Brain, Vol. 125, No. 2, 421-435,
February 1, 2002
© 2002 Oxford University Press
Oscillatory mechanism in primary sensory neurones
Department of Cell and Animal Biology, Institute of Life Sciences, Hebrew University of Jerusalem, Jerusalem, Israel and Department of Neurology, PVA/EPVA Neuroscience and Regeneration Research Center, Yale University School of Medicine, New Haven, CT, USA
Correspondence to: Professor M. Devor, Department of Cell and Animal Biology, Institute of Life Sciences, Hebrew University of Jerusalem, Jerusalem 91904, Israel E-mail: marshlu{at}vms.huji.ac.il
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Ectopic spike activity, generated at low levels in intact sensory dorsal root ganglia and intensified following axotomy, is an important cause of neuropathic pain. The spikes are triggered by subthreshold membrane potential oscillations. The depolarizing phase of oscillation sinusoids is due to a phasic voltage-sensitive Na+ conductance (gNa+). Here we examine the repolarizing phase for which K+ conductance (gK+) is implicated. In vivo, gK+ blockers have excitatory effects inconsistent with the elimination of oscillations. Indeed, using excised dorsal root ganglia in vitro, we found that gK+ block does not eliminate oscillations; on the contrary, it has a variety of facilitatory effects. However, oscillations were eliminated by shifting the K+ reversal potential so as to neutralize voltage-insensitive K+ leak channels. Based on these data, we propose a novel oscillatory model: oscillation sinusoids are due to reciprocation between a phasically activating voltage-dependent, tetrodotoxin-sensitive Na+ conductance and passive, voltage-independent K+ leak. In drug-free media, voltage-sensitive K+ channels act to suppress oscillations and increase their frequency. Numerical simulations support this model and account for the effects of gK+ block. Oscillations in dorsal root ganglia neurones appear to be based on the simplest possible configuration of ionic conductances compatible with sustained high frequency oscillatory behaviour. The oscillatory mechanism might be exploited in the search for novel analgesic drugs.
Keywords: dorsal root ganglion; ectopic firing; K+ channel block; neuropathic pain; membrane resonance; subthreshold oscillations
Abbreviations: 4-AP= 4-aminopyridine; AHP = after hyperpolarization; DRG = dorsal root ganglion; gNa+ = Na+ conductance; gK+ = K+ conductance; H–H = Hodgkin–Huxley; IK = delayed rectifier K+ current; Rin = input resistance; TEA = tetraethyammonium; TTX-S = tetrodotoxin sensitive; Vr = resting membrane potential
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Introduction |
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Somatosensory signals normally originate at peripheral afferent axon endings. Following nerve injury, however, somata of primary sensory neurones in segmental dorsal root ganglia (DRGs) become a significant source of ectopic afferent discharge (Kirk, 1974
; Wall and Devor, 1983; Burchiel, 1984; Kajander et al., 1992). Given the importance of this discharge for neuropathic dysaesthesiae and pain (Devor and Seltzer, 1999), detailed understanding of the electrogenic mechanism is a priority.
It has emerged that the ability of DRG somata to fire repetitively depends on their ability to generate subthreshold membrane potential oscillations. Action potentials are triggered when the amplitude of oscillation sinusoids reaches threshold. Only neurones with oscillations fire repetitively; others may fire at the onset of a depolarizing pulse, but activity is not sustained. Axotomy greatly increases the proportion of neurones with subthreshold oscillations and increases ectopic discharge (Study and Kral, 1996; Amir et al., 1999; Liu et al., 2000a, b).
The rising (depolarizatory) phase of oscillation sinusoids is due largely to an inward tetrodotoxin-sensitive (TTX-S) Na+ current (Amir et al., 1999; Pedroarena et al., 1999; Wu et al., 2001; Xing et al., 2001). Do voltage-activated K+ conductances (gK+) generate the falling (repolarizatory) phase? Certain evidence suggests that they might. For example, gK+ blockers reduce the resonance frequency of trigeminal ganglion somata, ultimately blocking resonance altogether (Puil et al., 1988, 1989). On the other hand, blocking gK+ does not eliminate ectopic afferent discharge. On the contrary, it triggers firing in immature and injured afferent axons, and accelerates firing in already active afferents (Devor, 1983; Burchiel and Russell, 1985; Eng et al., 1988). This can induce dysaesthesiae and pain (Lees, 1996; Chabal et al., 1989). Subthreshold oscillations are known to underlie ectopic firing at axonal sites of chronic demyelination (Kapoor et al., 1997), although it is not yet known whether this is also true in neuromas (or in normal sensory endings, for that matter). It is difficult to deduce from these and related observations whether gK+ plays a direct role in the oscillatory mechanism, or whether excitatory effects of gK+ blockers simply reflect depolarization induced by these reagents.
