Department of Neurology and Paralyzed Veterans of America/Eastern Paralyzed Veterans Association Neuroscience Research Center, Yale School of Medicine, New Haven 06510; and Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare, West Haven, Connecticut 06516
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ABSTRACT |
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Herzog, R. I.,
T. R. Cummins, and
S. G. Waxman.
Persistent TTX-Resistant Na+ Current Affects Resting
Potential and Response to Depolarization in Simulated Spinal Sensory
Neurons.
J. Neurophysiol. 86: 1351-1364, 2001.
Small dorsal root ganglion (DRG) neurons,
which include nociceptors, express multiple voltage-gated sodium
currents. In addition to a classical fast inactivating
tetrodotoxin-sensitive (TTX-S) sodium current, many of these cells
express a TTX-resistant (TTX-R) sodium current that activates near 70
mV and is persistent at negative potentials. To investigate the
possible contributions of this TTX-R persistent (TTX-RP) current to
neuronal excitability, we carried out computer simulations using the
Neuron program with TTX-S and -RP currents, fit by the Hodgkin-Huxley
model, that closely matched the currents recorded from small DRG
neurons. In contrast to fast TTX-S current, which was well fit using a m3h model, the persistent TTX-R current was not
well fit by an m3h model and was better fit using
an mh model. The persistent TTX-R current had a strong influence on
resting potential, shifting it from
70 to
49.1 mV. Inclusion of an
ultra-slow inactivation gate in the persistent current model reduced
the potential shift only slightly, to
56.6 mV. The persistent TTX-R
current also enhanced the response to depolarizing inputs that were
subthreshold for spike electrogenesis. In addition, the presence of
persistent TTX-R current predisposed the cell to anode break
excitation. These results suggest that, while the persistent TTX-R
current is not a major contributor to the rapid depolarizing phase of the action potential, it contributes to setting the electrogenic properties of small DRG neurons by modulating their resting potentials and response to subthreshold stimuli.
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INTRODUCTION |
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Dorsal root ganglion (DRG)
neurons are unique in expressing tetrodotoxin (TTX)-resistant sodium
currents, as well as the TTX-sensitive sodium currents that are widely
expressed in many types of neurons (Caffrey et al. 1992;
Kostyuk et al. 1981
; Rizzo et al. 1994
; Roy and Narahashi 1992
). One of these TTX-resistant
sodium currents is persistent and is characterized by a relatively
hyperpolarized voltage dependence and broad area of overlap between
activation and steady-state inactivation curves, which brackets
the resting potential of these cells (Cummins et al.
1999
). This TTX-resistant persistent current (TTX-RP) has been
attributed to NaN (NaV1.9) sodium channels, which
are preferentially expressed in C-type DRG neurons because the presence
of a serine at position 355 in the NaN sequence predicts TTX-resistance
(Dib-Hajj et al. 1998
); the persistent current is
present in patch-clamp recordings from TTX-treated DRG neurons from
SNS-null mice (Cummins et al. 1999
) that lack SNS, the
other TTX-resistant channel that has been identified in DRG neurons
(Akopian et al. 1999
); there are parallel changes in the
amplitude and density of the TTX-RP current and in the levels of NaN
mRNA and protein in DRG neurons in response to peripheral axotomy (all
down-regulated) and central axotomy (no changes) (Sleeper et al. 2000
); and there are parallel
changes in amplitude and density of the TTX-RP current, and of NaN mRNA
and protein levels, following exposure to glial cell-derived
neurotrophic factor (Cummins et al. 2000
).
It has been proposed that persistent sodium currents contribute to the
regulation of electroresponsiveness in neurons in which they are
present (Crill 1996). Based on the high density of the TTX-RP sodium current in DRG neurons, its relatively hyperpolarized voltage dependence, the overlap between activation and steady-state inactivation, and its persistent nature at negative potentials close to
resting potential, Cummins et al. (1999)
predicted that the persistent TTX-R current contributes to setting the resting potential and to subthreshold electrogenesis in small DRG neurons. Because the TTX-RP current exhibits slow activation kinetics
(Cummins et al. 1999
), it also might be predicted that
this current should not contribute substantially to the transient
inward current flow that accompanies the rising phase of the action
potential. However, experimental investigation of the contribution of
the TTX-RP sodium current to electrogenesis in DRG neurons is difficult
because there are no specific blockers for this current. Therefore in the present study we used computer simulations to test these hypotheses.
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METHODS |
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Whole cell voltage-clamp recordings from DRG neurons
Unless otherwise noted, parameters used in these simulations
were based on whole cell patch-clamp recordings of TTX-RP sodium currents from small (20-25 µm diam) DRG neurons. DRG cultures from
L4 and L5 ganglia of
SNS-null mice (Akopian et al. 1999) were established as
previously described (Cummins and Waxman 1997
; Cummins et al. 1999
). Animal care and surgical
procedures followed a protocol approved by the Animal Care and Use
Committee of Yale University.
Sodium currents in small DRG neurons were studied after short-term
culture (6-24 h). Whole cell patch-clamp recordings were conducted at
room temperature (~21°C) using an EPC-9 amplifier and the PULSE
program (v 8.01; both by Heka Elektronik, Lambrecht/Pfalz, Germany).
Fire-polished electrodes (0.8-1.5 M) were fabricated from 1.7-mm
capillary glass using a P-97 Puller (Sutter Instrument, Novato, CA).
The average cell capacitance in the present study was 23.7 ± 0.5 (SE) pF, n = 96. The access resistance was typically 1.5 ± 0.05 M
(n = 96). Voltage errors were
minimized using 80% series resistance compensation. Linear leak
subtraction was used for all recordings. The pipette solution contained
(in mM): 140 CsF, 1 EGTA, 10 NaCl, and 10 HEPES, pH 7.3. The standard
bathing solution was (in mM) 140 NaCl, 3 KCl, 1 MgCl2, 1 CaCl2, 0.1 CdCl2, and 10 HEPES, pH 7.3. Cadmium was included
to block calcium currents. The osmolarity of all solutions was adjusted
to 310 mosM.
