Effect of Na⁺ Flow on Cd²⁺ Block of Tetrodotoxin-resistant Na⁺ Channels

Tetrodotoxin (TTX)^* is a well-known blocker of voltage-gated Na⁺ channels. In mammalian central neurons many Na⁺ channels are selectively inhibited by nanomolar or subnanomolar external TTX. These channels are referred to as TTX-sensitive (TTX-S) channels. However, some other Na⁺ channels are much less sensitive to TTX, and require hundreds of nanomoles to hundreds of micromoles of TTX to produce the inhibition (TTX-resistant or TTX-R channels; Kleinhaus and Pritchard, 1976; Cohen et al., 1981; Lombet et al., 1982; Roy and Narahashi, 1992). In the nervous system, the dorsal root ganglion neurons contain abundant TTX-R channels (Kostyuk et al., 1981; Roy and Narahashi 1992; Akopian et al., 1996; Rush et al., 1998) which have been implicated to play an important role in the physiology and pathophysiology of pain transmission (Akopian et al., 1999; Kral et al., 1999).

In addition to TTX sensitivity, TTX-R and TTX-S channels are also different in the pore-blocking effect of transitional metal ions such as Cd²⁺ and Zn²⁺ (Frelin et al., 1986; Backx et al., 1992; Sheets and Hanck, 1992). In dorsal root ganglion neurons, 5 mM Cd²⁺ inhibits >85% of TTX-R currents yet inhibits only ∼30% of TTX-S currents (at 0 mV; Roy and Narahashi, 1992). In cardiac myocytes or Purkinje cells, which contain almost only TTX-R channels (the TTX-R channels in heart and in dorsal root ganglion neurons are distinct but closely related molecular clones, for reviews see Goldin et al., 2000; Goldin, 2001), 0.1–0.3 mM Cd²⁺ caused 50% inhibition of the Na⁺ current (IC50 = 0.1–0.3 mM; Visentin et al., 1990; Ravindran et al., 1991; Sheets and Hanck, 1992). But the IC50 of Cd²⁺ block of Na⁺ current in rat skeletal muscle, which contains almost only TTX-S channels, is 17 mM (Ravindran et al., 1991). It has been shown that one single amino acid at position 374 of the channel protein plays a critical role in both TTX and Cd²⁺ sensitivity. In TTX-S channels this amino acid is tyrosine (Y374), but in TTX-R channels it is cysteine or serine. TTX-R channels with a point mutation at this position (C374Y) show markedly decreased affinity to Cd²⁺, but increased affinity to TTX (Satin et al., 1992). Also, mutant (Y374C) TTX-S channels show markedly increased affinity to Cd²⁺, but decreased affinity to TTX (Backx et al., 1992).

The selectivity filter of the Na⁺ channel has been implicated to involve the DEKA ring in the pore (highly conserved aspartate, glutamate, lysine, and alanine in domain I, II, III, and IV of the channel protein, respectively), because mutations of the ring would significantly change ionic selectivity (Heinemann et al., 1992b; Favre et al., 1996). Interestingly, the foregoing cysteine residue (C374) is situated next to the aspartate residue in the DEKA ring (D373), and thus the Cd²⁺ blocking site is probably near or in the DEKA region. This is reminiscent of the case of Ca²⁺ channels, where Cd²⁺ is also a potent pore blocker and binds to an “EEEE” ring in the pore (one glutamate residue in each domain of the Ca²⁺ channel protein, at exactly the corresponding loci of the DEKA ring). This EEEE ring not only binds divalent ions much more tightly than the monovalent ions and thus confers the selectivity for Ca²⁺ ions (the “selectivity filter” of the channel), but also participates in the buildup of a “set” of contiguous ion binding sites capable of accommodating at least two Ca²⁺ ions simultaneously (Hess and Tsien, 1984; Kuo and Hess, 1993a,b; Yang et al., 1993, Ellinor et al., 1995).