Here, we have directly examined effects of three gK+ blockers on subthreshold oscillations. In addition, we determined the effects of shifting the reversal potential (and hence the driving force) for K+ ions. There were two aims: (i) to define the mechanism responsible for the repolarization of oscillatory sinusoids; and (ii) to determine how gK+ blockers modulate ectopic afferent discharge. We found that gK+ blockers have distinct facilitatory effects on membrane resonance and ectopic discharge independent of their effects on membrane potential. None eliminated the repolarizatory phase of oscillation sinusoids, indicating that voltage-gated K+ channels are not a necessary part of the oscillatory mechanism. Nonetheless, K+ current proved essential, as reducing K+ flux by manipulating the K+ driving force eliminated oscillations. Oscillatory behaviour in DRG neurones appears to be due to a novel mechanism involving inward current flow through a phasic TTX-S, voltage-dependent Na+ conductance (gNa+), reciprocating with outward current flow through a passive, voltage-independent K+ leak conductance.
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Material and methods |
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Electrophysiological preparation
We used Wistar-derived Sabra strain (Lutzky et al., 1984
) rats of both sexes (juveniles 2–4 weeks old, 30–75 g; adults 260–480 g). Data were combined as results were not related to sex or age. Animals were anaesthetized with pentobarbital sodium (Nembutal, 
60 mg/kg i.p.) and euthanized by carotid exsanguination. Protocols were approved by the Institutional Animal Care and Use Committee of the Hebrew University of Jerusalem following Israeli regulations concerning experiments on animals. DRGs L4 or L5 were excised with their dorsal roots, the spinal nerve and a variable length of sciatic nerve attached, and immersed in ice-cold Krebs solution containing NaCl 124 mM, NaHCO3 26 mM, KCl 3 mM, NaH2PO4 1.3 mM, MgCl2 2 mM and dextrose 10 mM, and saturated with 95% oxygen and 5% carbon dioxide (pH 7.4, 290–300 mos/mol). After 
1 h, during which time the solution gradually warmed to room temperature (20°C), ganglia were pinned in a recording chamber with a Silastic (from Dow-Corning, Seneffe, Belgium) floor and superfused with the Krebs solution to which 2 mM CaCl2 was added (1–3 ml/min, room temperature).
Sharp glass microelectrodes were used for intracellular recording and stimulation in current clamp mode (20–50 M
filled with 3 M KCl). In adult rats, penetration was facilitated by removing the dorsal surface of the DRG capsule using a fine blade. The K+ channel blockers tetraethylammonium (TEA, 2–10 mM, Sigma, St Louis, Mich., USA) or 4-aminopyridine (4-AP, 1 mM, Sigma, St Louis, Mich., USA) were added to the superfusion solution as noted in the Results. As an alternative means of blocking gK+, 2 M CsCl was sometimes used as the electrolyte in the recording pipette. Finally, in some experiments we altered the K+ concentration of the bath solution [K+]0, while maintaining osmolarity using symmetrical changes in [Na+]0, with appropriate controls (see Results). All cells reported here had a stable resting membrane potential that was more negative than –45 mV and an overshooting spike on intracellular (somatic) or extracellular axonal stimulation. Data were recorded digitally on magnetic videotape for off-line analysis.
Whole cell input resistance (Rin) was calculated from the linear portion of the current–voltage relationship in the hyperpolarizing range. Current–voltage curves were generated by intracellular current injection (100 ms pulses +0.2 to –1.2 nA in steps of 0.2 nA) through the bridge circuit of an Axoclamp-2A recording amplifier using pC LAMP software (v6.0.3, Axon Instruments, Foster City, Calif., USA). Sometimes only two current steps were used (0 and –1 nA). Other parameters measured were: (i) resting membrane potential (Vr); (ii) spike amplitude (from Vr); (iii) spike width at half maximal amplitude; (iv) amplitude of the afterhyperpolarization (AHP) following spikes; and (v) duration of the AHP (at 75% repolarization). The compound action potential evoked by sciatic/spinal nerve stimulation and monitored on the dorsal root using a suction electrode, served as an indicator of spike propagation through the ganglion.
Since the preparation did not permit determination of receptive fields, neurones were categorized by axonal CV (conduction velocity = propagation distance divided by spike latency) and shape of the intracellularly recorded action potential. Neurones were presumed to have a myelinated axon (A-neurone) if CV >1 m/s, and an unmyelinated axon (C-neurone) if CV 
1 m/s. Here we consider A-neurones exclusively. These were further characterized as Ainf neurones if analogue differentiation indicated an inflection on the falling limb of the spike, or A0 neurones if there was no such inflection. A0 neurones are predominantly low threshold Aß mechanoreceptors (including proprioceptors), while Ainf neurones include A
afferents, many of which are myelinated nociceptors (Gorke and Pierau, 1980; Koerber and Mendell, 1992; Villiere and McLachlan, 1996).
Some A0 neurones show sinusoidal subthreshold oscillations in their membrane potential either at Vr or upon depolarization (Amir et al., 1999). To analyse these oscillations, signals were band-pass filtered at 1 Hz to 10 kHz and digitized at 5 kHz. Oscillation frequency was quantified as power spectral density during 4 s spike-free epochs and processed using an FFT (Fast Fourier Transform) routine (CP Analysis v5.1, Datawave, Longmont, Col., USA). When the presence of action potentials interfered with FFT analysis, oscillation frequency was measured by inspection of shorter spike-free runs. The presence or absence of subthreshold oscillations was usually unequivocal, but if there was doubt we adopted the formal amplitude criterion of 1.5x the baseline noise present during brief pauses in the oscillations, and/or that there was a distinct peak in the FFT plot at the frequency expected from visual inspection of the voltage trace.