Protocols for characterization of the persistent TTX-R sodium current
The majority (typically ~85%) of small (<30 µm diam) rat
DRG neurons studied after <24 h in culture exhibit TTX-R sodium
currents. Distinct slow and persistent TTX-R currents can be observed
when the cells are held at 120 mV for several minutes before applying the test depolarizations. When the cells are held at more depolarized potentials, such as
50 mV, the persistent TTX-R current is attenuated by ultra-slow inactivation (Cummins et al. 1999
), and
the slowly inactivating, or slow, TTX-R current predominates. If the
currents obtained with the depolarized holding potential are digitally subtracted from the currents obtained with the hyperpolarized holding
potential, the persistent TTX-R sodium current can be seen in relative
isolation (see Fig. 1) (Cummins et al. 2000
). The slow
TTX-R current is not observed in transgenic Nav1.8 knock-out (SNS-null)
mice (Akopian et al. 1999
; Cummins et al.
1999
) and therefore is dependent on expression of functional
Nav1.8 sodium channel
-subunits. Because SNS-null neurons do not
express the slow TTX-R current, the total current recorded in SNS-null
neurons in the presence of 250 nM TTX is similar to that obtained in
rat small DRG neurons and wild-type mouse small DRG neurons (see Fig. 1) (Cummins et al. 1999
) using prepulse inactivation and
digital subtraction. Therefore we characterized the voltage-dependent and kinetic properties of the persistent TTX-R sodium currents in small
SNS-null DRG neurons.
All recordings were carried out with 250 nM TTX in the extracellular
solution from a holding potential of 120 mV. Prepulse inactivation
and digital subtraction was not used for the recordings of the
persistent TTX-R currents in SNS-null neurons. Because persistent TTX-R
sodium currents exhibit substantial voltage-dependent rundown and
ultra-slow inactivation, test pulses were given
5 s apart. The
voltage dependence of activation was measured with 200-ms depolarizing
test pulses to voltages ranging from
80 to +40 mV in 10-mV steps. The
time constants for activation (
m) and
inactivation (
h) were estimated using
Hodgkin-Huxley-type fits to the currents elicited with these
depolarizing test pulses. Single exponential fits to deactivating tail
currents were used to estimate
m at
hyperpolarized voltages. Tail currents were elicited by 25-ms
deactivation pulses to voltages ranging from
50 to
120 mV following
a 50-ms activation pulse to
40 mV. Due to the rundown that occurs
even at low pulse rates, we did not measure recovery from inactivation
kinetics for the persistent TTX-R sodium current. We assumed a Gaussian
distribution for
h. The voltage dependence of
steady-state inactivation was estimated with 500-ms prepulses to
voltages ranging from
130 to
10 mV in 10-mV steps followed by 20-ms
test pulses to
10 mV.
Protocols for characterization of the TTX-S sodium current
The voltage dependence of activation and steady-state
inactivation of the TTX-S sodium current were measured in adult rat small DRG neurons that expressed predominantly fast-inactivating sodium
currents. The neurons were held at 100 mV. The voltage dependence and
kinetics of these TTX-S currents are similar to those previously
reported for TTX-S currents in small DRG neurons (Cummins and
Waxman 1997
; Elliott and Elliott 1993
;
Roy and Narahashi 1992
). The voltage dependence of
activation was measured with 50-ms depolarizing test pulses to voltages
ranging from
80 to +40 mV in 5-mV steps. The time constants for
activation (
m) and inactivation
(
h) were estimated using Hodgkin-Huxley-type
fits to the currents elicited with depolarizing test pulses to voltages ranging from
50 to +40 mV. At more negative potentials (
120 to
60
mV),
h was estimated using single exponential
fits to the recovery from inactivation time course as previously
described (Black et al. 1999
; Cummins and Waxman
1997
). To determine the time course for recovery from
inactivation, cells were held at
120 mV, prepulsed to
20 mV for 20 ms to inactivate the TTX-S current, then brought back to the recovery
potential for increasing durations before the test pulse to
20 mV.
Data analysis
The electrophysiological data were analyzed using the PULSEFIT
(Heka Electronic) and ORIGIN (Microcal Software, Northampton, MA)
software programs. The peak conductance g for the TTX-S and persistent TTX-R sodium currents was calculated from the corresponding peak current obtained with the voltage dependence of activation protocols using the following equation
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Computer simulations
The electrical properties of small sensory neurons were
simulated using the NEURON program (version 4.2.1) (Hines and
Carnevale 1997). The definitions of channel properties for each
membrane mechanism were embedded in individual program modules written in the C programming language. Those modules were compiled in a format
that permitted importation into the Neuron program. The integration
method was Backward Euler at an integration time step dt of 0.02 ms.
Passive membrane properties of model neuron
Based on the electrically and microscopically measured values,
an isopotential cylinder with 3,000 µm2 surface
area and 24.3 pF capacitance was used. The specific resistance of the
cytosol, which was set to 200 /cm, did not affect function in the
isopotential model cell. Simulations were performed assuming a
temperature of 20°C, the temperature at which the experimental data
were recorded. Free ionic concentrations of sodium
([Na+]o = 145 mM;
[Na+]i = 12 mM) and
potassium ([K+]o = 4 mM;
[K+]i = 155 mM) were used
to calculate their Nernst reversal potential of +62.94 mV
(ENa) and
92.34 mV
(Ek), respectively.
By analogy to the Hodgkin-Huxley (HH) model of action potential
electrogenesis (Hodgkin and Huxley 1952), the linear
leakage current was defined as ILeak = gLeak*(V
ELeak), where
gLeak is the leak conductance,
V is the membrane potential, and
ELeak is the reversal potential for
the leak current. ELeak was set at
54.3 mV. The size of the current was adjusted so that its amplitude
corresponds to an input resistance of 300 M
:
gLeak = 0.00014 S/cm2. Values reported for the input resistance
of small DRG neurons range from 62 to 1,574 M
(Caffrey et al.
