INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Voltage-gated sodium channels are closely related to the other voltage-gated channels that are selective for potassium or calcium, but they excel in having very rapid activation and inactivation kinetics to guarantee the fast impulses of nerve and muscle (Hodgkin and Huxley, 1952; Armstrong, 1981; Hille, 1992; Marban et al., 1998; Armstrong and Hille, 1998). Their function is most commonly studied from ionic currents (I_Na) either measured on the single channel or whole-cell level. An additional and more direct insight into the gating machinery of voltage-dependent ion channels is obtained from the gating current (I_g), which was first recorded from sodium channels in the squid giant axon (Armstrong and Bezanilla, 1973; Keynes and Rojas, 1974; for recent reviews see Sigworth, 1994; Bezanilla and Stefani, 1998). I_g is generated by the displacement of charged voltage sensors inside the channel protein, a displacement that couples changes of the transmembranal electric field to the movement of gates that in turn control the permeability of the channel pore. An important finding of the studies by Armstrong and Bezanilla (1973, 1977) was that during inactivation part of the voltage sensors are immobilized and that the time course of recovery from fast inactivation and immobilization is identical. Therefore, gating currents appeared useful for the study of fast inactivation in sodium channels.

In a previous study, using a high-resolution voltage-clamp at the squid giant axon, I_g during the inactivation phase was recorded and correlated with the corresponding I_Na (Forster and Greeff, 1990; Greeff and Forster, 1991). These studies strongly suggested the necessity of a voltage sensor for the inactivation process, most likely segment S4 in domain 4 (D4). However, these experiments were limited to wild-type channels in a native preparation that also contained voltage-dependent potassium channels, and it was also assumed that all channels would produce ionic and gating current. It was, therefore, an important step to proceed to heterologous expression systems for designed channels and only a few endogenous voltage-gated channels. So far, evidence for an involvement or coupling of S4D4 in the inactivation process was demonstrated by ionic current experiments at mutant channels (e.g., Chahine et al., 1994; Chen et al., 1996; Ji et al., 1996; Kontis and Goldin, 1997). Gating current experiments from heterologously expressed voltage-gated channels have been exploited in the last years, mostly for potassium channels in Xenopus oocytes (e.g., Perozo et al., 1993, 1994; Bezanilla et al., 1994; Aggarwal and MacKinnon, 1996). For sodium channels, the expression was assumed to be too small and the sodium channel kinetics too fast (~5 times faster than in potassium channels) for the measurement of I_g by conventional two-electrode voltage-clamp recording techniques (Ruben et al., 1997). Sophisticated methods like the cut-open oocyte (Stefani et al., 1994; Stefani and Bezanilla, 1998), which has recently been used for I_g,Na studies combined with fluorescence (Cha et al., 1999) or the macropatch electrode used for the analysis of gating current fluctuations (Conti and Stühmer, 1989), so far have not permitted the direct quantitative correlation of ionic- and gating-currents for sodium channels. For voltage-gated calcium channels also expressed in transfected cells, such comparisons of gating-charge and ionic current have been successfully performed (Neely et al., 1993; Bangalore et al., 1996; Kamp et al., 1996; Josephson and Varadi, 1996; Jones et al., 1999). In a recent study using an optimized two-electrode voltage-clamp we succeeded in recording sodium channel I_g and I_Na from S4D4 mutated channels highly expressed in Xenopus oocytes, and could directly demonstrate the prominent role of this voltage sensor for inactivation (Kühn and Greeff, 1999).

In the above-mentioned paper and in Greeff et al. (1998) we already reported an obvious mismatch in the size of I_g as compared to I_Na. With the aim of clarifying the ratio of gating charge versus conductivity we carried out the present quantitative study measuring both signals simultaneously at the same oocytes. The straightforward two-electrode voltage-clamp technique (TEVC) allowed us to establish fast voltage steps at the whole oocyte, adequate for the recording of I_g (Greeff and Polder, 1998). As detailed now, asymmetry artifacts of the voltage-clamp were minimized and separated from I_g using special pulse protocols. Initially, the ratio of the total gating charge to ionic permeability was expected to be constant if all channels would gate and conduct ions. However, large variations of this ratio were found and always the number of conducting channels seemed to be smaller than the number of gating channels. In the compiled results, we observed a clear correlation with a change of the sodium equilibrium potential most likely caused by a high sodium influx at the channel density used. These data and specific tests strongly suggest that an increase of internal sodium, or rather the energetic stress needed to regulate the cytoplasmic concentration of free sodium, causes a decrease in sodium permeability by lowering the open probability of a fraction of channels with their gating machinery still intact. This finding is of relevance for the supposed ratio of gating charge versus ionic current for rat brain IIA sodium channels expressed in Xenopus oocytes, as well as channel modulation. Because the total gating current does not seem to be altered, the improved TEVC technique opens up new possibilities for studying the gating machinery of wild-type and mutant channels. Part of the results of the present study have been published in preliminary abstracts (Greeff et al., 1998; Greeff and Kühn, 2000).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Preparation of high-expression RNA

The gene of wild-type rat brain IIA sodium channel -subunit (rBIIA) used in this study was originally derived from cDNA plasmid pVA2580 (Auld et al., 1988) and transferred into high-expression vector pBSTA (both plasmids kindly provided by Dr. A. Goldin, Irvine, CA; see also Shih et al., 1998). This was performed by subcloning the SalI fragment of pVA2580 containing the open reading frame and 3' untranslated sequences of the sodium channel gene into the BglII site of vector pBSTA. For this purpose, both SalI- and BglII-generated single-stranded ends were partially filled with DNA polymerase I (Klenow fragment) in separate reactions. These reactions filled the first two bases of the 5' cohesive overhangs left by digestion by SalI and BglII, respectively, yielding fragments that were no longer self-complementary, but fully compatible with each other for ligation. The correct orientation of the subcloned insert was verified by restriction analysis and DNA sequencing. Plasmid pBSTA contains a T7 RNA polymerase promotor and Xenopus--globin 5' and 3' untranslated sequences. Capped, full-length transcripts were generated from SacII-linearized plasmid DNA using a T7 RNA in vitro transcription kit (Ambion Inc., Austin, TX). Oocytes (stage V-VI) from Xenopus laevis (NASCO, Ft. Atkinson, WI) were used. One day before injection of cRNA, the oocytes were defolliculated in a Ca²⁺-free solution containing 2 mg/ml collagenase (Boehringer, Mannheim, Germany), for 1-2 h at 18°C. Oocytes were microinjected with 20-80 ng of cRNA (50 nl) and maintained at 18 ± 1°C in modified Barth's solution (MBS in mM): 88 NaCl, 2.4 NaHCO₃, 1 KCl, 0.82 MgSO₄, 0.41 CaCl₂, 0.33 Ca(NO₃)₂, 10 HEPES-CsOH, pH 7.5, supplemented with 25 U penicillin, 25 µg/ml streptomycin sulfate, and 50 µg/ml gentamycin sulfate.