One might expect a similar molecular design of the pore near the DEKA and the EEEE rings based on the foregoing analogy between Na⁺ and Ca²⁺ channels. However, even the multiion nature of the Na⁺ channel is an unsettled issue. Early ²²Na⁺ flux ratio data (Begenisich and Busath, 1981) and the independence of Na⁺ channel selectivity of the mole fraction of the permeant ions (Green et al., 1987) would suggest that the Na⁺ channel is rarely occupied by two or more Na⁺. But Ravindran et al. (1991) maintained that the conductance–concentration behavior of muscle and heart Na⁺ channels favors a multiion model of Na⁺ permeation. The anomalous mole fraction behavior between Na⁺ and Ca²⁺ associated with mutations in the DEKA ring (Heinemann et al., 1992b; Teresa Perez-Garcia et al., 1997) also supports the possibility of ion–ion interaction in this pore region. The different blocking effect of internal spermine on Na⁺ channels in different directions of Na⁺ current flow also suggests ion–ion (Na⁺-spermine) interaction and multiion nature of the Na⁺ channel pore (Huang and Moczydlowski, 2001). Because previous studies on the block of Na⁺ channels by external Cd²⁺ or Zn²⁺ tend to ascribe the apparent voltage dependence of block entirely to the direct effect of membrane field on the blocking ion (e.g., Green et al., 1987; Ravindran et al., 1991; Backx et al., 1992; Sheets and Hanck, 1992), possible roles played by the permeating Na⁺ ions have remained unexplored. We therefore studied the effect of Na⁺ flow on Cd²⁺ block of TTX-R channels in dorsal root ganglion neurons in more detail. We found that the binding affinity of Cd²⁺ is significantly altered by the direction of Na⁺ ion flow, and at least 2 Na⁺ ions may coexist with the blocking Cd²⁺ ion in the presence of 150 mM ambient Na⁺. Thus, the pore of the TTX-R Na⁺ channels in dorsal root ganglion neurons is probably similar to the L-type Ca²⁺ channel pore in multiion nature and in the existence of a set of single-file ion binding sites located at the external pore mouth.

The dorsal root ganglia in the cervical and lumbar parts of the spinal column of 6–10-d-old Wistar rats were removed and put into Ca²⁺-free Tyrode's solution (150 mM NaCl, 4 mM KCl, 2 mM MgCl₂, and 10 mM HEPES, pH, 7.4), where the debris of nerves and connective tissues were removed from the ganglia. The cleaned ganglia were incubated in the dissociation medium (82 mM Na₂SO₄, 30 mM K₂SO₄, 3 mM MgCl₂, 10 mM HEPES, pH, 7.4) containing 1.25 mg/ml collagenase type I and 1.2 mg/ml protease type XXIII for 30–40 min. The enzyme action was terminated by washes with enzyme-free dissociation medium. The enzyme-treated ganglia were then triturated in dissociation medium with a fire-polished Pasteur pipette to release single neurons. Small neurons (18–30-μm diameter) with intact cell membrane but without attached satellite cells were picked for electrophysiological studies. Usually the isolated cells were used within 8 h of preparation.

The dissociated neurons were put in a recording chamber containing Tyrode's solution (Ca²⁺-free Tyrode's solution with 2 mM CaCl₂ added). Whole-cell voltage clamp recordings were obtained using pipettes pulled from borosilicate micropipettes (OD 1.55–1.60 mm; Hilgenberg, Inc.), fire polished, and coated with Sylgard (Dow-Corning). The pipette resistance was 1.5–2 MΩ when filled with one of the following three internal solutions. The “150 mM Cs⁺” internal solution was composed of 75 mM CsCl, 75 mM CsF, 3 mM MgCl₂, 10 mM HEPES, 5 mM EGTA, pH, 7.4. The “150 mM Na^+” and “150 mM Na⁺ + 150 mM Cs⁺” internal solutions had the same component except that 75 mM CsCl/75 mM CsF was replaced by 75 mM NaCl/75 mM NaF and 150 mM NaCl/150 mM CsF, respectively. After whole-cell configuration was obtained, the neuron was lifted from the bottom of the recording chamber and moved in front of an array of flow pipes emitting “150 mM Na⁺,” “150 mM Cs⁺,” or “150 mM Na⁺ + 150 mM Cs⁺” external solutions. The “150 mM Cs⁺” solution contained 150 mM NaCl, 2 mM MgCl₂, 2 mM CaCl₂, and 10 mM HEPES, pH, 7.4. The “150 mM Na⁺” and “150 mM Na⁺ + 150 mM Cs⁺” solutions had the same components except that 150 mM CsCl was replaced by 150 mM NaCl and 150 mM NaCl + 150 mM CsCl, respectively. In Fig. 5, C and D, when the cell had to be moved between the “150 mM Na⁺” and the “150 mM Na⁺ + 150 mM Cs⁺” solutions, 150 mM sucrose was specially added to the “150 mM Na⁺” solution to avoid abrupt osmolarity change and subsequent easy loss of the seal. CdCl₂ was dissolved in water to make a 500 mM stock solution, and then added to the external solution for a final concentration of 30–3,000 μM. All external solutions also contained 0.3 μM TTX, 1 μM nimodipine, and 0.5 μM ω-conotoxin MVIIC to block TTX-S Na⁺ and most Ca²⁺ currents. The residual Ca²⁺ currents, chiefly including the T-type Ca²⁺ currents, did not seem to produce significant contamination because the amplitude of transient Ca²⁺ currents was generally no larger than 0.2–0.3 nA at −20 mV and was even smaller at more positive test potentials (examined in an external solution composed of 150 mM tetraethylammonium chloride and 2 mM CaCl₂; unpublished data). It has been shown that the TTX-R channels in dorsal root ganglion neurons require more positive potentials than TTX-S channels to be activated and inactivated (Roy and Narahashi, 1992; Akopian et al., 1996; Rush et al., 1998). Moreover, the activation and inactivation kinetics at the same voltage (e.g., 0 mV) are both ∼3-fold slower in TTX-R channels than in TTX-S channels (Scholz et al., 1998). These parameters are helpful for the identification of the TTX-R currents. For example, the whole-cell TTX-R currents in rat dorsal root ganglion neurons typically show decaying time constants of ∼9, ∼7, and ∼2 ms at –20, 0, and 30 mV, respectively (Rush et al., 1998; Scholz et al., 1998). Thus, only those neurons in which the Na⁺ current decayed with the foregoing time constants (allowing a ±15% margin) to a sustained level no larger than 10% of the peak current were included for data analysis. Currents were recorded at room temperature (∼25°C) with an Axoclamp 200A amplifier, filtered at 10 kHz with four-pole Bessel filter, digitized at 20-μs intervals, and stored using a Digidata-1200 analogue/digital interface with the pCLAMP software (Axon Instruments, Inc.). All statistics were given as mean ± standard error of mean.

