores and the dynamic pores (Models 1 and 3). The experimental data are also plotted for comparison (open circles). Biionic conditions are indicated above each panel. The data for the symmetrical static pores and Model 2 are not shown, because they did not exhibit the concentration dependence as observed in the experiments.

The symmetrical static pores were rejected because they predicted nearly concentration-independent PX/PNa or the increase in PTl/PNa with increasing external [Tl+]. The static single-occupancy pore with asymmetric energy profiles could qualitatively reproduce both internal [K+]- and external [Tl+]-dependent decrease in PX/PNa, but not compatible with either the external [K+]-independent PK/PNa or the external [Na+]-dependent increase in PTl/PNa. For biionic conditions with a constant concentration ratio, static single-occupancy pore models always predict the concentration independent PX/PNa (Eisenman and Horn, 1983), whereas the biionic PTl/PNa values experimentally determined for the symmetrical concentrations (Na+ versus Tl+) or fixed concentration ratios (Na+ versus K+) were concentration-dependent (Figs. 5 and 6 F). The introduction of multiion occupancy into the 3B2S model, with or without ionic repulsion, did not improve the fit to the PX/PNa data.

Of the dynamic pore model subtypes, Model 1 was considered the best for the following reasons: 1) Model 1 is the simplest version with the minimum number of free parameters. 2) According to classic thermodynamics, the principle of microscopic reversibility must be considered for reversible transitions as in Model 2; however, Model 2 failed to simulate the concentration-dependent PX/PNa when parameter values were limited by the principle of microscopic reversibility. 3) Model 1, with only one binding site in the pore, can fit the PX/PNa data more satisfactorily than Model 3, which requires two extra binding sites for internal K+ and external Tl+ (Fig. 9).

The concentration-dependent PX/PNa data demanded asymmetric energy profiles of the dynamic pore. Under symmetrical ionic conditions, both K+ and Tl+ currents exhibited the almost linear (ohmic) I-V relation in the potential range from -20 to +50 mV, whereas the I-V plots for symmetrical Na+ (at 10 mM) revealed slight inward rectification at the potentials positive to +20 mV. Therefore, the energy profile for Na+ was assumed to be asymmetric, and those for Tl+ and K+ nearly symmetric. The inward rectification of Na+ currents required the external barrier to be lower than the internal one. The rate constant alpha Na was somewhat arbitrarily set at a lower value (Delta Galpha  = 15.0 RT), because the rapid transition in the Na+-occupied states yielded the [Na+]-dependent reduction in PX/PNa. (cf. Fig. 6, C and F).

Effects of vestibule surface charge on selective permeability of static pore

The vestibule surface potential VS is known to affect the permeability and selectivity of Na-channels; therefore, static pores linked with charged vestibules (i.e., static pore models with variable VS) may possibly account for the concentration-dependent PX/PNa data. In Fig. 10, the effects of VS and cation binding to the surface charge on PX/PNa are shown for the 3B2S static pore. The external and internal VS certainly affected PX/PNa for the asymmetrical static pore. However, the fit to the external [Tl+]- and internal [K+]-dependent PX/PNa was not improved by incorporating the surface charge binding effects of external Tl+ and internal K+ (Fig. 10, bottom). In conclusion, the vestibule surface charge did not enable the static pore model to provide reasonable fit to the PX/PNa data from the cardiac Na-channel.



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  		FIGURE 10   Influences of vestibule surface potentials on the biionic selectivity of the 3B2S static pore linked with charged vestibules. (Top-left) Decrease in VS by binding of monovalent cations to a fixed negative charge with different KD values. The VS at various concentrations of a binding cation was calculated for a given KD using the GCS analysis. The control VS for infinite KD (or in the absence of binding cations) was -76.6 mV. The smooth curves labeled by the KD values (in M) are the best fits with the Langmuir isotherm. (Top-right) IUC-concentration curves predicted for the different KD values. Amplitude of IUCs carried by Na+ in a single Na-channel (at -20 mV) was computed from the single-occupancy pore model with the energy profiles shown in Fig. 8, and plotted for individual KD values. The smooth curves are the best fits with Eq. 1. (Middle) Dependence of theoretical PX/PNa on the external or internal VS. The continuous lines show the PX/PNa predicted by the single- and double-occupancy pores with the best-fit parameters. Vrev was determined from the simulated I-V relation, then PX/PNa was calculated with Eq. 2. The VS values in both vestibules were first set equal to -75 mV as a control, and one of them was reduced to -50, -25, and then 0 mV. (Bottom) Effects of cation binding to the surface charge on the concentration dependence of PX/PNa. The continuous lines are the theoretical predictions by the charged vestibule model with the KD values 0.05, 0.5, 5.0 M and infinity (infinity ). The control VS in either side was assumed to be -75 mM. The experimental data are also plotted for comparison (open circles).

