Experimental and Modeling Study of Na+ Current Heterogeneity in Rat Nodose Neurons and Its Impact on Neuronal Discharge

J. H. Schild1 and D. L. Kunze2

1 Department of Physiology and Pharmacology, Oregon Health Sciences University, Portland, Oregon 97201; and2 Rammelkamp Research Center, MetroHealth Medical Center, Cleveland, Ohio 44109

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Schild, J. H. and D. L. Kunze. Experimental and modeling study of Na+ current heterogeneity in rat nodose neurons and its impact on neuronal discharge. J. Neurophysiol. 78: 3198-3209, 1997. This paper is a combined experimental and modeling study of two fundamental questions surrounding the functional characteristics of Na+ currents in nodose sensory neurons. First, when distinctly different classes of Na+ currents are expressed in the same neuron, is there a significant difference in the intrinsic biological variability associated with the voltage- and time-dependent properties of these currents? Second, in what manner can such variability in functional properties impact the discharge characteristics of these neurons? Here, we recorded the whole cell Na+ currents in acutely dissociated rat nodose sensory neurons using the patch-clamp technique. Two general populations of neurons were observed. A-type neurons (n = 20) expressed a single rapidly inactivating tetrodotoxin-sensitive (TTX-S) Na+ current. C-type neurons (n = 87) coexpressed this TTX-S current along with a slowly inactivating TTX-resistant (TTX-R) Na+ current. The TTX-S currents in both cell types had submillisecond rates of activation at room temperature with thresholds near -50 mV. The TTX-R current exhibited about the same rates of activation but required potentials 20-30 mV more depolarized to reach threshold. Over the same clamp voltages the rates of inactivation for the TTX-R current were three to nine times slower than those for the TTX-S current. However, the TTX-R current recovered from complete inactivation at a rate 10-20 times faster than the TTX-S current (10 ms as compared with 100-200 ms). Across the population of neurons studied the TTX-S data formed a relatively tight statistical distribution, exhibiting low standard deviations across all measured voltage- and time-dependent properties. In contrast, the same pooled measurements on the TTX-R data exhibited standard deviations that were 3-10 times larger. The statistical profiles of the voltage- and time-dependent properties of these currents then were used as a physiological guide to adjust the relevant parameters of a mathematical model of nodose sensory neurons previously developed by our group (Schild et al. 1994). Here, we show how the relative expression of TTX-S and TTX-R Na+ currents and the differences in their apparent biological variability can shape the regenerative discharge characteristics and action potential waveshapes of sensory neurons. We propose that the spectrum of variability robust reactivation characteristics of the TTX-R current are important determinants in establishing the heterogeneous stimulus-response characteristics often observed across the general population of C-type sensory neurons.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Sensory neurons exhibit a broad spectrum of functionally distinct Na+ currents (Caffrey et al. 1992; Nowycky 1992; Ogata and Tatebayashi 1993; Yoshida 1994). Na+ current classification most often is based upon voltage- and time-dependent properties and a relative sensitivity to the potent and specific Na+ channel antagonist tetrodotoxin (TTX). At one end of the spectrum are rapidly inactivating Na+ currents completely blocked by submicromolar concentrations of TTX (TTX-sensitive, TTX-S). At the other end of the spectrum are slowly inactivating Na+ currents only partially blocked or unaffected by micromolar TTX concentrations (TTX-resistant, TTX-R). Sensory neurons with a whole cell Na+ current exclusively composed of the fast TTX-S often exhibit sustained, almost stereotypical patterns of action potential discharge in response to current injections. In contrast,the discharge profiles for sensory neurons with both TTX-S and TTX-R Na+ currents are heterogeneous, ranging from single or very few action potentials through to sustained regular patterns of discharge (Bossu and Feltz 1984; Pearce and Duchen 1994; Rizzo et al. 1994; Stansfeld and Wallis 1985; Villiere and McLachlan 1996).

The role of the low threshold TTX-S Na+ current in the genesis of an action potential (threshold, upstroke velocity, peak voltage, etc.) has long been described (Hassard 1978). Although the voltage- and time-dependent properties of the TTX-R Na+ current have been well described, relatively little else is known regarding its role in neural activity (Yoshida 1994). Inflammatory agents that activate sensory fibers in vivo can also rapidly modulate the TTX-R Na+ current, giving rise to the suggestion that TTX-R may be an important regulator of nociceptor sensitivity (Akopian et al. 1996; Gold et al. 1996). However, it is not fully appreciated in what manner the TTX-R Na+ current may impact neuronal discharge. Furthermore, the functional role(s) for multiple inward Na+ currents in a single sensory neuron, each with distinctly different voltage- and time-dependent properties and the manner in which each shapes neuronal discharge are not well understood.

Here, we study the TTX-S and TTX-R Na+ currents in acutely isolated rat nodose neurons using the patch-clamp technique. In addition to characterizing voltage- and time-dependent properties, these experiments quantify the populational homogeneity for these distinct classes of Na+ currents. The TTX-S current data formed a relatively narrow statistical distribution, i.e., low standard deviations across all measured voltage- and time-dependent properties. In contrast, the same measurements on TTX-R current data were markedly heterogeneous, exhibiting standard deviations that were 3-10 times broader. These current and statistical data then were used as a physiological guide in adjusting parameters for the Na+ current expressions in a membrane model of nodose neurons previously developed by our group (Schild et al. 1994). Numerically, we assess the impact the relative strength of the TTX-S and TTX-R Na+ currents can have upon neuronal discharge characteristics. Furthermore, we demonstrate that across a population of cells, the heterogeneity of the TTX-R Na+ current, or neuromodulation of its voltage-dependent properties can give rise to a broad spectrum of firing properties and action potential waveshapes.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Neuron dissociation

The nodose ganglia of 1- to 3-day-old rat pups were excised surgically and immediately placed in chilled (5-10°C) nodose complete media (NCM) consisting of Dulbecco's Modified Engle's (DME)-F12 (Gibco BRL), 5% fetal bovine serum (Hyclone), 1% of a 1% stock of penicillin-streptomycin and 8 ng/ml nerve growth factor (Gibco), and 0.1% serum extender (Collaborative Research). After the extraction of 6-10 ganglia, the NCM was replaced by Earl's balanced salt solution (Gibco BRL) containing 0.5 mM ethylenediaminetetraacetic acid (EDTA), 1.5 mM CaCl2, 5 mg/ml trypsin, and 0.2 mg/ml L-cysteine (Sigma). After 30 min at 37°C, the trypsin solution was replaced with 37°C NCM containing 1.5 mg/ml each of trypsin inhibitor and albumin (Sigma). The ganglia were dispersed mechanically with aspiration pipettes and plated onto poly-D-lysine-coated substrates (Sigma, 10 mg/200 ml aqueous solution). The neurons were incubated in a 5% CO2-95% air, high humidity environment at 37°C for a minimum of 2 but not more than 10 h before recording. In a small number of experiments (n = 5), nodose neurons from 22- to 33-day-old rats also were studied. The dissociation procedure was similar except the intact ganglia were immersed in Earl's containing 1 mg/ml Type IIA collagenase (Sigma) and 30 U/ml papain (Sigma) for a period of 60 min at 37°C.

