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The Journal of Neuroscience, February 1, 2001, 21(3):1022-1032
Dynamics of Low-Threshold Spike Activation in Relay Neurons of
the Cat Lateral Geniculate Nucleus
Carolina
Gutierrez1,
Charles L.
Cox1,
John
Rinzel2, and
S. Murray
Sherman1
1 Department of Neurobiology, State University of New
York, Stony Brook, New York 11794-5230, and 2 Center for
Neural Science and Courant Institute of Mathematical Sciences, New York
University, New York, New York 10003
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ABSTRACT |
The low-threshold spike (LTS), generated by the transient
Ca2+ current IT,
plays a pivotal role in thalamic relay cell responsiveness and thus in
the nature of the thalamic relay. By injecting depolarizing current
ramps at various rates to manipulate the slope of membrane
depolarization (dV/dt), we found that an LTS occurred only if dV/dt exceeded a
minimum value of ~5-12 mV/sec. We injected current ramps of variable
dV/dt into relay cells that were
sufficiently hyperpolarized to de-inactivate
IT completely. Higher values of
dV/dt activated an LTS. However, lower
values of dV/dt eventually led to tonic
firing without ever activating an LTS; apparently, the inactivation of
IT proceeded before
IT could be recruited. Because the
maximum rate of rise of the LTS decreased with slower activating ramps
of injected current, we conclude that slower ramps allow increasing
inactivation of IT before the
threshold for its activation gating is reached, and when the injected
ramps have a sufficiently low dV/dt, the
inactivation is severe enough to prevent activation of an LTS. In the
presence of Cs+, we found that even the lowest
dV/dt that we applied led to LTS activation, apparently because Cs+ reduced the
K+ "leak" conductance and increased neuronal
input resistance. Nonetheless, under normal conditions, our data
suggest that there is neither significant window current (related to
the overlap of the inactivation and activation curves for
IT), rhythmogenic properties, nor
bistability properties for these neurons. Our theoretical results using
a minimal model of LTS excitability in these neurons are consistent with the experimental observations and support our conclusions. We
suggest that inputs activating very slow EPSPs (i.e., via metabotropic receptors) may be able to inactivate
IT without generating sizable IT and a spurious burst of action
potentials to cortex.
Key words:
low-threshold spike; thalamus; burst firing; T channel; window current; lateral geniculate nucleus
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INTRODUCTION |
The voltage-dependent,
low-threshold, transient Ca2+ current,
known as IT, is a ubiquitous property
found in all thalamic relay cells of all thalamic nuclei in all
mammalian species tested to date (Deschênes et al., 1984 ; Jahnsen
and Llinás, 1984a,b; Crunelli et al., 1989; Bal et al., 1995).
The status of IT is controlled by a
complex combination of voltage and time (Jahnsen and Llinás, 1984a,b; Zhan et al., 1999). IT is
inactivated when the membrane is maintained at a level more depolarized
than approximately  60 to 65 mV for 50-100 msec. This inactivation
is removed (i.e., IT is de-inactivated) by
sustaining a hyperpolarization more than approximately 65 to 70 mV
for 50-100 msec. If IT is inactivated when the cell is sufficiently depolarized, such as by a large EPSP, the cell responds with a stream of unitary action
potentials that characterizes tonic firing. If, instead,
IT is de-inactivated when a large
transient EPSP is evoked, then IT is
recruited, producing a large, transient
Ca2+ depolarization known as the
low-threshold spike (LTS). A high-frequency cluster of several action
potentials usually rides the crest of the LTS, and this characterizes
burst firing. Both tonic and burst firing are effective
relay modes during normal waking behavior (Guido and Weyand, 1995; Lenz
et al., 1998; Radhakrishnan et al., 1999; Ramcharan et al., 2000), and
the two modes represent different forms of transmission of information
to cortex (Sherman, 1996; Reinagel et al., 1999).
IT is thus an important property of
thalamic functioning that needs to be better understood.
One unresolved issue is whether a minimum rate of membrane
depolarization is required to activate an LTS. The activation and inactivation curves for IT overlap across
a limited range of membrane potentials, and it has been suggested that
when the membrane potential of a cell is within this range,
IT is generated in a sustained manner,
producing a "window current" (Coulter et al., 1989). A sizable
IT window current can underlie resonant or
rhythmogenic behavior in thalamic and other neurons and models (Puil
and Carlen, 1984; Wang et al., 1991). It can also lead to an N-shaped
steady-state current-voltage relation that, in turn, can lead to
"bistability" (Williams et al., 1997; Hughes et al., 1999). That
is, for some range of input current (between the "knees" of
the N) the membrane potential of the cell will sit stably on the
right or left "leg" of the N but not on the middle "leg." The
presence of a window current argues that there is no minimum rate of
depolarization that must be exceeded to generate
IT. However, it was reported recently that
very low frequencies of sinusoidal current injection failed to activate
an LTS, whereas higher (but not too high) frequencies of the same
amplitude reliably activated an LTS (Smith et al., 2000). This suggests
that a minimum rate of depolarization must be exceeded to generate
IT.
To resolve this question, we studied LTS activation (and indirectly
IT generation) in thalamic relay cells via
intracellular injection of current ramps that varied in their rate of
depolarization. We found that, under normal circumstances, the rate of
rise of the evoked voltage must exceed a minimum value to activate an LTS, and this has implications also for the presence of an
IT window current, rhythmogenesis, and bistability.