1992
; Scroggs et al. 1994
; Villiere and
McLachlan 1996
; Xu et al. 1997
). We
measured an input resistance of 289 ± 51 M
(n = 12) in small DRG neurons with potassium as the main intracellular
cation, which is close to the middle of this range.
Voltage-dependent currents
HH-type descriptions (Hodgkin and Huxley 1952) of
the various voltage-dependent currents were used for the simulations.
The time constant and infinity variables for the individual gates (x) in the HH descriptions of the voltage-dependent currents
were determined by the equations:
x = 1/(alphax + betax) and
xinf = alphax/(alphax + betax), where alpha and beta are the forward and
backward rates.
KDR POTASSIUM CURRENT.
The predominant potassium conductance in small DRG neurons is a delayed
rectifier (Safronov et al. 1996). Although other
potassium conductances may be present at lower levels in small DRG
neurons (Gold et al. 1996
; Safronov et al.
1996
; Scroggs et al. 1994
), the full complement
of potassium channels in cells expressing TTX-RP currents is unclear.
Because many small DRG neurons do not appear to express transient
potassium currents (Cardenas et al. 1995
), inward
rectifying potassium currents (Scroggs et al. 1994
), or
hyperpolarization-activated cation currents (Cardenas et al.
1995
) and to keep the model relatively simple, with as few
unconstrained variables as possible, the only potassium channel that
has been introduced into the model is a delayed rectifier potassium
channel (IKDR). The
KDR current was defined as:
IKDR = gKDR*n*(V
Ek), where
gKDR is the delayed rectifier
conductance and n is a dimensionless activation variable
that varies between 0 and 1. The kinetic characterization of the
channel described by Schild et al. (1994)
has been used
with alphan = 0.001265*(
+ 14.273)/{1
exp[(
+ 14.273)/
10]}; betan = 0.125*exp(
+ 55/
2.5); and
ninf = 1/{1+ exp[(
+ 14.62)/
18.38]}.
FAST-INACTIVATING TTX-S SODIUM CURRENT.
The majority of small (<25 µm diam) DRG neurons exhibit both TTX-S
and -R currents (Cummins and Waxman 1997). Although many small DRG neurons express the mRNA for more than one TTX-S sodium channel isoform (Black et al. 1996
), the physiological
signatures and relative levels of expression of different channel
isoforms within DRG neurons have not been determined, and most
patch-clamp studies on DRG neurons have recorded only a single
(presumably composite) TTX-S current (Cummins et al.
1997
; Elliott and Elliott 1993
; Kostyuk
et al. 1981
; Roy and Narahashi 1992
). In
accordance with these experimental results, only one TTX-S current,
which emulates the TTX-S current recorded from DRG neurons by
Cummins and Waxman (1997)
, is used here. We initially
introduced a TTX-S Hodgkin Huxley channel as derived from the squid
giant axon (Hines and Carnevale 1997
) into our model
cell. This simulated fast sodium channel, when combined with
gTTX-RP, produced membrane
oscillations in response to depolarizing stimuli. Since membrane
potential in most DRG neurons is stable and <5% of normal DRG neurons
display subthreshold oscillations (Liu et al. 2000
), we
therefore substituted a TTX-S channel that more closely matched the
TTX-S current recorded (Cummins and Waxman 1997
) from
small DRG neurons. The TTX-S sodium conductance from small DRG neurons
could be fitted to the conventional HH model for sodium conductance:
ITTX-S = gTTX-S
m*m*m*h*(V
ENa), where
gTTX-S is the fast inactivating TTX-S
sodium conductance and m and h are dimensionless
activation and fast inactivation variables that vary between 0 and 1 (Fig. 2B).
TTX-RP SODIUM CURRENT.
For consistency with the TTX-S current, we used a Hodgkin-Huxley model
to describe the persistent TTX-R sodium current. Because of the
limitations of this type of model, it was not possible to obtain a
perfect fit to both the h and the steady-state
inactivation data. Due to rundown and/or ultra-slow inactivation, there
is uncertainty in the experimental measurement of the voltage
dependence of steady-state inactivation. Since we have higher
confidence in our experimental
h data, the
final parameters were chosen such that the
h
(and the midpoint of steady-state inactivation) were closely
replicated. The trade-off is that the slope of steady-state inactivation may not be well described. However, inclusion of the
ultra-slow inactivation gate did not significantly alter the qualitative influences of ITTX-RP on
the behavior of the model neuron, indicating that the model is fairly
robust with regard to steady-state inactivation properties.
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RESULTS |
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Small spinal sensory neurons express a complex array of
voltage-dependent sodium channel mRNAs (Black et al.
1996; Dib-Hajj et al. 1998
). Recently we have
identified a TTX-RP current in small DRG neurons (Cummins et al.
1999
). This distinctive current (Fig.
1A), which is attributable to
NaN sodium channel alpha-subunits, has slow kinetics and, due to an
overlap between the voltage dependence of activation and fast
inactivation, generates persistent current at potentials around
65
mV. The TTX-RP sodium current
(ITTX-RP) is generally found
coexpressed with fast TTX-S sodium currents (Fig. 1B) in
small sensory neurons.
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To examine the functional role of
ITTX-RP, we developed a computer model
of a simplified DRG neuron (Fig. 2). The
model cell was defined with a membrane capacitance of 24.3 pF and an
input resistance of 300 M. The predominant potassium current in
small DRG neurons is a delayed rectifier (Safronov et al.