Electrophysiological techniques

The Na+ currents were acquired with the patch-clamp technique (8161 glass, 1-2 MOmega in normal saline) and a List EPC-7 voltage-clamp amplifier. The reference electrode was a low-resistance Ag-AgCl plug connected to the bath through a 150 mM KCl agar bridge. The electrode offset voltage and the liquid junction potential were compensated manually (see further text). After the formation of a gigaseal, the pipette capacitance also was nulled. Membrane rupture provided electrical access to the cell's interior. The adequacy of internal perfusion was monitored by successive voltage clamp steps to membrane potentials above the threshold for the major outward K+ currents in nodose neurons (Schild et al. 1994). The peak outward current steadily decayed as the intracellular medium equilibrated with the 0 mM K+ pipette solution. Generally, within 30-60 s from gaining intracellular access, the outward currents disappeared. The protocols then were performed in rapid succession. The voltage-clamp recordings consisted of a current-voltage (I-V) profile followed by a brief (2-3 min) test protocol (see RESULTS) and then a repeat I-V profile. To ensure the data were not influenced by Na+ current run-down, only those cells exhibiting consistent pre- and posttest I-V characteristics were included in the final analysis. The activation protocol consisted of voltage-clamp steps from a holding potential of -100-30 mV in 10-mV increments. Each clamp step was 40 ms in duration and applied once every 3 s. The inactivation protocol consisted of a 3-s conditioning pulse over a range of -100-10 mV in 10-mV increments. This was followed immediately by a voltage step from the conditioning potential to a membrane voltage corresponding to the peak I-V for that cell. Additional details on the recording protocols for each test are in the corresponding figure legends. The data were low-pass filtered (8 kHz, 4th order Bessel) and digitized (10 bits at 25 kHz) with the pClamp acquisition system (V5.5, Axon Instruments). All recordings were performed at room temperature (21-23°C).

Recording solutions

The Na+ solutions were similar to those of (Ikeda et al. 1986). The extracellular solution was (in mM) 50.0 NaCl, 10.0 MgCl2,10.0 N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES),25.0 dextrose, and nominally Ca+2 free (1-10 µM). The pH was adjusted to 7.4 using NaOH, which increased extracellular Na+ to approx 57 mM. The pipette solution was (in mM) 7.0 NaF, 140.0 N-methyl-D-glucamine, 2.0 tetraethylammonium-Cl, 2.0 MgCl2, 10.0 HEPES, 1.0 CaCl2, and 11.0 ethylene glycol-bis(beta -aminoethyl ether)-N,N,N',N'-tetraacetic acid for buffering intracellular Ca+2 to approx 10-8 M. The pH was adjusted to 7.3 using either HF or piperazine-N,N'-bis(2-ethanesulfonic acid). Osmolarities of the extracellular and pipette solutions were adjusted using either sucrose or mannitol to 340 and 310, respectively. In some experiments, a perforated patch (nystatin, 258 units/ml) was used to assess the time course of Na+ current rundown that may occur when using a ruptured patch (see RESULTS). Solution exchanges were performed using a gravity feed multibarrel pipette (approx 1 ml/min). For each day's experiments, the TTX was diluted to 1-100 µM from a 1 mM stock maintained at 4°C.

A central objective of our experimental recordings was to replicate as closely as possible the experimental conditions of Ikeda et. al (1986), who previously characterized the TTX-S and TTX-R Na+ currents in nodose sensory neurons. These authors did not account for the liquid junction potential in their measurements. In order that a direct and quantitative comparisons of data be possible, we also did not correct for the liquid junction potential when reporting our pooled measurements. However, for the model to produce action potentials at physiologically appropriate threshold voltages, it was necessary to offset the data values by -10 mV, an amount close to the liquid junction potential for our recording solutions.

Numerical analysis and simulations

The voltage-dependent activation and inactivation characteristics of the Na+ current records were analyzed using Hodgkin-Huxley type steady-state gating functions &mmacr; and &hmacr;, respectively. Steady-state characteristics were calculated from the current records using either a normalized Goldman-Hodgkin-Katz current equation or chord conductance. Both exhibited a sigmoidal voltage dependency described by
<FR><NU>1.0</NU><DE>1.0 + exp&cjs0362;<FR><NU><IT>V</IT><SUB>1/2</SUB><IT>−V</IT></NU><DE>S<SUB>1/2</SUB></DE></FR>&cjs0363;</DE></FR> (1)
where V1/2 is the membrane potential at half-activation and S1/2 is the reciprocal of the slope of the gating curve measured at V1/2. Time constants for both variables exhibited a putative Gaussian voltage dependency
<IT>A</IT>exp(−<IT>B</IT><SUP>2</SUP>(<IT>V − V</IT><SUB>peak</SUB>)<SUP>2</SUP>) + <IT>C</IT> (2)
where A scales the peak amplitude, B scales the functions width, Vpeak is the membrane potential at which tau m equals A, and C is an offset parameter. A nonlinear least-squares parameter estimation algorithm was employed to obtain good numerical fits to the activation, inactivation, reactivation, and time constant data (Schild et al. 1994). A parameter set was considered acceptable if the relative error, the normalized difference between a measured data point and that calculated using the modeling equations, was <1%. The parameter estimation routine assumes convergence when all free parameters in the equation set change by an amount <0.001%. For all data presented, error bars indicate 1 SD from the mean.

These parameters were used to update a membrane model of nodose neurons previously developed by our group (Schild et al. 1994). The ensuing numerical simulations had three main objectives. First, to further refine the parameter identification for the equations describing the TTX-S and TTX-R voltage-clamp data. Second, to study the individual roles of the TTX-S and TTX-R Na+ currents in action potential generation. Third, to assess the impact of the measured statistical spread in the voltage- and time-dependent properties of the TTX-S and TTX-R Na+ currents upon the capacity for regenerative discharge in nodose sensory neurons. The calculation of each model frequency data point was performed at the end of a 10-s simulation run, which is several times longer than the slowest system time constant. Details concerning the original model formulation and the primary data used in its development can be found elsewhere (Schild et al. 1994).

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

General observations

The Na+ currents from 107 nodose neurons formed two distinct populations. One group of cells (n = 20), classified as A type, exhibited a single fast inward Na+ current that was markedly sensitive to TTX (Fig. 1A). The remainingcells (n = 87), classified as C type, expressed both a TTX-S and a slower TTX-R inward Na+ current (Fig. 2A and inset of Fig. 1A). This phenotypic classification is consistent with the long-standing observation that peripheral sensory neurons exhibiting a singular fast TTX-S Na+ current give rise to myelinated axons, whereas those exhibiting both a TTX-S and TTX-R Na+ current have unmyelinated or lightly myelinated fibers (Stansfeld and Wallis 1985). Acutely isolated A-type neurons tended to have larger diameters than C-type cells (29.7 ± 8.1 µm, range: 22-50 µm, n = 15 vs. 24.7 ± 7.6 µm, range: 12-45 µm, n = 61, P < 0.025).