The amplitude, and hence detectability, of subthreshold oscillations is voltage-sensitive. We therefore routinely examined cells at Vr and then shifted the membrane potential (slow ramp and hold depolarization 20 mV/s, hold >2 s) until oscillations occurred or until more than –20 mV. Statistical evaluations (criterion P = 0.05) are based on two-tailed t-tests, Mann–Whitney U-tests, and significance of the 
2 or Fisher exact probabilities test using SigmaStat v2.0 (Jandel, San Rafael, Calif., USA). All means are given ± standard deviation.
Computational model
The electrophysiological results suggested a novel oscillatory mechanism which we tested in numerical simulations using a modified Hodgkin–Huxley (H–H) model of membrane excitability. Specifically, we modelled a 50 µm diameter isopotential cell using NEURON software (version 4.2.1; Hines and Carnevale, 1997; www.neuron.yale.edu). Specific membrane capacitance was 1 µF/cm2, specific longitudinal resistance 35.4 cm and temperature usually 20°C. Membrane electrical properties, including the various kinetic terms, were based on values from the reconstructed action potential of the squid giant axon (Hodgkin and Huxley, 1952). However, some values were modified to more closely resemble mammalian DRG neurones as follows.
(i) The maximal sodium conductance (gNa+max) was decreased to the range 15.0–41.0 mS/cm2 (Caffrey et al., 1992). (ii) The leak conductance was increased to the range 0.6–1.5 mS/cm2 (Scroggs et al., 1994). (iii) The reversal potential of the leak (Eleak) was usually set at –77.5 mV, to approximate the physiological K+ battery (Ek). To simulate changes in [K+]0, Eleak and Ek were varied together in the range –107 to –40 mV. (iv) In many runs gK+max was set to zero, neutralizing its effect. Prolonged depolarizing steps (usually 3 s, but with confirmation that oscillations persisted for >20 s) were given under current clamp conditions. We used the Crank–Nicholson second order accuracy method for integration (dt = 0.01 ms).
Finally, for accuracy of calculations, we followed the rule of thumb that the number of segments (computational compartments) should be section length/0.05 
(Luscher et al., 1994; Segev and Burke, 1998). Our cell model was thus a single computational compartment. The recording set-up and the basic structure of DRG A-neurones are shown in Fig. 1A and B.
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TEA and 4-AP enhance electrogenesis in DRG somata
TEA: basic effects and drug access
TEA (2–10 mM), a moderately selective blocker of the slow, sustained, delayed rectifier K+ conductance IK (Strong, 1990
; Safronov et al., 1996), had the expected effects of depolarizing the membrane, increasing Rin and increasing spike height and duration (measured at a constant membrane potential; Table 1 and Fig. C). In some neurones, an inflection developed on the falling phase of the action potential (arrow Fig. C; seven out of 25 A0 neurones tested) with spike duration occasionally reaching 10s or 100s of ms (Fig. D). The amplitude of the brief post-spike AHP decreased, and its duration increased, presumably due to the increased Rin and hence membrane time constant (
). In cells that originally had both brief and prolonged AHP phases (Amir and Devor, 1997), TEA gradually obliterated the obvious transition between the two (8 A0, 8 Ainf; Fig. C). Many cells showed a time-dependent ‘sag’ during hyperpolarizing pulses, reflecting the activation of an inwardly rectifying current. This was abolished by TEA (six out of six cells tested). These changes, which are consistent with many previous reports (e.g. Puil et al., 1988; Hille, 1992; Villiere and McLachlan, 1996), confirm that TEA successfully accessed the cell membrane.
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TEA: subthreshold oscillations
TEA did not block subthreshold oscillations; on the contrary, it facilitated them. Eleven A0 cells were tested before and after TEA application. Initially none had oscillations at Vr, but three began to oscillate when depolarized (thresholds = –52, –45 and –40 mV; oscillation frequency at threshold = 80, 83 and 103 Hz). TEA (10 mM) did not affect oscillation amplitude, but it reduced oscillation frequency (Fig. 3). Most strikingly, however, oscillations could now also be induced in five of the eight cells that did not oscillate previously (threshold = –49 ± 5 mV; Fig. 2). Overall, 73% of cells (eight out of 11) had oscillations in the presence of TEA. This compares with 27% (three out of 11) before drug application or 34% (22 out of 65) including a larger control sample from previous work (P = 0.02; Amir et al., 1999
).
