INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Previous studies have demonstrated that the hyperalgesia produced by 5HT and other inflammatory mediators involves protein kinase A (PKA)-mediated phosphorylation of tetrodotoxin (TTX)-resistant Na⁺ channels (Cardenas et al., 2001; Taiwo et al., 1992; Taiwo and Levine, 1992: England et al., 1996; Gold et al., 1996, 1998; Fitzgerald et al., 1999). However, the changes in Na⁺ channel function leading to increased nociceptor excitability have not been conclusively determined. England et al. (1996) proposed that the majority of the excitatory effect of PGE₂ on cultured neonatal sensory neurons was produced by a shift in the voltage of activation of TTX-resistant channels to more hyperpolarized potentials. Other studies found similar hyperpolarizing shifts in voltage of activation but also consistently observed large increases in peak Na⁺ conductance (Gold et al., 1996, 1998; Fitzgerald et al., 1999).

To further investigate this question, we used electrophysiological experiments in a subpopulation of nociceptor-like dorsal root ganglion (DRG) cells (type 2), in which we previously demonstrated that activation of 5HT₄ receptors coupled to a cAMP-dependent signaling pathway produces an increase in TTX-resistant Na⁺ currents (Cardenas et al., 1995, 1997, 2001). The type 2 DRG cells consistently express several characteristics of nociceptors including small diameter cell bodies, long duration action potentials, TTX-resistant Na⁺ current, and sensitivity to capsaicin (Cardenas et al., 1995, 1997; Harper and Lawson, 1985a,b; Holzer, 1991; Villiere and McLachlan, 1996). They also express a carbohydrate surface antigen (Gal1-4 GlcNAc-R), previously associated with a subpopulation of DRG sensory neurons terminating in the substantia gelatinosa (Del Mar and Scroggs 1996; Dodd and Jessell, 1985; Light and Perl, 1976, 1979).

The studies presented below suggest that in this subpopulation of acutely isolated DRG cells, 5HT increases TTX-resistant Na⁺ conductance and current activation and inactivation rate, whereas the voltage dependency of activation and channel availability is little affected. In addition, studies on the voltage dependency of Na⁺ current availability, time course of retrieval from inactivation, and inactivation of evoked currents suggest the presence of at least two inactivated states: one that is induced and retrieved rapidly (I_fast) and another that is induced and retrieved more slowly (I_slow).

To probe possible mechanisms underlying the 5HT induced increase in Na⁺ conductance, 40-ms Na⁺ current sweeps recorded before and after treatment with 5HT were fit with a minimal Na⁺ channel gating model:
in which I₁ and I₂ correspond to I_fast and I_slow, respectively. These studies indicated that 5HT produced a significant decrease in k_OI1 and a significant increase in k_C3O and k_I1I2. Subsequent computer simulations based on the above model, where k_OI1, k_C3O, and k_I1I2 were changed individually, suggested that the 5HT induced increase in Na⁺ conductance is primarily the result of a decrease in the rate of transition from the open state to I_fast (k_OI1). On the other hand, a 5HT induced increase in the transition from closed to open (k_C3O), and from I_fast to I_slow (k_I1I2) appeared to underlie the 5HT induced increases in the macroscopic activation and inactivation rates, respectively.

The increase in k_I1I2 by 5HT may also underlie the antagonism of the 5HT induced increase in Na⁺ current amplitude by long duration inactivation conditioning pulses (CPs). The increase in k_I1I2 by 5HT may enhance the transition of channels from I_fast to I_slow, during the course of the long (1 s) inactivation CPs. This may deplete the pool of channels in I_fast, relative to that present after long inactivation CPs in the absence of 5HT. The resultant reduction in the reopening of channels from I_fast could offset the increase in Na⁺ current amplitude via the 5HT-induced decrease in k_OI1.

The above findings fit well with previous studies showing that activation of the cAMP/PKA cascade simultaneously increases voltage sensitive TTX-resistant Na⁺ conductance and Na⁺ current activation and inactivation rate in nociceptors (Gold et al., 1996, 1998; Fitzgerald et al., 1999). Interestingly, another previous study suggested that PKA-dependent phosphorylation of TTX-sensitive Na⁺ currents in rat striatal neurons, which decreases Na⁺ conductance without affecting voltage of activation or inactivation, is associated with an increase in k_OI1 (d'Alcantara et al., 1999). Thus, changes in the transition between Na⁺ channel open and inactivated states may constitute a general mechanism by which Na⁺ currents are modulated. Our data regarding the antagonism of the 5HT-induced increase in Na⁺ current amplitude with long inactivation CPs suggests that development of drugs, which selectively induce or stabilize slow inactivation states of the TTX-insensitive Na⁺ channel, could be useful in reducing the hyperalgesia produced by inflammatory mediators.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Electrophysiology

Male rats (50-100 g), Sprague Dawley (purchased from Harlan) were rendered unconscious with methoxyflurane, decapitated, and DRG from lumbar and thoracic regions were dissected out. The ganglia were incubated at 36°C for 1/2 h in Tyrode's solution (composition below) containing: 1 mg/mL collagenase (Sigma, St. Louis, MO, Type 1A) and 2.5 mg/mL Dipase II (Roche, Basel, Switzerland). Individual DRG cell bodies were isolated by trituration and adhered to the bottom of a 35-mm petri dish, and superfused with Tyrode's solution containing: 140 mM NaCl, 4 mM KCl, 2 mM MgCl₂, 2 mM CaCl₂, 10 mM glucose, 10 mM HEPES, adjusted to pH 7.4 with NaOH.

All experiments were done at room temperature (23°C). Currents and voltages were recorded in the whole-cell patch configuration using an Axopatch 200A (Axon Instruments). Voltage commmands, and data acquisition and analysis were controlled using pClamp 8.0 (Axon Instruments, Union City, CA). Data were leak subtracted using the P/4 method. Electrodes were fabricated from soda lime capillary glass (Scientific Products, B4416-1) using a Narishige 2-stage vertical puller, coated with sylgard to ~200 µm from the tip, and fire polished to a final resistance of 0.8 to 2.0 M, using a Narishige microforge. For voltage clamp experiments, series resistance was estimated from capacity transients after compensation, as described previously (Scroggs and Fox, 1992). No data were included where series resistance resulted in greater than a 10-mV error in voltage commands.