Permeability properties of cardiac Na-channel as dynamic pore

The permeability properties of the cardiac Na-channel, as described by Model 1, are characterized as follows (see Fig. 8): 1) Conformation A has relatively low Na+ selectivity, whereas conformation B is highly Na+-selective. The selectivity sequence as determined from biionic PX/PNa is Na+ approx  Tl+ > K+ for A, and Na+ >> K+ > Tl+ for B. 2) The pore has relatively shallow wells for Tl+, the depth of which can be equal to that for Na+. The low Km for Tl+ is ascribable to the concentration-dependent shift in the distribution between A and B to favor the latter (with lower Tl+ permeability). 3) The transition rate constant alpha X depends on permeant cation species. The order of efficacy in facilitating the transition is Tl+ >=  K+ > Na+; thus, relatively impermeant cations are possibly more efficacious than the highly permeant cation Na+. 4) Native Na-channel pores undergo conformational transitions on a time scale of nanosecond order during cation permeation. These very fast transitions would not be detectable in the single-channel recording for which the theoretical lower limit of temporal resolution is of the order of 10 µs (Läuger, 1985).

Model 1 could clearly describe the mechanisms of the concentration-dependent selectivity changes as well as the low Km for Tl+ in IUC-concentration relation. Figure 11 shows the concentration-dependent kinetics of the dynamic pore and carried IUCs in the presence of external K+ or Tl+ alone. As external [K+] or [Tl+] increases, the steady-state probability of A decreases while that of B increases. It is evident that Km for IUC-concentration relation of the dynamic pore is affected by the concentration-dependent transition from A to B. The Km predicted for Tl+ currents is relatively low as observed in the experiments, because Tl+ induces the conformational transition to the Tl+ impermeable form B. As shown in Fig. 12, the concentration-dependent PX/PNa in the dynamic pore is attributable to the combined effects of the cation occupancy-induced transition to B with lower PX/PNa and the asymmetric energy profile for Na+ yielding the concentration-dependent change in the PX/PNa of A. The external [K+]-dependent increase in the PK/PNa of A was offset by the transition to B with lower PK/PNa. This explains why PK/PNa is apparently independent of the external [K+].



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  		FIGURE 11   Concentration-dependent kinetic behavior of Model 1 and carried IUCs in the presence of K+ (left) or Tl+ (right) only on the outside. (Top) State diagrams with the best-fit parameters. (Middle) Steady-state probabilities of A and B during the inward unidirectional passage of K+ or Tl+ at various external concentrations. (Bottom) Simulated IUC-concentration curves for K+ and Tl+. Amplitude of IUCs at -20 mV was calculated for the concentrations experimentally tested (<= 160 mM), then normalized to the Na+ current at 5 mM (cf. Fig. 4). The continuous lines labeled DP are the scaled predictions by the dynamic pore, being well approximated by Eq. 1 with the Km of 253 mM for K+, and 21.5 mM for Tl+. The experimental data are superimposed for comparison (open circles). Current-concentration curves for the pore fixed in A and B are also shown by the continuous lines labeled A and B, respectively.



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  		FIGURE 12   Mechanisms of the concentration-dependent selectivity changes as described by Model 1. (Top) State diagrams describing the permeation kinetics in the presence of two permeant cations, Na+ and K+ (left), or Na+ and Tl+ (right). (Middle) Steady-state probabilities of A and B under the different biionic conditions shown above the panels. The state probability at Vrev was computed for each biionic condition, and plotted against the concentrations of the test cations. (Bottom) Theoretically predicted PX/PNa for the dynamic pore (labeled DP) and for the pore fixed in A and B (labeled A and B, respectively). The biionic PX/PNa was determined from Vrev in the simulated I-V plot using Eq. 2. The experimental data are also shown for comparison (open circles).