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In the presence of TEA, oscillation frequency (at threshold) was 48 ± 6 Hz (n = 8), much slower than the 115 ± 25 Hz of controls (n = 22, P < 0.001; Figs and 3). TEA also attenuated the normal voltage-sensitivity of oscillation frequency in most cells. In drug-free medium, the frequency increases by 8.4 Hz for every 10 mV of depolarization (Liu et al., 2000
a), presumably due to the voltage sensitivity of IK (see model below). In the presence of TEA, four out of eight cells showed no frequency change (<1 Hz) over 10–20 mV of depolarization, and two others showed a small decrease with depolarization. Only two continued to show the expected increase in frequency with depolarization. The effects of TEA were reversed following return to the control bath medium (Fig. ). TEA (10 mM) was applied to eight (non-oscillating) Ainf neurones. This did not induce oscillations at Vr (–58.8 ± 7.3 mV) or on depolarization. TEA depolarized the cells (by a mean of 9.5 ± 5.2 mV) and had the other effects noted above with respect to A0 neurones, confirming membrane access by the drug.
TEA: repetitive firing
Most neurones with oscillations fire repetitively when depolarized a few mV beyond their oscillation threshold (Amir et al., 1999; Liu et al., 2000a). In the present study, two of the three cells that oscillated at baseline fired when further depolarized, and the third began to fire when TEA was applied. Likewise, firing was induced in three of the five neurones that began to oscillate in the presence of TEA. Firing threshold was 2.2 ± 1.3 mV positive of the oscillation threshold (n = 6). At threshold, cells fired either individual (singlet) spikes (n = 3) or intermittent bursts (n = 3). Bursting was usually evoked with deeper depolarization (Figs and 3). Spikes originated from the cell soma; they always emerged from the depolarizing phase of sinusoids and firing rate was modulated by intracellular current injection (Figs and 3).
4-AP
4-AP (at 1 mM) produces a relatively selective block of the transient K+ conductance IA (Castle et al., 1989; Strong, 1990; Hille, 1992; Safronov et al., 1996). As with TEA, 4-AP (1 mM) induced depolarization, increased Rin, abolished anomalous rectification, and increased spike height and duration (Table 1 and Fig. E). It also revealed an inflection on the falling phase of the spike in five out of seven A0 neurones tested. Finally, the AHP was increased in duration, its amplitude reduced and its peak delayed (four out of four A0 and one out of one Ainf neurones). These changes are expected (e.g. see Puil et al., 1989; Hille, 1992), and confirm cellular access of the drug. Oscillations were induced in one of 11 A0 cells tested after slight depolarization from Vr (threshold = –54 mV; Fig. ). As usual, amplitude and frequency of the oscillations were voltage-sensitive. Deeper depolarization gave rise to high frequency spikes. Both the oscillations and the spikes were eliminated when 4-AP was washed out (Fig. D and E). Discharge was also induced by 4-AP in an additional six of these 11 cells, but in the absence of oscillations. Activity in these cells proved to originate at the cut nerve end rather than in the cell soma.
Intracellular Cs+ induces low frequency oscillations
Cs+, which blocks K+ conductance by steric hindrance at the ion channel pore, suppresses a wider spectrum of K+ channel types than either TEA or 4-AP (Hille, 1973; Castle et al., 1989; Strong, 1990). Particularly, it blocks sustained voltage-gated K+ conductances spared by 10 mM TEA.
Drug access
Progress of the block was monitored by changes that unfolded as Cs+ ions diffused into the cell from the CsCl-filled microelectrode. These changes were not seen when KCl-filled electrodes were used (five experiments interleaved among the Cs+ experiments, duration 30–45 min) or in prior studies (Amir et al., 1999; Liu et al., 2000a). Specifically, Cs+ led to a slow depolarization in most neurones, increased spike height in some, increased Rin and increased spike width, often with the appearance of an inflection on the falling phase of the spike. It also reduced AHP amplitude and increased AHP duration (Table 1). These changes were first detectable 5–10 min after impalement and appeared to be still progressing at 35 min (Fig. ). The extent and kinetics of the changes varied with the baseline oscillatory phenotype of the neurone tested (see below).
Subthreshold oscillations
Like TEA and 4-AP, Cs+ tended to facilitate oscillations, not prevent them. As usual, few of the neurones sampled had oscillations when first impaled (two out of 44; Vr = –63.0 and –53.5 mV, respectively), although an additional five oscillated on depolarization. Over the first 5–20 min, as Cs+ entered the cells, 15 initially non-oscillating cells began to oscillate (on depolarization). With time, threshold for generating oscillations drifted towards Vr (Fig. B). Oscillations in these 22 neurones were as described above (‘typical’). Interestingly, another 14 developed distinctive ‘slow’ oscillations (on depolarization), beginning about 5 min after impalement. This left only eight of the original 44 A0 cells (18%) silent after 35 min of Cs+ diffusion.
The 14 slow oscillating neurones were distinctly different from those with typical oscillations. Although oscillation amplitude was normal (1.6 ± 0.5 mV near the initial threshold of –29.4 ± 9.9 mV, n = 14), frequency was exceptionally low from the moment of first detection (36.8 ± 20.5 Hz for four neurones detected within 5 min, 33.9 ± 14.0 Hz considering all 14). In all 14, oscillation frequency proceeded to decline with time (Fig. C).