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MATERIALS AND METHODS |
General methodology. General methods for tissue
preparation were similar to those used routinely in our laboratory (Cox
et al., 1998). Briefly, cats (4-8 weeks old) were deeply anesthetized with an intramuscular injection of ketamine (25 mg/kg) and xylazine (1 mg/kg). A craniotomy was made overlying the thalamus, and a block of
tissue containing the lateral geniculate nucleus was removed and placed
in a cold oxygenated solution containing (in mM): 2.5 KCl,
1.25 NaH2PO4, 10.0 MgCl2, 26.0 NaHCO3, 11.0 glucose, and 234.0 sucrose. The tissue block was then sliced into
400-µm-thick sections in either the coronal or sagittal plane. The
slices were placed in a holding chamber with artificial CSF (ACSF)
containing (in mM): 126.0 NaCl, 2.5 KCl, 1.25 NaH2PO4, 2.0 MgCl2, 2.0 CaCl2, 26.0 NaHCO3, and 10.0 glucose; slices were gassed with
95% O2 and 5% CO2 to a
final pH of 7.4. After incubation for at least 2 hr, individual slices
were transferred to an interface-style recording chamber that was
maintained at 32 ± 1°C and through which ACSF continually
flowed at a rate of 1-1.5 ml/min.
Intracellular recordings were obtained from relay cells from the
lateral geniculate nucleus by use of the whole-cell configuration. Recording pipettes had a tip resistance of 4-8 M when filled with
the following intracellular solution (in mM): 117 K-gluconate, 13 KCl, 1.0 MgCl2, 0.07 CaCl2, 0.1 EGTA, and 10.0 HEPES. Current-clamp recordings were made with an Axoclamp 2A amplifier (Axon Instruments, Foster City, CA), and the bridge was continually monitored and adjusted
to compensate for membrane potential changes caused by the passage of
current through the recording electrode throughout each experiment.
Data were digitized and stored on an IBM-compatible computer and
videotape for off-line analyses. A 10 mV correction for the junction
potential was applied to the membrane potential of all cells during
data analysis (Hagiwara and Ohmori, 1982).
The model. Our experimental observations (see Results) (Zhan
et al., 1999) demonstrated that the basic response properties of
Ca2+ spikes were similar in the presence
or absence of TTX (Jahnsen and Llinás, 1984a,b;
Hernández-Cruz and Pape, 1989). Thus, as before (Zhan et al.,
1999), we use a minimal Hodgkin-Huxley type of model that neglects the
primary currents involved in generating and shaping action potentials.
Our model includes those currents that we believe capture the essence
of our observed activation of Ca2+ spikes.
The current balance equation is:
where IT is the "T-type"
low-threshold Ca2+ current,
IA is a transient
K+ current,
Ih is the hyperpolarization-activated
"sag" current, the leakage components
(IK-leak and
INa-leak) are ohmic,
Iapp represents any current injected
into the cell, V is membrane potential (in millivolts),
t is time (in milliseconds), and C is total
capacitance, equal to 290 pF, corresponding to a cell model with a
surface membrane area of 29,000 µm2. We
used the formulations for IT,
IA, and Ih
found in the computer program Cclamp of Huguenard and McCormick (1994)
and based on their previous voltage-clamp data (summarized in McCormick
and Huguenard, 1992). The model uses the Goldman-Hodgkin-Katz
formulation for IT as:
where PT is the maximum
permeability of an open channel (30 cm3/sec); z = 2;
Caint and Caext are the
concentrations of Ca2+ inside and outside
the cell, respectively (assumed fixed in our model at 50 nM and 2 mM, respectively);
and F, R, and T are Faraday's constant, the gas constant, and absolute temperature, respectively (Hille, 1992). The transient K+ current is
given by:
with the reversal potential VK = 105 mV and gA = 2 µS unless stated
otherwise. The sag current is given by:
with the reversal potential
Vh = 40 mV. As noted in Results, the
conductance gh was quite small (<1 nS)
for the relay cells of the cat's lateral geniculate nucleus under
study here. The leakage currents are given by:
and:
where gNa-leak = 2.65 nS,
gK-leak = 7 nS, and
VNa = 45 mV. The general form for the
gating dynamics of the voltage-gated channels is:
where x = mT,
hT, mA,
hA, or r with:
The specific parameter values (in millivolts) are:
and
and the "time-constant" functions are:
and:
We adjusted the gating rates to 33.5°C from Cclamp's set
condition of 23.5°C by using a temperature correction factor,  , of 3.
All computed results shown here were obtained with the above minimal
model by use of the software XPPAUT (found at
http://www.pitt. edu/~phase/). For numerical integration we used
the fourth-order, adaptive-step Runge-Kutta method in XPPAUT (with
error tolerance, 10 5).
Computations were performed on a Linux/Unix Pentium II workstation.
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RESULTS |
Experimental observations
We recorded from 33 neurons of the cat's lateral geniculate
nucleus. All of these neurons exhibited overshooting action potentials; their resting membrane potentials were 63 ± 7.1 mV (here and below, this refers to the mean ± SD), and their input resistances were 105 ± 32.5 M. On the basis of electrophysiological
criteria, including the presence of LTSs and relatively small
depolarizing sag responses (see below) to hyperpolarizing pulses, these
were all deemed to be relay cells. For further confirmation of relay cell recordings, five of the neurons were filled with biocytin and
after the recording were visualized after histological processing. All
five cells exhibited the characteristic morphology of relay cells
rather than interneurons (Guillery, 1966; Friedlander et al., 1981). Of
the overall sample of 33 cells, 13 were studied strictly as controls
(i.e., without additional drugs), 1 was studied also in the
presence of TTX, and the remaining 6 were studied also in the
presence of Cs+.