Electrophysiological recording

Two-electrode voltage-clamp recordings were performed 1-15 days after cRNA-injection with a TEC-05 (npi-electronics, Tamm, Germany) that had been modified in collaboration with R. H. Polder from npi-electronics for optimal series resistance (R_s) compensation and fast charging of the membrane capacitance (Greeff and Polder, 1998). Intracellular electrodes contained an agarose cushion (Schreibmayer et al., 1994), were filled with 3 M KCl, and had resistances between 100 and 200 k. Macroscopic ionic- and gating-current signals were recorded using a PDP-11/73 (Digital Equipment Corp., Maynard, MA) controlled 16-bit A/D and 12-bit D/A interface (CED, Cambridge, UK). The oocytes were clamped at a holding potential of 100 mV for at least 5 min to ensure recovery of slow inactivation before recording started.

R_s compensation was adjusted for critical settling of the capacitance transients within 100-200 µs (Greeff et al., 1982). The charging of the membrane was then speeded up optimally without subsequent ringing, which would distort the gating currents. At the same time a reduction of voltage errors due to large ionic currents was achieved. In our study the macroscopic ionic currents were large and prone to R_s errors in two respects, as seen in the Results. First, at all voltages, for the capacitance as well as for the ionic current, a voltage error occurs, being the product of uncompensated R_s and current size. Second, in the very nonlinear voltage range of the sodium activation curve around 40 mV, such voltage errors distort the normal activation more pronouncedly than in the more linear region above 0 mV. This behavior is especially prominent for membrane regions that are not well space-clamped. In our experiments we improved our technique in this respect. In the early phase the oocytes were pressed against the chamber floor, which could lead to a bottom region of the membrane with a different series resistance, resulting in space-clamp errors. In the later experiments the cells were slightly lifted, which seemed to create better space-clamp conditions. Compare the "escaping" sodium current traces (see Figs. 3 and 5) and the better-recorded I/V curves (see Fig. 6). A further relevant point was that wein contrast to the situation assumed in the methodical study by Baumgartner et al. (1999)placed the current electrode tip deep into the cell to achieve a more homogeneous spatial charging of the membrane. As we could check on the recorded capacitance transient, an eccentric position of the electrode showed up as a slow tail that could not be compensated critically, an observation known to us from squid axon experiments. For the calculation of R_s and its uncompensated part, dummy studies were performed. Reliably, we could estimate the uncompensated part from the speed of the critically compensated transient. In contrast to the situation in the cell, this could be confirmed in the dummy by comparing the voltage levels due to DC-current at the point of current injection and between the series resistance and the membrane resistance in parallel to the capacitance. Corresponding calculations for the experimentally observed ionic currents will be given in the Results. In order to know the clamping speed, we routinely stored the capacitance transients.

No analogous subtraction was used because the 16-bit ADC had a sufficiently fine resolution for digital subtraction of the large linear transient and leak currents by scaled averages from pulses below 100 mV (for basic protocols see Bekkers et al., 1984). Reduction of the remaining asymmetry was achieved by finding a compromise between clamping speed and asymmetry, i.e., low-pass-filtering the command signal at 5 kHz (8-pole Bessel filter, Frequency Devices, Haverhill, MA, U.S.A.). Recorded signals were low-pass filtered at 5 kHz (8-pole Bessel filter, Frequency Devices) and sampled at 10 or 20 kHz. Data analysis was performed on the PDP-11/73; permeability calculations were done in MathCad (MathSoft, Inc., Cambridge, MA). The experiments were carried out in MBS solution at different bath temperatures (8-15 ± 1°C) and in some cases a fraction of Na⁺ was replaced by an equimolar amount of choline, as indicated in the experiments. For the recording of gating currents, either 2 µM tetrodotoxin (TTX; RBI Research Biochemicals International, Natick, MA, U.S.A.) was added or recordings were performed at the sodium reversal potential as described in the text.

Permeability calculations

During the course of the experiments for this study the problem arose that sodium ionic currents obtained under different conditions, such as varying external and internal sodium concentrations, had to be compared. Furthermore, for an estimate of the number of conducting channels the published figures for single channel currents had to be used that had been obtained at conditions favorable for single channel recording, i.e., in a voltage region of 60 to 10 mV. In order to avoid the above-mentioned distortions due to R_s errors in the nonlinear voltage region, we adopted the method of obtaining the conductance around the sodium reversal potential E_Na. For the comparison of such different experimental data we transformed the current and conductance G_Na to permeability P_Na. This, as discussed later on, despite not being the perfect method, is a very good method for an estimate of the amount of open channels independent of both the sodium concentration and the voltage range of the test-pulse.

According to the Goldman-Hodgkin-Katz-theory, the current I_Na that flows through open channels with a given P_Na depends on the pulse potential V and the sodium concentrations on either side of the membrane, [Na⁺]_i and [Na⁺]_e, as follows (see, e.g., Hille, 1992, Eq. 13.5):

(1)

where K equals F/(R*T) with their usual meanings, and z is the valence. In our experiments the internal sodium concentration was unknown, but was derived from the experimentally observed reversal potential assumed to correspond to the sodium equilibrium potential E_Na using the Nernst equation. Substituting [Na⁺]_i = [Na⁺]_e/exp(E_Na * K) and setting z = 1 in Eq. 1 one obtains:

(2)

Often the ionic currents are expressed as current per area of membrane, and then the permeability has the dimension of distance per time. In our approach we preferred to compare the absolute currents of whole oocytes with currents through single channels and expressed the permeability by the volume that is cleared per time. A typical figure for the single channel current from cell attached recordings at an oocyte in ND96 bath containing 96 mM sodium is reported to be 0.9 pA at V = 30 mV at room temperature (same sodium channel clone rBIIA as in our study; Goldin, 1991). Assuming a typical E_Na of +51 mV corresponding to a reasonable figure of 12 mM for [Na⁺]_i, we calculated the single channel permeability P_Na by solving Eq. 2 and obtained P_Na equal to 5.8 · 10⁵ pl/s. This figure as also the figure for the more familiar conductance  = i_Na/(V  E_Na) equal to 11 pS will be used for the estimate of the number of conducting channels in the Discussion.