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FIG. 1. Voltage-clamp records of the tetrodotoxin-sensitive (TTX-S) Na+ current. A: current records from a neonatal nodose neuron exhibiting exclusively the fast, TTX-S Na+ current (ITTX-S). Clamp voltage indicated next to each current trace. Holding voltage was -100 mV. Inset: TTX-S current component of the total Na+ current in a cell exhibiting both the TTX-S and TTX-resistant (TTX-R) currents. B: current-voltage characteristics for a neuron exhibiting exclusively ITTX-S. Current was blocked effectively by 10 µM TTX. C: average normalized current-voltage characteristics of the TTX-S current (n = 10) recorded in neonatal nodose neurons and the I-V data from the subtracted TTX-S records presented in A (square ). Here and throughout RESULTS, error bars indicate 1 SD from mean.


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FIG. 2. Voltage-clamp records of the TTX-R Na+ current. A: current records from a neonatal nodose neuron exhibiting the slow, TTX-R Na+ current (ITTX-R) in the presence of 10 µM TTX. Clamp voltage indicated next to each current trace. Holding voltage was -100 mV. Note that the time base is 4 times longer than that for ITTX-S (Fig. 1A). Inset: TTX-R ITTX-R recorded from a juvenile (33-day-old) rat using the same voltage-clamp protocol. B: normalized current-voltage characteristics for an example TTX-R current blocked by extracellular perfusion with Zn2+. When extracellular Na+ was replaced with an equimolar concentration of N-methyl-D-glucamine, the entire Na+ current was eliminated. C: averaged and normalized current-voltage characteristics of the TTX-R current from neonatal rats (black-square, n = 20) was similar to the TTX-R current data from a juvenile rat (square ) presented in A.

Current-voltage characteristics

Under voltage clamp, the TTX-S current (ITTX-S) in A-type neurons (Fig. 1A) exhibited a transient response that was typical of the large, fast inward Na+ current in sensory neurons (Bossu and Feltz 1984; Caffrey et al. 1992; Ikeda et al. 1986). The current rapidly activated at membrane potentials greater than -50 mV. Above approx 0 mV the current followed an ohmic reduction in peak magnitude as the clamp voltage approached the Na+ reversal potential (ENa = -53 mV). The whole cell current was blocked by submicromolar TTX, which was reversible even at high concentrations (Fig. 1B). The TTX-S component of the total inward Na+ current for C-type neurons (Fig. 1A, inset) was similar to theITTX-S in the A-type cells. Although the TTX-S current component in C-type cells was typically smaller than that in A-type cells the normalized current-voltage (I-V) relationships of the two Na+ currents were nearly indistinguishable (Fig. 1C). However, we would caution against undue speculation that the ITTX-S in A- and C-type neurons arise from the same class of Na+ ion channel. This is because linear subtraction often cannot adequately separate the TTX-S and TTX-R Na+ current components from the whole cell record (note outward directed traces, Fig. 1A, inset).

In sharp contrast to the ITTX-S, the TTX-R current(ITTX-R) had an I-V profile that was shifted 20-30 mV toward more depolarized potentials and a slower rate of inactivation (Fig. 2). No partial block of this slow Na+ current was observed even at high concentrations of TTX (50-100 µM). The TTX-R current was blocked in a graded fashion by increasing concentrations of Zn+2 (Fig. 2B). An EC50 of approx 400 µM agrees with the relatively low divalent sensitivity exhibited by TTX-R currents in nodose sensory neurons (Ikeda and Schofield 1987). The TTX-R current also was studied with acutely isolated juvenile nodose neurons (n = 5, 27-33 days old). No significant difference was noted between the voltage- and time-dependent properties of the TTX-R Na+ currents in neonatal and juvenile rat (Fig. 2C and inset in Fig. 2A). Thus as in other sensory neurons, postnatal ontogenic development appears to not significantly alter Na+ channel voltage- and time-dependent properties as is often the case with channel expression (Ogata and Tatebayashi 1992).

Variability in activation and inactivation properties

The steady-state activation and inactivation of both the TTX-S and TTX-R currents were well described by the &mmacr;(V) and &hmacr;(V) functions, respectively (Fig. 3 and Table 1). Average (n = 10) V1/2 and S1/2 values for the ITTX-S &mmacr;(V) were -31.62 ± 0.99 and -6.98 ± 1.39, respectively. The TTX-S current began inactivating around -90 mV and was inactivated completely by -30 mV. Average (n = 10) V1/2 and S1/2 for &hmacr;(V) were -65.99 ± 2.4 and 5.97 ± 0.81, respectively. The steady-state activation window [i.e., the area of overlap of the &mmacr;(V) and &hmacr;(V) curves] for ITTX-S was <20 mV wide and never exceeded a peak level of 0.05 (Fig. 3A). In contrast, ITTX-R activated at much more depolarized potentials, requiring membrane voltages in excess of +20 mV to reach full activation. Average (n = 20) V1/2 andS1/2 for &mmacr;(V) were -11.29 ± 4.62 and -5.54 ± 1.10, respectively. The TTX-R current began inactivating around -60 mV and was inactivated completely by 0 mV. Average (n = 10) V1/2 and S1/2 for &hmacr;(V) were -31.00 ± 6.4 and 5.20 ± 0.61, respectively (Fig. 3B). The activation window forITTX-R was considerably larger than that for TTX-S, spanning nearly 40 mV with a typical peak magnitude of 0.2. Voltage steps within this prominent activation window evoke asustained (i.e. noninactivating) TTX-R Na+ current (Fig. 2A, -20 mV current trace).


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FIG. 3. Stead-state activation [&mmacr;(V), black-square] and inactivation [&hmacr;(V), bullet ] for TTX-S and TTX-R Na+ currents from A- and C-type neurons, respectively. Mean data values were calculated using a normalized chord conductance. Calculations of normalized permeability using the Goldman-Hodgkin-Katz current equation produced similar results (not shown). Boltzmann curves are best fits to the mean TTX-S (n = 10) and TTX-R (n = 20) data using the parameters listed in Table 1. For both panels, the shaded regions demarcate the span of the Boltzmann curves across the entire data set. Relative least-squares error for a numerical fit to any single record was <1%.

 
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TABLE 1. Summary of TTX-S and TTX-R voltage-dependent properties

The degree of homogeneity in the steady-state characteristics of the TTX-S and TTX-R currents (Fig. 3, shaded regions) was strikingly different even though the &mmacr;(V) and &hmacr;(V) functions for all data sets were fit numerically to the same level of precision. The pool of activation and inactivation gating functions for the TTX-R data set spanned a substantially broader range of voltages than for the ITTX-S. Indeed, the coefficient of variation (CV) for the pooled V1/2 activation and inactivation voltages for the TTX-R data was 14 and 6 times greater, respectively, than the same measures using the TTX-S data (Table 1). Interestingly, the CVs for all other measures from the data were approximately the same for both Na+ currents with the exception of the pooled TTX-R inactivation time constant, which had a CV that was nearly twice that of the TTX-S data.