1996
), and therefore we introduced a delayed rectifier
potassium conductance gKDR into the
simplified DRG cell model. In addition to
gKDR and a leak conductance
(gLeak), the basic model cell for all
simulations also contained a fast TTX-S sodium conductance
(gTTX-S; see following text), which
emulates the experimentally recorded TTX-S sodium current in these
cells. Computer simulations were carried out using this model with and
without the addition of gTTX-RP.
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Model of ITTX-R persistent sodium current
The kinetics of TTX-RP sodium current were characterized by
fitting data obtained with whole cell voltage-clamp recordings (Cummins et al. 1999) from small DRG neurons from
SNS-null mice to a classical Hodgkin and Huxley (1952)
kinetic model. To describe the transient changes in sodium conductance
in squid giant axons, Hodgkin and Huxley (1952)
used a
m3h model, with three particles of activation
(m) and one of inactivation (h). However, TTX-RP
current data from voltage-clamp experiments were not well fit with a
m3h model (Fig. 3,
A, C, and E). The best fit to the
values measured by patch clamp was achieved using a mh model, with only
one activation particle and one inactivation particle (Fig. 3,
B, D, and F). We compared the mh and
m3h fits to TTX-RP currents in SNS-null neurons
elicited by
40- and
20-mV test depolarizations. In 19 of 20 neurons, the root mean square deviation between the fit and the data
(RMS value) was lower for the mh fit than the m3h
fit for the currents elicited by the
40-mV depolarization. For the
currents elicited by the
20-mV depolarization, the RMS value was
lower for the mh fit in 17 of 20 neurons. The RMS value for the mh fit
was 39% smaller at
40 mV (P < 0.001) and 62%
smaller at
20 mV (P < 0.005) than the RMS value for
the m3h fit. We also fit TTX-RP currents elicited
in rat DRG neurons by
40-mV test depolarizations. The RMS value was
lower for the mh fit in 20 of 20 neurons, and the average improvement
over the m3h fit was 47 ± 4%
(P < 0.001). The Hodgkin and Huxley mh fits to TTX-RP
currents recorded from SNS-null neurons were used to estimate
h over the range of
70 to +40 mV
(n = 8; Fig. 2G). The mh fits were also used
to estimate
m over the range of
40 to +40 mV
(n = 8; Fig. 2E). Single exponential fits to
deactivating tail currents, elicited following a 50-ms pulse to
40
mV, were used to estimate
m over the range of
120 to
50 mV (n = 3; Fig. 2E).
Steady-state inactivation (n = 16) and activation
(n = 13) data on the TTX-RP sodium current (Fig.
2C) was obtained from SNS-null neurons as previously
described (Cummins et al. 1999
). The estimated values
for
m and
h,
together with the data on steady-state activation and steady-state
inactivation, were used to determine the forward and backward reaction
rates (
and
; see METHODS) for activation and
inactivation. The TTX-RP currents (ITTX-RP) simulated using these
calculated parameters are shown in Fig.
4A. These simulated currents
are similar to persistent TTX-R sodium currents recorded from SNS-null
DRG neurons (see Fig. 1A). The model value for peak
conductance, gTTX-RPmax, was adjusted
so that it reflects the experimentally measured value of 11 nA for
persistent sodium currents in small rat DRG neurons of 11.05 ± 1.6 nA (n = 64; cell capacitance = 23.9 ± 0.7 pF).
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Model of fast TTX-S sodium current
Although it is probable that many small DRG neurons express more
than one fast TTX-S sodium channel isoform (Black et al. 1996), only one fast TTX-S sodium current
(ITTX-S) is used here. This current
matches the presumably composite TTX-S sodium current that is typically
recorded from small DRG neurons (Cummins and Waxman
1997
; Elliott and Elliott 1993
; Roy and
Narahashi 1992
). TTX-S sodium currents in small DRG neurons
exhibit slow recovery from inactivation (Cummins and Waxman
1997
; Elliott and Elliott 1993
), but previous
models for TTX-S sodium currents do not adequately reproduce this
property. Steady-state activation and inactivation of TTX-S currents
was measured in adult small rat DRG neurons that predominantly
expressed TTX-S sodium currents (n = 6). We used
m3h Hodgkin and Huxley fits to current traces
elicited in these neurons by 50-ms depolarizations to voltages ranging
from
50 to +40 mV to estimate
m and
h (Fig. 2, D and F,
respectively). Recovery from inactivation was measured as previously
described (Cummins et al. 1998
) in eight adult small rat
DRG neurons to estimate
h at potentials from
140 to
60 mV. The estimated values for
m
and
h, together with the data on steady-state
activation and inactivation, were used to determine the forward and
backward rates for activation and inactivation of TTX-S sodium currents (Fig. 2B). As can be seen in Fig. 2, B, D, and
F, there is a good correspondence between the parameters
estimated from TTX-S currents recorded from adult small rat DRG neurons
and those obtained from the TTX-S sodium current model. At
80 mV,
h is 87 ± 9 ms (n = 5)
for TTX-S currents from DRG neurons and
h for
our model TTX-S sodium current is 77 ms. The model value for peak
conductance, gTTX-S-max, was adjusted
so that it reflects the experimentally observed current density
(~1,000 pA/pF) for fast TTX-S sodium currents in small DRG neurons
(Cummins and Waxman 1997
). Figure 4C shows
simulated ITTX-RP and
ITTX-S together, for comparison with
Fig. 1C.
Resting cell properties
ITTX-RP CONTRIBUTES TO RESTING POTENTIAL.
On the basis of the wide overlap between activation and steady-state
inactivation, which brackets resting potential, Cummins at al.
(1999) predicted that the TTX-RP sodium current should contribute to resting potential. To test this hypothesis, we examined resting potential in the simulated cells with and without the addition
of ITTX-RP currents. The baseline for
all simulation experiments is a model cell that contains the three
conductances, gTTX-S,
gKDR, and
gLeak. The resting membrane potential
of this system in its equilibrium state was initially set to
70 mV by adjusting gKDR-max. When
gTTX-RP is added to the model cell at a maximal current density of 453 pA/pF, a depolarizing shift in the
resting potential to
49.1 mV was observed. This depolarizing influence is a result of the sustained opening of persistent TTX-R channels at negative potentials. At
49.1 mV, the steady-state current
in the persistent TTX-R channels is 15.8 pA/pF in the model DRG neuron.
