INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

A step depolarization of the nerve membrane potential from its resting level (-60 mV) elicits a sodium ion current, I_Na, which is activated typically within a millisecond, followed by inactivation of the current on a time scale of several milliseconds (Hodgkin and Huxley 1952a). These results are well described by the Hodgkin and Huxley (1952b) model of I_Na. Their model also predicts a small amplitude steady-state, or persistent, current given by the overlap between activation and inactivationthe so-called "window" current (Attwell et al. 1979). Over the past 20 years, a persistent Na⁺ current (I_NaP) has been found in neurons from various regions of the mammalian brain that is not adequately described by the Hodgkin and Huxley (1952b) window current model (Crill 1996). In particular, the threshold of I_NaP is 10-15 mV below threshold of the classical Na⁺ current; this has led some investigators to suggest that it might originate from a set of ion channels within the nerve membrane that are distinct from those underlying I_Na, even though I_Na and I_NaP are both blocked in a similar manner by tetrodotoxin (Crill 1996). Rakowski et al. (2002) have reported careful measurements of I_NaP from squid giant axons, the preparation used by Hodgkin and Huxley (1952a), which they attributed to the I_Na channel. The analysis of their results in this report supports the alternative conclusion, namely that most of I_NaP originates from a subset of I_Na channels that lack the gating mechanism of the I_Na channel. In particular, the measurements of slow inactivation of I_Na given in the following text would appear to exclude the possibility that I_NaP is attributable to the I_Na channel, except for a small portion in the 60- to 40-mV range.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The measurements of I_Na in Fig. 2 were carried out in squid giant axons (Loligo pealei) using axial wire voltage-clamp and intracellular perfusion techniques described elsewhere (Clay and Shlesinger 1983). The extracellular solution consisted of (in mM) 425 NaCl, 10 KCl, 50 MgCl₂, 10 CaCl₂, and 10 Tris-HCl (pH 7.6). The intracellular perfusate in this experiment consisted of (in mM) 300 CsF (which effectively blocks I_K), 20 Na glutamate, 15 Na₂HPO₄, and 400 sucrose (pH 7.3). This solution is referred to as the 300 Cs perfusate. In other experiments to test for possible effects of intracellular F on Na⁺ channel gating the intracellular perfusate consisted of (in mM) 50 Na glutamate, 250 K glutamate, 25 K₂HPO₄, and 400 sucrose (pH 7.3)0 Cswith an extracellular solution consisting of (in MM) 300 KCl, 135 NaCl, 50 MgCl₂, 10 CaCl₂, and 10 Tris-HCl. The temperature of the extracellular solution was 5°C maintained constant to within 0.1°C by a Peltier device located within the experimental chamber. The persistent current predicted by the Vandenberg and Bezanilla (1991b) model of I_Na gating (APPENDIX) was calculated with the Mathematica software package (Wolfram 1999).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The I_NaP results of Rakowski et al. (2002) are reproduced in Fig. 1. These measurements were carried out by holding the preparation in voltage clamp at the potentials indicated on the abscissa during application of tetrodotoxin (TTX) at a final concentration of 0.2 µM. The currents shown are the difference between the holding current prior to TTX application and after wash-in of the toxin. The difference current is present at potentials as negative as 90 mV with a maximal (inward) amplitude of approximately 4 µA/cm^-2 at 50 mV. The curve describing the data (Fig. 1, ) is given by

(1)

where Na_i and Na_o are the intra- and extra-cellular sodium ion concentrations, respectively (Na_i = 0.05 M; Na_o = 0.425 M). By comparison, the maximal peak I_Na amplitude elicited with voltage steps from a holding potential of 100 mV is approximately 0.8 mA/cm^-2, which occurs at approximately +5 mV (Vandenberg and Bezanilla 1991a). As noted in the preceding text, the Hodgkin and Huxley (1952b) model qualitatively describes the primary features of I_Na gating. However, several groups have shown that it is an inadequate quantitative model (reviewed by Patlak 1991). An alternative model provided by Vandenberg and Bezanilla (1991b) for I_Na in squid axons (APPENDIX) successfully describes macroscopic ionic currents, single-channel currents, and gating currents in this preparation. Their model also predicts a sustained, or persistent, I_Na component (Fig. 1, - - -). This result clearly provides an inadequate description of I_NaP. In particular, it has a maximal amplitude of approximately 25 µA/cm^-2 at 15 mV, whereas I_NaP has a maximum amplitude of 4 µA/cm^-2 at 50 mV.