Shift of inactivation

During prolonged patch recording, the voltage-dependent inactivation of Na+ currents paradoxically shifts toward more hyperpolarized values (Fig. 4, worst case examples). Although others have observed this phenomena, its underlying mechanisms are unknown. However, the shift may be indicative of rundown of a modulated system, possibly through a loss by dialysis of critical but as yet unidentified intracellular factor(s). Often, we observed a shift of ~10-15 mV within 10 min of going whole cell. The magnitude of the &hmacr;(V) shift was about the same for both the TTX-S and TTX-R currents. During the time course of the shift no significant changes were detected in the S1/2 values or decay characteristics of both currents. Perforated patch recording slows the onset of the time-dependent shift, but the V1/2 of &hmacr;(V) eventually reaches the same hyperpolarized potential as observed in the dialyzed cells (Fig. 4). Because the voltage dependence of Na+ channel gating is quite steep (Fig. 3), such a shift dramatically limits the recruitment of whole cell Na+ current (INa). As a technical measure toward reducing the influence this may have on our results, we analyzed only those data collected within the first 2-3 min of going whole cell and only when consistent control records before and after a test protocol were observed.


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FIG. 4. Time-dependent shift of stead-state inactivation (extreme examples). Although the cells were held at -100 mV the steady-state inactivation characteristics of the TTX-S current (curves labeled &hmacr;TTX-S) exhibited a shift of about -15 mV within 5-10 min of going whole cell. open circle  and bullet , inactivation protocols performed at 2 and 5 min, respectively, after going whole cell. This same phenomena is also apparent in the TTX-R inactivation curves (curves labeled &hmacr;TTX-R). Here, 2 different neurons are shown, 1 using the whole cell (triangle  and black-triangle) and the other perforated patch (open circle  and bullet ) recording configurations. A shift of about the same magnitude occurs in both cells but over a somewhat slower time course when using the perforated patch technique. During the time course of the shift, no significant change was observed in the slope factors of the computed &hmacr;(V) functions (------).

Time course of activation and inactivation

On average, the ITTX-S activated about twice as fast as the ITTX-R but the distribution of activation time constants (tau m) for both currents overlapped (Fig. 5, Table 1). The pooled inactivation time constants (tau h) for both currents were significantly different (P < 0.01). Beyond approximately -20 mV, the average tau h for ITTX-R was anywhere from three to nine times larger than that for the TTX-S current. Even at different membrane potentials but where the normalized activation and inactivation levels were the same (compare Figs. 3 and 5), the time course of the TTX-R current was always slower and considerably more variable than that of the TTX-S current.


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FIG. 5. Time constants for the TTX-S (A) and TTX-R (B) currents. Curves are best fits to the mean activation (tau m, black-square) and inactivation (tau h, bullet ) time constant data measured directly from the current records. TTX-S time constant parameters are tau m: A = 1.15, B = 0.06, Vpeak = -40.0, and C = 0.21 and tau h: A = 18.0, B = 0.043, Vpeak = -62.5, and C = 1.35. TTX-R time constant parameters are tau m: A = 1.45, B = 0.058, Vpeak = -14.5, and C = 0.26 and tau h: A = 10.75, B = 0.067, Vpeak = -13.5, and C = 3.15. Distribution of time constants more hyperpolarized than peak responses are model projections (see text). left-right-arrow , typical range of resting membrane potentials for these neurons; *, SD that exceeds the bounds of the ordinate.

Although we assume a Gaussian distribution of time constants, those to the left of (more hyperpolarized relative to) peak values are model projections. Protocols for assessing Na+ ion channel activity subthreshold to whole cell current activation were not performed. However, both our measured and model projected time constant values are well within the range of voltage-dependent values reported in the literature (Elliott and Elliott 1993; Ikeda et al. 1986; Ogata and Tatebayashi 1993). Our modeling results (see further text) indicate that during the course of an action potential, the TTX-R current significantly lags behind the TTX-S current transient. On account of its relatively depolarized steady-state characteristics and large activation window, this lag results in a substantial TTX-R inward Na+ current over the majority of the downward phase of the spike trajectory. Our numerical simulations will demonstrate how this effect and the extensive variability associated with the TTX-R current (Figs. 3B and 5B) can alter dramatically the action potential wave shape and maximum discharge rate of C-type sensory neurons.

Recovery aspects

The time-dependent recovery characteristics of the TTX-S and TTX-R currents in A- and C-type cells, respectively, were investigated using a paired pulse protocol (Fig. 6). From a holding voltage of -100 mV, a pair of voltage-clamp steps were applied to the cell. Both steps had the same amplitude of either -20 or 0 mV, which are close to the peak of the I-V relationship for the TTX-S and TTX-R currents, respectively (Figs. 1 and 2). The steps were 40 ms in duration, sufficient for complete inactivation of even the slower TTX-R current (see Fig. 2). The pair of steps were separated by an interval ranging from 1 to 1,000 ms, which was repeated once every 3,000 ms. Both Na+ currents exhibited slow and fast components of recovery that could not be satisfactorily described by first through third-order exponential functions (Fig. 6). The time constants of the slow recovery component for both currents were on the order of several hundred milliseconds, requiring 1,000-2,000 ms for both currents to return to control magnitudes. However, this slower component of recovery accounted for no more than 5-10% of the peak magnitude of either current. For both the TTX-S and TTX-R currents, the vast majority of recovery occurred shortly after the initial control pulse. However, the rates of recovery for the two currents were significantly different. The TTX-S current required ~150 ms to return to within 80% of control magnitude (Fig. 6A). In contrast, the TTX-R recovered from complete inactivation almost immediately, requiring only a few milliseconds to return to within 80% of control levels (Fig. 6B). Such a complex recovery trajectory has been observed in both nodose and dorsal root ganglia (DRG) sensory neurons but the underlying mechanisms are unknown (Bossu and Feltz 1984; Ogata and Tatebayashi 1993).


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FIG. 6. Reactivation characteristics of TTX-S and TTX-R currents in A- and C-type neurons, respectively. Membrane potentials for the control and test voltage-clamp pulses were selected to elicit a peak current response from the particular cell under test. Generally, -20 and 0 mV for the TTX-S and TTX-R Na+ currents, respectively (see Figs. 1 and 2). Time between paired pulses (Delta T) was varied as the cell was held at -100 mV. Pulse pairs were applied once every 3 s. Averaged data points (black-square) represent the percent ratio of the peak current produced by the test and control pulses for the TTX-S (A, n = 4) and the TTX-R (B, n = 8) Na+ currents. bullet  (B), data from a single neuron where analogue compensation was sufficient to permit brief values of Delta T. Insets: example current records.

Peak Na+ current

Capacitance normalized peak magnitudes of the ITTX-S in A-type and the ITTX-R in C-type neonatal nodose neurons were approximately equal (Fig. 7). The TTX-S current present in A-type cells was generally larger than the TTX-S Na+ current in C-type neurons (P < 0.025). Although the data varied considerably, the ITTX-S in the C-type cells was typically smaller than its TTX-R counterpart (P < 0.05). The variability in peak current magnitude is not surprising given the number of factors that are known to influence Na+ channel density, such as the age of the animal, the enzymatic dispersion methodologies, and even the relatively brief time in the culturing chamber (2-10 h).


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FIG. 7. Normalized peak Na+ current in A-type (TTX-S, shaded column) and C-type (TTX-S and TTX-R, dark columns) nodose neurons from 1- to 3-day-old rats. TTX-S current records from the C-type neurons were calculated as the difference between the responses before and after the application of 10 µM TTX. TTX-S component of the C-type cells was generally smaller than its TTX-R counterpart (P < 0.05) and rarely larger than the TTX-S current in A-type neurons (P < 0.025). As the subtraction procedure is less than optimal (see inset, Fig. 1A, and text), the normalized C-type TTX-S current should be considered only as an approximation.