Effect of rate of depolarization on activation of
low-threshold spikes
Activation of LTSs in geniculate relay cells can readily be
accomplished by depolarizing the neuron after it has been sufficiently hyperpolarized to de-inactivate IT. Here,
we were especially interested in activating
IT and the LTS with current injected to
depolarize the cell at various rates. To do this, we used depolarizing
current ramps for which we varied the rate of rise of the ramp (or
dV/dt) while keeping the initial and final
depolarization constant. In other words, the final amplitude of current
injected was kept constant, but the duration of the ramp was varied
between 0.8 and 20 sec. To ensure full de-inactivation of
IT, the geniculate neurons were
hyperpolarized to membrane potentials more hyperpolarized than 80 mV
before the application of current ramps. These ramps depolarized the
cells sufficiently to pass through the zone of IT activation and, with rare exceptions,
continued to depolarize the cells sufficiently to evoke tonic firing in
the absence of TTX.
Figure 1 shows a typical experiment
performed in a geniculate relay cell before TTX application. Four
current ramps were injected into the cell, with
dV/dt decreasing from top to
bottom (i.e., Fig. 1, from A to D).
Note that in all cases, tonic firing was eventually evoked when the
depolarizing ramp reached the threshold for action potentials. However,
LTSs were evoked only from the faster ramps (Fig.
1A,B) and not from the slower ones (Fig.
1C,D). Furthermore, there is not even a hint that the slower
ramps activate any IT in the voltage
region in which LTSs are evoked from faster ramps. That is, there is no
discernable "bump" indicative of a subthreshold LTS (but see
below). Thus, with a sufficiently low dV/dt, the firing mode of this cell was
switched from burst to tonic without activating a burst. In other
words, it is possible with a sufficiently low value of
dV/dt to start with completely de-inactivated IT and then to proceed to
inactivate IT without ever activating an
LTS. This failure to evoke LTSs and thus
IT from sufficiently low depolarizing
values of dV/dt was seen in every one of
the 33 relay cells we studied. All 33 cells showed a fairly sharp and
repeatable threshold for the minimum dV/dt needed to activate an LTS in individual cells, and the mean ± SD
of the threshold dV/dt was 9.1 ± 3.5 mV/sec. We found no correlation between the threshold
dV/dt and neuronal input resistance
(p > 0.1). Each of the following figures
illustrates this in a different geniculate relay cell to emphasize the
generality of this observation.
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Figure 1.
Responses of a geniculate cell (top
trace of each panel) to injected current
ramps (bottom trace of each
panel). The vertical dashed line shows
the beginning of each ramp, which culminated in 650 nA of injected
current. The initial holding potential in each case was 80 mV
(indicated by the horizontal dotted line), and each
response ended with tonic firing. A-D, Series of ramps
of increasing duration and thus decreasing
dV/dt. The faster ramps of
A and B activated LTSs and associated
bursts of action potentials, whereas the slower ramps of
C and D failed to activate LTSs.
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To analyze quantitatively the voltage response to the current ramps,
three different measurements were calculated: the slope of
depolarization (dV/dt), the maximum rate
of rise of the LTS, and LTS threshold. Because measurements of the
maximum rate of rise of the LTS might be compromised by the presence of
action potentials, these measurements were limited to the 14 cells
studied in the presence of TTX. The measures of
dV/dt and LTS threshold were made on all cells.
Figure 2 illustrates how these measures
were made in a cell studied in the presence of TTX. First, we obtained
the voltage response of the cell to the injected current ramp (Fig.
2A) and temporally differentiated it (Fig.
2B). In the differentiated trace, a baseline voltage
was established in the region before onset of the current ramp (Fig. 2,
between vertical lines 1 and 2, with line
2 marking the beginning of the current ramp). The upper and lower
confidence limits encompassing 95% of all data points in the baseline
region were then calculated. We defined LTS threshold in all cells as
the first of at least five consecutive voltage points sampled at 200 Hz
(for the illustrated cell, sampling ranged between 200 and 400 Hz) for
which the differentiated trace exceeded the upper confidence limit
(Fig. 2, vertical line 3). The
dV/dt was calculated from a linear
regression of the voltage response between vertical lines 2 and 3 in Figure 2A. The correlation coefficients of the regression lines ranged between 0.97 and 0.99, indicating that the voltage response during this time was quite linear.
Finally, the maximum rate of rise of the LTS was determined from the
differentiated trace (Fig. 2B, arrow).
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Figure 2.
Determination of LTS threshold, LTS amplitude, and
dV/dt. A, Voltage response (top
trace) to injection of current ramp (bottom
trace) to a cell in the presence of TTX. B,
Differentiated voltage trace in A. The region bounded by
lines 1 and 2 indicates the baseline
response (in which no current was passed) and in which the upper 95%
confidence limit was determined (see text for details). The LTS
threshold was determined by extrapolating this confidence limit to the
point at which 5 consecutive bins in the differentiated trace exceeded
it. This point, indicated by line 3, provides the
estimate of the LTS threshold. The slope
(dV/dt) of the voltage response
was then measured from the onset of the current injection (line
2) to the LTS threshold (line 3). Finally, the
amplitude of the LTS was made by subtracting the voltage at the peak of
the LTS by the voltage of the extrapolated gray line
under the peak (arrows in A).
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Figure 3, A and B,
shows the responses evoked from current ramps of differing
dV/dt values in another geniculate relay
cell before and after TTX application. Both with and without TTX, ramps with a faster dV/dt activated
low-threshold spikes (Fig. 3A,B, top three
traces), whereas those with a slower
dV/dt did not (Fig. 3A,B,
bottom two traces). Note that occasionally more than one LTS
was evoked (Fig. 3A, second trace from
top); we saw evidence of double and triple LTSs in 12 of the
33 cells studied.
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Figure 3.