For most voltage clamp experiments on TTX-resistant Na⁺ currents the patch electrodes were filled with a solution (internal solution) containing: 120 mM CsCl, 5 mM 2Na-ATP, 0.4 mM 2Li-GTP, 5 mM MgCl₂, 5 mM ethylene glycol-bis (-aminoethylether)-N,N,N',N',-tetraacetic acid (EGTA), 1.86 CaCl₂, 20 (N-[2-hydroxyethyl]piperazine-N'-[2-ethanesulfonic acid]) (HEPES), adjusted to pH 7.4 with CsOH. Total [Ca²⁺]_i was calculated to be 100 nM. For isolation of Na⁺ currents, the external solution contained: 50 mM NaCl, 112.5 mM tetraethylammonium chloride (TEA), 2 mM CaCl₂, 0.5 mM CdCl₂, 10 mM HEPES, and 0.0005 mM TTX, pH 7.4 with TEA-OH.

Additional internal and external solutions were used in experiments on Na⁺ current activation designed to mimic conditions present in experiments of Rush et al. (1998) and Gold et al. (1996). For the Rush et al. (1998) conditions, the internal solution contained: 110 mM CsF, 5 mM MgCl₂, 10 mM NaCl, 11 mM EGTA, and 10 mM HEPES, pH 7.2 with CsOH. The external solution contained: 82.5 mM Choline-Cl, 20 mM TEA, 32.5 mM NaCl, 5 mM CsCl, 5 mM MgCl₂, 0.1 mM CaCl₂, 5 mM Glucose, 10 mM HEPES, 0.0005 mM TTX, pH 7.2 with NaOH. For the Gold et al. (1996) conditions, the internal solution contained: 140 mM CsCl, 6 mM NaCl, 4 mM MgCl₂, 0.1 mM CaCl₂, 11 mM EGTA, 10 mM HEPES, 2 mM 2Na+ATP, 1 mM 2Li+GTP, pH 7.2 with Tris-base. The external solution contained: 65 mM Choline-Cl, 40 mM TEA, 35 mM NaCl, 5 mM MgCl₂, 0.1 mM CaCl₂, 10 mM Glucose, 10 mM HEPES, 0.0005 mMTTX, pH 7.4 with NaOH. Solutions were changed around the cell under study by means of a small glass capillary tube placed near the cell in the bath as described earlier (Cardenas et al., 1997). Most chemicals and salts were obtained from Sigma. ATP and GTP were obtained from Boehringer Mannheim.

Experiments were restricted to type 2 DRG cells, which were identified (in Tyrode's solution) by the expression of an I_A-like current that was evoked upon repolarization to 50 mV after a 787-ms hyperpolarization to 90 to 110 mV (Cardenas et al., 1995, 1997). However, with Cs⁺ replacing K⁺ in the pipette solution to block K⁺ currents, the A current was inward rather than outward. The data shown in the results section have not been corrected for liquid junction potential.

Estimation of voltage dependency of activation

The voltage where 1/2 of the Na⁺ current was activated (V_1/2) was estimated from amplitudes of Na⁺ currents evoked every 7 s by 40-ms test potentials to 55 mV through +50 mV (in 5-mV increments) from a holding potential of 60 mV. The peak current amplitudes observed at the different test potentials were converted to macroscopic conductance (g) using the relationship g = I/(V_R  V_M), in which V_R is the apparent reversal potential of the Na⁺ current in our system ( +45 mV), and V_M is the test potential. Best fit values for V_1/2 and the slope factor k were estimated by fitting the Boltzmann relationship: g = g_max/(1 + exp((V_1/2t  V_M)/k)) to the macroscopic conductance observed at different test potentials, using a Gauss-Newton least squares iteration program (Systat, SPSS Inc.). For conversion from current to conductance, estimations of V_1/2, and plotting current-voltage and conductance-voltage relationships, all voltages were corrected for the effects of series resistance, which was measured from capacity transients recorded from each cell after series resistance compensation.

Estimation of voltage dependency of current availability

Availability curves were generated by giving 100-ms or 1-s conditioning potentials (CPs) to 0 mV through 140 mV or 120 mV, respectively, from a holding potential of 60 mV. Immediately after each CP, the DRG cells were given a test potential to +5 mV (peak current) to evaluate the amount of current available for activation. After each test pulse the leak was measured at the CP voltage and was subtracted from the preceding current using the P/4 method (P-Clamp, Axon Instruments). In between each cycle (consisting of CP + test pulse + leak) the cells were returned to the holding potential of 60 mV for 5 s (for graphical representation of the protocols see insets Fig. 3, B and D). The current amplitudes recorded from each cell were individually normalized relative to I_max observed in each cell, and fitted with a double Boltzmann function I = f₁/(1 + exp((V_M  V_h1)/k₁)) + f₂/(1 + exp((V_M  V_h2)/k₂)), in which the fitting parameters f₁ + f₂ = I_max = 1, and V_M = the CP potential. Best-fit values V_h1 and V_h2 and the slope factors (k₁ and k₂) were estimated using the Gauss-Newton least squares iteration program.

View larger version (36K): [in this window] [in a new window]   FIGURE 1   Effects of 5HT on the voltage dependency of activation of TTX-resistant Na+ current in type 2 DRG cells. (A) Family of averaged Na+ currents evoked with 40-ms depolarizations to voltages ranging from 25 mV to +25 mV, under control conditions (1) and after treatment with 10 µM 5HT (2). Each current record is the average from 11 experiments. The currents were recorded in the presence of 500 nM TTX. (B) Plot of current versus test potential, under control conditions () and after treatment with 5HT (). Each data point is the average of 11 experiments ± SE. (C) Plot of normalized macroscopic conductance versus voltage constructed from the data in B as described in the Materials and Methods. Each data point represents the average normalized conductance from 11 experiments ± SE. The line through the average data points represents the fit achieved with a Boltzmann function as described in the Materials and Methods. The values of V1/2 and k for control and 5HT conditions generated by the Boltzmann fit to the average data points were similar to the corresponding average values of V1/2 and k reported in the results. For B and C, the position of the data points along the x axis has been corrected for series resistance.