It will be further useful to consider the first derivative dI_Na/dV of Eq. 2 to obtain the permeability from the conductance around E_Na, which is measured reliably also at high channel expression, because around E_Na the ionic currents remain small and are only subject to linear R_s errors (discussed in the Results). From Eq. 2 follows by differentiation:

(3a)

where

(3b)

(3c)

(3d)

The relevance of these computations is shown graphically in Fig. 1 based on the single channel data from above: single channel current i_Na of 0.9 pA at V = 30 mV at room temperature, cell-attached recording from an oocyte with sodium concentrations [Na⁺]_e of 96 mM (Goldin, 1991), and a typical [Na⁺]_i of 12 mM.

View larger version (12K): [in this window] [in a new window]   FIGURE 1   Single channel conductance iNa (A) and its derivative diNa/dV (B) versus pulse potential as calculated from Eqs. 2 and 3 assuming a constant permeability for the channel of 5.8 · 105 pl/s and asymmetrical, typical [Na+]e/[Na+]i of 96/12 mM corresponding to ENa of +51 mV. The different figures for the cord conductance s(c, 30), the slope conductance at various voltages, and especially s(ENa) at ENa, are discussed in the text.

The cord conductance i_Na/(V  E_Na) would give  = 11 pS (straight line s(c, 30)). The ionic current through an open channel according to Eq. 2 depends on voltage and the asymmetrical sodium concentrations. Therefore, the slope conductance dI(V)/dV varies, which is visible in Fig. 1, A and B. Around the equilibrium potential E_Na of +51 mV the slope dI(V)/dV equals 6.55 pS (tangent s(E_Na), in 1 A; level in 1 B), while it would be ~16 pS at 30 mV, which is between 22 pS at very negative and 2.8 at very positive voltages (current determined by either external or internal concentration only). The slope conductance dI/dV at E_Na (the observed E_rev) was experimentally obtained, and from its value together with V = E_Na one obtains the figure for P_Na using Eq. 3, which simplifies because T1 and T3 become zero:

(4)

The permeability P_Na does not depend on the sodium concentrations of the solutions adjacent to the conducting channels, but indicates how much volume is cleared per time, while the current and the conductance also depend on the ion content of this volume. Therefore, experimental data obtained with varying external or internal concentrations can directly be compared via P_Na.

To test the usefulness of P_Na, it will be necessary to fit an equation to I_Na versus V when a whole family of sodium currents for different voltages is obtained. Simply fitting a Boltzmann curve to G_Na versus V would not fit well, and especially would not account for different ionic concentrations. Therefore, we decided to combine the conversion of current to permeability and the Boltzmann relation. For this purpose Eq. 2, which reflects the change of the current at different voltages and sodium concentrations for a constant permeability P_Na corresponding to a constant number of open channels, is now multiplied with the Boltzmann term raised to the third power. In that way, the voltage-dependence of open probability is incorporated similar to the Hodgkin and Huxley formalism (Hodgkin and Huxley, 1952), but for the peak sodium currents uncorrected for inactivation, as it is often used:

(5)

where V' is the half-activation voltage and A the slope factor.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Expected size and identification of sodium channel gating current: increase of channel expression

The known properties of ionic- and gating-current from sodium channels of squid and other preparations are used here for a first estimate of the expected size of the gating current (I_g) (Fig. 2). During activation, charged voltage sensors (S4 segments) move along the electric field in the channel protein and, by coupling to a gating structure, control the opening of the pore (Stühmer et al., 1989; Yang and Horn, 1995; Yang et al., 1996). The individual S4 movements are assumed to occur between energetically favorable states (Fig. 2 B). According to the present understanding a channel has to go through a number of closed states (C₀, C₁, C₅), separated by charge-producing transitions before the channel pore is open for sodium ions to pass (state O in state diagram of Fig. 2 B). Voltage-dependent transitions produce specific amounts of charge displacement (q_0-5), around 1 electron charge (e_o), that cause single channel gating current shots (i_g in Fig. 2 C) which, however, are far too small to be detected individually. In the open state, a single channel ionic current (i_Na) of ~1 pA flows (equivalent to ~5000 sodium ions/ms), until the inactivation gate closes the channel. The sum of these stochastic single channel signals is measured as the total macroscopic ionic current (I_Na) and gating current (I_g) of all channels in the cell membrane. I_Na shows an activation and an inactivation phase, I_g occurs mainly during the activation phase (Fig. 2 C). Each channel produces a constant amount of gating charge per channel (q = q₀ + q₁ + . . . q₅) the size of which is still a point at issue, estimations ranging from 4 to 6 (Hille, 1992; Sigg and Bezanilla, 1997) to 12 e_o (Hirschberg et al., 1995). A mean value of 8 e_o will be assumed in the Discussion. A further phenomenon specific for sodium channels is gating charge immobilization. In a two-pulse protocol with a short interpulse interval at holding potential, the second pulse will elicit no transient I_Na, but still a fraction of gating current (I_{g, n}) that is assumed to occur from channels switching quickly between inactivated states (Armstrong and Bezanilla, 1977; Bekkers et al., 1990) or, with respect to molecular structure, only part of the voltage sensors, are able to return while the pore is still closed by the inactivation h-gate. Part of the structure responsible for inactivation and immobilization is most likely the cytoplasmic loop connecting domains D3 and D4 (Vassilev et al., 1988; Stühmer et al., 1989; Patton et al., 1992). Recent work suggests that the S4 voltage sensors in D1 and D2 are free to move during inactivation, while those in D3 and D4 are immobilized (Cha et al., 1999) and our own results suggest that it is S4D4 that controls the movement of the loop (Greeff and Forster, 1991; Kühn and Greeff, 1999).

View larger version (31K): [in this window] [in a new window]   FIGURE 2   Schematic working model illustrating the essential features of sodium channel ionic and gating currents. (A) Cross-section of the -subunit of the sodium channel protein, with its four domains D I-D IV (D I is omitted to lay open the pore); each domain has 6 putative membrane-spanning segments S1-S6 (not detailed). The S4 segments of D I-D III control the m-gates (shown for D II), whereas segment S4 of D IV is coupled to the h-gate. The molecular mechanisms of this coupling are treated elsewhere (Kühn and Greeff, 1999). The highly specific, external sodium channel blocker tetrodotoxin (TTX) is depicted in its assumed functional position. The outward movement of the S4 voltage sensors caused by depolarization is indicated by arrows. (B) State diagram assuming 6 closed states (C0 to C5) with quantal displacement charges of activation (q0 to q5), the open state (O), and several inactivated states (I); qh, quantal displacement charge O to I. (C) Signals during a test pulse that activates and inactivates the sodium channels, a short gap at holding potential, and a second pulse occurring when the channels are still inactivated. Abbreviations: Vp, command voltage pulses; Vh, holding potential; q0-5, qh, quantal gating charges of the S4 voltage sensors that cause the single channel gating current shots (ig) due to the movements of the voltage sensors for the activation and inactivation gates, respectively; Ig, macroscopic gating current of the total number of channels; Ig,n, nonimmobilized fraction of Ig; iNa, single channel sodium ionic current; INa, macroscopic sodium ionic current; INa,n, remaining, noninactivating fraction of sodium current after inactivating prepulse.