Voltage responses to ramps of injected current
before and during TTX application. Conventions are as described in
Figure 1. A, Responses before TTX application. Faster
ramps (top 3 traces) activate LTSs, but slower ramps
(lower 2 traces) do not. B, Responses
during TTX application. Faster ramps (top 3 traces)
activate LTSs, but slower ramps (lower 2 traces) do not.
C, Relationship between LTS amplitude and depolarizing
slope for data in B. D, E, Relationship
between LTS amplitude and depolarizing slope for two other geniculate
cells. Max, Maximum.
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Figure 3C plots, for the cell illustrated in Figure 3,
A and B, the relationship between the maximum
rate of rise of the LTS (measured in the presence of TTX) and the
dV/dt resulting from the injected current
ramp. Figure 3, D and E, plots the same
relationship for two other geniculate relay cells. In each of these
examples, there is a significant positive correlation between the
dV/dt of the ramp and the maximum rate of
rise of the LTS. Overall, the relationships shown in Figure
3C-E were representative of the 14 cells studied in this
manner in the presence of TTX; of these, 12 had a highly significant
correlation (p < 0.001 or p < 0.01), 1 had a relationship that was close to significance (0.1 > p > 0.05), and only 1 had a relationship that was
clearly insignificant (p > 0.1). A lower value
for the maximum rate of rise of the LTS indicates that there is more
inactivation of IT, and the correlation of
this with dV/dt suggests that slower
values of dV/dt produce more inactivation
of IT before activation of an LTS. We thus
conclude that the reason that even lower values of
dV/dt fail to activate an LTS is because
these permit enough IT inactivation to
leave an insufficient number of de-inactivated T channels to support an LTS.
We noticed that the transition from a
dV/dt that was subthreshold for activating
an LTS to a suprathreshold one was not only sharp but in most cases the
LTS varied little in amplitude after being activated (see Zhan et al.,
1999). We found such an activation of the LTS in response to ramps in
21 of the 33 cells (see also Fig.
4A). In the remaining
12 cells, the LTS amplitude appeared to be graded over a narrow range
of dV/dt values near threshold (see Fig.
4B). However, although not illustrated here, partial LTSs such as those illustrated in Figure 4B were not
reliably evoked, because repeated trials with the same
dV/dt might evoke no partial LTS at all,
and this is in contrast to the extremely reliable full-blown LTSs
activated at greater dV/dt values.
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Figure 4.
Responses of two different geniculate cells in TTX
to injected ramps producing slower
dV/dt values from
left to right. A, Cell
showing all-or-none LTS to faster ramps (6 traces on the
left) and no LTS to slower ones. B, Cell
showing a partial LTS (4th trace from
left) as a transition between all-or-none LTSs (3
traces on the left) and no discernable LTS
(6 traces on the right).
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Thresholds for low-threshold spikes
Figure 5A shows another
example of a geniculate relay cell with LTSs being activated only by
ramps with higher values of dV/dt. In this
example, the threshold for activating the low-threshold spike (Fig.
5A, arrows; see also Fig. 2) is remarkably
constant (ranging <5 mV) despite the varying
dV/dt values of the ramps. Among all cells
observed (n = 22), the LTS thresholds varied <10 mV.
For this same cell, Figure 5B shows the scatter plot of
dV/dt versus voltage threshold for
activation of the low-threshold spike, and Figure 5, C and
D, shows this relationship for two other geniculate relay
cells. The LTS thresholds for the cells in Figure 5, B and C, appeared to be independent of the slope of the
depolarization. This observation was true for 18 of 22 cells. For the
remaining four cells, there was a significant negative correlation
between dV/dt and LTS threshold (e.g.,
Fig. 5D). Why only some cells showed such a correlation is
unclear, but it is worth emphasizing that, in any given cell, the range
of voltage thresholds was quite small.
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Figure 5.
Reliability of LTS thresholds with different
current ramps. A, Responses of a geniculate cell to
injected current ramps producing lower
dV/dt values from
left to right. Arrows
indicate the threshold for each LTS (see Fig. 2 for how these were
determined). B, Relationship between slope of the
voltage ramp and threshold for activating the LTS for the cell
illustrated in A. Only slopes fast enough to activate an
LTS are considered. C, D, Plots as in B
for two other geniculate cells.
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Effect of the K-leak conductance and/or
IA on activation of low-threshold spikes
It has been argued that there is a range of membrane potentials
for thalamic relay cells in which the activation and inactivation curves for IT overlap (see introductory
remarks) (see also Coulter et al., 1989; Williams et al., 1997). If so,
then a relay cell with a membrane potential within that voltage range
should experience this window current and the regenerative
nature of IT. If this voltage range and
window current are large enough, the cell should fire repeated,
spontaneous LTSs or exhibit bistability. If a significant window
current existed, we should expect to see evidence of it in all of our
ramps, including those with a dV/dt too
low to activate an LTS. As noted above, the slowest ramps for each cell
that failed to evoke an LTS also failed to show any sort of
irregularity in the voltage response as the threshold for the LTS was
crossed, so that any IT or window current
that might have been activated as we traversed the critical voltage
range was either too small to be detected or masked by other currents.
Nonetheless, several recent studies suggest that thalamic relay cells
do have a window current that leads to bistability in membrane
properties (Williams et al., 1997; Hughes et al., 1999) However, this
bistability was dependent on a relatively high apparent input
resistance, consistent with a very small resting K-leak conductance and
attenuation of the hyperpolarization-activated mixed cation current
Ih (Williams et al., 1997). We have tried to test this idea for six geniculate relay cells by adding a relatively low concentration of Cs+ (2-10
mM) to the bathing solution during the recordings
to block both K+ channels, therefore
blocking the K-leak conductance and IA
(McCormick and Pape, 1990) and also increasing input resistance; this
also blocks Ih (McCormick and Pape, 1990).