Slow oscillating neurones also had other peculiarities that set them apart. For example, although the duration of the (fast) AHP was no different on first impalement than in typically oscillating cells (Table 1; P > 0.2), a higher than normal proportion had a second-phase, prolonged AHP (10 out of 14 versus three out of 22; P < 0.01). Their most striking peculiarity, however, was the 15-fold increase that developed in their spike width (originally 0.8 ± 0.2 ms; 11.6 ± 8.9 ms after 35 min). In comparison, spike width in neurones with typical oscillations increased from 0.7 ± 0.3 ms to only 3.2 ± 5.0 ms, on average. In the presence of Cs+, the mean frequency of typically oscillating neurones declined from 90 ± 29 Hz to 47 ± 15 Hz, while in the slow oscillating neurones the decline was from 33.9 ± 14 to 16 ± 10 Hz (n = 14). Slow and typical oscillating cells had the same initial Vr, spike height, spike duration and Rin (P > 0.05).
Slow oscillating neurones appeared within 20 min of electrode penetration; no additional ones were recruited after that time. Measurements of microelectrode resistance gave no indication that a consistently larger tip orifice was used for the slow oscillating neurones (P > 0.2). Thus, they are not simply cells into which Cs+ entered rapidly and reached higher concentrations. We suspect that the slow oscillating neurones represent a distinct subclass of DRG A0 neurones.
Repetitive discharge
Whether typically or slow oscillating, all these neurones fired repetitively when depolarized 2–3 mV beyond the threshold for evoking oscillations (36 out of 36 A0 cells; Fig. B). The spikes originated in the cell soma (not the distal axon) as they emerged from oscillatory sinusoids; their frequency increased with depolarization and spiking was eliminated by hyperpolarization. In the typically oscillating cells, the threshold for evoking repetitive firing drifted towards more negative values as Cs+ diffused into the cell, paralleling the drift in threshold for evoking oscillations (Fig. B). This drift was less pronounced in the slow oscillating cells.
Near threshold, the discharge rate was low and the interspike interval was irregular. Singlet spikes were triggered only every few oscillations. Nonetheless, the firing rate was proportional to oscillation frequency; cells with slow oscillations fired at a lower rate than the cells with typical oscillations [2.1 ± 1.2 impulses/s (n = 14) versus 9.2 ± 6.8 impulses/s (n = 19), P < 0.001]. In most cases (24 out of 36), depolarization beyond threshold led to the appearance of bursts. In slow oscillating cells, these bursts were often prolonged.
Elimination of oscillations using elevated [K+]0
K+ is the only major ion in the system with a reversal potential negative to the membrane potentials at which oscillations were observed. Hence, it is the only ion able to draw the membrane back in the hyperpolarizing direction when the depolarizing Na+ conductance inactivates. The equilibrium potential for Cl– in DRG neurones is about –20 mV (Deschenes et al., 1976; Gallagher et al., 1978; Oyelese and Kocsis, 1996). It is very likely, therefore, that the repolarizing phase of oscillation sinusoids is due to the outward flow of K+ ions. Since blocking of gK+ with TEA, 4-AP and Cs+ failed to eliminate the oscillations, the remaining logical possibility is K+ flow through voltage-insensitive leak (background) channels (Hille, 1992; Lesage and Lazdunski, 2000; Goldstein et al., 2001). As no blockers are available for these channels, we tested this possibility by manipulating the K+ reversal potential. Specifically, increasing [K+]0, which shifts the K+ reversal potential in the depolarizing direction, reduces the driving force on K+ ions at the (depolarized) potentials at which oscillations were observed (Hille, 1992). This is expected to attenuate oscillations and ultimately eliminate them.
Effects of elevated [K+]0 were tested in nine A0 neurones that had oscillations in the normal bath medium ([K+]0 = 3 mM; Vr = –58.2 ± 6.2 mV). Oscillations were measured at –41.4 ± 4.8 mV; four cells discharged (in bursts) at this potential. Increasing [K+]0 to 40 mM caused depolarization of 21.3 ± 8.1 mV from Vr (in 20–50 s, n = 3); increasing [K+]0 to 30 mM caused depolarization of 18.0 ± 6.4 mV (in 45–120 s, n = 5). Under these conditions, oscillations declined in amplitude and then vanished (n = 8). Neither returning to the membrane potential at which oscillations were first detected or to Vr, nor applying further depolarization (to –20 mV), restored the oscillations (Fig. A). Burst firing was likewise eliminated (n = 4). Most cells continued to spike on step depolarization, although spike amplitude was sometimes reduced. In the remaining cell [K+]0 was increased to 20 mM. This did not eliminate oscillations, but it reduced both amplitude and frequency (Fig. B). Finally, in four neurones [K+]0 was reduced to zero. This did not eliminate or attenuate oscillations (Fig. C).