Starting the experiments in search of gating currents, initially a rough comparison of peak amplitudes of the macroscopic currents to be expected from N channels with single channel current i_Na was made. The ionic current is expressed as

(6)

and p^o is the probability of a channel to be open at peak time; p^o is ~0.5 for voltages of 0 mV and above as determined directly by the method of nonstationary fluctuation analysis at the node of Ranvier (Sigworth, 1980), in squid (Bekkers et al., 1986), and neuroblastoma cells (Bulatko and Greeff, 1995). F^a equals 1 if all channels that produce gating current are a homogenous population with the same normal probability p^o. This is assumed at first, but if some channels keep their pore closed for some reason or bypass the open state, F^a will be between 0 and 1; this would correspond, e.g., to modulated channels (Bulatko and Greeff, 1995) or to channels with their pores closed by TTX. The gating charge of N channels, each contributing q, equals:

(7)

I_g occurs mostly during the time t_p to peak of I_Na. We found that I_g was of nearly triangular shape, especially when filtered, and then the following approximation for its peak is useful:

(8)

Injection of large amounts (30-80 ng) of cRNA from conventional vectors yielded an average maximal inward current I_{Na, peak} at voltages ~10 mV of ~5 µA (unpublished data). Taking i_Na as 0.9 pA (Goldin, 1991) and p^o as 0.5, we calculate from Eq. 6 a total channel number N of 11 × 10⁶ per oocyte. Assuming all these channels to be fully functional (F^a = 1), t_p = 1 ms (for the applied test-voltage) and q = 8 e_o, one would expect from Eq. 8 an I_g,peak of ~0.03, µA which gives a ratio for I_Na,peak/I_g,peak of ~160:1. This fits with other estimations around 100:1 for mammalian sodium channels expressed in Xenopus oocytes (unpublished, from personal discussions). Such a small gating current would be hardly detected in the baseline noise of a two-electrode voltage-clamp. Therefore, our primary aim was to increase the density of channels by applying a high-expression vector designed for Xenopus oocytes that had already been successfully used for potassium channels (Perozo et al., 1993); the cRNA contains code-flanking -globin, a 3'-end poly-A tail and 5'-end cap. With this technique we could increase I_Na,peak by a factor ~10 with maximal amplitudes of between 50 and 150 µA (typical recordings Fig. 5 A), and we expected for I_g,peak 0.3-0.9 µA.

Very fast clamp and short asymmetry: unexpectedly large putative gating current

Because sodium gating currents were expected to be very fast, we initially tried to speed up the clamp as fast as possible and would even accept some asymmetry artifacts due to some nonlinearity in recording and subtraction of the capacitance transients. It was possible to speed up the charging of the whole oocyte membrane to a settling time of the capacitance transient in ~60 µs (Fig. 3); this, however, caused transients I_c with amplitudes of 500-600 µA. These fast and large transients obtained for the forward pulses were not subtracted well using subtraction pulses between 100 and 150 mV. The resulting asymmetry artifacts gave erratic zigzag lines of ~10-20 µA (Fig. 3 D). This contamination might obscure the gating current with respect to amplitude, but since it lasts only 60 µs it could be blanked, still leaving time to display the slower gating current (demonstrated in Fig. 3, D and E; expanded time base). As a result, the putative gating current can be clearly identified even in the nonexpanded traces of Fig. 3 A. It showed typical gating current properties: always flowing outward in contrast to the ionic current and occurring in <1 ms before the peak of the ionic current. The size of several µA, however, was unexpectedly large, being nearly of equal amplitude as the ionic currents, so we had serious doubts about its origin.

View larger version (32K): [in this window] [in a new window]   FIGURE 3   Recordings with a voltage-clamp tuned for speed and critical Rs compensation. (A) Testpulses from 50 to +30 mV in steps of 10 mV; pulses for subtraction of linear components were between 100 and 150 mV; note the escaping trace at 40 mV. (B-E) signals of 30, 0, +30 mV on expanded timescale; the vertical dotted lines indicate the settling time of the membrane voltage. (B) Capacitance transients (Ic) and (C) their integral, which reflects the time course of charging the cell membrane (Vm) to the command voltage. (D) Signal traces of membrane current Im = INa + Ig + contamination show the zigzag due to non-ideal subtraction of the capacitance transients of forward test pulse and linear subtraction pulse. The zigzag is followed by putative outward gating currents and ionic sodium currents, which change polarity when Vp crosses the sodium reversal potential. (E) Same as D but data points during nonlinear subtraction of transients were blanked. Experiment T18M.I; temperature 8°C.

These experiments also demonstrated the performance of our TEVC with respect to speed and linearity. It is possible to charge the large membrane capacitance of 200-280 nF within <100 µs. The integrated transients represent the time course of the voltage at the very membrane as it is charged to the command voltage (Fig. 3 C). From their 10-90% rise-time of 23 µs the time constant is calculated as 23/2.3 = 10 µs (Horowitz and Hill, 1980). This allows us to obtain an estimate of the remaining series resistance, which was not compensated as R_s,r = /C_m = 10 µs/0.25 µF equal to 40 . As detailed above, this method to estimate R_s was verified on a dummy and should also be representative for the I_Na traces. However, the observed escaping trace at 40 mV would then only suffer from a voltage error of 8 µA times 40 , equal to 0.32 mV, which would not explain this distortion. At this early stage of the experiments we were not so conscious about electrode positioning and contact area of the oocyte with the bottom of the chamber. We now assume that the charging of the membrane was not perfectly homogeneous with respect to space-clamp, which allows small membrane areas to produce uncontrolled ionic-current (see Methods for improvement). More important was a reduction of the artifact due to nonlinear subtraction of the huge transients. From studies on dummy membranes we noticed that this asymmetry occurred mainly during the fast changes (large time derivative) in the capacitance transient. Therefore, our next strategy was to slow the clamp such that it still would be adequate for gating-current recording.