Estimation of the time course of removal of inactivation

Type 2 DRG cells, held at 80 mV, were given CPs to 0 mV, which alternated between 60 ms and 1 s in duration. No current was evoked by a test potential to +5 mV immediately after (no delay) either duration of inactivation pulse. To estimate the time course of removal of inactivation, the 60-ms and 1-s CPs were followed by repolarization to 80 mV for times ranging from 5 ms to 5 s (delay). Then after the various delays, test potentials to +5 mV were given to assess the recovery of the Na⁺ current from inactivation (for a graphical representation of the protocol see the inset in Fig. 5 B). The cells were returned to the holding potential of 80 mV for 10 s between each cycle (which consisted of CP + delay + test pulse) to reset the channels. The current amplitudes recorded from each cell were individually normalized relative to I_max observed after a 5-s delay in each cell and were fit with a rising triple exponential function; f₁ × (1  exp(t/₁)) + f₂ × (1  exp(t/₂)) + f₃ × (1  exp(t/₃)), in which the fitting parameters f₁ + f₂ + f₃ = I_max = 1 and t represents the delay period.

View larger version (18K): [in this window] [in a new window]   FIGURE 2   Effects of 5HT on macroscopic activation and inactivation rates of evoked TTX-resistant Na+ currents. (A) Effects of 5HT on peak Na+ current in 12 type 2 DRG cells used for analysis of macroscopic activation and inactivation rates. The current records corresponding to control conditions and 5HT treatment are each averages of current records from 12 experiments. In turn, each of the 12 current records included in the average control and 5HT sweeps, are averages of 5 to 10 individual currents recorded under control conditions or after treatment with 5HT. (B) Same current records as in A, except that the peak control current amplitude has been scaled up to match peak current amplitude observed after 5HT treatment. (C and D) Plots of 1 (C) and 2 (D) describing the macroscopic rates of Na+ current inactivation, versus test potential used to evoke the Na+ currents, under control conditions () and after treatment with 5HT (). Values of 1 and 2 were derived by fitting falling double exponential functions to the inactivating portion of the averaged current records shown in Fig. 1 A, corresponding to test commands of 10 mV through +20 mV.

Computer modeling

The simulations and analyses with the models were made with the Matlab (The MathWorks, Inc.) software. Na⁺ current traces obtained under control conditions and during the peak effect of 5HT were analyzed by curve fitting using a model describing the gating mechanism of the Na⁺ channel as follows. The model, defined by kinetic transitions between different channel states (closed, open, or inactivated), was mathematically described by a system of first order differential equations:

(1)

in which X_i was the fraction of channel population in state i, and k_ij was the first order kinetic constant characterizing the conversion of state i to state j. These differential equations were numerically integrated by using the Runge-Kutta algorithm. This procedure gave the time course of the fraction of channel population in the open state, i.e., the open probability p_o(t). To fit the model to the experimental data, the measured Na⁺ current (I(t)) had to be numerically transformed into open probability, using the theoretical relationship:

(2)

in which N and i referred to the total number of channels and to the current of a single open channel, respectively. Practically, the value of the scaling factor i N could not be determined, because N was unknown in our experiments. To circumvent this problem, we referred to a study showing the voltage and time dependencies of the open probability of TTX-resistant Na⁺ channels in frog DRG cells (Yakehiro et al., 2000) and assumed that, at a given test potential, the maximal open probability with respect to time (p_{o, max}) corresponded to the peak amplitude of Na⁺ current (I_max). Thus, the following normalization was applied:

(3)

(4)

For example, the control current trace I(t) (Fig. 6 A), which was obtained using a depolarization step from 60 mV to +5 mV, was transformed to the open probability p_o(t) (Fig. 6 B) using a maximal open probability p_{o, max} of 0.32. The calculation of this p_{o, max} value was based on the Yakehiro et al. (2000) report, which determined from single channel studies that the maximal conductance for TTX-resistant Na⁺ channels in frog DRG cells corresponded to an open probability of 0.4. The control current recorded from the type 2 DRG cell illustrated in Fig. 6 A was evoked using a depolarization to +5 mV, which corresponded to the voltage where 80% of the maximal conductance observed in this cell, as determined from a study of its current-voltage relationship. Thus, the p_{o, max} of 0.32 for the peak of this current represents 80% of 0.4. 

View larger version (34K): [in this window] [in a new window]   FIGURE 3   Effect of 5HT on the voltage dependency of availability of TTX-resistant Na+ currents in type 2 DRG cells. (A and C) Na+ currents evoked by a test potential to +5 mV after 1-s CPs to 0 mV through 120 mV (A) or 100-ms CPs to 0 mV through 140 (C), under control conditions (1), and after treatment with 5HT (2). The current records are averages from five experiments in A and six experiments in C. (B and D) Plot of average normalized current amplitude taken from (A or C), versus conditioning potential for control conditions () and after 5HT treatment (). For each cell included in B or D, the current was normalized to 1 relative to the largest current (Imax) observed through the range of CPs. The line passing through the averaged data points represents the fit to these points achieved with a double Boltzmann function as described in the methods. The values of Vh and k generated by fits to the averaged data points were similar to the average values of Vh and k generated by double Boltzmann fits to data from individual cells (Table 1). The insets in B and D are the protocols used to generate the currents in A and C, respectively, and are described in the Materials and Methods and text. The error bars represent the standard error of the mean.

The kinetic parameters k_ij of the model were estimated by an iterative procedure searching for the set of parameter values generating the minimal deviation (least square fitting) between the experimental curve p_o(t) and the theoretical curve given by numerical integration of the differential equations.

Statistical analysis was done using a two tailed paired t-test for comparison of pairs of responses observed in one group of cells. The student's t-test was used to make comparisons between mean responses from two different treatment groups. Also, analysis of variance was used in more complicated situations when two or more mean responses for a particular variable were to be compared between two treatment groups, and were likely influenced by two factors such as 5HT and voltage. All statistical analyses were carried out using Systat (SPSS Inc). The data in the results section are written as the mean ± SE.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Effect of 5HT on voltage of activation

Voltage of activation of TTX-resistant Na⁺ currents in type 2 DRG cells was studied using different pipette and external solutions for comparison with analogous data collected in other laboratories. When using pipette and external solutions made up as per Rush et al. (1998) (see Materials and Methods), V_1/2 averaged 8.7 mV ± 2.9, the slope constant k averaged 7.7 ± 0.8, and g_max averaged 28.6 ± 10.1 nS (n = 4, data not shown). Similar values for V_1/2 (10.3 mV ± 1.1), k (6.2 ± 0.3), and g_max (26.2 ± 5.3 nS) (n = 9, data not shown) were observed when the pipette and external solutions were switched to those used in a study by Gold et al. (1996) (see Materials and Methods). However, when Na⁺ currents were recorded with the pipette and external solutions used throughout this study, V_1/2 averaged 0.3 ± 0.6 mV, k averaged 6.5 ± 0.4, and g_max averaged 13.6 ± 2.5 nS (n = 11) (Fig. 1, B, and C). The shift of V_1/2 in the depolarizing direction relative to values obtained using the solutions of Rush et al. (1998) or Gold et al. (1996) can be largely explained by the inclusion of 2 mM Ca²⁺ in our external solution to improve seal stability (Hille, 1992). Also, the smaller g_max observed in the present study may be attributed to the presence of 400 µM Cd²⁺, which was included to block Ca²⁺ entry. At the concentration of 400 µM, Cd²⁺ could be expected to produce a partial blockade of TTX-resistant Na⁺ channels (Akopian et al., 1996; Roy and Narahashi, 1992).