Resting potential depends in a nonlinear manner on the number of available TTX-RP channels
Although the mean amplitude of the
ITTX-RP current in small rat DRG
neurons was ~11 nA, the ITTX-RP
amplitude ranged from 0 to 42 nA (n = 64) and thus can
vary from cell to cell. To further explore the effect of
gTTX-RP on resting potential, we
examined the resting potential of the model cell with different
densities of persistent TTX-R channels. Figure
5A shows that the relationship between resting potential and density of persistent TTX-R channels is
not linear. A 50% reduction in TTX-RP channel density alters the model
cell's resting potential by only 2.5 mV. Looked at another way, 50%
of the TTX-RP conductance contributes 87% of the depolarization seen
at 100% conductance. Even with the TTX-RP current density set at just
20% of the average peak current density measured in DRG neurons (20% × 460 pA/pF = 92 pA/pF), the resting potential of the model cell
was still depolarized by 6.3 mV. As
gTTX-RP approaches the average peak
current density value observed in patch-clamped DRG neurons (460 pA/pF), resting potential approaches an asymptote, so that there is
little further depolarization on additional increase of the
conductance. In the model cell, it appears that the depolarizing shift
in resting potential caused by ITTX-RP
is limited by two factors: ITTX-RP is
persistent in the range where the voltage dependence of steady-state
activation and inactivation overlap, generating window currents, but
inactivates slowly at more depolarized potentials and
IKDR is more strongly activated when
the cell is depolarized beyond 50 mV. Thus the activation of delayed
rectifier potassium currents and the inactivation of
ITTX-RP at potentials positive to
50
mV can limit the depolarizing influence of
ITTX-RP.
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Ultra-slow inactivation gate affects resting potential
As is the case with other voltage-dependent sodium currents, the
TTX-RP sodium current in DRG neurons appears to exhibit ultra-slow inactivation (Cummins et al. 1999). Ultra-slow
inactivation, which can be modeled using an ultra-slow inactivation
gate, has been described in skeletal muscle sodium channels
(Kirsch and Anderson 1986
) and some neuronal channels
(Rudy 1978
; Rush et al. 1998
), and in
several preparations it has been shown to be distinct from fast
inactivation in terms of kinetics and voltage-dependent properties.
Studies on the persistent TTX-R sodium current in DRG neurons
(Cummins et al. 1999) suggest that ultra-slow
inactivation significantly reduces the amplitude of the persistent
TTX-R sodium current in DRG neurons at
60 mV. Therefore we asked
whether an ultra-slow inactivation gate would alter the impact of
gTTX-RP on resting potential of the
model DRG neuron. Because the persistent TTX-R currents in DRG neurons
exhibit time-dependent run-down, ultra-slow inactivation properties of
the current have been difficult to fully characterize. We assumed that
ultra-slow inactivation of ITTX-RP is
similar to that described for other voltage-dependent sodium channels
(Cummins and Sigworth 1996
; Ogata and Tatebayashi 1992
), and the midpoint of steady-state ultra-slow inactivation was initially set at
73 mV. These simulations showed that the presence of an ultra-slow inactivation gate (s gate) diminishes the
amplitude of ITTX-RP at voltages near
resting potential, and the resting membrane potential of the model DRG
neuron equilibrates at a more negative potential of
56.6 mV. The
underlying steady-state ITTX-RP is 8.2 pA/pF. As seen in Fig. 5A, the addition of the s gate to the
gTTX-RP model does not alter the basic
relationship between resting potential and
ITTX-RP current density but rather modulates the asymptotic value for resting potential.
To further examine the possible influence of the s gate on the contribution of gTTX-RP to resting potential, we introduced a variable that parallel shifted the midpoint of steady-state ultra-slow inactivation along the voltage axis (Fig. 5B). As seen in Fig. 5C, the resting potential of the model DRG neuron becomes more negative as the midpoint of steady-state ultra-slow inactivation is shifted in the negative direction. Therefore in theory at least, modulation of the voltage dependence of ultra-slow inactivation of ITTX-RP might be a more effective mechanism for regulating resting potential than altering gTTX-RP channel density.
Active properties
GTTX-RP CONTRIBUTES TO SUBTHRESHOLD
RESPONSES.
The NEURON simulation environment allows the introduction of multiple
"point processes" into the cell. These are idealized current clamp
or voltage-clamp electrodes, which do not have any spatial extension.
By introducing a current-clamp electrode and a voltage-clamp electrode
at the middle position of the cell, the cell can be held at a specific
potential, before applying a current pulse, to observe the response of
the system. Using this technique, we examined the effect of
gTTX-RP on the simulated cells'
responses to sub- and suprathreshold depolarizations. For these
simulations, gTTX-RP with ultra-slow
inactivation (midpoint set at 73 mV) was utilized. We first applied a
10-ms depolarizing stimulus of 500 pA to a cell containing
gTTX-S at its resting potential of
70 mV. This produced a depolarizing response, which peaked at
39.04
mV. We then applied the same stimulus to a cell containing
gTTX-S and
gTTX-RP at its resting potential of
56.6 mV. In this cell, the stimulus resulted in a depolarization that peaked at
28.99 mV (Fig. 6, A and B).
|
ITTX-RP IS THE MAIN SODIUM CURRENT CONTRIBUTING TO THE SUBTHRESHOLD RESPONSE. Figure 6, A and B, indicates that the response to a depolarizing response is larger in a cell that produces both ITTX-RP and ITTX-S, but these results do not differentiate the relative contributions of TTX-RP and -S channels to this enhanced depolarization. To address this issue, we plotted the conductances of the two sodium currents in response to the 500-pA depolarizing stimulus. As seen in Fig. 6, C and D, the primary contribution to the increased conductance associated with the depolarization in a cell with gTTX-S and gTTX-RP is that of gTTX-RP (gmax 234 µmS/cm2), and the TTX-S current contributes only marginally (gmax 41 µmS/cm2) to the conductance increase associated with the enhanced subthreshold depolarization. These findings demonstrate that, during the subthreshold depolarization, gTTX-RP is much larger than gTTX-S and indicate that ITTX-RP can act as an amplifier of subthreshold depolarizations.