Slightly slower and improved voltage-clamp with little asymmetry confirms large gating current

To decide whether the observed asymmetrical charge displacement had its origin in clamp artifacts or actually reflects charge movement in sodium channels, we reduced the clamp asymmetries by compromising on the speed and applied special protocols for the separation of the two possible sources for asymmetry current. Improvements on the technical side were as follows: 1) slowing the command pulse from the D/A converter by feeding it through an 8-pole Bessel low-pass filter set at 5 or 3 kHz; 2) checking all gain stages in the voltage-clamp to avoid any saturation of an amplifier with respect to gain and slew rate; 3) using low-resistance electrodes of 100-200 k. These means resulted in a capacitance transient of a much smaller amplitude and roughly triangular shape, as seen in noninjected control oocytes (Fig. 4, A and B). The 10-90% rise-time was ~180 µs, corresponding to a time constant of 180/2.3 = 80 µs when the command pulse was rounded at 5 kHz, and the resulting signal filtered again at 5 kHz for reduction of noise before A/D conversion. In an analogy to the above calculation, a remaining R_s of some 300  would be obtained. This, however, is an upper limit as checked on a dummy because the rounding of the command pulse and low-pass filtering of the recorded transient mask the effective R_s compensation. Escaping ionic current traces still were sometimes observed for large currents (40 µA in Fig. 5 A), but often with well-placed electrodes the I/V curves were only a little distorted (compare Fig. 6). The nonlinearity in the subtraction of the capacitance transient was greatly reduced. A full transient of 200 µA amplitude resulted in an asymmetry of <1 µA of various shape. Typically, we obtained a fast downward spike during the rising phase of the ON-transient (Fig. 4 A), but asymmetries lasting slightly longer than the transient and in the direction of I_g could also be seen (Fig. 4 B). Analog subtraction of the transient before digitization did not improve the transient cancellation and was not necessary, because our 16-bit ADC had enough resolution to avoid digitization noise in the records. We regarded this amount of clamp asymmetry as acceptable in view of the large gating current, but carried out further test protocols to distinguish real gating current from the overlapping asymmetry in channel-expressing cells.

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Sodium ionic and gating currents versus clamp-asymmetries with and without inactivating prepulse from noninjected control cells (A, B) and cRNA-injected cells (C-F). (A) Difference of capacitance transients for test pulses of 13 ms duration to 40 mV up to +40 mV in steps of 10 mV from a holding potential (Vh) of 100 mV; subtraction pulse between 120 mV and 150 mV with its transient (Ic) shown scaled to the +40 mV testpulse: full transient of 150 µA, corresponding difference 0.88 µA, duration as full transient, equal in ON and OFF. (B) Another example with an outward asymmetry that in addition lasts longer than the full transient, amplitudes 196 and 1.4 µA; the asymmetry is shown for the same test pulse with and without inactivating prepulse. (C) Recordings of INa in MBS solution with and without inactivating prepulse to +20 mV for 20 ms; interval of 2 ms at Vh; test pulse to 20 mV for 13 ms. (D) Gating current with medium-sized contamination as in control cell of A, recorded in MBS containing 2 µM TTX; no inactivating prepulse; series of test pulses from 80 mV to +80 mV in steps of 20 mV, pulse duration 13 ms. (E) Same as D but with 20 ms inactivating prepulse to 0 mV; interval at Vh 1 ms; Ig,off of inactivating prepulse included in time window. (F) Difference resulting from digital subtraction of recordings in E from those in D; Ic capacitance transient for pulse to +80 mV. Timescale: 4 ms bar as in E for all panels except for B 1 ms. Recordings taken at a holding potential Vh of 100 mV; temperature 8°C.

View larger version (22K): [in this window] [in a new window]   FIGURE 5   Estimation of gating charge and sodium conductance around the sodium reversal potential for high sodium channel expression. (A) Simultaneous recording of ionic and gating currents without TTX for test pulses of 40 to +60 mV in steps of 10 mV; Vh  100 mV. (B) Recordings as in A but 2 mV steps from +14 to +22 mV, expanded time scale. (C) Trace at ENa of 16 mV displays gating current and its integral gives the total gating charge Qg. Capacitance transient Ic reflects speed of voltage-clamp. The trace at 16 mV subtracted from the other traces leaves the pure sodium currents around ENa (see text). (D) Peak sodium currents of C plotted against pulse potential; the slope dINa/dV gives a conductance GNa of 0.91 mS. Cell No. P27S10; temperature 8°C.

View larger version (16K): [in this window] [in a new window]   FIGURE 6   Peak sodium currents versus voltage in three different external sodium concentrations fitted by permeability rather than conductance. Recordings for testpulses of 50 to +60 mV in steps of 10 mV, Vh 100 mV, critical Rs compensation, and subtraction of linear components applied as described. External solution was changed by perfusion and contained in sequence 11 mM, 20 mM, and 90 mM [Na+]e made from MBS solution and choline+ replacing sodium. The fitted Eq. 5 gave the following parameters for these three [Na+]e respectively: ENa equals +4.0, +15.1, and +46.2 mV from which, using the Nernst equation, [Na+]i was calculated as 9.4, 11.0, and 15 mM; maximal sodium permeability PNa equals 9.1, 8.6, and 6.6 × 109 l/s; V' equals 27.2, 28.1, and 27.2 mV; the slope A equals 11.7, 10.3, and 7.4 mV. Experiment Q19J; temperature 15°C.

The strongest proof for the identification of the sodium gating current was obtained by checking for the typical partial immobilization of sodium gating charge as detailed schematically above (Fig. 2 with references). As the experiment in Fig. 4, C-F shows, a test pulse to 20 mV did elicit a large ionic current with a clear activation and inactivation phase. The same pulse applied after an inactivating prepulse to +20 mV for 20 ms elicits no or few ionic currents (depending on the duration of recovery during the gap at holding potential) and only reopens a variable amount of noninactivating sodium channels (Fig. 4 C). Gating currents were recorded after the addition of 2 µM TTX to the bath with test pulses ranging from 80 mV to +80 mV in steps of 20 mV, first in the absence of an inactivating prepulse (Fig. 4 D). The same pulses applied after an inactivating prepulse demonstrated a reduction of the ON-gating currents by ~50% (Fig. 4 E). Typically, this nonimmobilized gating current I_g,n displays a faster time course compared to the total I_g,t. The clamp asymmetry of several µA was relatively large in this particular experiment (also chosen to better demonstrate the procedure) and it clearly did not change when a prepulse was applied (compare Fig. 4, D and E). This is expected for a clamp asymmetry, as can also be seen for the control cell in Fig. 4 B. The immobilization of our gating current signal in contrast to clamp asymmetry is evident after subtraction of the traces without and with a prepulse (Fig. 4 F).