View larger version (26K): [in this window] [in a new window]   FIGURE 4   Effect of CP duration on Na+ current availability and modulation by 5HT. (A and B) Comparison of availability curves generated with 1-s CPs versus 100-ms CPs, under control conditions (A) and after treatment with 5HT (B). (C) Test currents evoked under control conditions (dashed line) and after treatment with 5HT (solid line), after 100-ms and 1-s CPs to 30 mV. The current records corresponding to 1-s and 100-ms CPs are averages from five and six experiments, respectively. (D) Average 5HT induced changes in the amplitude of currents evoked after 100-ms conditioning potentials (, n = 6) or after 1-s conditioning potentials (, n = 5). The data for A to D was taken from the experiments depicted in Fig. 3, A to D. The error bars indicate the standard error of the mean.

When the above mentioned 11 type 2 DRG cells were exposed to 10 µM 5HT peak Na⁺ current was increased by 50 ± 9% from a control level of 438 ± 79 pA, to 614 ± 95 pA (Fig. 1, A1 and A2). The maximal Na⁺ conductance was increased 39 ± 9.0% by 5HT from the control level of 13.6 ± 2.5 nS to 17.3 ± 2.3 nS. After treatment with 5HT the V_1/2 for the conductance-voltage relationship was shifted by 2.9 ± 1.0 mV (p = 0.005, paired t-test), but the slope factor (k) was not significantly affected (k = 6.5 ± 0.4 under control conditions and 5.9 ± 0.4 after treatment with 5HT) (Fig. 1 C). However, in five additional control type 2 DRG cells tested, V_1/2 was significantly shifted by 2.8 mV ± 0.7 mV as a result of waiting for ~5 min between control I-V curves (p = 0.02, paired t-test). The apparent reversal potential was also shifted by a similar amount. When V_1/2 observed after 5HT treatment was corrected individually for each of the 11 DRG cells, based on a drift rate of 0.0092 mV/s, the difference before and after 5HT treatment became +0.2 ± 1.2 mV. Thus, drift artifact could account for the change in V_1/2 observed before and after 5HT treatment. The gradual drift of the voltage of activation to more negative voltages was likely an artifact of the whole-cell patch configuration (Fernandez et al., 1984).

Effects of 5HT on the macroscopic rate of activation and inactivation of evoked Na⁺ currents

In addition to increasing peak Na⁺ current amplitude and conductance, 5HT also produced small but significant increases in the macroscopic rate of activation and inactivation. In the 12 experiments included, 10 µM 5HT increased peak Na⁺ current by an average of 53 ± 9.6% (Fig. 2 A). The 5HT induced increase in inactivation rate became more apparent visually when the peak amplitudes of the control and 5HT current records were normalized (Fig. 2 B). Times to peak current and inactivation rate of peak current were analyzed in current records averaged from 5 to 10 individual 40-ms currents recorded before and after 5HT. Current segments, starting 1 to 3 ms after peak current to the end of the test potential, were fitted with falling exponential functions. The data was not normalized nor changed in sign. A double exponential function [a × (exp(time/₁)) + b × (exp(time/₂))] gave better fits than single or triple exponential functions. Under control conditions, ₁ averaged 4.22 ± 0.25 ms and was significantly reduced by 5HT to 3.76 ± 0.19 ms (p = 0.0001, paired t-test, n = 12). ₂ was also significantly reduced by 5HT from 88.6 ± 14.1 ms under control conditions to 61.8 ± 9.8 ms after treatment with 5HT (p = 0.03, paired t-test). 5HT also produced a significant increase in the proportion of the fit associated with ₁ from 71.6 ± 4.1% under control conditions to 78.2 ± 1.8% after treatment with 5HT (p = 0.04, paired t-test).

View larger version (35K): [in this window] [in a new window]   FIGURE 5   Effects of 60-ms and 1-s CPs on recovery from inactivation and modulation of Na+ current amplitude by 5HT. (A) Currents evoked after delays of 5 ms to 5 s after 60-ms CPs under control conditions (1) and after treatment with 5HT (2), or after 1-s CPs under control conditions (3), and after treatment with 5HT (4). The currents are averages from four cells. (B) Plot of average normalized current amplitudes (taken from B) against delay time. The current amplitudes were normalized to 1 for each cell included, relative to the current observed at the 5-s delay (Imax). The open and closed circles represent control conditions and 5HT treatment, respectively for the 60-ms CPs, and the open and closed triangles represent control conditions and 5HT treatment, respectively for the 1-s CPs. The line through the average data points represents the fit to these points achieved with a triple exponential. The variables ( and f) generated by fitting the triple exponential function to the averaged data points were similar to the average values of  and f generated by triple exponential fits to data points in individual experiments. The inset is the protocol used to generate the currents from A and is described in the methods. Test currents evoked after a 100-ms delay under control conditions (dashed line) and after 5HT treatment (solid line), following a 60-ms CP (upper panel) or a 1-s CP (lower panel). Each current trace is the average of four experiments. (D) Effects of 5HT on Na+ current amplitude at different delay times after 60-ms CPs () or 1-s CPs (). Each point represents the average from four experiments. The error bars indicate the standard error of the mean.

Double exponential functions were also fitted to the inactivating portion of the averaged current records shown in Fig. 1, A1 and A2 to analyze the effect of 5HT on the inactivation of Na⁺ currents evoked by different test potentials. ₁ decreased as test potential became more positive, as did the reduction in ₁ produced by 5HT (Fig. 2 C). A similar pattern was observed for ₂ (Fig. 2 D).

In addition to increasing inactivation rate, 5HT also produced a slight but significant increase in the activation rate of the Na⁺ current, as judged by the time required for the current to peak (data not shown). In the same 12 cells depicted in Fig. 2 A and B, the current peaked 2.178 ± 0.082 ms after initiation of the test potential under control conditions, which was slightly but significantly later than the average time to peak of 2.066 ± 0.079 observed after treatment with 5HT (p = 0.02, paired t-test).