For the six cells we studied, the mean input resistance was elevated by
Cs+ from 115 to 142 M, or by 23%.
We repeated the ramp protocols before and during exposure to
Cs+ in six geniculate relay cells (Fig.
6). In control conditions, we repeated
our typical result: larger dV/dt values
evoked an LTS (Fig. 6A, top three traces),
whereas smaller ones did not (Fig. 6A, bottom
two traces). In the presence of Cs+
(6 mM), the smallest
dV/dt still evoked LTSs, and typically
several LTSs were evoked (Fig. 6Bi). Ramps with even
smaller dV/dt values continued to evoke
LTSs (Fig. 6Bii,iii), and indeed, we never were able to ramp the injected current slowly enough to avoid activation of LTSs.
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Figure 6.
Effect of Cs+ on activation of
LTSs. A, Responses of a geniculate cell before
application of Cs+. The rate of the ramp is
indicated to the right of each trace. As
in other cells, only faster ramps activate LTSs. B,
i-iii, Responses of the same cell to ramps after application
of Cs+. Now, even the smallest
dV/dt values that we applied
activated LTSs, and these included
dV/dt values much slower than
those used before Cs+ application.
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Our observations suggest that it may be possible in a thalamic
relay cell under physiological conditions to inactivate
IT without activating an LTS if the cell
is depolarized slowly enough. Depolarization is normally achieved via
synaptically generated EPSPs, but the typical EPSP activated via
ionotropic receptors seems too fast to prevent activation of an LTS,
and it has been demonstrated that such EPSPs activated from stimulation
of the optic tract do indeed activate LTSs (Scharfman et al., 1990). However, relay cells also are innervated by inputs that activate metabotropic receptors, which are associated with much slower EPSPs,
perhaps slow enough to inactivate IT
without an LTS. One problem with this is that the most prominent of
these, a glutamatergic input from cortex that activates metabotropic
glutamate receptors and a cholinergic input from the parabrachial
region of the brainstem that activates muscarinic receptors, produce an
EPSP by reducing a K+ conductance (for
review, see McCormick, 1992). Figure 6B
suggests that, if the reduction in the K+
conductance is large enough, LTSs may always be generated even with
metabotropic receptor activation.
We tested for this possibility with the application of
1-aminocyclopentane-1,3-dicarboxylic acid (ACPD), a general
agonist for metabotropic glutamate receptors, to three geniculate
cells. Figure 7 illustrates the basic
result we observed in all cells tested. ACPD was applied after the cell
was initially hyperpolarized (to 70 mV), at which level
IT is effectively de-inactivated. Thus
depolarizing pulses activate LTSs and bursts of action potentials. Application of ACPD then depolarizes the cell slowly enough to inactivate IT, because depolarizing pulses
now activate individual action potentials in tonic-firing mode, and no
LTS was generated during this depolarization. It is important to note
that the slow depolarization seen with ACPD activation is a result
of both the slow kinetics associated with activation of
metabotropic receptors and the diffusion time of the agonist to
the receptor sites; that is, synaptic activation of these receptors
would likely produce a faster response. Nonetheless, the results
summarized in Figure 7 indicate that the reduction in the
K+ conductance associated with ACPD
application is not so large that de-inactivation of
IT is necessarily associated with
activation of an LTS.
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Figure 7.
Effect of ACPD application on response mode. The
cell has initially been hyperpolarized to 70 mV (horizontal
dashed lines in all traces) so that
IT is de-inactivated. In the slower
time base (top trace), responses to current injection
are shown, and three of these (a-c) are shown at a
faster time base in the bottom traces. For
a, before ACPD application, and c, after
the membrane has returned to its previous hyperpolarized level, the
response is in burst mode with LTSs. For b, after the
ACPD has depolarized the cell, the response is in tonic mode. Notice
that, during the transition from burst to tonic mode after ACPD
application, no LTS was activated.
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Theoretical observations
In a previous paper, we studied, both experimentally and
theoretically, latency and threshold properties of LTS excitability (Zhan et al., 1999). For addressing these issues, a minimal
Hodgkin-Huxley type of model for the LTS was helpful. Sodium spiking
was excluded because it did not influence the features of interest in
that study, nor does it here (e.g., Figs. 3-5). We used a reduced
version of the model developed by McCormick and Huguenard (McCormick
and Huguenard, 1992; Huguenard and McCormick, 1994) for thalamic relay cells. Currents for generating
Na+-K+
action potentials were neglected as well as some other
K+ currents that played only a minor role
for a single LTS. This same model (see Materials and Methods) is used
here. It contains a T-type low-threshold
Ca2+ current
(IT), a transient
K+ current
(IA), and leakage currents
(IK-leak and
INa-leak); for some simulations (see
below) we included a sag current (Ih).
Figure 8 shows that the response of the
model to current ramps of various speeds, starting from a
hyperpolarized holding state, compares well with our observed behaviors
of thalamic relay cells (Figs. 1, 3-6). For ramps rising fast enough,
an LTS is generated, but this does not occur for ramps that rise too
slowly. Note, in this reduced model, IA,
which is the only voltage-gated K+ current
in the model, alone controls the LTS amplitude. Of course, the model
does not go into tonic-firing mode even with strong depolarization,
because the Na+-spiking mechanism has been
ignored. At the holding state for this simulation,
IT was de-inactivated
(hT = 1). During the ramp depolarization,
hT can drop substantially (data not shown)
even before the LTS upstroke. For example,
hT is ~0.3 at the upstroke of the LTS
for the second case of Figure 7 before the voltage reaches the
threshold for the activation gating variable m. If the ramp
speed is too slow, hT drops so much that
the current is prevented from activating. This behavior is in close
agreement with the basic conclusion reached from the experimental
observations (e.g., Fig. 3).