Fig. 1 A shows sample outward TTX-R Na⁺ currents from a dorsal root ganglion cell. 300 and 1,000 μM external Cd²⁺ reduces the peak of Na⁺ currents in a dose-dependent fashion, with no obvious effect on the timing of the peak current or the macroscopic decaying kinetics of the currents. At different membrane potentials from −20 to 40 mV, the relative peak currents in 30–3,000 μM of Cd²⁺ are plotted in Fig. 1 B. The relative current in a fixed concentration of Cd²⁺ remains roughly similar between membrane potentials −20 and 40 mV, although there may be a slight tendency for the relative current to become larger at more positive potentials (especially for Cd²⁺ concentrations 300 μM or higher, where the inhibitory effect is relatively large, so that the forgoing slight tendency is more clear). This finding indicates minimal apparent voltage dependence of Cd²⁺ block in this experimental configuration. Fig. 1 C plots the relative current against Cd²⁺ concentration. Each set of data can be reasonably fitted by a one-to-one binding curve. The dissociation constants from the fitting curves are only slightly different between −20 and 40 mV, roughly e-fold increase per ∼230 mV depolarization (Fig. 1 D).

Fig. 2 A shows sample inward TTX-R Na⁺ currents in the control solution and in the presence of 300–1,000 μM external Cd²⁺. The blocking effect of Cd²⁺ on the inward currents is much stronger than that on the outward currents in Fig. 1. At different membrane potentials from −20 to 40 mV, the relative peak currents in 30–3,000 μM of Cd²⁺ are plotted in Fig. 2 B. Again, the inhibition is clearly Cd²⁺ concentration dependent, yet not very sensitive to changes of the membrane potential. Most interestingly, one may readily note that over the same voltage range (−20 to 40 mV), 30–3,000 μM Cd²⁺ produces a much larger inhibitory effect on inward (Fig. 2 B) than on outward (Fig. 1 B) Na⁺ currents. Fig. 2 C plots the relative current against Cd²⁺ concentration. Each set of data is again reasonably fitted by a one-to-one binding curve. However, the absolute values of the apparent dissociation constants here are nearly one order of magnitude smaller than those obtained with outward current in the same voltage range (Fig. 1 C). Fig. 2 D further shows that the dissociation constants are only mildly voltage-dependent between −20 and 40 mV in this experimental configuration, with e-fold increase per ∼140 mV of depolarization.