In order to maintain physiological osmolarity of the bath solution in these experiments, [Na+]0 was reduced by an amount equivalent to the increase in [K+]0. In principle, this change might attenuate oscillations due to the (slightly) reduced driving force on Na+ ions. To control for this possibility, [Na+]0 was reduced by 30 or 40 mM and replaced with choline, leaving [K+]0 at 3 mM. Oscillations persisted unchanged (n = 9 cells; Fig. A).
Simulation of the oscillatory process
Oscillatory model
The depolarizing phase of oscillation sinusoids is due to a TTX-S inward Na+ current on the grounds that oscillations are blocked when [Na+]0 is replaced by choline, or when the Na+ channel blockers lidocaine or TTX are applied. Oscillation frequency remains fixed until final block occurs (Amir et al., 1999; Pedroarena et al., 1999; Wu et al., 2001; Xing et al., 2001). Oscillations are unaffected by Ca2+ channel blockers. Our failure to eliminate or even attenuate oscillations using gK+ blockers means that voltage-sensitive K+ channels are not essential for repolarization. Rather, repolarization appears to be due to voltage-insensitive K+ leak (‘background’) conductance (Hille, 1992; Lesage and Lazdunski, 2000; Goldstein et al., 2001).
These data lead us to the following oscillatory model. In the presence of IK blockers, subthreshold oscillations result from activation of a voltage-sensitive TTX-S Na+ conductance with rapid activation, inactivation and repriming kinetics, reciprocating with repolarization due to ohmic K+ leak. This configuration is not unlike that in mammalian PNS nodes of Ranvier. In lower vertebrates, voltage-gated K+ channels and K+ leak both contribute to spike repolarization. In mammals, in contrast, nodal repolarization following Na+ channel inactivation is due primarily to the large K+ leak conductance present at the node (Chiu et al., 1979; Hille, 1992).
To gain further confidence in the viability of this model, we simulated it using the H–H formalism, but with values of gNa+max and leak appropriate to the mammalian DRG (see Material and methods). In the simulations, prolonged voltage steps were applied to potentials at which we typically saw oscillations in DRG neurones in vitro. In the first series, gK+max was set to zero to simulate the presence of gK+ blockers. After a brief transient, depolarization produced sustained subthreshold oscillations of the membrane potential at frequencies and amplitudes characteristic of those observed in DRG cells in the presence of TEA, 4-AP or Cs+. Just as in live cells, oscillation frequency increased with depolarization (Fig. A; oscillation frequencies, upper to lower trace, are: 42, 38, 33, 24 and 0 Hz). Likewise, the simulated neurones showed a preferred membrane potential at which oscillation amplitude was maximal (–45.4 mV in Fig. A; Amir et al., 1999; Liu et al., 2000a). We conclude that the proposed model is feasible.
Facilitation of oscillatory behaviour by IK block
Our basic oscillatory model engages only a single active channel, gNa+. Nonetheless, voltage-sensitive K+ conductances are in fact normally present in DRG neurones, and blocking them affects ectopic electrogenesis: it excites ectopic neuropathic discharge, increases the proportion of neurones with oscillations and reveals oscillations at more negative membrane potentials. These facilitatory effects are independent of, and in addition to, excitation due to membrane depolarization. Two factors may play a role. First, since IK block slows the repolarization kinetics of oscillation sinusoids, a larger proportion of the transient Na+ channels present will have become reprimed and available for activation. Secondly, because of the increase in Rin caused by the K+ channel block (Table 1), those Na+ channels that are activated generate a larger voltage excursion and hence make oscillatory sinusoids more prominent at any given membrane potential.
Effects of IK on the prevalence of oscillatory neurones were simulated. We began with a cell configuration that oscillated in the absence of any voltage-dependent K+ channels (gK+max = 0.0 mS/cm2), and then reintroduced the classical H–H delayed rectifier K+ conductance using incrementally increasing values of gK+max (from 0.0 mS/cm2 to values beyond the maximum reported in DRG neurones, 2.0 mS/cm2; Everill et al., 1998; Fedulova et al., 1998). Membrane potential was held constant, near the value that yielded maximal amplitude oscillations. As gK+max increased, oscillation amplitude decreased (and frequency increased). For values of gK+max 0.5 mS/cm2 oscillatory behaviour was eliminated (Fig. B). This is consistent with the progressive recruitment of oscillating cells in vitro by gK+ block. Interestingly, oscillations could be restored in the continued presence of gK+max >0.5 mS/cm2 by slightly reducing the K+ leak (from 1.5 mS/cm2 to 1.4 mS/cm2; Fig. C). This suggests that the heterogeneity of oscillatory behaviour in different DRG neurones in drug-free medium might, among other things, be related to the baseline leak conductance of the cells.
Role of IK in controlling oscillation frequency
In addition to inducing oscillations in quiescent cells, TEA and Cs+ reduced oscillation frequency from the range of 60–140 Hz to the range of 30–60 Hz. We explored this action by simulating a neurone with high frequency oscillations in the presence of relatively high IK (gK+max = 1.0 mS/cm2, K+ leak was 1.4 mS/cm2). Oscillation frequency (at threshold) was 99 Hz, consistent with values in drug-free medium in vitro. As gK+max was reduced from 1.0 to 0.25 mS/cm2, frequency fell to 39 Hz and threshold shifted to more negative values, consistent with in vitro results (Fig. C).