View larger version (14K): [in this window] [in a new window]   Fig. 1. Persistent sodium current (INaP) in squid giant axons. The data are the INaP results of Rakowski et al. (2002) taken from Fig. 10 of their paper. The symbols (closed squares and closed triangles) refer either to 425/0 or 425/50 (sodium ion concentrations), respectively, with 425 mM extracellular Na+ and either 0 or 50 mM intracellular Na+. The curve describing these results is given by 4.34 (V/24) (Nai exp(V/24)-Nao)/((exp(V/24)1)(1+exp((V +65)/7)) with Nao = 0.425 M and Nai = 0.05 M. [This expression is virtually unchanged over the voltage range of the measurements (100 to +10 mV) with Nai = 0.05 M replaced by 0 M.] The dashed curve represents the steady-state current predicted by the Vandenberg and Bezanilla (1991b) model - the VandB model -, as described above (APPENDIX). The ordinate for the INaP results is on the left. The ordinate for the dashed curve is on the right.

One factor that is missing from the preceding analysis is slow inactivation of I_Na (Rudy 1978). These results are illustrated in Fig. 2. In this experiment, the membrane potential was stepped from a holding level of 90 mV to intermediate levels between 90 and 0 mV for various times (t) from milliseconds to tens of seconds followed by a 7-ms step to 0 mV with 300 mM intracellular Cs to block I_K (METHODS). Currents elicited by the second step are shown superimposed in Fig. 2, top, for a prepulse to 55 mV with the duration of the prepulse indicated alongside each record. The classical rapid inactivation reached a quasi-steady level at 55 mV within approximately 20 ms (T = 5°C). No additional inactivation was observed with t < 8 s. Slow inactivation occurred with t in the 10- to 50-s range, as indicated by Fig. 2, top. A rest interval of 5 s at 90 mV was sufficient to allow for recovery from inactivation, both fast and slow, as evidenced by test steps directly from 90 to 0 mV after the rest interval (not shown). The two phases of inactivation are further illustrated by a plot of the relative peak I_Na amplitude on a logarithmic scale (Fig. 2, middle). Steady-state inactivation was determined by holding at the potentials indicated in Fig. 2, bottom, (100 to 40 mV) for 5 min followed by a step to 0 mV (results labeled "true steady-state inactivation"). No additional inactivation was observed for times more than 5 min. Consequently, currents observed in the steady-state at any given potential after 5 min, such as the results from Rakowski et al. (2002), are referred to here as persistent current. Also shown in Fig. 2 are the classical, or standard, inactivation results obtained with a holding potential of 100 mV and a 50-ms prepulse to the potentials indicated (Fig. 2, bottom), followed by a step to 0 mV. These results (labeled "HH") are described by the Hodgkin and Huxley (1952b) inactivation curve, _h/(_h + _h) with _h = 0.14 exp[(V + 60/20)] and _h =1/{1 + exp[0.1(V + 30)]}. Steady-state inactivation is described by _sh/[(_h + _h)( _s + _s)], where _s and _s are the slow inactivation parameters, with _s = exp[0.1(V + 57)] and _s = exp[0.1(V + 57)]. As indicated by Fig. 2, bottom, the net effect of the slow process in the steady state is to shift inactivation leftward on the voltage axis and to steepen the slope of this relation at its midpoint. The results in Fig. 2, bottom, were not noticeably temperature dependent. Moreover, results similar to those shown in Fig. 2, top, were obtained without CsF in the perfusate (300K_i/300K_o as described in METHODS), which suggests that Na⁺ gating in these experiments was not affected by intracellular F.