Model exploration of TTX-R function

Our experimental recordings document the marked differences between both the average and the statistical distribution of the voltage- and time-dependent properties of the TTX-S and TTX-R currents. These data raise two essential questions regarding the functional aspects of TTX-S and TTX-R currents in sensory neurons. First, in what manner does each current contribute to the action potential threshold, wave shape and regenerative discharge characteristics of sensory neurons? Second, what functional impact can the broad distribution of voltage- and time-dependent properties of the TTX-R current have upon a C-type neuron's capacity for repetitive discharge? These questions cannot be easily answered experimentally. At a minimum, this would require extensive changes in both the extracellular and pipette solutions to perform a suite of electrophysiological investigations of whole cell Na+ current dynamics and action potential discharge properties in the same cell. As a result, we have turned to mathematical modeling to explore the potential impact these biophysical characteristics may have upon sensory neuron function. Here, we used a comprehensive mathematical model of A- and C-type sensory neurons previously developed by our group (Schild et al. 1994). Parameter sets were identified for the two Na+ currents using both the mean population data (Figs. 3 and 5) and individual TTX-S and TTX-R current records (Fig. 8). The remaining modeling parameters were either identical to the original work or noted in the figure legends.


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FIG. 8. Numerical reconstruction of TTX-S and TTX-R Na+ currents. Selected TTX-S and TTX-R current records from A- and C-type cells, respectively, were reproduced using the parameter estimation routine (see METHODS). Identified parameters then were used in a model of these nodose sensory neurons (Schild et al. 1994) to predict the firing properties of these particular cells. For the TTX-S current, the activation parameters are:V1/2 = -37.75, S1/2 = -6.98, A = 1.2575, B = 0.625, Vpeak = -39.0, and C = 0.175 and for inactivation: V1/2 = -65.99, S1/2 = 5.97, A = 25.5, B = 0.035, Vpeak = -72.5, and C = 1.05. Maximum TTX-S whole cell conductance is &gmacr;Na,f = 35 nS. For the TTX-R current, the activation parameters are: V1/2 = -15.29, S1/2 = -6.54, A = 1.35, B = 0.075, Vpeak = -13.5, and C = 0.395 and for inactivation: V1/2 = -28.39, S1/2 = 5.2, A = 14.75, B = 0.05, Vpeak = -18.5, and C = 2.25. Maximum TTX-R whole cell conductance is &gmacr;Na,s = 25 nS.

Relative magnitudes of TTX-R and TTX-S currents

For our numerical simulations, adjustments in peak Na+ current magnitude were made in terms of the relative number of TTX-R to TTX-S Na+ channels, henceforth referred to as TTX-R/TTX-S. The conductance and density of TTX-R and TTX-S Na+ channels in nodose sensory neurons presently are unknown. A reasonable estimate of Na+ channel density about the soma of mature rat DRG neurons is ~100-150/µm2 with TTX-R and TTX-S single channel conductances of 3.4 and 6.3 pS, respectively (Caffrey et al. 1992; Roy et al. 1994). Here, we vary the relative number of 3.4 pS TTX-R and 6.3 pS TTX-S Na+ channels between 0 and 100 so that the total combined channel density always equals 100/µm2. The TTX-S and TTX-R currents were simulated using the mean V1/2, S1/2, and time-constant values calculated from the data (Figs. 3 and 5 and Table 1). For all simulations presented, all remaining modeling parameters were held constant. For each TTX-R/TTX-S the C-type model neuron was driven by a series of 0-1,500 pA current steps for 10 s, at the end of which the instantaneous firing frequency (IFF, reciprocal of the time between two successive action potentials) was calculated.

TTX-R/TTX-S and firing threshold

The impact the TTX-R/TTX-S has upon action potential threshold is summarized in a three-dimensional plot outlining the C-type model cell's capacity for repetitive discharge at low stimulus intensities (Fig. 9). There are four general areas of interest within this near threshold region that exhibit disparate patterns and rates of action potential discharge. Region 1 is termed stable. Here, stimulation elicits either a subthreshold response (unshaded region, Fig. 9) or a single action potential that recovers to a stationary membrane potential.


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FIG. 9. Near-threshold stimulus response characteristics of a C-type model neuron as function of TTX-S and TTX-R Na+ channel densities. Nominal Na+ parameter values are the same as those identified for the mean current and time constant data (see legends of Figs. 3 and 5, Table 1). The C-type neuron was modeled with a maximum of 100 Na+ channels/µm2. Number of TTX-R Na+ channels was varied inversely relative to the number of TTX-S channels so that total channel density was always was equal to 100/µm2. A mean cell diameter of 24.7 µm was assumed for the C-type neuron model. All modeling equations and parameters were the same as those presented in Schild et al. (1994) with the exception of the following differences in maximum whole cell conductances (in nS): &gmacr;K = 37.5, &gmacr;K,Ca = 17.5, &gmacr;A = 25.0, &gmacr;D = 15.0, &gmacr;Ca,t = 3.5, &gmacr;Ca,n = 10.0, &gmacr;Ca,b = 0.175, and &gmacr;Na,b = 0.35. All data points on the mesh surface were taken at the end of a 10-s simulation run. Shaded bands demarcate 2.0-Hz increments in instantaneous firing frequency. Small dotted trace, 65 and 35% of the total number of Na+ channels are TTX-R and TTX-S, respectively; solid circle, irregular bursts in response to a near threshold step current, see Fig. 11, inset 1.

Region 2 is termed unstable-periodic. Here, the firing pattern exhibited by the model neuron is occasionally irregular, such as eliciting a short burst of action potentials for 1-2 s before terminating (e.g., Fig. 11, inset 1). As the proportion of the total whole cell Na+ current (INa) that is TTX-R moves away from 100%, both the minimum step current required for repetitive discharge and the minimum sustainable IFF decrease. This occurs because of the increasing contribution of the TTX-S current, which has an activation threshold well below that of the TTX-R current and closer to the -50 to -60 mV resting potential of these cells (Figs. 1-3). An abrupt firing threshold followed by a region of high gain that spans regions 1 and 2 are nonlinear characteristics of the Hodgkin-Huxley formulations (Hassard 1978). As the stimulus intensity increases, the IFF of the model neuron increases but in an irregular manner and only over a limited range of frequencies. The irregular IFF is a consequence of the complex interplay between the multiple outward K+ currents present in these neurons and the slowly inactivating TTX-R Na+ current. This effect was most prominent when the majority of the INa was composed of the TTX-R current. For example, neurons with a Na+ channel distribution that is between 80 and 100% TTX-R require between 30 and 150 pA to elicit an action potential and between 55 and 500 pA to initiate and sustain repetitive discharge. The high threshold for repetitive discharge is a consequence of the depolarized activation properties of the TTX-R current (Fig. 2) and insufficient regenerative TTX-S current to sustain oscillations. The large activation window (Fig. 3B), slow rates of inactivation (Fig. 5B), and nearly instantaneous recovery properties (Fig. 6B) of the TTX-R function to sustain this current during the downward phase of the action potential. The TTX-R inward Na+ current delays repolarization, thereby increasing the action potential duration, which, in turn, increases the recruitment of total outward K+ current ultimately limiting the maximum IFF.


