Current Clamp and Modeling Studies of Low-Threshold Calcium
Spikes in Cells of the Cat's Lateral Geniculate Nucleus
X. J.
Zhan,1
C. L.
Cox,1
J.
Rinzel,2 and
S.
Murray
Sherman1
1Department of Neurobiology, State
University of New York, Stony Brook, 11794-5230; and
2Center for Neural Science and Courant Institute
of Mathematical Sciences, New York University, New York, New York 10003
 |
ABSTRACT |
Zhan, X. J.,
C. L. Cox,
J. Rinzel, and
S.
Murray Sherman.
Current clamp and modeling studies of low-threshold calcium
spikes in cells of the cat's lateral geniculate nucleus. All
thalamic relay cells display a voltage-dependent low-threshold
Ca2+ spike that plays an important role in relay of
information to cortex. We investigated activation properties of this
spike in relay cells of the cat's lateral geniculate nucleus using the combined approach of current-clamp intracellular recording from thalamic slices and simulations with a reduced model based on voltage-clamp data. Our experimental data from 42 relay cells showed
that the actual Ca2+ spike activates in a nearly
all-or-none manner and in this regard is similar to the conventional
Na+/K+ action potential except that its voltage
dependency is more hyperpolarized and its kinetics are slower. When the
cell's membrane potential was hyperpolarized sufficiently to
deinactivate much of the low-threshold Ca2+ current
(IT) underlying the Ca2+ spike,
depolarizing current injections typically produced a purely ohmic
response when subthreshold and a full-blown Ca2+ spike of
nearly invariant amplitude when suprathreshold. The transition between
the ohmic response and activated Ca2+ spikes was abrupt and
reflected a difference in depolarizing inputs of <1 mV. However,
activation of a full-blown Ca2+ spike was preceded by a
slower period of depolarization that was graded with the amplitude of
current injection, and the full-blown Ca2+ spike activated
when this slower depolarization reached a sufficient membrane
potential, a quasithreshold. As a result, the latency of the evoked
Ca2+ spike became less with stronger activating inputs
because a stronger input produced a stronger depolarization that
reached the critical membrane potential earlier. Although
Ca2+ spikes were activated in a nearly all-or-none manner
from a given holding potential, their actual amplitudes were related to
these holding potentials, which, in turn, determined the level of
IT deinactivation. Our simulations could
reproduce all of the main experimental observations. They further
suggest that the voltage-dependent K+ conductance
underlying IA, which is known to delay firing in many cells, does not seem to contribute to the variable latency seen in
activation of Ca2+ spikes. Instead the simulations indicate
that the activation of IT starts initially with
a slow and graded depolarization until enough of the underling
transient (or T) Ca2+ channels are recruited to produce a
fast, "autocatalytic" depolarization seen as the Ca2+
spike. This can produce variable latency dependent on the strength of
the initial activation of T channels. The nearly all-or-none nature of
Ca2+ spike activation suggests that when a burst of action
potentials normally is evoked as a result of a Ca2+ spike
and transmitted to cortex, this signal is largely invariant with the
amplitude of the input activating the relay cell.
 |
INTRODUCTION |
One of the most important cellular properties
exhibited by thalamic relay neurons is a voltage-dependent, transient,
low-threshold Ca2+ conductance, leading to depolarization
via Ca2+ entry through T-type Ca2+ channels
(Crunelli et al. 1987
; Jahnsen and Llinás
1984a
,b
). This Ca2+ current thus is known as
IT, and it produces a low-threshold spike
referred to here as the "Ca2+ spike."
IT can be activated by a depolarizing input,
such as an excitatory postsynaptic potential (EPSP), but only if the
membrane already has been hyperpolarized sufficiently for
50-100 ms
(Jahnsen and Llinás 1984a
). This is because at
more depolarized potentials, IT is
inactivated and a period of hyperpolarization is required to
remove the inactivation or deinactivate
IT. In regard to its transient nature, the
low-threshold Ca2+ conductance underlying
IT behaves much like the Na+
conductance underlying the conventional action potential except the
voltage sensitivity of IT operates in a more
hyperpolarized range and its kinetics are slower.
The importance of IT derives from the fact that
the large, depolarizing Ca2+ spike that it produces usually
reaches threshold for activating conventional
Na+/K+ action potentials, producing a brief
burst of firing (Jahnsen and Llinás 1984a
,b
). This
is known as the burst mode of firing and reflects the
response of a relay cell to depolarizing inputs when the cell is
initially hyperpolarized. When the cell is depolarized initially so
that IT is inactive, the cell responds to the
same depolarizing inputs with a steady stream of unitary action
potentials, and this is known as the tonic mode of firing
(Huguenard and McCormick 1992
; Jahnsen and
Llinás 1984a
,b
; McCormick and Huguenard
1992b
; Steriade and Llinás 1988
). Both
firing modes are a ubiquitous property of relay cells throughout the
mammalian thalamus, and both firing modes have been seen during both in
vitro and in vivo recording, the latter including recording from awake,
behaving animals (Ghazanfar and Nicolelis 1997
;
Guido and Weyand 1995
; Guido et al. 1992
,
1995
; Sherman and Guillery 1996
). It is now clear that the different patterns of firing represented by burst and
tonic firing provide different types of relays of information to
cortex. Because the firing mode is determined by the inactivation state
of IT at the time an activating, depolarizing
input, such as an EPSP, arrives at a relay cell, it is of great
interest to understand how IT behaves.