We were then in a position to embark on a detailed quantitative comparison of sodium channel gating- and ionic-current and to check whether their ratio would be a constant. For this purpose we systematically measured I_g and I_Na from the same oocytes. Fig. 5 A shows a family of ionic and gating currents for a series of test-pulses ranging from 40 to +60 mV in steps of 10 mV obtained under optimized conditions at 8°C, where the fast sodium channel currents are slow compared to the capacitance transient. Despite more cautious R_s treatment and electrode positioning, for the large ionic currents of some 30 µA proper control of space-clamping was still a problem, as the escaping trace at 40 mV shows. However, as can be clearly seen, the ionic current changes its polarity from inward to outward when crossing the equilibrium potential for sodium at ~+23 mV, in this case. In contrast, the gating current that precedes the ionic current is always flowing along the polarity of the test-pulse. We took advantage of this by stepping in small increments across the reversal potential (Fig. 5 B). Then, the ionic currents are small despite the large number of activated channels and only subject to linear R_s errors in this part of the I/V-curve, and at exactly E_Na no net ionic current flows, leaving an almost pure gating-current signal. From these recordings we obtained at the same time the total gating current I_g,t and the sodium conductance dI_Na/dV at E_Na. Initially, we considered applying partial TTX block of the sodium channels to reduce the ionic current and thus avoid R_s errors. The partial reduction by TTX, however, is not well defined due to use-dependent block (Patton and Goldin, 1991; Conti et al., 1996). Furthermore, the simultaneous recording of I_Na and I_g,t ensured that no channel loss could occur while waiting for the TTX to block. To demonstrate the absence of sodium ionic contamination we did control experiments where we compared the gating current at E_Na before applying TTX and quickly after adding it to the bath (see Fig. 10 A, inset).

For the analysis of ionic conductance, the gating current trace is subtracted from the family of traces around E_Na to obtain practically pure ionic currents, since the gating current hardly changes in contrast to the ionic current over this small voltage range (Fig. 5 C). The comparison in Fig. 5 C of the time courses of the capacitance transient (I_c), I_g,t, and I_Na shows that the clamp is fast enough to record the gating current, which in turn has practically come to zero at the peak time of the sodium current, as expected. The I_Na versus voltage plot in Fig. 5 D shows that in this experiment the conductance dI_Na/dV at E_Na was 0.91 mS. It may be noted here that the measured reversal potential is not subject to R_s errors, because no current is flowing but the conductance dI_Na/dV of 0.91 mS corresponds to a resistance of 1.1 k, and here an R_s of 200-300  has some effect. This will be discussed below, as well as the question whether E_rev represents E_Na (I/V curves Fig. 6 and compiled data of Table 1 in the Discussion).

Quantitative comparison of sodium permeability and gating charge

During the course of the experiments where we recorded the gating current at E_Na we repeatedly had to determine E_Na. We soon noticed that this reversal potential decreased from initial values ~+40 to +50 mV down to +15 mV, especially when the experiment lasted up to an hour or more. For instance, the two runs displayed in Fig. 5, A and B were from the same cell and separated by 17 min, while E_Na changed from +23 to +16 mV. It could even happen that after one determination of E_Na it would decrease by a few millivolts while running an experiment of some 3-5 min. This was manifested by an increasing outward ionic current that contaminated the initially pure gating current. The most likely explanation was a sodium influx either caused by I_Na through activated channels or, alternatively, by a small but continuous leak at the holding potential with its large driving force. Below, experimental evidence in support of the latter hypothesis is given. Thus, to obtain the amount of conducting channels we were faced with the problem that the cytoplasmic sodium concentration [Na⁺]_i, and hence its driving force, would continuously change in one experiment and within the pool of experiments. We, therefore, also used low extracellular sodium concentrations by partial replacement of sodium by the nonpermeating cation choline. In addition, we did not use the sodium conductance for an estimate of the number of open channels, but the sodium permeability, which should depend less on the concentration of sodium on either side of the membrane (see Methods).

Fig. 6 shows a validity test for the use of P_Na as a figure proportional to the number of activated channels at varying sodium concentrations. The three I_Na versus V curves were obtained for pulses between 40 and +60 mV in steps of 10 mV in three different bath solutions to change [Na⁺]_e in a rapid sequence from 11 mM to 20, and finally 90, mM. The I/V curves, and especially E_Na, changed from +4.0 and +15.1 to +46.2 mV. Assuming the sodium channels to conduct only Na⁺ ions, [Na⁺]_i was calculated from the Nernst equation as 9.4, 11, and 15 mM, respectively. Should the sub-Nernstian low E_rev of +4 mV or +15.1 mV be explained by a partial selectivity for choline, its relative permeability P_Ch/P_Na would have to be 0.08 or 0.18, respectively, which appears unrealistically high. The internal K⁺ also cannot explain the changes of [Na⁺]_i, but might shift the absolute values slightly by an almost constant amount. The data were fitted by Eq. 5, which combines a Boltzmann equation for voltage dependence of gating with P_Na and should be independent of [Na⁺]_i/e. Indeed, maximal P_Na is rather constant, being 9.1, 8.6, and 6.6 × 10⁹ l/s in sequential order. The midpoint of activation (V' in Eq. 5) being 27.2, 28.1, and 27.2 mV, as well as the indicator of the voltage dependence, the slopes A of 11.7, 10.3, and 7.4 mV do not vary much. They most probably indicate some distortion by R_s errors in the linear and more so in the nonlinear voltage ranges. Taking only dI/dV from the pair of data points across each E_rev, one would obtain for G_Na 0.39, 0.47, and 0.98 mS, and for P_Na 10.0, 8.5, and 8.2 nl/s (note the steeper slope of the data points versus fitted curve). A correction for an uncompensated rest of R_s of 200  (the linear distortion as discussed above) would change G_Na to 0.424, 0.518, and 1.22 mS, and P_Na to 10.9, 9.3, and 10.2 nl/s. In conclusion, P_Na around E_Na appears to be a rather good estimate for the number of open channels in varying sodium concentrations, and R_s errors appear to lead to an underestimation of P_Na by ~8% for G_Na in the range of 0.5 mS and by ~25% in the range of 1 mS.

The next step was to measure I_g and G_Na and check whether the ratio of P_Na/Q in different cells and conditions was constant. For this purpose, we performed experiments as demonstrated in Fig. 5. E_Na, G_Na at E_Na and [Na⁺]_e were used as input for Eq. 4 in order to calculate the maximal permeability P_Na. The resulting figures from three batches of injected oocytes are given in Table 1, together with the experimental conditions and cell properties. At 90 mM external sodium, the equilibrium potential E_Na dropped substantially to different levels during the experiments and, as calculated from the Nernst equation, [Na⁺]_i increased to values of 15 up to 41 mM. In contrast, low external sodium concentration leads to a more stable intracellular sodium concentration at a reduced level (see Table 1).