GTTX-RP DOES NOT CONTRIBUTE
SUBSTANTIALLY TO INWARD CURRENT FLOW DURING THE RISING PHASE OF THE
ACTION POTENTIAL.
To examine the effect of gTTX-RP on
cell excitability, we first compared thresholds to depolarizing stimuli
in cells containing gTTX-S with a
resting potential of 70 mV and cells containing gTTX-S and
gTTX-RP with a resting potential of
56.6 mV. Using 2-ms stimuli in 10-pA increments, we observed graded
responses with a higher threshold for generation of overshooting action potentials in a cell containing gTTX-S
and gTTX-RP with a resting potential
of
56.6 mV (840 pA) compared with a cell containing gTTX-S with a resting potential of
70 mV (800 pA) that displayed an all or none behavior. In response to
a 1,500-pA current injection, action potential overshoot in a cell
containing gTTX-S and
gTTX-RP with a resting potential of
56.6 mV was smaller (21.4 mV) than in a cell containing
gTTX-S with a resting potential of
70 mV (45.4 mV), and a depolarizing afterpotential was present in the cell containing gTTX-RP (Fig.
7, A and B,
top).
|
Presence of gTTX-RP does not induce repetitive firing in response to sustained depolarizing stimuli
The response of cells with and without gTTX-RP to sustained (30 ms) depolarization is shown in Fig. 8. Neither cell with gTTX-RP nor without gTTX-RP fired repetitively in response to these long-lasting stimuli (Fig. 8). We were unable to evoke repetitive firing even when stimulation amplitudes were increased to 5,000 pA (not shown). Thus the addition of gTTX-RP to a cell containing gTTX-S does not, in itself, support repetitive firing in response to sustained depolarizing stimuli.
|
Anode break responses
Caffrey et al. (1992) observed anode break
excitation, i.e., rebound excitation occurring on termination of
hyperpolarizing pulses, in small DRG neurons. Although our model did
not include an A current or inward rectification, we reasoned that as a
result of its depolarized hinf curve,
gTTX-RP might contribute to anode break electrogenesis. We thus attempted to elicit anode break excitation in the model neurons with and without
gTTX-RP. Figure 9A shows the response of a
cell with only gTTX-S to 50-ms
hyperpolarizing current injections of
120,
160, and
200 pA,
respectively. After the end of the pulses, the membrane potential
passively returns to its equilibrium potential at
70 mV without any
overshooting depolarization. In Fig. 9B, the same
hyperpolarizing pulses were applied as before, but the model cell also
contained gTTX-RP. The small stimulus
(
120 pA) hyperpolarizes the cell only to
86.2 mV, compared with
90.7 mV in the simulation without
gTTX-RP. Following termination of the
hyperpolarizing pulse, there is a rebound depolarization to
25.5 mV,
after which the cell gradually passively repolarizes toward its
equilibrium resting potential. Release from a stronger hyperpolarizing
pulse (
160 pA) evokes a longer rebound depolarization, so that the
firing threshold is reached at about
25 mV, and an action potential
with overshoot is generated. After this short 3-ms action potential,
the cell returns gradually to its resting potential. An even faster and larger anode break spike which peaks close to 32 mV is evoked at the
end of a
200-pA hyperpolarizing pulse (Fig. 9B), which did
not elicit any response in the model cell with only
gTTX-S (Fig. 9A).
|
Although anode break excitation was seen in model cells containing
ITTX-RP and
ITTX-S, it is critically dependent on
the presence of the TTX-S channels. The fast spikes that were evoked by
the last two pulses could be suppressed by taking the fast TTX-S
current out of the model cell, mimicking the effect of TTX addition to the bath solution in physiological experiments (Fig. 9C)
(Caffrey et al. 1992). Despite the absence of the fast
spike in the model cell without
gTTX-S, the model cell containing
gTTX-RP still responded at the end of
hyperpolarizing pulses by depolarizing to
26.2 mV. Although action
potentials are not generated, the recovery from depolarization after
the pulse was similar to that observed when the cell contained both
gTTX-RP and
gTTX-S, and membrane potential
returned with a similar time course to resting potential. The effect of
blocking ITTX-S on rebound excitation
in the model cell is similar to the experimentally observed effect of
TTX on anode break excitation in small rat DRG neurons described by
Caffrey et al. (1992)
.
Time course of rebound excitation parallels recovery of gTTX-RP
TTX-RP channels are known (Cummins et al. 1999) to
recover gradually from ultra-slow inactivation. We therefore expected
that anode-break excitation might be time dependent. To test this
hypothesis, the anode break response was also examined in simulations
employing
200-pA hyperpolarizing pulses of different duration. In
these simulations, another interesting effect of addition of
gTTX-RP was observed (Fig.
10). In the simulations with
gTTX-RP in the model cell, increasing
duration of the
200-pA pulses causes the anode break response to
evolve from an initially subthreshold depolarization (5- and 15-ms
hyperpolarizing pulses), into one that triggers a rebound overshooting
action potential (following hyperpolarizing pulses of 25, 35, and 45 ms). The time course of the development of anode break excitation is
similar to that for recovery of
ITTX-RP from inactivation
(Cummins et al. 1999
).