In the foregoing experiments we have used very different internal and external Na⁺ concentrations to obtain preponderant outward (150 mM internal Na⁺ and 0 mM external Na⁺, Fig. 1) or inward (150 mM external Na⁺ and 0 mM internal Na⁺, Fig. 2) Na⁺ current through TTX-R channels. The very different inhibitory effects of Cd²⁺ at the same range of test potentials suggest that Cd²⁺ inhibition of Na⁺ current is chiefly dependent on the direction of ionic flow rather than on membrane voltage. To confirm that the observed inhibitory effect is indeed ascribable to the direction of Na⁺ flow but not to the different external and internal solutions used in different experiments, we studied the inhibitory effects of Cd²⁺ in an experimental condition with equimolar (150 mM) internal and external Na⁺. Now the effects of external Cd²⁺ on both inward and outward TTX-R currents could be documented in the same neuron with different test pulse potentials. Fig. 3 A shows sample sweeps at test potentials of −20 and 20 mV, respectively. Fig. 3 B shows representative peak I-V plots in control and in the presence of 300–1,000 μM external Cd²⁺. The I-V curves are of very similar shape and it is evident that the inhibitory effect on the inward current is significantly larger than that on the outward current.

Fig. 4 A summarizes the inhibitory effect of external Cd²⁺ at various potentials with equimolar (150 mM) Na⁺ on both sides of the membrane. Similar to the findings in Fig. 1 B, the inhibitory effect of external Cd²⁺ on outward Na⁺ currents shows at most a very slight voltage dependence and only equivocally becomes weaker with more positive potentials between 10 and 50 mV. In contrast, the inhibitory effect of Cd²⁺ on the inward currents is obviously weaker with more depolarization between −30 and −10 mV, showing much stronger voltage dependence than that in Fig. 2 B. Fig. 4, B and C, shows the dissociation constants of Cd²⁺ block in each voltage. In outward Na⁺ current the voltage dependence here is roughly similar to that observed in Fig. 1 D, whereas in inward Na⁺ currents the apparent voltage dependence here is much stronger than that in Fig. 2 D. The simplistic fittings for the apparent voltage dependence of the data points in outward currents and those in inward currents in Fig. 4 C are obviously two discontinuous functions and, thus, may not be a rational analysis of the data. We have already seen that the absolute magnitude of the affinity (dissociation constants) of the blocking Cd²⁺ ion is very much different in different directions of net ionic flow (Figs. 1 and 2). In Fig. 4 C, and in comparison with Fig. 2 D, we further see that even the apparent voltage dependence of Cd²⁺ block is dependent on not only the direction of net ionic flux, but also the ion species in ambient solutions (and thus the permeating ions in the pore). These findings strongly indicate that Cd²⁺ block is profoundly influenced by the movement of other permeating ions, rather than by just a simple effect of the transmembrane field. This flux-coupling phenomenon implies that Cd²⁺ binds to a set of single-file ionic sites in the TTX-R Na⁺ channel pore where the other permeating ions also bind to. Based on the flux-coupling equation (Hodgkin and Keynes, 1955), a better quantitative treatment of the data in Fig. 4 C could be done with all the data points well described by one continuous function (see discussion).

There is very shallow voltage dependence of external Cd²⁺ block in Figs. 1 and 2, where there is preponderant Na⁺ efflux and influx, respectively. This would imply a Cd²⁺ blocking site located very shallowly in the external part of the conduction pathway. If there is indeed a set of ion binding sites at the external pore mouth of the TTX-R channels underlying the flux-coupling phenomenon, it would be desirable to see whether physiological concentrations (∼150 mM) of Na⁺ could so significantly occupy all of these sites as to affect the binding of Cd²⁺ from the external solution to the blocking sites. In the presence of 150 mM internal Na⁺, the dissociation constants in the presence of net outward currents is only slightly smaller in 150 mM external Cs⁺ (Fig. 1) than in 150 mM external Na⁺ (Fig. 4). This point is reexamined in Fig. 5 A, which plots the blocking effect of Cd²⁺ at 40 mV (data from Figs. 1 and 4), where there should be preponderant Na⁺ efflux and thus roughly the same unbinding rate of the blocking Cd²⁺ ion in both cases. The blocking effect at 40 mV is roughly similar, or at most only equivocally different, implying either of the two following possibilities. Probably neither 150 mM external Na⁺ nor 150 mM external Cs⁺ so significantly occupies all of these externally located ionic sites as to affect the binding rate of Cd²⁺. Alternatively, 150 mM external Na⁺ and 150 mM external Cs⁺ both may significantly occupy all of the ionic sites in this pore region and thus affect the Cd²⁺ binding rate, but roughly to the same extent. To differentiate between these two possibilities, we repeated the experiments in symmetrical 150 mM Na⁺ plus 150 mM Cs⁺ (Fig. 5 B), where the apparent dissociation constant of external Cd²⁺ is generally similar to those in Fig. 4 B and remains very much flow-dependent. This finding strongly argues against the second possibility given above. We therefore conclude that 150 mM external Na⁺ (or 150 mM external Cs⁺) cannot so significantly occupy all sites in this multiion single-file pore region as to remarkably decrease the binding rate of Cd²⁺. When studying the effect of the additional 150 mM external Cs⁺, we also noted that external 150 mM Cs⁺ seems to inhibit the inward but not the outward Na⁺ current (Fig. 5, C and D). This inhibitory effect probably is not related to changes in surface potential or channel gating, because the I-V plots remain very much the same in shape (see the legend of Fig. 3 B). The similar ∼25% inhibition at −40 to −10 mV, where there are inward currents, and the lack of discernible blocking effect at positive potentials, where there are outward currents, further support that the inhibition is also a flow-dependent block produced by 150 mM Cs⁺, rather than an effect related to surface potential or gating change. Although 150 mM external Cs⁺ does not significantly occupy all of these ion binding sites, the flow-dependent blocking effect of 150 mM external Cs⁺ does suggest interactions between Cs⁺ and the single-file multiion region at the external pore mouth.