Voltage-insensitive leak conductance
Passive leak, apparently associated with a variety of K+ permeable channels, is ubiquitous in sensory neurones. In the absence of effective pharmacological blockers, we demonstrated its participation in the oscillatory behaviour of DRG neurones by altering [K+]0 and hence the driving force on K+. The same result was obtained in H–H simulations (Fig. D). High frequency oscillations (99 Hz) were obtained as above (K+ reversal potential EK = –77 mV), and then EK was varied. Stepwise reduction in EK, simulating increased [K+]0 (at a constant membrane potential), reduced oscillation amplitude until oscillations vanished entirely. Increasing EK, simulating decreased [K+]0, increased the amplitude (and frequency) of oscillations (Fig. D). Interestingly, sustained subthreshold oscillations did not occur in simulations in which IK was present, but the leak conductance was blocked (tested in the range gK+max = 0–2 mS/cm2; gleak = 0.0 mS/cm2).
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Discussion |
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Our main goal was to define the oscillatory mechanism in DRG A0 neurones. Previous work indicated that the depolarizing (positive-going) phase of oscillatory sinusoids is due to an inward TTX-S Na+ current; Ca2+ currents do not appear to contribute significantly (Amir et al., 1999
; Pedroarena et al., 1999; Wu et al., 2001; Xing et al., 2001). Here, we focused on the repolarizing (negative-going) phase with the aims of: (i) completing the description of the oscillatory mechanism; and (ii) revealing how gK+ blockers excite ectopic afferent discharge in vivo. We found that gK+ antagonists do not block subthreshold oscillations; on the contrary, they facilitate oscillations and spiking. The prominent facilitatory effects of TEA and Cs+ compared with 4-AP indicate a special role for IK. Manipulating EK and hence neutralizing all K+ currents, including those not affected by the blockers, did stop oscillatory behaviour. These results suggest an essential role for voltage-insensitive background K+ channels.
Together, the data reveal a novel oscillatory mechanism. In the presence of IK block, oscillations are due to inward current passing through a rapidly activating, inactivating and repriming TTX-S voltage-sensitive Na+ conductance (depolarizing phase), alternating with outward current passing through the ohmic K+ leak conductance (repolarizing phase). In drug-free medium, this canonical oscillatory mechanism is modulated by the voltage-sensitive K+ conductance IK, which has the effect of increasing the frequency of oscillations and reducing their prevalence at physiological potentials. In natural cells, there may well be additional minor modulation of resonance by other conductances such as gCa2+, IH (hyperpolarization-activated inward current) and persistent gNa+ (Llinas, 1988; Elliott, 1997; Schild and Kunze, 1997; Hutcheon and Yarom, 2000; Yagi et al., 2000). The proposed model constitutes perhaps the simplest possible configuration of ionic conductances compatible with sustained high frequency oscillatory behaviour (Hutcheon and Yarom, 2000). To the best of our knowledge, no such oscillatory mechanism has been demonstrated previously in any other neuronal type.
Other modes of oscillatory behaviour in primary sensory neurones
Puil and collaborators (Puil et al., 1988, 1989) proposed that resonance in trigeminal ganglion neurones is due to reciprocal activation of a TTX-resistant Na+ conductance and a TEA-sensitive K+ conductance, presumably IK. This was based on the observations that resonance was unaffected by TTX (1 µM), the removal of [Ca2+]0 or the addition of Ca2+ channel blockers, and was suppressed by TEA. Their model clearly does not apply to DRG A0 neurones. On the other hand, primary somatosensory neurones of the mesencephalic nucleus of the trigeminal nerve (MesV) do appear to resemble those of the DRG (Pelkey and Marshall, 1998; Pedroarena et al., 1999; Wu et al., 2001).
‘Slow oscillating’ DRG neurones appear to represent a distinct subclass of DRG A0 neurones (see Results). Cs+, which acts by blocking the K+ channel pore, suppresses a wider spectrum of K+ channel subtypes than either TEA or 4-AP (Hille, 1973; Castle et al., 1989; Strong, 1990). We speculate that the slow oscillating neurones possess a unique transient K+ conductance(s), sensitive to Cs+ but not to TEA or 4-AP, which normally contributes to the termination of the action potential. In another study, we encountered a few cells with slow oscillations (on depolarization, three out of 93 sampled) in the absence of Cs+ (Amir et al., 2002).
Ion channels, effects of axotomy and significance for chronic pain
Na+ conductance
Our model calls for a TTX-S Na+ channel with rapid activation, inactivation and repriming kinetics, and with availability in the voltage range –30 to –70 mV. At least two Na+ conductances meeting these requirements have been described in medium and large DRG neurones (Caffrey et al., 1992; Rizzo et al., 1994; Everill et al., 2001). Activation and inactivation occurs in a time frame of 5 ms, fast enough to support oscillations as fast as 140 Hz. Moreover, since repriming of TTX-S currents takes <20 ms (for 50% recovery, further reduced by axotomy), there should always be a pool of channels available (Cummins and Waxman, 1997; Everill et al., 2001). A possible difficulty lies at the most depolarized part of this range (positive to –40 mV), where most TTX-S Na+ channels are expected to be inactivated. We offer two solutions. First, it is very likely that Na+ channels in the initial segment and proximal stem axon contribute to oscillation currents. The membrane potential here would be somewhat more negative than in the soma proper. Secondly, there may be a contribution by TTX-resistant Na+ channels, which remain available at more positive potentials (see below).