View larger version (18K): [in this window] [in a new window]   Fig. 2. Slow inactivation of INa. Top panel: currents elicited by the two step protocol illustrated in the inset of the middle panel. Membrane potential was stepped from 90 to 55 mV for time t followed by a step to 0 mV. Currents elicited by the second step are shown superimposed for various t indicated alongside each record. A rest interval at 90 mV of 5 s was used between each application of the protocol. The scales represent 3 ms and 0.25 mA/cm2. Middle panel: semi-logarithmic plot of peak INa from the top panel as a function of t. Prepulse potential was 55 mV. The result for time [yen] was obtained after holding the potential at 55 mV for 5 min. The theoretical curve describing these results corresponds to 0.37 + 0.35 exp(-t/1) +0.28 exp(-t/2), where 1 =10 ms and 2 =54 s. Bottom panel: voltage dependence of INa inactivation. The closed circles (labeled HH) represent fractional inactivation with a 50 ms duration prepulse to the voltages indicated on the abscissa. The closed squares represent fractional inactivation obtained by holding at the potentials indicated for 5 min. The error bars represent ± SD (n = 4). The curve describing the HH results is given by h/(h+h) with h = 0.14 exp((V + 60)/20) and h = 1/(1 + exp(0.1(V + 30))). These expressions were taken from Hodgkin and Huxley (1952b) with their h multiplied by a factor of 2. The curve describing the results labeled "true steady-state inactivation" is the product of h/(h+h) and s/(s+s) with s = exp(0.1(V + 57)) and s = exp(0.1(V + 57)).

The steady-state, or persistent, current in the Vandenberg and Bezanilla (1991b) model with slow inactivation taken into account is the product of Fig. 1, - - -, and _s/(_s+_s), and is represented by the curve labeled a in Fig. 3. This result, in turn, was subtracted from the I_NaP data in Fig. 1, giving the modified I_NaP results in Fig. 3. The only significant changes occurred between 60 and 40 mV (open symbols). The other I_NaP results were unchanged because the predicted contribution of the sustained I_Na component to I_NaP is virtually nil outside the 60 to 40 mV range. The modified results in Fig. 3 represent that portion of I_NaPthe major part of I_NaP measured by Rakowski et al. (2002)which is attributable here to a set of channels that are distinct from I_Na.

View larger version (10K): [in this window] [in a new window]   Fig. 3. Persistent sodium current, INaP, with the contribution from INa removed. The curve through the data are the same as the solid curve in Fig. 1. Curve a is given by the product of the persistent current predicted by the Vandenberg and Bezanilla (1991b) model, the dashed curve in Fig. 1, and the slow inactivation process, i.e., s/(s+s). This is the predicted contribution of INa to INaP. The INaP results in Fig. 1 are shown here corrected according to curve a. That is, each data point in Fig. 1 at each respective potential was reduced by an amount predicted by curve a. The only results affected were in the 60 to 40 mV range, as indicated by the open symbols.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Rakowski et al. (2002) presumed that their I_NaP results in squid axons were attributable to the classical Na⁺ channel given that I_NaP reversed near the theoretical sodium ion equilibrium potential, E_Na; tetramethylammonium ions (TMA) and n-methylglutamate ions (NMG) were both impermeant; and I_NaP had a tetrodotoxin sensitivity similar to that of I_Na. However, these results are insufficient to exclude the possibility that I_NaP is attributable to a channel mechanism distinct from I_Na. Indeed, the relationship between I_Na and I_NaP has been an ongoing debate for several years (Crill 1996; Huguenard 2002). One hypothesis is that I_NaP is attributable to transitions of the conventional transient Na⁺ channels to noninactivating gating modes as demonstrated for heart and skeletal muscle Na⁺ channels by Patlak and Ortiz (1985; 1986) and in brain neuron Na⁺ channels by Alzeheimer et al. (1993) and Segal and Douglas (1997). In the latter studies, the noninactivating gating modes were extremely rare and too short-lived to be associated with I_NaP (Magistretti et al., 1999). Moreover, Magistretti et al. (1999) found that the single-channel conductance of I_NaP from stellate cells in the entorhinal cortex was significantly higher than transient openings, 19.7 pS as compared with 15.6 pS. Furthermore, I_NaP is preferentially diminished by the anticonvulsant phenytoin relative to the effects of this agent on I_Na (Segal and Douglas 1997), which further supports a distinct ion channel mechanism for I_NaP. Recently, Taddese and Bean (2002) have shown that persistent Na⁺ current in isolated tuberomammillary neurons in the 60- to 40-mV range may be attributable to an allosteric gating mechanism of the transient I_Na channel. The analysis provided here of the Rakowski et al. (2002) measurements is also consistent with a contribution of I_Na to persistent current in the 60- to 40-mV range. Outside of this range I_Na appears an unlikely candidate for I_NaP given that 90 to 60 mV is below threshold of I_Na and that slow inactivation removes contributions of I_Na to persistent current for V > 40 mV.