Effect of 5HT on Na⁺ current availability

The effect of 5HT on the voltage dependency of availability of TTX-resistant Na⁺ current was also studied in type 2 DRG cells. For these experiments the cells were given CPs to various voltages from a holding potential of 60 mV. After each CP and subsequent test potential, the cells were returned to 60 mV for 5 s to reset the channels (see insets, Fig. 3, B and D). Presumably CPs positive to 60 mV induced inactivation, whereas CPs negative to 60 mV removed inactivation.

In a group of six cells receiving 100-ms CPs, I_max averaged 379 ± 33 pA under control conditions and was increased to 578 ± 38 pA (56 ± 14%) after treatment with 5HT (Fig. 3, A1 and A2). Similarly, in another group of five cells receiving 1-s CPs, 5HT increased I_max by 51 ± 9% from an average of 1141 ± 446 pA under control conditions to 1613 ± 551 pA after treatment with 5HT (Fig. 3, C1 and C2). Control current amplitude, observed at 60 mV without a CP differed between the two groups to a similar degree as I_max. Thus, the difference in the average control I_max values between the two groups of cells appeared to be due mainly to sampling error rather than CP duration.

Availability curves were plotted individually for each of the cells receiving 100-ms or 1-s CPs (before and after 5HT), by plotting Na⁺ current amplitude current (normalized to 1.0 relative to I_max) against conditioning potential (Fig. 3, B and D). The availability curves generated by either protocol appeared to be biphasic and were well fit by double Boltzmann functions. Treatment with 5HT did not significantly effect the voltage of Na⁺ current availability, as judged by the estimates for V_h1 and V_h2 generated by the fitting procedure (Table 1). Also, the values obtained for the slope constant k were not changed significantly by 5HT (Table 1).

5HT did, however, produce a significant overall decrease in the normalized current amplitudes for both 100-ms and 1-s CPs (Fig. 1, B and D), which appeared to be most prevalent around the first shoulder of the availability curves corresponding to V_h1 (p = 0.001 and 0.00004, respectively; 2-way analysis of variance (ANOVA) for 5HT effect with mV as the second factor). There was also a trend toward smaller values for the fitting parameter f₁ after treatment with 5HT, which possibly reflects the noticeable reduction in normalized current amplitude around V_h1. A decrease in f₁ after 5HT treatment was observed in four of the five cells given 1-s CPs and five of six cells given 100-ms CPs. However, this putative effect of 5HT did not reach significance, possibly due to the small sample sizes (p = 0.095 and 0.081 for 1-s and 100-ms CPs, respectively; paired t-test).

Effect of CP duration on Na⁺ current availability

In contrast to 5HT treatment, variation in CP duration did have a significant effect on k and V_h values generated by Boltzmann fits to the availability curves (Fig. 4, A and B). Because values of V_h and k were not significantly affected by 5HT, the data for control and 5HT treated conditions were grouped for statistical analysis. The average k₁ and k₂ values associated with the 1-s pulses (5.7 ± 0.3 and 12.1 ± 0.4, respectively; n = 10) were significantly smaller than those (6.4 ± 0.2 and 15.2 ± 0.7, n = 12) associated with the 100-ms CPs (p = 0.045 and 0.001, respectively, Students t-test).

View larger version (37K): [in this window] [in a new window]   FIGURE 6   Effects of SHT on the estimates of kinetic rate constants for the transitions described in Model 2 using computer modeling of Na+ current traces. (A) Representative current records showing the increase of TTX-resistant Na+ current by 5HT in a type 2 DRG cell held at 60 mV and stepped to +5 mV. (B) Open probability time course was calculated using a scaling factor S = 1048 pA, and a line was fitted to the data according to Model 2 as described in the Materials and Methods. (C) Scatter plots of the kinetic parameters for 12 individual neurons with the following mean values under control conditions () and in the presence of 5HT (), respectively: kC1C2 = kC2C3 = kC3O = 1744 ± 46 s1 and 2137 ± 68 s1, kOC3 = 345 ± 14 s1 and 314 ± 63 s1, kOI1 = 1441 ± 126 s1 and 742 ± 88 s1, kI1O = 579 ± 50 s1 and 482 ± 87 s1, kI1I2 = 280 ± 21 s1 and 466 ± 41 s1, and kI2I1 = 29 ± 4 s1 and 31 ± 5 s1. kCO and kI1I2 were significantly increased, and kOI1 was significantly decreased in the presence of 5HT, whereas the other parameters were not changed significantly. Twelve current sweeps recorded under control conditions and after 5HT treatment (taken from the experiments depicted in Fig. 2 A) were used for modeling.

Values for V_h1 and V_h2 also differed significantly between the groups of cells given 1-s versus 100-ms CPs (Fig. 4, A and B). V_h1 averaged 36.3 ± 0.6 mV (n = 10) for the 1-s CPs, which was significantly more negative than the average of 33.9 ± 0.8 mV (n = 12) for the 100-ms CPs (p = 0.02, Students t-test). V_h2 averaged 76.8 ± 1.6 mV (n = 10) for the 1-s CPs, which was significantly more positive than the average of 89.0 ± 3.1 mV (n = 12) for the 100-ms CPs (p = 0.003, Students t-test).

Effect of CP duration on the modulation of the Na⁺ current by 5HT

The increase in Na⁺ current, usually observed after treatment with 5HT, was markedly antagonized by 1 s, but not 100-ms CPs, to depolarized potentials. As illustrated in Fig. 4 C, 5HT increased Na⁺ current by 35 ± 12% after a 100-ms CP to 30 mV, which was similar to the 41 ± 12% increase in Na⁺ current produced by 5HT in the absence of a 100 ms CP (n = 6). In contrast, 5HT increased Na⁺ current by only 5 ± 6% after a 1-s CP to 30 mV, which was significantly less than the 29 ± 8% increase in Na⁺ current produced by 5HT in the absence of a 1-s CP (p = 0.02, paired t-test; n = 5). The 5HT induced increase in Na⁺ current amplitude was also reduced significantly more by 1-s CPs compared with 100-ms CPs, over the range of CP potentials from 110 mV to 20 mV (Fig. 6 D; p = 0.0003, 2-way ANOVA for CP duration with mV as the second factor).