In Fig. 3 B, we have argued the insignificant effect of 300–1,000 μM Cd²⁺ on the surface potential related to channel gating. To have a more quantitative measurement of the effect of Cd²⁺ on surface potential or on the gating machinery of TTX-R Na⁺ channels, the inactivation curve of the channel is documented in 100–3,000 μM Cd²⁺. Fig. 6, A and B, show that 100–300 μM Cd²⁺ does not definitely shift or change the curve. 1,000 μM Cd²⁺ causes a shift of ∼1.5 mV, and 3,000 μM Cd²⁺ causes a shift of ∼4 mV. These changes in the inactivation curve, whether they are related to changes in the surface potential or to a direct effect of Cd²⁺ on the gating machinery of the channel, are so small that correction for such changes seems unnecessary. In all experiments so far we have deliberately included 2 mM Ca²⁺ and 2 mM Mg²⁺ in the external solution to minimize possible surface potential changes in the presence of high concentrations of Cd²⁺. To check for any major effect of the added Ca²⁺, we repeated some experiments in 5 mM external Ca²⁺, which probably induces changes in surface potential for a few mV and shift the I-V relationship (e.g., the voltage where the current start to be discernible) to the right in the voltage axis accordingly (unpublished data). Thus, the TTX-R currents are probably far from fully activated at potentials more negative than −20 mV. Similar to the rationales given in the legend of Fig. 4, we therefore did not quantify the inhibitory effect of Cd²⁺ in 5 mM external Ca²⁺ at potentials more negative than −20 mV (Fig. 7). For characterization of Cd²⁺ block in high external Ca²⁺ over a wider voltage range, we not only studied the block in symmetrical 150 mM Na⁺ (Fig. 7 A), but also in 150 mM external Na⁺ and 150 mM internal Cs⁺ (Fig. 7 B). The apparent dissociation constants of Cd²⁺ in both inward and outward currents are very similar to those obtained in 2 mM external Ca²⁺, and the strong flow dependence is clearly preserved. These findings are consistent with the very high (∼50 mM) previously reported IC50 of Ca²⁺ or Mg²⁺ on Na⁺ currents (Ravindran et al., 1991). The presence of 2 mM external Ca²⁺ or Mg²⁺ (which usually has a less remarkable effect on surface potential than Ca²⁺) is thus unlikely to distort the major findings of this study.