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Figure 8.
Simulated voltage responses to ramps of injected
current at various speeds. LTS generation does not occur for very slow
ramps. The model is a minimal biophysical description and does not
include currents for generating
Na+-K+ action potentials (see
Materials and Methods). The holding potential is 91.5 mV, and the
ramp speeds are 50, 100, 200, and 300 pA/sec.
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To understand the involvement of K+
currents in these phenomena, we simulated the effect of blocking
IA and
IK-leak. In Figure 9A, where both currents are
blocked, an LTS is evoked for even the slowest ramps. In fact, for the
slowest ramp, the model cell shows nearly steady subthreshold
oscillations, reflecting the rhythmogenic effect of the window current
of IT. These results agree with our
electrophysiological experiments, demonstrating that one or both
K+ currents must override the regenerative
property of the window current. Notice that the LTSs have higher
amplitude in Figure 9A than in Figure 8 now that
IA has been blocked. Also, in the absence
of these outward currents, we had to apply more anodal current to hold
the cell hyperpolarized to approximately 90 mV. Finally, the ramp
speeds are lower by a factor of 10 or more than are those in Figure
8.
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Figure 9.
Effects of blocking either or both of the two
K+ currents of the model on the voltage response of
the model to current ramp input. A, Blocking of
IA and
IK-leak leads to LTS generation at even very
slow ramp speeds. The computed LTSs are large because
IA is absent. B, Only
IA is blocked here. As in the control
case (compare Fig. 6), there is a minimal ramp speed below which no LTS
is activated. C, Blocking only
IK-leak enables LTS generation at any ramp
speed. The ramp speeds in A and C are 1, 5, 10, and 30 pA/sec; in B, they are 50, 100, 300, and
500 pA/sec. The holding conditions are as follows: in
A and C, Ihold
is 0.36 nA, and Vhold is approximately
87.4 mV; in B, Ihold is
0.27 nA, and Vhold is approximately 91.4
mV.
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Using our computer model, we can selectively block either current to
identify the primary contributor to masking of the window current. In
Figure 9B, we simulate the block of
IA with
IK-leak intact, and this restores the
feature of the control case that LTS generation requires that the ramp
stimulus be fast enough. The ramp speeds here are comparable with those
in the control case, and the slowest ramp fails to activate an LTS.
This simulation shows that IK-leak
alone can still mask the influence of the window current. Indeed,
blocking IK-leak but not
IA (Fig. 9C) enables LTS
generation for all ramp speeds. The subthreshold behavior in this case
is very similar to that in Figure 9A, particularly the
slow-rising phase of voltage and the timing of the LTS upstroke. However, the amplitudes are less in Figure 9C because
IA is present.
To see more directly the masking effect of
IK-leak we plot in Figure
10A the steady-state
current-voltage relation
ISS(V) versus V. The prominent N-shape in the control case is caused by
the outward window current of IA; it
disappears when IA is blocked. The
lowermost ISS curve is with both
K+ currents blocked. This reveals the
window current of IT, which makes
ISS modestly N-shaped in the
hyperpolarized regimen, and this is seen better in the magnification of
Figure 10B. It suggests the possibility of
bistability in this reduced model, in which K+ currents have been eliminated. Now
imagine the trajectory of the membrane potential in Figure
10B during the ramp. Before the LTS the
voltage-current pair rises upward along the left leg of the N. As the
ramp current passes above the knee, the voltage is no longer at the
pseudo steady state but increases rightward rapidly toward the right
leg of the N. During this transient phase the activation gating
variable of IT outraces the inactivation process, and an LTS is generated. Thus the N-shape accounts for the
~20 mV jump in voltage from just before to just after the leading LTS
in the ramp responses in Figure 9A and the smaller jumps in
Figure 9C. Note that this N-shape is also partially
preserved when IA is present.
Interestingly, this model with IA present and IK-leak blocked has a double
N-shape.
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Figure 10.
Steady-state current-voltage relation,
ISS versus V, for the model,
showing the effects of blocking either or both of the two
K+ currents of the model. A, Large
"bump" in ISS in the voltage range of
60 to 40 mV is caused by the (outward) window current of
IA. The modest "trough" in
ISS at approximately 70 mV is caused by
the (inward) window current of IT at
steady state. This N-shaped region of ISS is
seen better in the magnification in B. B,
Part of A is magnified.
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Although the window current, by creating an N-shaped
ISS(V), can
destabilize the membrane over a certain voltage range, this is not the
only possible destabilization mechanism. Resonance and rhythmicity are
also possible, even with a monotonic
ISS(V), as occurs in
the standard Hodgkin-Huxley model (Rinzel, 1978). Modest parameter
changes in our minimal model in this low-conductance hyperpolarized
voltage range can evoke either mechanism or both (Fig. 9A,
see the near-sustained oscillations after the LTS, and with voltage
jump, for the slowest ramp). Apparently relay neurons with different
parameter values (i.e., in different preparations) are also capable of
either or both when masking conductances are blocked. In our case the
destabilization appears more like resonance (with multiple LTSs and no
jump); in other experiments bistability (and sometimes oscillations)
are seen (Williams et al., 1997; Hughes et al., 1999).
Although we do not illustrate the point with a figure here, we have
explored computationally the potential effect of
Ih on LTS generation for slow ramp inputs.