Time course of removal of inactivation

In another series of experiments we studied the interaction of 5HT with the time course of removal of inactivation. For these experiments, type 2 DRG cells were given alternating 1-s and 60-ms CPs to 0 mV, which produced maximal inactivation. After various delay periods (5 ms-5 s), during which the membrane potential was returned to 80 mV, the amplitude of currents evoked by a command to +5 mV were recorded as a measure of how much inactivation had been removed. The cells were held at 80 mV for 10 s between each cycle of CP, delay, and test potential to reset the channels (see inset, Fig. 5 B).

After a 5-s delay after 60-ms CPs, the test current amplitude (I_max) averaged 1407 ± 453 pA under control conditions was increased to 1855 ± 444 pA (+41 ± 14%) after treatment with 5HT (Fig. 5, A1 and A2). Current amplitude was reduced gradually by an average of 55% as the delay was shortened incrementally to the shortest time of 5 ms (Fig. 2, A1 and A2). A somewhat different pattern was observed regarding 1-s CPs. 5HT increased I_max by +36 ± 12% (from 1354 ± 438 pA to 1736 ± 432 pA), similar to that observed regarding 60-ms CPs. However, I_max was reduced by 96% after a 5-ms delay (Fig. 5, A3 and A4).

Plots of current amplitude (normalized to 1 relative to the peak amplitude observed with a delay of 5 s) versus delay were fitted with exponential functions to extract time constants for the rate of recovery (Fig. 5 B). The data was best fit by a triple exponential function. The average values for  and the associated fitting parameters generated by individual fits for each of the four experiments are given in Table 2. In summary, the fitting procedure generated three distinct time constants () in the proximity of 2, 100, and 1000 ms.

View this table: [in this window] [in a new window]   TABLE 2   Comparison of  and f values for removal of inactivation induced by 60-ms and 1-s CPs before and after 5HT

Effects of CP duration on the removal of inactivation

Varying the CP duration strongly affected the magnitude of the fitting parameters associated with the different time constants. The fitting parameter (f₁) associated with the fastest time constant (₁) was in the order of 50-fold smaller for the 1-s CPs versus the 60-ms CPs (Table 2). Conversely, the fitting parameters (f₂ and f₃) associated with the second and third time constants (₂ and ₃) were ~40% and 100% larger, respectively, for the 1-s CPs versus the 60 ms CPs (Table 2). These effects of CP duration were significant under control conditions as well as after treatment with 5HT (paired t-test, p = 0.02 for f₂, control or 5HT, and p = 0.0002 for f₃, control or 5HT).

Effect of 5HT on the time course of removal of inactivation

Comparison of several parameters measured for control and 5HT treatment conditions suggest that 5HT slowed removal of inactivation. As illustrated in Fig. 5 B, 5HT produced an overall significant decrease in the normalized current amplitudes for 1-s CPs, but not for 60-ms CPs (p = 2.2 e¹¹ and 0.53, respectively; 2-way ANOVA for 5HT effect with delay as the second factor). There was also a trend toward increased values for ₃ after treatment with 5HT that reached significance for the 1-s CPs, and approached significance for the 60-ms CPs (Table 2; paired t-test, n = 4, p = 0.01 and 0.07, respectively). The increase in ₃ was accompanied by a larger fitting parameter (f₃), in four of four cases for the 1-s CPs and three of four cases for the 60-ms CPs. The change in f₃ approached statistical significance for the 1-s CPs (p = 0.053, paired t-test, n = 4).

Effect of CP duration on the modulation of the Na⁺ current by 5HT

As with the above described availability experiments, modulation of Na⁺ current by 5HT was significantly affected by CP duration. At the delay time of 100 ms after 60 ms CPs, the Na⁺ current was increased by an average of 40.3 ± 13% by 5HT, which was similar to that observed in the absence of a CP (39 ± 12.3%) (Fig. 5 C). In contrast, for the same delay after 1-s CPs, the Na⁺ current was only increased by 3.3 ± 11%, which was significantly less than in the absence of a CP (p = 0.02, paired t-test, n = 4) (Fig. 5 C). Also, 1-s CPs significantly suppressed the 5HT induced increase in Na⁺ current relative to that observed regarding 60-ms CPs, when all delay periods were grouped together (Fig. 5 D; p = 0.000002, 2-way ANOVA for 5HT effect with delay as second factor).

Computer modeling experiments

Computer modeling experiments were carried out to gain insight into possible mechanisms that could underlie the increase in TTX-resistant Na⁺ current by 5HT. The current records from the 12 type 2 DRG cells depicted in Fig. 2 A were used for the computer modeling experiments. Various molecular models with different numbers of closed and inactivated states were tested for their ability to fit peak TTX-resistant Na⁺ currents recorded from type 2 DRG cells held at 60 mV. The simplest model that provided a good fit consisted of three closed states, one open state, and two inactivated states (model 1). Models with fewer closed or inactivated states were not able to accommodate quantitatively the activation shapes of the 40-ms current records.

View larger version (13K): [in this window] [in a new window]   Model 1

When Model 1 was fitted to the experimental data, there appeared to be dependencies between the different kinetic parameters of the activation pathway and between the parameters of the two inactivation pathways. As in other studies (d'Alcantara et al., 1999), the dependencies were eliminated by simplifying the model; equating all the kinetic constants of the transitions leading to the open state (k_C1C2 = k_C2C3 = k_C3O) and neglecting the reverse transitions between closed states (k_C2C1 = k_C3C2 = 0). This hypothesis reflects the fact that the experimental data were not informative enough for estimating these constants individually.

Because of their mutual dependence, it was impossible to estimate the kinetic parameters of both inactivation pathways from a single experimental trace. However, the availability experiments suggested that 5HT did not significantly affect the voltage dependency of availability of TTX-resistant Na⁺ channels in type 2 DRG cells (Fig. 3, Table 1). Because the principal objective was to identify the possible modifications of the gating mechanism responsible for an increase in Na⁺ current, we removed the possibility of inactivation from the closed state in the model. The above manipulations led to the following operational model:
Model 2

To estimate the effects of 5HT on channel kinetics, p_o(t) curves were generated for peak currents recorded under control conditions and in the presence of 5HT (holding potential 60 mV) for each of 12 type 2 DRG cells, using Eq. 3 as described in Materials and Methods (Fig. 6, A and B). Then the six unknown independent parameters were estimated for each cell under control conditions and during peak effect of 5HT by fitting the model to the p_o(t) curves as described in the methods (Fig. 6 B).