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FIG. 11. Impact of measured variations in the voltage dependence of the TTX-R Na+ current activation and inactivation (Fig. 3) upon the C-type model neuron discharge. V1/2 values for the &mmacr;(V) and &hmacr;(V) functions were varied by ±1 SD about their mean (Table 1). Here, &gmacr;TTX-S = 0.43 µS and &gmacr;TTX-R = 0.43 µS, which corresponds to Fig. 9 (Dotted trace; see text). All other model equations and parameters are identical to those used in Fig. 9. Shaded region outlines the current-frequency relationship when both the TTX-R and the TTX-S gating functions were adjusted by ±1 SD (Table 1). Vertical calibration, -80 mV for the action potential traces and -3 nA for the current traces; Dotted trace, 0 mV potential. Horizontal calibration is 200 ms or indicated with each trace.

Region 3 is termed stable-periodic. Here, the model neuron exhibits regular and well-defined action potential discharge that grades smoothly with increasing stimulus intensity. Over the span of region 3, the neuron functions much like a proportional encoder although the trajectories are not quite linear. Both the discharge gain and the maximal IFF steadily increase with an increasing proportion of TTX-S channels contributing to the somal INa. As a result, the maximum sustainable IFF is strongly dependent upon the proportion of TTX-S in the INa. For a 500-pA step current, a C-type neuron with a 100% TTX-R INa discharges at 10 Hz, whereas exactly the same model cell but with a 100% TTX-S INa discharges at nearly 40 Hz.

When the number of TTX-R channels falls below ~50% of the total the C-type model neuron becomes autoactive (region 4). Again, this is because the activation window for ITTX-S lies very close to the resting membrane potential of these cells (Fig. 5A, left-right-arrow ). The resting TTX-S Na+ current is large enough to initiate and sustain oscillations, i.e., spontaneous discharge, with an IFF that parallels an increasing contribution of the TTX-S current. This emergence of spontaneous activity at low TTX-R/TTX-S is consistent with experimental evidence, suggesting that neuronal hyperexcitability may be the result of a selective loss of TTX-R channels accompanied by a simultaneous increase in the number of TTX-S channels (Rizzo et al. 1995).

TTX-R/TTX-S variability and neural discharge

Our experimental results have quantified the statistical boundaries for a broad range of voltage- and time-dependent properties associated with the whole cell TTX-R and TTX-S Na+ currents (Figs. 3-7, Table 1). Using these features as a physiological guide in our numerical simulations, we explore the potential impact such diversity may have upon the discharge characteristics of A- and C-type nodose sensory neurons. For the A-type neuron simulations, we use a slightly higher TTX-S Na+ channel density of 140 channels/µm2 to replicate the rapid upstroke velocity in A-type action potentials (Schild et al. 1994). For the C-type neuron simulations, the relative number of TTX-R and TTX-S channels was fixed at 65 and 35% of the total, respectively (note dotted trace in Fig. 9). On account of the differences in single channel conductances, these values correspond to nearly identical maximum whole cell TTX-R and TTX-S conductances. The V1/2 parameters associated with both the &mmacr;(V) and &hmacr;(V) Na+ channel-gating functions were adjusted ±1 SD about their mean values (Fig. 3, Table 1). To reduce the number of possible modeling scenarios, we adjust the V1/2 of &mmacr;(V) and &hmacr;(V) simultaneously. All other modeling parameters were held constant and for the C-type neuron were the same as those used in Fig. 9.

A-TYPE MODEL NEURON. With an increasing suprathreshold step current the A-type neuron asymptotically approaches a maximum 80 Hz IFF. Beyond this peak, the IFF begins to decrease even in the face of increasing stimulus current. The outward K+ currents are major factors in limiting the peak IFF but the TTX-S Na+ current (ITTX-S) dynamics are also critically important. With an increasing step current magnitude, there is a concomitant reduction in peak afterhyperpolarization (AHP). This is, in part, due to the voltage- and time-dependent characteristics of the K+ currents as well as the passive properties of the neuron in response to the steady current injection. A reduction in AHP means there is an ever-increasing percentage of the membrane trajectory that is more depolarized than the activation window of ITTX-s (compare Fig. 10, insets 1 and 2). Less of this current recovers from inactivation and coupled with the slow reactivation characteristics of ITTX-S (Fig. 6A), the net effect is a steadily decreasing peak INa. Adjustments of ±1 SD to the V1/2 values for the &mmacr;(V) and &hmacr;(V) functions were rather unremarkable. There was a modest broadening of the near threshold region (<= 100 pA) but the reminder of the current-frequency relationship essentially scaled up or down depending upon whether the V1/2 values were shifted in a hyperpolarizing or depolarizing direction, respectively.


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FIG. 10. Impact of measured variations in the voltage dependence of the TTX-S Na+ current activation and inactivation (Fig. 3) upon the A- model neuron discharge. V1/2 values for the &mmacr;(V) and &hmacr;(V) functions werevaried by ±1 SD about their mean (Table 1). Maximum whole cell TTX-S Na+ conductance (&gmacr;TTXS) for the A-type neuron was 2.5 µS. All other modeling equations and parameters were the same as those presented in Schild et al. (1994) with the exception of the following differences in maximum whole cell conductances (in nS): &gmacr;K = 27.5, &gmacr;K,Ca = 42.5, &gmacr;A = 350.0, &gmacr;D = 400.0, &gmacr;Ca,t = 0.1, &gmacr;Ca,n = 1.0, &gmacr;Ca,b = 0.085, and &gmacr;Na,b = 1.0. Vertical calibration bars correspond to -80 mV and -12 nA for action potential traces and ITTX-S records, respectively. Dotted trace, 0 mV potential for all action potential traces that were captured at the end of a 10-s simulation. Horizontal calibration is 100 ms.

C-TYPE MODEL NEURON. The simulation protocols summarized in Fig. 9 were repeated but with ±1 SD adjustments to the V1/2 values for the TTX-R current. The results defined a parametric volume outlining an activity manifold for the C-type model sensory neuron (shown here as a 2-D plot, Fig. 11). The IFF corresponding to the mean V1/2 values (solid black trace, Fig. 11) follows the same trajectory as the dotted trace in Fig. 9. With an increasing suprathreshold step current, the C-type neuron asymptotically approaches a maximum 28 Hz IFF. Beyond this peak, the IFF begins to decrease even in the face of increasing stimulus current much in the same manner and for much the same reasons as the A-type model (Fig. 10). Shifting only the V1/2 of the TTX-R &mmacr;(V) and &hmacr;(V) functions by ±1 SD had essentially no effect on threshold. Likewise, the current-frequency relationship and patterns of C-type action potential activity over the lower stimulus intensities (0-600 pA) were unchanged across the ±1 SD parameter adjustments (mean and ±1 SD traces overlap and see Fig. 11, inset 2). This lack of an effect on threshold and discharge is not surprising given the relatively depolarized activation characteristics of the ITTX-R (Fig. 3B). Furthermore, the high action potential peak recruits a large net outward K+ current, producing deep AHPs that, in turn, enabled ITTX-S to recover partially from inactivation. As a result, for the particular TTX-R/TTX-S examined here and only over these lower stimulus intensities the TTX-S current was responsible for setting discharge threshold and to a large extent the current-frequency relationship of theC-type cell. Even though the TTX-S current is much smaller than its TTX-R counterpart, it activates at lower membrane potentials and accelerates membrane depolarization toward the activation window of the TTX-R current (Fig. 11, inset 1). When both the TTX-R and TTX-S gating functions were shifted, there was a modest but functionally significantchange in discharge characteristics (note shaded region, Fig 11) similar to that observed in the A-type model(Fig. 10).