For these simulations we used the model for
Ih as developed previously (McCormick and
Huguenard, 1992) (see Materials and Methods). With a maximal
conductance gh set to a value (10 nS) at
the lower end of the range reported by Huguenard and McCormick for rat
thalamic relay cells, we find that LTS generation is precluded for very
slow ramps regardless of whether or not
IK-leak is present. This strong inward
but nonregenerative current swamps the small window current of
IT. As mentioned above, these relay
neurons have a small depolarizing sag in response to hyperpolarizing
current pulses. In four neurons, we have conducted voltage-clamp
recordings to estimate gh in these
neurons. In these cells the average gh was
0.3 nS and ranged from 0.1 to 0.5 nS. This small depolarizing sag is
observed in all cat LGN relay cells and does not appear to be a result
of experimental manipulation (i.e., whole-cell recording), because
recordings from interneurons indicate large depolarizing sag responses
with similar recording procedures. Furthermore, there does not appear
to be a time-dependent run-down of the sag response. When using the
much smaller value of gh of 1 nS (which is
still larger than what we observe experimentally in geniculate relay
cells), we find that our results are essentially unchanged from Figures
1 and 2. This agreement between experimental and theoretical
results supports the idea that Ih is quite
small in cat thalamocortical relay neurons.
| |
DISCUSSION |
We have shown in geniculate neurons that, to activate an LTS
(which we take as implying IT generation),
the activating input must exceed a minimum rate of depolarization or
dV/dt. Our experimental observations of
this behavior have been supported and extended by use of model thalamic
relay cells that also offer insights into the voltage-dependent
conductances underlying this phenomenon.
Space-clamp issues
We recorded from and injected current into the soma, whereas many
or most of the T channels underlying IT
reside in the dendrites (Zhou et al., 1997; Destexhe et al., 1998; Zhan
et al., 2000). Because geniculate neurons have extensive dendritic
arbors (Guillery, 1966; Friedlander et al., 1981), space-clamp
limitations could affect interpretation in two related ways: (1) when
we hyperpolarize the soma to completely de-inactivate
IT, the hyperpolarization at dendritic
locations is probably less, and (2) the ramps applied at the soma
likely produce ramps in dendrites with a lower voltage amplitude and
thus a corresponding reduction in dV/dt.
However, for several reasons, we do not believe that these factors
affect our basic conclusions. Because we observe LTSs with applied
ramps of a sufficiently fast dV/dt, at
least many if not all dendritic T channels must have been
de-inactivated. Furthermore, although ramps may differ in absolute
amplitude and dV/dt at different dendritic
locations, it is still the case that relative speeding up or slowing
down of dV/dt from injections in the soma
determines whether or not an LTS is activated. Thus even with
space-clamp limitations, our basic conclusion that LTS activation
requires a minimum dV/dt seems sound.
Our theoretical results for an electrotonically compact (space-clamped)
cell model support the conclusion that the minimum dV/dt requirement depends on the relative
amount of masking of the window current related to
IT. With sufficient masking of
IT or inadequate
IT one expects accommodation, by which we
mean failure to respond, to a very slow ramp. Accommodation may be
precluded by manipulations that block or partially block the
conductances that mask IT. In a
distributed cable structure one should also expect the phenomenon of
accommodation to depend on the degree of masking, although more
unmasking might be required to preclude accommodation. Theoretical
results for a simplified excitable membrane model show that the
critical level of an excitability parameter (analogous to voltage
threshold or degree of masking) beyond which accommodation is possible
for very slow ramps is greater for the space-clamped case than for
local stimulation in a cable (Rinzel and Keener, 1983).
Window current
If the inactivation and activation curves for
IT overlap, a membrane potential held
within the overlapped voltage range will generate some
IT, and the result is a steady-state
window current (Coulter et al., 1989; Williams et al., 1997). If this
occurs, under certain conditions, it can also lead to bistability or
resonance or oscillations of the membrane potential (Hutcheon et al.,
1994; Puil et al., 1994; Manor et al., 1997; Williams et al., 1997). The presence of a window current and these nonlinear dynamic response properties could have important functional implications regarding integration of afferent synaptic activity in thalamic relay cells.
However, if a minimum dV/dt is needed to
activate an LTS, then a window current cannot occur to any appreciable
extent, because this current by definition can be generated by a
steady-state (i.e., dV/dt = 0)
voltage within the window. Also, a window current should create a
deviation in the slope of the voltage response to the slow current
ramps we used, and this was never observed in our experiments without
Cs+. Of course, it is possible that the
window currents are so small that they are below our resolution to
detect, but if so, such a window current would have rather limited
functional significance.
However, with Cs+ we found that even the
slowest ramps activated LTSs. There are at least two possible and
perhaps related explanations for this. One is that the
Cs+, by reducing the
K+ conductances, increases the apparent
membrane resistance. This, in turn, increases the amplitude and
dV/dt of the background fluctuations in
membrane potential, many of which are caused by spontaneous synaptic
events (Cox et al., 1998). Thus the voltage ramps evoked by the current
injections are not perfectly smooth but instead include small
fluctuations, and these would be amplified because of the presence of
Cs+, perhaps enough to activate an LTS.
The other possibility derives from the experiments and theories that
reveal mechanisms for dynamic destabilization (bistability, resonance,
and oscillations) in certain parameter and stimulus ranges. In
particular, we note that membrane bistability occurs in relay neurons
only after suppression of Ih and
IK-leak (Williams et al., 1997; Hughes
et al., 1999). By reducing both
IK-leak and
Ih with Cs+,
we have created experimental conditions that would promote observing the bistability. Although we did evoke LTSs with all ramps used in the
presence of Cs+, we did not observe any
obvious bistability in the voltage responses to these very slow current
ramps, such as lasting tail responses on the LTSs. Destabilization in
this case may be caused by resonance.