The estimates of the six parameters, under control conditions and after treatment with 5HT, are summarized in Fig. 6 C for each of 12 cells. The parameters k_C3O and k_I1I2 were both significantly increased by 23 ± 4% and 67 ± 15% from their control values (p = 0.00001 and 0.0007, respectively, paired t-test), and the parameter k_OI1 was significantly decreased by 48 ± 6% of the control values (p = 0.0007, paired t-test). We did not detect a significant change in the other three parameters.

The effects of 5HT on k_C3O, k_OI1, and k_I1I2 appeared to be reversible. In 8 of the 12 cells the Na⁺ currents recorded following washout of the 5HT for an average of 10 min were again fitted to see if the effects of 5HT on the rate constants changed back toward control levels. In these eight cells, 5HT increased peak Na⁺ current by 174 ± 31 pA (54 ± 14% increase), and the current was decreased by 245 ± 99 pA by the end of the washout period. Regarding these same eight cells, 5HT decreased k_OI1 from a control level of 1317 ± 105 s¹ to 738 ± 125 s¹, which returned to 1459 ± 211 s¹ over the washout period. k_C3O and k_I1I2 averaged 1777 ± 55 s¹ and 280 ± 28 s¹, under control conditions, respectively, were increased by 5HT to 2204 ± 77 s¹ and 486 ± 54 s¹, and fell to 1804 ± 69 s¹ and 348 ± 26 s¹, respectively over the washout period. For all three rate constants, the changes produced by 5HT as well as the changes produced by washout relative to 5HT conditions were significant (p < 0.05 for all, paired t-test with Bonferroni adjustment for multiple comparisons). On the other hand the values for k_OC3, k_I1O, and k_I2I1 were not significantly affected by 5HT or washout relative to control conditions.

As illustrated in Figs. 1 B and 7, A and B, 5HT produced a much larger relative increase in Na⁺ currents evoked with smaller test potentials compared with those evoked with larger test potentials. Additional modeling experiments were carried out to see if the 5HT induced changes in k_C3O, k_OI1, and k_I1I2 regarding peak Na⁺ currents were conserved regarding currents evoked by different test potentials. As illustrated in Fig. 7, A1 and A2, TTX-resistant Na⁺ currents, which were evoked by different test potentials ranging from 10 mV to +5 mV, were well fit by Model 2, before and after treatment with 5HT. (For this modeling the averaged current records illustrated in Fig. 1 A were used.) However, for some other test potentials, the Model 2 did not fit well (see Discussion; data not shown). For these reasons, the effects of 5HT on the rate constants are presented below only for currents evoked by test potentials ranging from 10 mV to +5 mV.

View larger version (32K): [in this window] [in a new window]   FIGURE 7   Effect of varying test potential on the 5HT induced changes in kC3O, kOI1, and kI1I2. (A) Fit of Model 2 to Na+ channel open probability for current records obtained using test potentials ranging from 10 mV to +5 mV. The corresponding averaged current records shown in Fig. 1, A1 and A2, were used for transformation into open probability and fitting. The po, max corresponding to each test potential under control conditions was derived from the averaged g-V plot shown in Fig. 1 C. (B) Percent increase in TTX-resistant Na+ current produced by 5HT for different test potentials. (C to E) Estimates of kC3O, kOI1, and kI1I2 for different test potentials, under control conditions (circles) and after treatment with 5HT (squares). (F-H) Plots of percent change in kC3O, kOI1, and kI1I2 produced by 5HT versus percent increase in TTX-resistant Na+ current produced by 5HT for different test potentials. Percent change in kOI1 was significantly correlated with percent change in Na+ current produced by 5HT, whereas percent change in kC3O and kI1I2 were not. Pearson correlation coefficients = 0.995, 0.960, 0.928, and p = 0.03, 0.24, 0.43, respectively for kOI1, kC3O, and kI1I2 (Bonferroni adjustment for multiple comparisons).

For the most part, the changes in k_C3O, k_OI1, and k_I1I2 produced by 5HT regarding peak Na⁺ current (Fig. 6) were also observed regarding Na⁺ currents evoked by smaller test potentials (Fig. 7, C-E). The 5HT-induced change in k_OI1 appeared to most closely parallel the effects of 5HT on Na⁺ current, becoming smaller as the amplitude of the test potential was increased (compare Fig. 7, B with D). The percent change in k_OI1 produced by 5HT was significantly correlated with the percent change in Na⁺ current produced by 5HT, whereas percent changes in k_C3O and k_I1I2 were not (Fig. 7, F-H).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Electrophysiological studies

One the main goals of the present study was to better characterize the TTX-resistant Na⁺ conductance expressed by type 2 DRG cells to facilitate comparisons with TTX-resistant Na⁺ currents observed in other preparations. A comparison of the TTX-resistant Na⁺ channel in type 2 DRG cells with the TTX-R1, TTX-R2, and TTX-R3 subtypes proposed by Rush et al. (1998) is presented in Table 3. The voltage dependency of activation of the TTX-resistant Na⁺ current in type 2 DRG cells was carried out in the same solutions used in the Rush et al. (1998) study. Given corrections to our data for junction potential (7 mV) and corrections to the data of Rush et al. (1998) for series resistance (+4 mV, their estimate), the V_1/2 of activation for TTX-resistant Na⁺ current in type 2 DRG cells most closely matches that of the TTX-R2 subtype (Table 3).

View this table: [in this window] [in a new window]   TABLE 3   Comparison of TTX-resistant Na+ currents expressed by type 2 DRG cells to three subtypes of TTX-resistant Na+ currents proposed by Rush et al. (1998)

We studied the availability of the TTX-resistant Na⁺ current in type 2 DRG cells using a voltage command protocol identical to that used by Rush et al. (1998), but using different internal and external solutions that reduced rundown and improved seal stability in our system. Given corrections to our data for junction potential (6.8 mV) and for the presence of 2 mM Ca²⁺ in our external solution (10 mV), the V_h1 and V_h2 values we observed regarding availability most closely resembled those of the TTX-R2 channel (Table 3). In addition we observed biphasic availability curves similar to those reported for TTX-R2 subtype in the Rush et al. (1998) study, where a significant proportion of the fit was associated with the more negative V_h2. In contrast the TTX-R1 subtype exhibited availability curves that appeared mostly monophasic, and when fit with double Boltzmann functions, over 90% of the fit was associated with the more depolarized V_h1 (Table 3).