It is important to note that this lack of effect upon threshold and the entire current-frequency relationship is strongly dependent upon the TTX-R/TTX-S. To just initiate repetitive discharge in a neuron with a mix of 90% TTX-R and 10% TTX-S channels, a minimum step current of 0.2 nA is required at -1 SD, whereas at +1 SD, the same model cell requires ~1.0 nA. Thus for cells with greater than ~80-90% TTX-R Na+ channels, the ±1 SD adjustments in V1/2 can have an effect on threshold and the current-frequency relationship is markedly attenuated (Fig. 9).

As the stimulus intensity increases, two essential response features emerge. First, for the mean parameter values the IFF abruptly decreases to a rate less than half that produced with lower stimulus strengths. This transition occurs because with increasing step current magnitude there is a concomitant reduction in peak AHP as well as the TTX-S current. On account of its relatively depolarized inactivation characteristics (Fig. 3B), the TTX-R current is unaffected by the stimulus induced elevation in AHP. For example, a 0.4-nA stimulus (Fig. 11, inset 2) produces repetitive action potentials with peak TTX-R and TTX-S currents of -5.2 and -1.1nA, respectively. In contrast, a 1.0-nA stimulus (Fig. 11, inset 3) produces repetitive action potentials with peak TTX-R and TTX-S currents of -4.2 and -0.25 nA, respectively. Thus the abrupt reduction in IFF with increasing stimulus strength marks the transition from the TTX-S to the TTX-R current as the primary regenerative inward Na+ current which results in lower frequency oscillations for reasons discussed earlier (Fig. 9).

The second prominent feature is the dramatic difference between the mean and ±1 SD simulations at higher stimulus intensities. Shifting both the &mmacr;(V) and &hmacr;(V) functionsby -1 SD (shaded line, Fig. 11) dramatically increased the capacity of the C-type model neuron to handle large magnitude stimuli as compared with simulations using the mean parameter values (compare Fig. 11, insets 3 and 4). This occurs because the -1 SD shift in the TTX-R activation window increases the peak magnitude of ITTX-R over the upstroke of the action potential by nearly 25% (4.2 vs. 5.4 nA). This has a multitude of subtle effects such as increasing peak upstroke velocity of the action potential (60 vs. 87V/s), increasing its peak-to-peak height (92 vs. 103 mV) as well as increasing the peak in total outward K+ current (5.3 vs. 6.1 nA). Although the additional K+ current increases the depth of the AHP by only about -5 mV, this is sufficient to increase the recovery from inactivation of the TTX-S thereby increasing the its peak magnitude by 50% (0.25 vs. 0.38 nA). Collectively, these changes in action potential dynamics extend the functional capacity of the C-type model neuron at elevated stimulus intensities. Shifting the TTX-R activation window by +1 SD has essentially the opposite effect (Fig. 11, dotted trace and inset 5).

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

The voltage- and time-dependent dynamics of the inward Na+ currents from acutely isolated rat nodose sensory neurons were characterized using the patch-clamp technique. Two general populations of neurons were identified according to electrophysiological and morphological characteristics (Figs. 1 and 2). A-type neurons (n = 20) singularly expressed a fast TTX-S current with dynamics that were relatively homogeneous across the cell population. C-type neurons (n = 87) expressed two Na+ currents, a slow TTX-R Na+ current as well as a TTX-S current that was similar to the TTX-S expressed in A-type neurons (see inset, Fig. 1). The details of our experimental observations are in excellent agreement with earlier reports on the Na+ currents in nodose sensory neurons (Bossu and Feltz 1984; Ikeda et al. 1986). A close examination of the statistical distribution of Na+ current dynamics revealed striking differences in the degree of homogeneity across the TTX-R data as compared to the TTX-S data. Across our sample of TTX-R currents, the activation threshold ranged from -45 to -25 mV, peak I-V responses occurred anywhere from -10 to 10 mV and decay time constants at peak I-V varied by >40% (Figs. 2, 3B, and 5B).

Our pooled data is consistent with that of other investigations of sensory neuron Na+ currents (Bossu and Feltz 1984; Elliott and Elliott 1993; Ikeda et al. 1986; Ogata and Tatebayashi 1993). We only can speculate as to why these earlier studies did not observe a such a broad spectrum of voltage- and time-dependent properties as the possibilities range from differences in recording methodologies to the age of the animal at time of recording. However, the heterogeneity of the TTX-R Na+ current has been observed elsewhere (Rizzo et al. 1994). It is important to note that such extensive cell-to-cell variability was not apparent in our TTX-S data (Figs. 1, 3A, and 5A), which exhibited standard deviations that were comparable with those reported by others (Bossu and Feltz 1984; Elliott and Elliott 1993; Ikeda et al. 1986; Ogata and Tatebayashi 1993).

Heterogeneity is not a technical artifact

The particular data analyzed here were selected because the individual experimental recordings met stringent criteria (e.g., similar electrode properties, comparable access resistances, consistent pre- and posttest controls, adequate voltage clamp, brief recording period, etc.). This ensured that the recording conditions for A- and C-type neurons were nearly identical and reduced the influence of technical factors upon result statistics. The normalized TTX-S and TTX-R currents in A- and C-type cells, respectively, were about the same magnitude (Fig. 7). However, because the larger diameter of A-type neurons, the absolute magnitude ofITTX-S in these cells was often 20-40% larger than the INa of C-type neurons. If the variabilities associated with the ITTX-R were induced experimentally (e.g., variability across electrode access resistances, loss of space clamp, etc.), then one could expect the larger INa of the A-type neurons to exhibit a broader range in voltage properties than the smaller C-type neurons. As the exact opposite was observed (Fig. 3 and Table 1), we conclude that the diversity in the voltage- and time-dependent properties of the TTX-R Na+ current is not an artifact of the recording procedure.

It is reasonable to assume that such a continuum of properties reflects a diffuse family of molecularly distinct TTX-R Na+ ion channels. Unfortunately, both our experimental procedures and the mathematical formalisms lack the complexity to make this distinction. However, our analysis of the whole cell data offers several indirect lines of evidence that such a scenario may be unlikely. For example, the normalized I-V relationships for the TTX-S Na+ currents from A- and C-type cells were nearly indistinguishable (Fig. 1C). Furthermore, if the total TTX-R current is derived from a much broader family of Na+ channels than the TTX-S current, then it is unlikely that the CVs for the slope factors and the time constants would be of comparable size, whereas the CVs for V1/2 would differ by as much as an order of magnitude (Table 1). Equally as plausible is that functionally related TTX-R Na+ channels express a relatively homogeneous molecular structure but that these channels are under extensive neuromodulatory control. This is consistent with the experimental evidence documenting the several millivolt G-protein-mediated shifts in the voltage-dependence of Na+ channel gating (Scheuer 1994). It is unknown to what extent such neuromodulatory mechanism may be responsible for the observed voltage- and time-dependent variabilities (Figs. 3-6). Thus the biological mechanisms underlying the diversity exhibited by our TTX-R Na+ current data presently remains unresolved. However, the impact of such differential properties upon neurosensory integration and the potential physiological strategies surrounding the concurrent expression of TTX-S and TTX-R Na+ channels in C-type sensory neurons can be explored numerically (Figs. 9-11).