The enhancement of oscillatory behaviour and spiking by axotomy may partly reflect increased maximal TTX-S gNa+ (Rizzo et al., 1996) combined with accelerated repriming that occurs following axotomy (Cummins and Waxman, 1997; Everill et al., 2001). These changes, in turn, may be due to the upregulation of brain type III Na+ channel mRNA transcripts (Nav1.3) in DRG neurones (Waxman et al., 1994; Boucher et al., 2000). We note, however, that in the absence of axotomy, type III Na+ channels are expressed at low levels; thus, one of several other candidate channels probably contributes to oscillations in intact ganglia, perhaps type I (Nav1.1) or PN4 (Nav1.6) (Waxman et al., 1999; Goldin, 2001; Everill et al., 2001).
Two TTX-resistant Na+ channel subtypes, PN3/SNS (Nav1.8) and NaN/SNS2 (Nav1.9), have attracted particular attention recently as potential targets for analgesic drugs because they are unique to the DRG. PN3/SNS, at least, is expressed in some large diameter neurones (A0) (Renganathan et al., 2000). Unfortunately, since both are TTX-resistant, they contribute at most only a small fraction of total gNa+ in A0 neurones, are strongly downregulated by axotomy and have relatively slow kinetics. They are unlikely to be the main Na+ channel type responsible for the depolarizing phase of oscillatory sinusoids. Nevertheless, they might still contribute sufficient Na+ current that blocking them would suppress oscillations and ectopic firing, and yield analgesia.
K+ conductance
TEA and Cs+ caused a negative shift in the threshold for eliciting oscillations, presumably by blocking IK. This increased the prevalence of oscillations at all membrane potentials, including Vr. The intense ectopic spike discharge and pain generated in vivo by gK+ block (references in Introduction) probably derives from this effect, combined with membrane depolarization.
In addition to facilitating oscillations, IK block reduced oscillation frequency. Part of this slowing may be due to the negative (hyperpolarizing) shift in the threshold at which oscillations could be elicited. In the Cs+ experiments, for example, oscillation threshold of typically oscillating neurones shifted by –22 mV (Fig. B). Based on the known relation of membrane potential to oscillation frequency (0.84 Hz/mV; Liu et al., 2000a), a 22 mV shift is expected to lower oscillation frequency by 18 Hz. The actual decline was 45 Hz, however, so other factors must also contribute. For example, IK is expected to accelerate the depolarizing phase of oscillation sinusoids by reducing . Likewise, by summing with the K+ leak conductance, IK hastens the repolarizing phase of sinusoids. In this context, progressive activation of IK by depolarization accounts for the monotonic increase in oscillation frequency that occurs as cells are depolarized (Amir et al. 1999; Liu et al., 2000a). It also explains the fact that TEA eliminated the voltage- sensitivity of oscillation frequency in most cells.
The facilitation of oscillatory behaviour by K+ channel block is more than an experimental tool; it may be an important factor in ectopic hyperexcitability following axotomy. Specifically, it has recently been discovered that axotomy leads to reduced expression of K+ channel mRNA in DRG neurones and to a 50% reduction in IK (Everill and Kocsis, 1999; Ishikawa et al., 1999). This change may be as important as the upregulation of gNa+ for the facilitation of subthreshold oscillatory behaviour, ectopic spiking in injured DRG A0 neurones and neuropathic pain (Kocsis and Devor, 2000).
Chronic pain
Our results suggest that axotomy induced dysregulation of Na+ and K+ channel expression in DRG A0 neurones, and of vectorial transport of the channel proteins, are key contributing factors to oscillatory behaviour, ectopic afferent discharge and consequent sensory abnormalities in neuropathy. Classically, pain sensation is considered to be the exclusive domain of C- and A- nociceptors. However, a substantial literature now points to activity in large diameter, myelinated, Aß afferents (which correspond to the A0 neurones studied here) as major players in both inflammatory and neuropathic pain (Campbell et al., 1988; Devor and Seltzer, 1999; Woolf and Salter, 2000). The unique oscillatory mechanism revealed here, and the ectopic afferent discharge that it occasions, may thus be a primary cause of neuropathic paraesthesias and pain. Correspondingly, the oscillatory mechanism might provide fertile ground for the development of novel analgesic drugs.
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The study was supported by grants from the United States–Israel Binational Science Foundation (M.D. and J.D.K.), the National Institutes of Health (NS 06208) and the Medical and Rehabilitation Services of the Department of Veterans Affairs (J.D.K). C-N.L. received a Golda Meir postdoctoral fellowship.
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