The ratio of P_Na/Q_t, which we initially expected to be constant, clearly varied substantially by more than a factor of 4 within a single batch of oocytes. We noticed that this ratio became smaller when E_Na dropped and the calculated [Na⁺]_i increased. This is better seen in the graphical representation of the tabulated figures for P_Na/Q_t and [Na⁺]_i (Fig. 7 A; batch 1 in Table 1). The data follow a hyperbolic relation that becomes linear in the log-log plot (Fig. 7 B). The increase of [Na⁺]_i could also be reversed when after an incubation in 73 mM external sodium concentration this was lowered to 20 mM (experiments P27S10 and P27S11 in Table 1 and asterisks in Fig. 7). The experimentally induced reduction of [Na⁺]_i from 39 back to 14 mM occurred within a time of ~20 min and was accompanied by a nearly threefold increase of the P_Na/Q_t ratio, pretty close to the overall trend of the data from the whole batch.

View larger version (11K): [in this window] [in a new window]   FIGURE 7   Graphical presentation of the varying ratio of sodium permeability and gating charge versus the corresponding internal sodium concentration, from data in Table 1. (A) Batch 1, no TTX during time of sodium channel expression. Asterisks mark two experiments at the same cell with 73 mM (arrow 1) and 20 mM (arrow 2) [Na+]e in the bath. The fitted hyperbola is of the form Y = A/X + B. (B) Log-log plot of the same data of batch 1 in the linear plot (filled symbols) and additionally the data from batches 2 and 3 in Table 1 (open symbols). Inset indicates [Na+]e in the bath and whether 2 µM TTX was added during expression. Lines were fitted by eye.

From these observations we suspected that oocytes with such a high expression of sodium channels (as derived from I_g) would leak some sodium ions into the cell along the concentration gradient. This might occur either continuously, through a few open channels but a large driving force at the holding potential of 100 mV or, in addition, due to the inflow during the pulses. This would force the cell to actively pump sodium ions out for its homeostasis, which represents an energetic stress for the cell. As a result, the permeability of some channels would be down-modulated by an as yet unknown mechanism, whereas the gating charge of these channels remained undisturbed. Therefore, we hypothesized that a similar sodium load also stresses the cells during the days of incubation, because at the typical resting potential of 15 to 30 mV it is rather likely that a fraction of channels stays open and the electrochemical driving force for sodium leads to a persistent sodium influx. Consequently, to reduce the cytoplasmic sodium load, we added 2 µM TTX to the incubation solution. For the voltage-clamp experiment, the cells were washed and transferred into MBS without TTX and with 90 or 10 mM sodium. This resulted in an increase of the permeability/gating-charge ratio which, however, still was dependent on the internal sodium concentration (Table 1, Fig. 7 B; batches 2 and 3). For the pool of our data, the P_Na/Q_t varied by a factor of 10-20, which is much larger than simple experimental variation and, therefore, indicated a clear dependence on the influx of sodium or its cytoplasmic accumulation.

Experiments to compare sodium influx and increase of cytoplasmic sodium

The above-calculated free cytoplasmic sodium concentration from E_rev indicates a substantial increase of [Na⁺]_i during the experiment. As suggested, this might be due to leak at holding potential or I_Na during the pulses. We have performed the following checks on this: 1) comparison of the integrated leak during the experiment with the calculated change of [Na⁺]_i; 2) use the inactivation deficient mutant IFM/QQQ and application of repeated long pulses to produce a substantial influx by pulses; 3) comparison of agarose-cushion electrodes and open-tip ones filled with NaCl for their leak into the center region of the oocyte and check the resulting changes in E_rev. For all these calculations it was important to know the freely accessible space in an oocyte. According to the in-depth studies on amphibian oocytes by Horowitz (e.g., Horowitz and Paine, 1979) Na⁺ distributes quickly into the sucrose-accessible space. This cytoplasmic space represents ~30% of the cell water, while the vesicular structures, most prominently the yolk vesicles, may actively accumulate sodium (Dick and Fry, 1975). For the oocytes used in our experiments of 1.3 mm diameter and a calculated volume of 1.15 µl we assume an average water content of 75% and obtain 0.25 µl for the freely accessible space. Fig. 8 A shows for a typical experiment the leak-current I-hold at V_h of 100 mV during the whole experiment. Assuming this current to be all Na⁺-influx into the freely accessible space, the resulting change of [Na⁺]_i is calculated. The filled circles in Fig. 8 A were measured over the time where also E_Na (E_rev) was determined and used to estimate [Na⁺]_i by the Nernst equation (Fig. 8, B and C). Between the two open circles marked by 1 and 2 asterisks, TTX was applied to the bath. In this experiment most of the leak was blocked, suggesting that indeed the leak would be carried by Na⁺ ions through sodium channels. (At present, we cannot be conclusive about the TTX-sensitive part of the leak because we normally extended the experiments until the leak was too high for reasonable clamping.) Then, the mean leak integrated over this period was 0.32 µA and the resulting change in [Na⁺]_i, or as indicated in Fig. 8 D, [ion]/min in the accessible space would be 0.77 mM/l/min. This was then directly compared with the change of [Na⁺]_i as obtained from the data in Fig. 8 C, i.e., 0.26 mM/l/min. The results of similar experiments with a smaller and a larger leak are shown in Fig. 8 D. In experiment 3 (Fig. 8, D and E) G_Na was also determined several times during the marked increase of internal sodium and P_Na calculated. G_Na showed a slight decrease and the plotted P_Na showed a clear inverse relationship similar to the pool of experiments in Table 1. This will be further treated in the Discussion.

View larger version (33K): [in this window] [in a new window]   FIGURE 8   Comparison of leak current at holding potential and free internal sodium [Na+]i as calculated from the observed reversal potential Erev for three experiments done in constant [Na+]e of 90 mM. (A) Experiment 1 with typical leak or holding current of medium size (I-hold) at Vh of 100 mV, typically increasing during the experiment. It could be almost totally blocked by TTX at the end in this experiment (TTX given between the circles marked by * and **). The filled circles correspond to the time when Erev was also measured as given in (B) for the calculation of [Na+]i using the Nernst equation (C). (D) From the mean I-hold, 0.32 µA for experiment 1, distributing into a free accessible space of 0.25 µl in the oocyte (see text), the expected change of ion-concentration per minute is indicated and compared to the observed change in free [Na+]i as obtained from the data in C. Similarly obtained data are shown for 2 other experiments with either a small and constant leak of ~0.1 µA (experiment 2) or a rather large leak (experiment 3). (E) For experiment 3 the changing figures for PNa around Erev were determined and displayed versus the cytoplasmic free [Na+]i as calculated at the indicated times from the interpolated Erev.