We have characterized the inhibitory effect of external Cd²⁺ on the TTX-R Na⁺ currents in rat dorsal root ganglion cells. When there is Na⁺ on one side of the membrane and Cs⁺ on the other side, the ionic flow through the channel is either preponderantly outward (Fig. 1) or inward (Fig. 2), and in both cases there is little voltage dependence on Cd²⁺ inhibition. The very shallow voltage dependence is roughly similar to what was observed in Cd²⁺ block of cardiac Na⁺ channels (Sheets and Hanck, 1992), and suggests little intrinsic voltage dependence of Cd²⁺ block. On the other hand, the inhibitory effect of Cd²⁺ is closely correlated with the direction of Na⁺ current flow. At −20 to 40 mV, the dissociation constant of Cd²⁺ is 200–300 μM in the presence of preponderant Na⁺ influx (Fig. 2 D), consistent with what was reported before with similar experimental configurations (Visentin et al., 1990; Ravindran et al., 1991; Sheets and Hanck, 1992). In contrast, the dissociation constant of Cd²⁺ is nearly one order of magnitude larger in the presence of preponderant Na⁺ efflux at exactly the same voltage range (Fig. 1 D). The different apparent voltage dependence of Cd²⁺ block in inward currents in Figs. 2 and 4, as we have pointed out in the results section, also substantiates the flux-coupling phenomenon and thus significant interactions between movements of the blocking Cd²⁺ ion and the coexisting Na⁺ ions. Thus, Cd²⁺ probably binds to a set of single-file ion binding sites at or near the external mouth of the pore, where Na⁺ and even Cs⁺ ions also bind to. The affinity between Na⁺ and the sites in this pore region, however, is not high (150 mM external Na⁺ does not seem to saturate or significantly occupy all sites in this region; Fig. 5, A and B). The low affinity of Na⁺ to this pore region may partly explain why some previous studies (e.g., Green et al., 1987; Sheets and Hanck, 1992) fail to observe significant flow dependence of Cd²⁺ or Zn²⁺ block of Na⁺ channels. The symmetrical 20–30 mM Na⁺ used in those studies could be too low to have enough occupancy of this pore region to produce vivid flux-coupling effect. Also, batrachotoxin (BTX) was used to prolong single channel openings in some studies (Green et al., 1987; Ravindran et al., 1991). Because BTX might alter the cation binding sites in the Na⁺ channel pore (Khodorov, 1985; Green et al., 1987), features of single-file multiion permeation may be altered in the presence of BTX.

If external Cd²⁺ binds to the TTX-R channel pore, it would be interesting to consider whether the blocking Cd²⁺ can only exit back to the external side, or it could also exit to the internal side, in which case Cd²⁺ becomes a “permeant blocker” of the channel. Because the binding rate of Cd²⁺ is not much different in different experimental conditions (Fig. 5, A and B), the different apparent dissociation constants in different conditions is most likely ascribable to the different unbinding rate (off rate) of the blocking Cd²⁺ ion. Thus, the small voltage dependence of the dissociation constants in preponderant outward and inward Na⁺ flow (Figs. 1 D and 2 D) suggests little intrinsic voltage dependence of the exit of the blocking Cd²⁺ ion. We have been describing the flow as “preponderantly” rather than “exclusively” inward or outward because the permeability ratio between Cs⁺ and Na⁺ is small but not exactly negligible (0.016, Chandler and Meves, 1965; <0.013, Hille, 1972). Also, Cs⁺ currents through Na⁺ channels (against Na⁺ ions on the other side of the membrane) can be observed if appropriate electrochemical gradient is applied (unpublished data), and Cs⁺ may also interact with the set of ion binding sites at the external pore mouth (Fig. 5, C and D). Thus, the ionic flux through the pore should be only mostly but not strictly outward or inward in Figs. 1 and 2. If the movement of the blocking Cd²⁺ in the single-file region is coupled to (”controlled” by) the movement of Na⁺ ion, then the overall exit rate of the blocking Cd²⁺ ion from the region should be a weighted average (weighted according to the relative chances of moving in each direction) of its “absolute” inward and outward exit rates (“absolute” means the exit rate if Cd²⁺ is absolutely moving in that particular direction). If there were a huge energy barrier for Cd²⁺ internal to this single-file region and Cd²⁺ essentially could only exit back to the external side, then the overall unbinding rate of Cd²⁺ would be the product of the absolute outward exit rate of Cd²⁺ and the relative tendency of moving outward of the ions in this single-file region. Because the tendency of moving outward versus moving inward of the blocking Cd²⁺ ion (and the other permeating ions in this single-file region) must be very small, but would increase exponentially as the membrane potential goes more positive in the presence of preponderant inward current (see Eq. 1 below), the overall unbinding rate, and therefore the apparent dissociation constant of Cd²⁺ with preponderant inward Na⁺ current in Fig. 2, would have been extremely small yet strongly voltage dependent. This is inconsistent with the findings that the dissociation constants in Fig. 2 lack significant voltage dependence and are ∼9-fold smaller than those in Fig. 1. Thus, the exit of Cd²⁺ could not be strictly outward. Instead, Cd²⁺ seems to exit the single-file region either inwardly or outwardly, with the chances of moving in either direction determined by Na⁺ flow.