Our data regarding removal of inactivation also suggests that type 2 DRG cells express the TTX-R2 Na⁺ channel. As described in the results section, we observed that triple exponential functions fit the time course of removal of inactivation better than the double exponential functions used by Rush et al. (1998). On the other hand, when we fit our data with double exponential functions we got fast and slow time constants very similar in magnitude to those observed by Rush et al. (1998) for the TTX-R2 channel (Table 3). Furthermore over 50% of the overall fit was attributed to the slow time constant, similar to the scenario observed for the TTX-R2 channel (Table 3). In contrast, removal of inactivation from the TTX-R1 channel could be explained mostly by a rapid rate of retrieval (Table 3).

A final observation is that both the TTX-resistant Na⁺ current in type 2 DRG cells and the TTX-R2 subtype exhibit pronounced use-dependence, in contrast to the TTX-R1 subtype (Table 3). The term "use-dependence" was coined by Rush et al. (1998) to stand for the decrease in peak Na⁺ current amplitude produced by evoking peak Na⁺ currents at a rate of 1 Hz. As illustrated in Table 3, the TTX-R2 subtype and the TTX-resistant Na⁺ current expressed by type 2 DRG cells exhibit pronounced use-dependence, whereas this phenomena is seen to a much lesser degree regarding the TTX-R1 subtype (Cardenas et al., 2001; Rush et al., 1998).

Several observations suggest the existence of multiple inactivation states of the TTX-resistant Na⁺ channel in type 2 DRG cells. The observation that a double exponential function was required to fit the inactivation of evoked Na⁺ currents fits with the idea of multiple inactivated states. The different time constants describing this inactivation may reflect transitions from the open state to different inactivation states. Also, the observation that the availability curves were biphasic suggests the possibility of multiple inactivation states. One possibility is that the values of V_h1 and V_h2, generated when fitting double Boltzmann functions to the data, represent 1/2 inactivation for one inactivation state versus another, although there could be other interpretations. A third piece of evidence is the observation of three rates of removal of inactivation, which may correspond to transitions from different inactivation states to closed states.

More specifically, several additional observations suggest the hypothesis that there are two inactivation states, one (I_fast) that is induced and retrieved faster than the other (I_slow). As mentioned above, evoked Na⁺ currents inactivated according to two time constants averaging 3 ms and 88 ms. The more rapid time constant may reflect the transition from the open state to an initial inactivation state, which in conformational terms, is closest to the open state. The slower time constant may reflect a slower transition from the initial inactivation state to a subsequent inactivation state, which is farther from the open state.

The steeper availability curves generated with long versus short CPs also fits with the hypothesis of I_fast and I_slow states. For submaximal potentials, the 1-s CPs could be expected to induce and retrieve more channels to and from the inactivated state, due to the additional time available for transitions to and from I_slow. The result of this would be steeper curves both for induction and retrieval of inactivation.

Varying CP duration had significant effects on V_h1 and V_h2, in the availability experiments, which can also be explained in terms of I_slow and I_fast. Due to more time available for transitions to I_slow, V_h1 could be expected to be more negative for 1-s CPs because less positive voltages would be required to induce the inactivated state in 1/2 of the channels not already inactivated at the holding potential of 60 mV. Similarly, due to more time available for transitions from I_slow to closed, V_h2 could be expected to be more positive for 1-s CPs because less negative voltages would be required to remove inactivation from 1/2 of the channels that are inactivated at 60 mV.

The effects of CP duration on fitting parameters in the removal of inactivation experiments also fit with the hypothesis of I_fast and I_slow. In these experiments, the fitting parameters associated with the three time constants describing removal of inactivation, represent the proportion of the total fit attributed to each time constant. Thus, based on fitting parameter values, 1-s CPs (compared with 60-ms CPs) induced dramatically less inactivation than was removed according with the fastest time constant, and significantly more inactivation than was removed according to the two slower time constants (Table 2). One interpretation of this could be that the 1-s CPs initially induced a greater number of channels into I_slow, which was removed according to the slower time constants.

Thus, the hypothesis that fits the data best overall is that there are two inactivated states, I_fast and I_slow, illustrated below in Model 3:

View larger version (16K): [in this window] [in a new window]   Model 3

Model 3 holds that I_fast is induced and retrieved rapidly with time constants in the proximity of 2 to 4 ms. On the other hand, I_slow is induced with a time constant averaging 88 ms for depolarizations that evoke peak Na⁺ current, and is retrieved according to two time constants in the proximity of 100 ms and 1 s. The two time constants for retrieval of I_slow, could possibly represent transitions from I_slow to different closed states. The time constants for induction and retrieval of I_fast and I_slow in Model 3 are based on the inactivation of evoked Na⁺ currents and the removal of inactivation experiments and on the assumption that the rates of induction of I_fast and I_slow from the closed state resemble their rates of induction from the open state. They are meant to be theoretical approximations only. The assumption that I_slow is retrieved to different closed states (not necessarily C₁ and C₂) is based on earlier work indicating that multiple rates of retrieval from inactivation can represent transitions from one inactivation state to different closed states (Vandenberg and Bezanilla, 1991; Goldman, 1995).

The hypothetical scenario that I_slow undergoes transitions to different closed states was adopted solely to match up our observations that two time constants best described inactivation of evoked Na⁺ currents, whereas three time constants best described removal of inactivation. Other scenarios could serve this purpose equally well, such as hypothesizing that I_fast undergoes transitions to different closed states. In any case, the observation of three time constants in the removal of inactivation experiments suggests an alternate hypothesis: there are three inactivation states, possibly exhibiting fast, intermediate, and slow rates of induction and retrieval. However, if this were the case, one might expect to find a third slow component of inactivation in the records of evoked Na⁺ currents, that corresponds to the slowest time constant for removal of inactivation. Such a slow component was not detected in the Na⁺ current records, despite much effort in this behalf. In addition, the previous work of Vandenberg and Bezanilla (1991) and Goldman (1995) suggest that different time constants for retrieval do not necessarily correspond to distinct inactivation states.

The characteristics of the inactivation states incorporated into Model 3 fit with the phenomenon of use-dependence first described by Rush et al. (1998). As mentioned above, the term "use-dependence" was applied by Rush et al. (1998) to describe the rapid decline in TTX-R2 Na⁺ current amplitude that occurs when peak Na⁺ currents are evoked at a rate of 1 Hz using 30-ms-long test potentials. We have observed a similar degree and rate of use-dependence regarding the TTX-resistant Na⁺ currents in type 2 DRG cells (Cardenas et al., 2001). Use-dependence could be explained by induction, during the 30-ms test potentials, of a slowly retrieved form of inactivation. This inactivation could accumulate over the course of a 1-Hz