The change of internal free sodium due to influx was always found to be ~2-4 times larger than that obtained from the change in E_rev. The following explanations were mainly considered. 1) The seemingly too large leak influx may not consist only of Na⁺ or 2) distribute into a larger freely accessible space than assumed, or 3) some of the increased sodium is pumped actively back into the bath or into the intracellular vesicles. The active pumping appears to be the most likely mechanism. The percentage of freely accessible space is rather well documented and shows only little variation. As a further check to let Na⁺ specifically enter the cell, we used the noninactivating mutant IFM/QQQ at high expression. While the normal I_Na of wild-type at a relatively low stimulus rate during an experiment had a negligible influx, with this mutant 200-ms-long pulses at a frequency of 1/s for 1000 sweeps were applied. In this way we obtained a substantial influx from well-defined current plateaus of exactly measurable size (4-10 µA) for 200 ms followed by a duty cycle of 800 ms, which allowed for diffusion. In several experiments we found the change of [Na⁺]_i due to influx to be again 2-4 times larger, i.e., 1.5-3 mM/l/min versus 0.4-0.8 mM/l/min as obtained from the change in E_rev. It thus appears very likely that the Na⁺ influx provokes a pump activity of ~1-2 mM/l/min with a stoichiometric consumption of 1:3 of 1-2 mM ATP/min in order to keep the internal sodium at low levels. In further experiments using 3 M NaCl-filled coarse tip electrodes with or without an agarose cushion we could demonstrate that without agarose a fast leakage of sodium in the central region leads to changes of E_rev that indicated a change of [Na⁺]_i under the membrane by 3-4 mM/l/min. While these experiments demonstrate the fast diffusion within the cell, they did not allow us to control and quantify the influx and concentration as well as in the voltage-controlled QQQ mutants. In these latter experiments we could further observe during the quantified Na⁺-influx and decrease of E_rev that the conductance dI/dV at E_rev became smaller, which will be treated further in the Discussion when estimating the number of open channels from either G_Na or P_Na.

Properties of the unexpectedly large gating current

Our results indicated the presence of a large proportion of channels with a very low open probability that produced gating current. Therefore, we had to consider and to exclude whether 1) the gating current would be changed to an abnormal gating current, or 2) that most of the channels would remain in normal inactivated states, not producing ionic current but still gating current by the nonimmobilized parts of the voltage sensors. To check on this, we performed double-pulse experiments in order to compare the recovery of ionic- and gating-currents and the size of immobilization. As known from other preparations and shown schematically in Fig. 2, the gating current of the inactivated and immobilized channels represents 40-50% of the total gating current produced by recovered channels, has faster kinetics, and no slow rising phase. We checked for this by applying optimal recording conditions, small asymmetry, and a low temperature of 8°C to slow the fast gating-current in relation to the speed of the clamp (given by the capacitance transient). The recording was done in quick succession for the gating current at E_Na and the ionic current at a potential ~10-30 mV below E_Na to get sodium currents of a size not subject to R_s errors. It has to be recalled that the recovery time course is determined by the potential during the interpulse interval (100 mV) and not by the potential of the test pulse. Fig. 9, A and B show the superimposed traces of I_Na and I_g of the test pulse for a series of recovery periods of 60, 1, 2, 3, 5, . . . up to 60 ms after the same inactivating prepulse. For the shortest intervals there is still the gating-current from those channels switching between inactivation states. Frequently, there is some ionic-current when not all channels are inactivated that shows up as a noninactivating plateau of ionic current. With increasing recovery more and more channels produce ionic-current, which activates and inactivates in the normal way. The corresponding I_g traces seem to grow faster initially because during the shortest gap even the fast equilibration between the inactivated states could not finish and, consequently, I_g,on is small. The full gating-current of immobilized channels can be seen after 2 ms recovery (3rd trace) and clearly shows a steeper and shorter time course than that of fully recovered channels with a prominent rising phase. This corresponds very well to the results of similar experiments where high-resolution gating-currents were recorded in the squid giant axon (Greeff et al., 1982).

View larger version (18K): [in this window] [in a new window]   FIGURE 9   Comparison of recovery of sodium ionic- and gating-current from inactivation or immobilization, respectively. (A, B) Single cell experiment; no TTX had been used and the recordings were done within a few minutes: gating currents at ENa of +42 mV first (B); and 12 min later at a test potential of +10 mV the ionic currents (A). Otherwise identical protocols: inactivating prepulse to +40 mV for 20 ms; Vh and recovery at 100 mV, recovery gaps were (in ms) 60, 1, 2, 3, 5, 8, 15, 20, 40, and 60; linear subtraction pulses between 100 and 130 mV. Critical Rs compensation; duration of the capacitance transient (not shown) gives the speed of the clamp and is reflected in the fast rise of Ig, which is followed by a genuine slow rise. (C) Recovery of peak sodium current (INa) and integrated gating currents (Qg), normalized to maximal values; single-exponential fits to the plotted data (except 1 and 2 ms points, compare D and text) gave rec of 12.8 and 11.4 ms for INa and Qg, respectively. (D) Isochronic plot of Qg versus INa for all data points (circles), 3 to 60 ms recovery data points are close to linear fit (squares). Experiment P25S2; MBS-solution; temperature 8°C.

For further analysis of the recovery experiments we compared the time course of recovery of I_Na,peak and the integrated gating charges Q_g. In Fig. 9 C these data are shown individually versus the recovery time, while Fig. 9 D displays the same data as a phase plot of Q_g versus I_Na,peak. As can be seen in the phase plot, after the shortest recovery gaps of 1 and 2 ms, both quantities recover in parallel, as indicated by the straight line. This corresponds to similar time constants of 11.4 and 12.8 ms for Q_g and I_Na,peak, respectively. In this particular experiment the percentage of nonimmobilized gating current (Q_n) from inactivated channels being 4.6 nC after 3 ms or 4.0 nC extrapolated back to zero recovery time is 57 or 66%, respectively, in comparison to the fully recovered gating-current. In order to check on this more thoroughly we calculated this ratio for the experiments from Table 1. The average ratio of Q_n/Q_t is 44 ± 14% (SD, n = 18) which agrees well with the above-quoted figures from other preparations (Armstrong and Bezanilla, 1977; Greeff et al., 1982). Note that in batch 1 at 8°C, 1 ms recovery gave a percentage of 21 to 33% (*Q_n/Q_t marked in Table 1) which supports the finding of Fig. 9 D, namely that at this temperature even Q_n does not fully recover; in batches 2 and 3 at 15°C a 1-ms recovery is sufficiently long. The important conclusion is that we certainly do not see a variation in Q_n/Q_t corresponding to the 5- to 20-fold variation in the P_Na/Q_t ratio. This suggests that the unusually large gating currents behave normally with respect to immobilization and recovery, as will be treated further in the Discussion