A critical feature of this analysis is slow inactivation. This mechanism has been reported by several groups (Almers et al. 1983; Hirschberg et al. 1995; Kirsch and Anderson 1986; Ruben et al. 1992; Rudy 1978; Simoncini and Stuhmer 1987). The original measurements in squid giant axons of Rudy (1978) differ significantly from the results of Fig. 2 of this report. In particular, Rudy (1978) found that slow inactivation was half-maximal at 30 mV, whereas the midpoint for this process in this study is 57 mV (Fig. 2). This difference in results is probably attributable to a difference in experimental protocol. Rudy (1978) measured the recovery of the Na⁺ conductance after a long-lasting depolarization of the membrane potential, whereas the onset of this process from a negative holding potential was used in these experiments. A straightforward way of measuring slow inactivation in the steady-state is to hold the membrane potential for several minutes at various levels and then measure peak inward current with a test pulse to 0 mV, a procedure that has been used for muscle Na⁺ channels (Almers et al., 1983; Simonichi and Stuhmer 1987). This study appears to be the first in which this protocol has been used in squid giant axons (Fig. 2). The results suggest that inactivation of I_Na is complete at 40 mV. A similar result was reported for rat muscle Na⁺ channels heterologously expressed in HEK-293 cells (Cummins and Sigworth 1996). Whole cell recordings cannot exclude the possibility that a small component of the Na⁺ conductance remains active in the steady-state for V > 40 mV. The single-channel recordings of Hirschberg et al. (1995) more compellingly demonstrate complete inactivation, at least for V > 20 mV. In other words, any sustained Na⁺ current for V > 20 mV would, in the spirit of this report, be attributable to an I_NaP channel distinct from I_Na. Conversely, the results of Hirschberg (Hirschberg et al. 1995) also demonstrate a small activation of Na⁺ conductance for V < 60 mV, even for potentials as negative as 90 mV, which would be consistent with an identification of I_NaP with I_Na in this potential range. However, activation of I_Na for V < 60 mV in squid giant axons is not predicted by the Vandenberg and Bezanilla (1991b) model (Fig. 1). Moreover, Correa and Bezanilla (1994) found a very minimal activation of I_Na channels in steady state even at moderately depolarized potentials, such as 40 mV. They did not report single Na⁺ channel openings at 90 mV in steady-state conditions.

Persistent Na⁺ current appears to underlie oscillatory activity in mammalian brain neurons, such as the theta rhythm in the entorhinal cortex (Alonso and Llinas 1989; Silva et al. 1991; White et al. 1995). The role of I_NaP in squid giant axons under physiological conditions is unknown. It appears to cause spontaneous rhythm firing of action potentials with slightly elevated intracellular pH (pH_i > 7.7) (Clay and Shrier 2001). The axon has a small, nonselective cation conductance, sometimes referred to as a leak conductance, that is permeable to both Na⁺ and K⁺ and is activated by intracellular protons (Clay and Shrier 2001, 2002). A similar conductance was originally reported in rat dorsal root ganglion neurons by Bevan and Yeats (1991) with a proton binding site on the external rather than the intracellular side of the membrane. Intracellular perfusates in the squid giant axon with slightly alkaline pH remove this component, thereby allowing the negative slope character of I_NaP to destabilize the resting state of the axon (Clay and Shrier 2001, 2002).

The molecular basis of I_NaP has yet to be determined. It could be mediated either by a novel  subunit isoform not yet cloned or by one of the genes that are known to encode I_Na (Magistretti et al. 1999). Heterologous expression of cloned Na⁺ channel subunits will, quite likely, resolve this issue.