    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Relationship between cation permeation and gating mechanisms

The voltage-dependent gating parameters exhibited the hyperpolarizing and depolarizing shifts during the consecutive perfusions of different external test solutions. The depolarizing shift is known to reflect the surface charge effects of cations (Makielski et al., 1987; Hanck and Sheets, 1992b), whereas the hyperpolarizing shift corresponds to the spontaneous negative shift in Na-channel kinetics (Kimitsuki et al., 1990; Hanck and Sheets, 1992a). According to Dani (1986), large organic cations are less effective in screening vestibule surface charges than smaller metal cations; replacement of TMA molecules (empty  approx  6.0 Å) by group Ia cations (empty  = 1.56-3.30 Å) is expected to diminish VS (by 10-20 mV for the total substitution of 150 mM). Thus, the size effect of cations on the vestibule surface charge screening may partly contribute to the depolarizing shift in gating kinetics.

Only Tl+ induced the significant depolarizing shifts in the kinetic parameters (see Figs. 2 and 3). These positive shifts would not be due to the surface charge screening effect of Tl+ in the external vestibule because the replacement of TMA by the smaller cation K+ only caused slight depolarizing shifts. The concentration-dependent parallel shifts in Tl+ current kinetics suggest the surface charge binding effect of external Tl+ rather than a direct effect on the gating machinery.

Hille (1972) reported that the voltage dependence of Na-channel activation shifted to the depolarizing direction by a few millivolts when external Na+ (at 110 mM) was replaced by other monovalent cations such as K+. This positive shift in the activation kinetics could not be ascribed to the surface charge effects because there were no significant changes in either the steady-state availability or the inactivation time constant. Similarly, Yamamoto et al. (1985) showed that the gating kinetics of squid axon Na-channels is appreciably affected by permeant cation species. The permeant ion-dependent gating behavior has also been demonstrated for Ca- and K-channels (Matteson and Swenson, 1986; Shuba et al., 1991; Demo and Yellen, 1992; Gómez-Lagunas and Armstrong, 1994; Kiss and Korn, 1998), the previous reports suggesting that occupancy of binding-sites by cations affects gating kinetics. In contrast to the report by Hille (1972), however, no comparable effects of external K+ on activation or other kinetic parameters were observed in this study. Within the concentration range tested (<= 160 mM), the cardiac Na-channel gating appeared to be independent of permeant cation species as well as concentrations on the outside.

Selective permeability of cardiac TTX-insensitive Na-channel

Cardiac Na-channel is substantially permeable to Rb+ and Cs+

It has been reported that native TTX-sensitive Na-channels are not measurably permeable to either Rb+ or Cs+ (Hille, 1972, 1975; Ebert and Goldman, 1976). In contrast, the present study, in which Rb+ and Cs+ currents flowing through the Na-channel were directly recorded as IUCs, demonstrated that the native cardiac Na-channel is substantially permeable to both Rb+ and Cs+ (see Fig. 1). There are few available data for comparison on the selectivity of native TTX-insensitive Na-channels. However, a report from the biionic Vrev measurement for canine cardiac Purkinje cells provided a PCs/PNa value of 0.020 (Sheets et al., 1987), which is close to (slightly bigger than) those determined in this study (see Table 3). These data possibly indicate that cardiac TTX-insensitive Na-channels are less selective to Na+ and more permeable to both Rb+ and Cs+ than TTX-sensitive ones.

Huang et al. (1979) compared the selectivity of BTX-activated Na-channels for alkali cations in two neuroblastoma cell lines, N18 (TTX-sensitive) and C9 (TTX-resistant). Although there was no qualitative difference in the selectivity sequence, the relative permeability to K+, Rb+, and Cs+ of the TTX-resistant channel was a little greater than that of the TTX-sensitive isoform. That report, together with our finding, implies that the relatively low selectivity of TTX-insensitive Na-channels is a general property of the Na-channel family, which holds even after BTX treatment. It is not reasonable to compare our data with those obtained from the single-channel recordings for toxin-modified Na-channels because the treatment with toxins such as BTX is known to change the conductivity and selectivity of Na-channels (Khodorov, 1985; Garber and Miller, 1987; Green et al., 1987).

Thallous ion is highly permeant with apparently high affinity

Compared with group Ia cations, Tl+ apparently exhibited the high affinity (low Km) for the cardiac TTX-insensitive Na-channel and for the neuronal TTX-sensitive one (Table 3). Hille (1972) sugg