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DISCUSSION |
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Small DRG neurons are unique in expressing a persistent TTX-R
sodium current (Cummins et al. 1999). Our simulations
utilized the NEURON program and incorporated data on voltage dependence and rate constants for activation and inactivation, which were derived
from patch-clamp studies on the TTX-R sodium current in these neurons
(Cummins et al. 1999
; Dib-Hajj et al.
1999
). Although single channel recordings from the persistent
TTX-R channel in DRG neurons are not available, we used the available
data from whole cell patch clamp and matched the peak conductance of
the persistent TTX-R current in the model to experimentally observed values. We modeled the time constants of activation and inactivation of
ITTX-RP by fitting experimental data
(Cummins et al. 1999
) to a classical HH model to
determine
m and
h. In
our simplified model, we lumped all TTX-S currents into a single
current that matches the experimentally observed (presumably composite)
TTX-S current in these cells (Cummins and Waxman 1997
).
Like all simulations, our modeling depends on a number of assumptions
about channel densities, kinetics, and voltage dependence of the
conductances within the modeled neuron. Because we were interested in
the simple question, how does the expression of persistent TTX-R
current alter the behavior of a neuron, and because we did not want to
introduce other unconstrained variables, we did not attempt to model
calcium currents or the slowly inactivating TTX-R sodium current
produced by SNS (NaV1.8) channels. The persistent TTX-R sodium current that we modeled here has very different properties from the current produced by SNS. Schild and Kunze
(1997) have suggested that the slowly inactivating
TTX-R sodium currents in nodose neurons may modulate action potential
waveshapes of sensory neurons, but because of their different
characteristics, these two distinct currents are likely to play
different roles in electrogenesis. Because there is uncertainty about
the potassium conductances in these cells (Cardenas et al.
1995
; Gold et al. 1996
; Safronov et al.
1996
; Scroggs et al. 1994
), we also included a
single relatively well-defined potassium conductance in our model. We
could have inserted additional conductances, but this would have
introduced additional unconstrained variables and we wanted to limit
them. Despite the limitations inherent in this and all computer models, we believe the present results provide important qualitative
predictions about the effects of persistent TTX-R sodium current in DRG
neuron physiology.
Hodgkin and Huxley (1952) found a best fit when m was
raised to the third power (m3h) in their model of
sodium currents in the squid giant axon. In contrast, we found a best
fit for a single activation particle (mh) for the TTX-RP current. As
seen in Fig. 3, mh provided a better fit for both activation and
inactivation. Although our use of the mh model may seem at variance
with traditional approaches, it is notable that in a study on gating
properties of sodium channels in DRG neurons, Ogata and
Tatebayashi (1993)
found that TTX-R currents were fit by a mh
model. A number of other studies also revealed deviation from the
classical m3h model. For example, in a
patch-clamp study of nodes of Ranvier from rabbit sciatic nerve,
Chiu et al. (1979)
found that sodium currents were best
fit to m2h kinetics, whereas frog nodal sodium
currents were fit by m3h kinetics.
Sontheimer and Waxman (1992)
found that sodium currents in stellate spinal cord astrocytes were best fit by a
m4h model, while the currents from pancake
astrocytes were best fit by a m3h model. Although
the molecular substrate for these differences has not been delineated,
it is interesting that the amino acid sequence for rat NaN includes
fewer charged residues within the S4 segments of DII and DIII, compared
with fast sodium channels (Dib-Hajj et al. 1998
). This
observation, together with the strikingly different kinetics and
voltage-dependent properties of the persistent TTX-R channel
(Cummins et al. 1999
), suggests that its gating may
involve mechanisms that are different from those of traditional, transient sodium channels.
We included a component of ultra-slow inactivation to reflect the
experimental observations. Consistent with patch-clamp results which
suggest that ~95% of ITTX-RP is
inactivated at a resting potential of 60 mV (Cummins et al.
1999
), we observed a downward shift in the curve relating
membrane potential to gTTX-RP when ultra-slow inactivation was included compared with the curve without ultra-slow inactivation. The introduction of ultra-slow inactivation produced a reduction in the depolarizing effect of
ITTX-RP similar to the reduction in
depolarizing effect that is produced by a >90% decrease in density of
TTX-R persistent channels. We found that irrespective of whether slow
inactivation was included, the presence of
gTTX-RP produced a significant (>10
mV) depolarizing shift in resting potential. This depolarizing
contribution to resting potential was present without, and with,
ultra-slow inactivation (although the magnitude of the shift was
reduced by ~30%, when ultra-slow inactivation was included). The
steady-state TTX-R current that maintained this depolarization in the
model neuron was small, being only 9.21 pA/pF. The relatively large
depolarizing effect of ITTX-RP, even
when ultra-slow inactivation was included, reflects the nonlinear
relationship between resting potential and density of persistent TTX-R
channels (Fig. 5A) and, as suggested by Cummins et
al. (1999)
, may have a functional advantage, in that a large
number of channels with a low open probability might produce a small
yet more consistent current (and hence a more stable membrane
potential) than a smaller number of channels with a higher open probability.
Our observation that ITTX-RP has a
significant effect on resting potential confirms prior results, which
demonstrated that in optic nerve axons, a persistent sodium conductance
contributes to resting potential, which shifts by ~5% in a
hyperpolarizing direction when the persistent current is blocked
(Stys et al. 1993). An effect of
ITTX-RP on resting potential, even
with ultra-slow inactivation, is consistent with the idea that because
there are so few channels of any kind that are active near resting
potential, even small persistent currents can have a significant effect
on resting potential (Crill 1996
). We cannot exclude the
possibility that Na+ influx via persistent
channels leads to an increase in activity of
Na+/K+-ATPase that in turn
exerts a hyperpolarizing influence (Stys et al. 1993
);
consistent with this latter suggestion,
Na+/K+ATPase has been
shown to contribute to activity-dependent hyperpolarization in the
axons of DRG neurons (Bostock and Grafe 1985
) and in
optic nerve axons (Gordon et al. 1990
). A number of
studies (Ritchie and Straub 1957
; Serra et al.