We have argued that differences in the apparent dissociation constants of Cd²⁺ could signal differences in the unbinding rates of the blocking Cd²⁺ ion. The dissociation constant of Cd²⁺ with most preponderant Na⁺ influx (213 μM at −20 mV, Fig. 2 C) and that with most preponderant Na⁺ efflux (1,839 μM at 40 mV, Fig. 1 C) together indicate an ∼9-fold difference between the absolute inward and outward exit rates of the blocking Cd²⁺ ion (assuming complete Na⁺ flux coupling of Cd²⁺ movement). This difference would suggest that the internal energy barrier (the barrier internal to the single-file pore region containing the set of ion binding sites) for the “permeating” Cd²⁺ ion is ∼2.2 RT higher than the external energy barrier based on the reaction rate theory (Zowlinski et al., 1949). The asymmetrical and much slower inward exit rate of the blocking Cd²⁺ also explains the seemingly different voltage dependence of Cd²⁺ block on the inward and outward currents in symmetrical 150 mM Na⁺ (Fig. 4 C), which is otherwise very difficult to envision with a direct effect of transmembrane field on the blocking Cd²⁺ ion. Because Na⁺ flux would not be so preponderant in one direction in the vicinity of the reversal potential (0 mV in Fig. 4), the relatively small but not negligible Na⁺ efflux in net inward current at −10 or −20 mV, along with the ninefold faster absolute outward exit rate of Cd²⁺, could make the overall Cd²⁺ unbinding rate much faster than one would have imagined considering only inward exit of the blocking Cd²⁺ ion. In contrast, the equal amount of “contaminating” Na⁺ influx in net outward current at 10 or 20 mV will have only slight or even negligible effect because of the much slower absolute inward exit rate of Cd²⁺ (see below for a more detailed quantitative treatment of this issue). The higher internal barrier for Cd²⁺ and the flux coupling of Cd²⁺ movement in this single-file region may also explain why previous studies (e.g., Yamagishi et al., 1997) fail to show block of the pore by 100 μM internal Cd²⁺, although we have argued that Cd²⁺ is a permeant blocker. If there are no additional low-affinity (nonblocking) ionic sites located between the internal solution and the externally located single-file Cd²⁺ blocking sites, the on rate (binding rate) of internal Cd²⁺ would be ninefold slower than that of equimolar external Cd²⁺ (at 0 mV). Given the same Cd²⁺ off rate (unbinding rate) controlled by ionic flux (the bound Cd²⁺ ion should not know where it comes from), the apparent dissociation constant (which should be the ratio between the off rate and the on rate) of internal Cd²⁺ in blocking the TTX-R channel would be at least ∼9-fold larger than those of external Cd²⁺, and thus would be ∼2 mM in inward current and ∼20 mM in outward current. If there are additional internal low-affinity ionic sites also bearing flux coupling or other intense ion–ion interactions, the apparent dissociation constant for the internal Cd²⁺ will be even larger, especially in inward currents (see the examples in L-type Ca²⁺ channels; Kuo and Hess, 1993a). Thus, 100 μM internal Cd²⁺ might be too low a concentration to have a discernible blocking effect on either inward or outward Na⁺ currents.

Fig. 4 C shows that a simplistic analysis considering only the direct effect of membrane electrical field on Cd²⁺ is incapable of describing all of the data points with one function. If Cd²⁺ affinity is actually directly and closely related to Na⁺ flux, a quantitative analysis based on flux-coupling considerations may be more appropriate. The original flux-coupling equation (Hodgkin and Keynes, 1955; Hille, 1992) is:

where [S,internal] and [S,external] denote concentrations of the internal and external permeant (Na⁺) ions, respectively. Z and Vrev denote the charge and reversal potential of the permeant ions, respectively. n denotes the number of permeating (Na⁺) ions in this single-file region. V denotes the membrane potential in mV and F, R, T have their usual meanings (RT/F = 25 mV if T = 25°C. Here we have assumed the single-file nature to be complete to facilitate further analysis and calculation. If the single-file ionic movement is not absolute, the deduced number of ions in this region may be different, but the essence of flux-coupling remains the same). In symmetrical (150 mM, Figs. 3 and 4) Na⁺ on both sides of the membrane, Eq. 1 is simplified to:

We have argued that the direction of Cd²⁺ exit from this single-file region is “controlled” by the direction of Na⁺ current flow, and thus the overall exit rate (J) of Cd²⁺ would be a weighted average of the absolute inward exit rate (Ji) and the absolute outward exit rate (Jo):