TTX-S Na+ current and neural discharge

The resting potential for nodose and indeed for most sensory neurons falls between -50 and -60 mV. Generally, this means that <20% of the total TTX-S Na+ channel population is available for generating an action potential from rest (Fig. 3A). The TTX-S current has an activation window that spans <20 mV and never exceeds a peak level of 0.05. Also, >150 ms are required for the TTX-S current to recover to within 80% of its initial magnitude (Fig. 6). Collectively, these factors limit the overall excitability and the dynamic range of A-type neural discharge (Fig. 10). For A-type neurons (Fig. 3A) or C-type neurons with a significant TTX-S component (Fig. 9), both threshold and maximum IFF are markedly influenced by the slope of the TTX-S &hmacr;(V) and, to a lesser extent, the &mmacr;(V) functions. Slight changes in the membrane resting potential or peak AHP can alter dramatically the number of TTX-S Na+ channels available for the subsequent action potential. The relatively modest variability in the voltage-dependent activation of the TTX-S current (Table 1) can alter the threshold characteristics of A-type neural discharge (Fig. 10). However, the impact of these changes upon the current-frequency characteristics of A-type neurons is far less than that for C-type neural discharge (Figs. 9-11).

TTX-R Na+ current and neural discharge

The steady-state profiles for the TTX-R current were 20 to 30 mV more depolarized than those for the TTX-S current, and thus the full compliment of TTX-R Na+ channels is available at rest potentials (Fig. 3). The activation window for ITTX-R spanned nearly 40 mV and was nearly seven times larger than that of the TTX-S current. The rate of activationof ITTX-R was moderately slower than that of ITTX-S, whereas its rate of inactivation was four to six times slower (Figs. 2 and 5). As was first reported by Bossu and Feltz (1984) for cranial sensory neurons, recovery of the TTX-R current was nearly instantaneous in comparison with that of the TTX-S current (Fig. 6). Collectively, these factors ensure the availability of the slow TTX-R Na+ channels over a wide range of dynamic activity, membrane voltages and stimulus magnitudes. Elliott and Elliott (1993) have proposed that cells with a large TTX-R component would be slowly adapting. Our modeling results appear to support this conclusion as we have shown that the TTX-R Na+ current can maintain an active and potentially dominant role in C-type neural discharge in the presence of strong depolarizing stimuli. Considering its broad range of voltage- and time-dependent properties (Figs. 3 and 5), nearly instantaneous recovery (Fig. 6), and capacity to dramatically alter C-type neural discharge (Figs. 9 and 10), we conclude that the TTX-R Na+ current is a major factor underlying the continuum of action potential waveshapes and discharge properties characteristic of C-type nodose sensory neurons (Stansfeld and Wallis 1985).

It is well known that the major families of outward K+ currents responding to membrane depolarization (e.g., delayed rectifier, transient outward K+, and calcium-activated K+) can have a similar impact upon neuronal discharge as we have shown here for the TTX-R Na+ current. However, the activation threshold for most voltage-dependent K+ currents is very near or slightly more depolarized than the activation voltage of the TTX-S Na+ current. As a result, modulation of K+ channel properties tends to effect both the minimum stimulus to elicit an action potential and the current-frequency relationship of the neuron. However, because ofthe rather depolarized activation characteristics of the TTX-R current (Figs. 2 and 3), it is possible to impart rather dramatic changes in neural discharge without appreciably altering the input stimulus necessary for action potential generation (Fig. 11).

Potential clinical significance of TTX-R

Trophic nerve growth factors are necessary to sustain the differential expression of TTX-S and TTX-R Na+ channels (Yoshida 1994). In a subset of DRG neurons, maturation brings about an increase in TTX-S with a simultaneous decrease in TTX-R Na+ channels, presumably guided by physiological factors associated with the neuron's functional development (Roy and Narahashi 1992). Axotomy also induces considerable changes in the electrophysiological characteristics of sensory neurons; this has been shown to involve a selective loss of TTX-R and a simultaneous enhancement of TTX-S Na+ currents (Rizzo et al. 1995). Our simulation results demonstrate the manner in which neuronal excitability is influenced by the relative number of TTX-S and TTX-R Na+ channels (Fig. 9). When the number of TTX-R Na+ channels falls to less than about half of the total, the C-type model neuron becomes autoactive, assuming the combined density of the 3.4 pS TTX-R and 6.3 pS TTX-S Na+ channels remains constant. This is because the restingTTX-S Na+ current is large enough to initiate and sustain regenerative oscillations. Such hyperexcitability has long been associated with injured sensory nerve fibers (Wall and Devor 1983). A potential method in the management of neuropathic pain may involve site directed upregulation of TTX-R Na+ channel expression. Alternatively, the selective modulation of the voltage-dependence of Na+ channel activation and inactivation could bias sensory neurons toward a lower activity state (Fig. 11). If such interventions could gradually decrease hyperexcitability without blocking nerve conduction, as happens with most local anesthetic agents, then it may be possible to lessen the severity of pain perception while maintaining an ability to detect and encode neurosensory information.

Physiological relevance of TTX-R

Across species and sensory modalities myelinated afferent fibers generally function in a deterministic manner, often exhibiting low-activation thresholds and encoding sensory information with a high degree of fidelity and repeatability. Just as ubiquitous are the higher thresholds, the lower maximal discharge rates, and continuum of action potential waveshapes and discharge properties exhibited by C-type afferent fibers: characteristics that are well represented in our numerical simulations. Modulation of TTX-R Na+ ion channel density and/or voltage- and time-dependent properties enables the C-type sensory neuron model to be tuned anywhere within a broad manifold of activity (Figs. 9 and 11). If TTX-R Na+ ion channels are present at the terminal endings of C-type afferents, then rather modest changes in TTX-R properties could have dramatic effects upon the dynamic range of sensory encoding.

Throughout the general population of sensory neurons the range of chemosensitivities exhibited by C-type cells is substantially broader than that for A type (Leal-Cardoso et al. 1993), possibly implicating a more integrative role in sensory processing for unmyelinated than for myelinated sensory afferents. It is intriguing to speculate that the TTX-R Na+ current may function to increase the neural capacity of C-type afferents (Figs. 9 and 11) to encode a broader range of sensory inputs.

    ACKNOWLEDGEMENTS

  This work was supported by National Heart, Lung, and Blood Institute Grants HL-07676 and HL-09242 to J. H. Schild and HL-36850 to D. L. Kunze J. H. Schild also is supported currently by American Heart Association Grant 9630277N.

    FOOTNOTES

  Address for reprint requests: J. H. Schild, Dept. of Electrical Engineering---IUPUI, 723 West Michigan St. SL160, Indianapolis, IN 46241 E-mail: jhs{at}engr.iupui.edu

  Received 19 May 1997; accepted in final form 26 August 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society