However, although our experimental observations cannot reveal details
of the conductances involved in these phenomena, our modeling studies
do so. They show that blockade by Cs+ of
IK-leak but not of
IA is responsible for allowing the slowest ramps to activate an LTS. As for Ih, the
modeling also shows that blockade of a large
Ih by Cs+
could also account for this phenomenon, but our experimental observations are that geniculate relay cells in the cat (as
opposed presumably to many other thalamic relay cells) have such a
small Ih that this is not really a factor
for these cells. We thus conclude that blockade by
Cs+ of
IK-leak is mainly responsible for the
observation that, with Cs+, even the
slowest ramps evoke an LTS; IK-leak is
the principal masking agent for the window current of
IT.
Significance of a minimum dV/dt for control
of response mode
An important factor of the dV/dt of
an evoked EPSP is the nature of the postsynaptic receptor involved.
Ionotropic receptors are associated with fast postsynaptic potentials
(PSPs), whereas activation of metabotropic receptors produce much
slower PSPs. The major neurotransmitters producing EPSPs in geniculate
relay cells are glutamate and acetylcholine, and each can activate both ionotropic and metabotropic receptors (for review, see Sherman and
Guillery, 1996). Regarding glutamatergic inputs, retinal afferents activate only ionotropic receptors and thus fast EPSPs, but cortical afferents also activate metabotropic glutamate receptors and can thus
evoke slow EPSPs. Ionotropic (nicotinic) and metabotropic (muscarinic)
cholinergic receptors are activated via axons from the parabrachial
region of the brainstem.
For a thalamic relay cell in burst mode, the present results are
consistent with evidence that EPSPs generated via ionotropic receptors
are fast enough to activate LTSs and burst firing (Scharfman et al.,
1990). They also suggest that EPSPs via metabotropic receptors may be
slow enough to inactivate IT and thus
convert a relay cell from burst to tonic mode without activating a
burst, although an important caveat to this is offered in the next
paragraph. We have shown in Figure 7 that, although EPSPs generated in
these relay cells via metabotropic receptors involve a reduction in IK-leak (McCormick and Von Krosigk,
1992), this reduction is sufficiently limited (see also Fig. 9) that
the resulting slow depolarization fails to elicit an LTS. EPSPs via
metabotropic glutamate receptors effectively switch firing modes from
burst to tonic (McCormick and Von Krosigk, 1992; Godwin et al., 1996),
but the experiment shown in Figure 7 involves bath application of a
metabotropic glutamate agonist, and there has as yet been no test to
see whether synaptic activation of metabotropic glutamate or muscarinic
receptors will perform the switch without activating a burst.
Obviously, the switch from tonic to burst mode involves
hyperpolarization that would not produce spurious firing in the relay cell. The mechanism we suggest, involving a slow EPSP via metabotropic receptors, can do the opposite, but also without producing any spurious
burst response relayed to cortex. Whether this regularly occurs for
geniculate relay cells may be doubted. This is because retinal ganglion
cells have background firing rates of 10-60 Hz (Bullier and Norton,
1979), and the fast EPSP generated by each retinal action potential is
fairly large (~2-3 mV) (Bloomfield and Sherman, 1988). Thus,
although activation of metabotropic receptors from modulatory inputs
might produce a very slow EPSP, it seems likely that fast EPSPs from
retina would be superimposed on this and would activate an LTS. A burst
of action potentials would likely be relayed to cortex, but this is not
really a spurious signal, because it would, in this scenario, always be
activated by a retinal input.
Thus although it is questionable whether relay cells in the lateral
geniculate nucleus can be switched from burst to tonic firing without a
burst being activated, the possibility does exist for other thalamic
nuclei, providing that the driver inputs (i.e., those equivalent to
retinogeniculate inputs) have sufficiently low spontaneous activity.
Also, for cortical or brainstem inputs to do this would require that
mainly only metabotropic and not ionotropic receptors are activated.
How different patterns of active cortical or brainstem inputs activate
the different receptor types is presently unknown, but it is plausible
that, within each pathway, a subset of axons may primarily activate
only metabotropic receptors. Suprathreshold driver input, which carries
the basic information to be relayed to cortex, evokes only fast EPSPs,
meaning that it will always fire a relay cell in burst or tonic mode, and thus driver input has limited capabilities of switching modes. On
the other hand, in some thalamic nuclei, cortical and parabrachial inputs operating via metabotropic receptors may be able to perform the
trick of pure mode switching uncomplicated by unnecessary extra action potentials.
| |
FOOTNOTES |
Received Aug. 2, 2000; revised Oct. 26, 2000; accepted Nov. 13, 2000.
This research was supported by United States Public Health Service
Grant EY 03038 and National Science Foundation Grant MS 0078420. Additional support was provided by the National Institutes of Health
Intramural Programs of the National Institute of Diabetes and Digestive
and Kidney Diseases and the National Institute of Neurological Diseases
and Stroke. We thank Susan Van Horn for her excellent technical assistance.
Correspondence should be addressed to S. M. Sherman, Department of
Neurobiology, State University of New York, Stony Brook, NY 11794-5230. E-mail: s.sherman{at}sunysb.edu.
| |
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Copyright © 2001 Society for Neuroscience 0270-6474/01/2131022-11$05.00/0
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R. Dodla, G. Svirskis, and J. Rinzel
Well-Timed, Brief Inhibition Can Promote Spiking: Postinhibitory Facilitation
J Neurophysiol,
April 1, 2006;
95(4):
2664 - 2677.
[Abstract]
[Full Text]
[PDF]
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TOP
ABSTRACT
INTRODUCTION
![<FR><NU><UP>d</UP>x</NU><DE><UP>d</UP>t</DE></FR>=<FR><NU>&phgr;[x<SUB>∞</SUB>(V)−x]</NU><DE>&tgr;<SUB>x</SUB>(V)</DE></FR>,](/content/vol21/issue3/fulltext/1022/img007.gif)
Compound via MeSH