1999
) suggest that
Na+/K+-ATPase activity can
produce a hyperpolarization, even after single action potentials, in C
fibers, and this hyperpolarization would be expected to partially
relieve the resting inactivation of
gTTX-RP. The distribution of NaN
channels along the trunks of C fibers (Fjell et al.
2000
) (where the larger surface:volume ratio would favor an
increase in intracellular Na+ concentrations) is
consistent with such a role.
Although definitive data on resting potential in various subclasses of
DRG neurons are not yet available, it is interesting that using sharp
microelectrodes Caffrey et al. (1992) found a more
depolarized resting potential (
51.3 ± 13.6 mV) in small (<30
µm diam) DRG neurons compared with large cells (>50 µm;
68.4 ± 6.6 mV). This may provide a possible correlate for the
selective pattern of expression of NaN, which is present in small DRG
neurons, but not in larger cells (Dib-Hajj et al. 1998
;
Fjell et al. 1999
). We found that when we modeled the
TTX-S sodium current that is recorded (Cummins and Waxman
1997
) in small DRG neurons and included it in our model,
resting potential was stable. This matches the experimental finding
(Liu et al. 2000
) that membrane potential in ~95% of
normal DRG neurons is stable. However, when the model incorporated a
different TTX-sensitive fast sodium channel, derived from the squid
giant axon (Hines and Carnevale 1997
), we observed oscillations in membrane potential.
Sodium-dependent potential oscillations have been observed in
demyelinated dorsal column axons (Kapoor et al. 1997)
and in axotomized DRG neurons (Liu et al. 2000
) and may
contribute to inappropriate spontaneous firing that is associated with
neuropathic pain. Changes in the expression of mRNA and protein for
TTX-S sodium channels with the expression of previously unexpressed channels (Black et al. 1999
; Dib-Hajj et al.
1996
; Waxman et al. 1994
), accompanied by
changes in TTX-S sodium currents (Black et al. 1999
;
Cummins and Waxman 1997
) have been observed in
axotomized DRG neurons. Because the inappropriately expressed sodium
channels, and their currents, have not been fully characterized in
axotomized neurons, we did not attempt to model them in the present
study. Our results suggest that the expression of appropriate mixtures of sodium channels within normal DRG neurons results in
stable resting potential. Our results do not, however, rule out the
possibility that dysregulation of sodium channel expression following
axonal injury, with the deployment of inappropriate mixtures of sodium channels, may lead to membrane instability and inappropriate
spontaneous activity.
Activation of sodium channels at potentials that are subthreshold for
spike electrogenesis has been shown to amplify depolarizing inputs,
such as excitatory synaptic inputs, in a number of types of neurons
(Lipowsky et al. 1996; Llinas and Sugimori
1980
; Parri and Crunelli 1998
; Schwindt
and Crill 1995
; Stafstrom et al. 1984
; Stuart and Sakmann 1995
). Our observations indicate that
ITTX-RP can amplify the response to
subthreshold depolarizing inputs. Although the contribution of
different sodium channel subtypes to the sodium current produced at the
sensory terminals of DRG neurons has not been studied, the available
immunocytochemical evidence suggests that TTX-RP channels may be
deployed close to, or at, sensory terminals of some spinal sensory
neurons (Coward et al. 2000
; Fjell et al.
2000
). Such a localization, close to the trigger zone for spike
initiation within sensory neurons, would poise the persistent TTX-R
sodium channels to amplify generator potentials.
We observed a higher threshold for action potential generation in cells
containing gTTX-RP, a difference that
could be accounted for the depolarizing shift in the resting potential,
which would tend to inactivate TTX-S sodium channels in these cells.
Although a higher threshold in cells that contain an additional sodium channel may at first sight seem surprising, this result is consistent with molecular biological and patch clamp observations (Dib-Hajj et al. 1998; Sleeper et al. 2000
), which
demonstrated a downregulation of NaN sodium currents and persistent
sodium currents in axotomized DRG neurons. Because the steady-state
inactivation curve of the TTX-S sodium current in small DRG cells is
relatively hyperpolarized, there may be a significant subpopulation of
inactivated TTX-S channels at rest and the degree of inactivation
should be sensitive to small shifts in potential close to resting
potential (Caffrey et al. 1992
). The present results
support the suggestion (Cummins and Waxman 1997
) that
reduction in persistent sodium currents might result in a
hyperpolarizing shift in resting potential that could remove
inactivation from TTX-S channels, thus contributing to the
hyperexcitability that is seen in these cells following axotomy.
In summary, the present results suggest that although the persistent TTX-R sodium current in small DRG neurons does not contribute substantially to inward current flow during the steep rising phase of the action potential, it contributes a depolarizing influence to resting potential and amplifies subthreshold inputs. We thus predict that the persistent TTX-R channels play a role in shaping the electroresponsiveness of these cells. Once knockout mice or specific blockers for the TTX-RP current are available, these results based on simulations in a model neuron can be tested in a physiological milieu in situ.
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ACKNOWLEDGMENTS |
---|
R. I. Herzog was an Eastern Paralyzed Veterans Association (EPVA) Spinal Cord Research Fellow.
This work was supported in part by grants from the National Multiple Sclerosis Society, and from the Rehabilitation Research Service and Medical Research Service, Department of Veterans Affairs. We also thank the EPVA and the Paralyzed Veterans of America for support.
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FOOTNOTES |
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Address for reprint requests: S. G. Waxman, Dept. of Neurology LCI 707, Yale School of Medicine, 333 Cedar St., New Haven, CT 06510 (E-mail: stephen.waxman{at}yale.edu).
Received 5 December 2000; accepted in final form 15 May 2001.
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REFERENCES |
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