Because fraction of outward flux = (outward flux)/(outward flux + inward flux), and fraction of inward flux = (inward flux)/(outward flux + inward flux), Eqs. 2 and 3 can be combined and we have:

Because of the insignificant effect of 150 mM ambient Na⁺ on the binding rate of Cd²⁺ (Fig. 5 A), the dissociation constants at different membrane potentials should be roughly linearly correlated with the exit rates, and Eq. 4 could be rewritten as:

where D is the observed dissociation constant, and Do and Di are the apparent dissociation constants when Cd²⁺ exclusively exits outwardly and inwardly, respectively. Fig. 8 A shows a best fitting curve, using Eq. 5, to the data points from Fig. 4 C, giving Do = 2,400 μM, Di = 260 μM, and n = 2.2. Curves with the same Do and Di yet different n values (n = 1, 2, or 3) are also drawn to demonstrate the different slope with different n values. It is evident that the curves with n = 2 or 3 stay reasonably close to the data points, whereas the curve with n = 1 describe the data poorly. Fig. 8 B shows that Eq. 5 with similar parameters may also describe the data in either preponderant outward or inward Na⁺ currents in Figs. 1 D and 2 D, where the apparent voltage dependence of the dissociation constants should approximate that at the two boundary conditions (very positive and very negative potential ranges) in Fig. 8 A, and is indeed shallow in both cases. The e-fold increase of K_app,o per ∼230 mV of depolarization in Fig. 1 might be close to the “true” voltage dependence of Cd²⁺ binding affinity, because the blocking Cd²⁺ coming from outside now exits mostly back to the outside. The Cd²⁺ binding site thus could be located in the pore at electrical distance ∼0.05 from the outside (Woodhull, 1973). This very superficial location is consistent with the findings that the key amino acid residue responsible for external Cd²⁺ binding is also a critical residue responsible for the binding of TTX, a much bulkier external pore blocker presumably incapable of going deep into the pore (Backx et al., 1992; Satin et al., 1992; Terlau et al., 1991). We conclude that the blocking Cd²⁺ probably binds to a single-file multiion region at the external pore mouth. This region may accommodate at least two coexisting Na⁺ ions (in 150 mM ambient Na⁺, Fig. 9) and is connected to the bulk solution by a wide vestibule.

In L-type Ca²⁺ channels the carboxylate groups (e.g., glutamate residues, Kuo and Hess, 1993a,b; Yang et al., 1993; Ellinor et al., 1995) are responsible for the binding of Cd²⁺ with very high affinity (micromolar dissociation constants), whereas in TTX-R channels sulfhydryl or hydroxyl groups (e.g., cysteine or serine residues, Backx et al., 1992; Heinemann et al., 1992a, Akopian et al., 1996) are probably involved in the binding of Cd²⁺ with lower affinity (submillimolar to millimolar dissociation constants). Despite these differences, there are striking similarities in the pore structure around the Cd²⁺ binding site between Ca²⁺ and TTX-R Na⁺ channels. In both channels, Cd²⁺ binds to a single-file region at the external pore mouth, which contains a set of ionic sites capable of accommodating at least two permeating ions simultaneously, and more or less involving the “selectivity filter” of the channel (the EEEE and the DEKA rings for Ca²⁺ and Na⁺ channels, respectively). This is consistent with the finding that mutation of many amino acid residues in the vicinity of each of the DEKA residues into cysteine would enhance the blocking effect of Cd²⁺ on Na⁺ channels, suggesting extended loop structure and thus capability of accommodating multiple ions near the DEKA region of the pore (Chiamvimonvat et al., 1996; Yamagishi et al., 1997). In this regard, one may also note that there seems to be multiion occupancy with significant interaction between permeating K⁺ ions at the external pore mouth of an inward rectifier K⁺ channel (Shieh et al., 1999). Moreover, Miller (1996) has proposed that the narrow single-file selectivity region of some K⁺ channels may be connected to the bulk solutions by a wide vestibule, because in some K⁺ channels the selectivity determining deep-pore residues are accessible to large peptide blockers or polar thiols from the external or internal side of the membrane (Pascual et al., 1995; Naranjo and Miller, 1996). It would be interesting to see whether such a multiion region at the external pore mouth is a more general functional design shared by different cationic channels.

This work was supported by grant NSC-90-2320-B-002-154 from the National Science Council, Taiwan. Chi-Pan Hsieh is a recipient of the MD Ph.D./DDS Ph.D. predoctoral fellowship RE90M003 from the National Health Research Institute, Taiwan.