Since the first descriptions of IT and burst
firing in thalamic neurons, which involved intracellular recording in
current-clamp mode (Jahnsen and Llinás 1984a
,b
),
much of the quantitative and systematic study of
IT has involved voltage-clamp recording, often in acutely dissociated cells and usually in rodents (Coulter et al. 1989
; Hernández-Cruz and Pape 1989
).
The main advantage of this approach is that it permits a more complete
description of the voltage dependency and kinetics of a
voltage-dependent conductance, such as that associated with
IT. Such data have enabled the development of
Hodgkin-Huxley-like models that reproduce many properties of Ca2+ spikes (Crunelli et al. 1989
;
Destexhe et al. 1998
; Huguenard and McCormick
1992
, 1994
; McCormick and Huguenard 1992
;
Wang et al. 1991
; Williams et al. 1997
).
However, among those aspects that have not been studied systematically
in current-clamp mode, experimentally and including comparison with
theory, is the nature of threshold for Ca2+-spike generation.
The main purpose of the present study is to do this for relay cells of
the lateral geniculate nucleus, the thalamic relay of retinal input to
cortex, using current-clamp recording from in vitro slice preparations.
We have found that the sensitivity for generation of Ca2+
spikes is surprisingly high, with nearly all-or-none threshold behavior, and that these spikes and their associated bursts of action
potentials occur with quite long latency near threshold. We compare our
experimental data with simulations from a cellular model based on
published voltage-clamp data. Also, our recordings are from the cat
thalamus and the model is derived from voltage-clamp studies of rodent
thalamus, so our comparisons also serve to test the generality of the
behavior of IT across species.
 |
METHODS |
Slice preparation
All intracellular recordings were made from relay neurons of the
cat's lateral geniculate nucleus in an in vitro thalamic slice
preparation. Young animals (4-8 wk old) of either sex were handled in
compliance with approved animal protocols. Briefly, animals were
anesthetized deeply with a mixture of ketamine (25 mg/kg) and xylazine
(2 mg/kg) and mounted in a stereotaxic device. We then opened a
rectangular area of skull overlying the lateral geniculate nucleus and
removed a block of tissue containing the lateral geniculate nucleus.
After placing this block in oxygenated cold slicing solution (see next
section), we killed the animal with an overdose of pentobarbital
sodium. Thalamic slices (400-500 µm thick) were cut in a coronal or
sagittal plane with a vibrating tissue slicer and placed in a holding
chamber for
2 h before recording. Individual slices were transferred
to an interface type recording chamber and continuously superfused with
warm oxygenated physiological solution (see next section). The tissue
was maintained at 33°C for all recordings.
Solutions
The slicing solution was used throughout the tissue preparation
until the slice was transferred to the holding chamber. It contained
(in mM) 2.5 KCl, 1.25 NaH2PO4, 10.0 MgCl2, 0.5 CaCl2, 26.0 NaHCO3, 11.0 glucose, and 234.0 sucrose. The physiological solution used in the
holding and recording chamber for intracellular recording contained (in
mM) 126.0 NaCl, 2.5 KCl, 1.25 NaH2PO4, 2.0 MgCl2, 2.0 CaCl2, 26.0 NaHCO3, and
10.0 glucose; and it was gassed with a mixture of 95%
O2-5% CO2 to a final pH of 7.4. In some
experiments, the Na+ channel blocker, tetrodotoxin (TTX;
0.5-1 µM), was added to the bath to block conventional
Na+/K+ action potentials. The intracellular
recording electrodes were filled with a solution that was either 3 M
KAc or 1 M KAc with 2-5% neurobiotin.
Electrophysiological recordings and data analysis
We obtained intracellular recordings in current-clamp mode from
the geniculate relay cells using sharp electrodes. Recording electrodes
were pulled to an impedance of 40-80 M
at 100 Hz when filled with
the aforementioned solution. An Axoclamp 2A amplifier was used in
bridge mode to enable current-clamp recordings. During the recordings,
we adjusted an active bridge circuit to balance the drop in potential
produced by passing current through the recording electrode. Current
protocols were generated using either AxoData or pClamp on a laboratory
computer, and the data were stored digitally with a temporal resolution
of 0.2 ms. Cells were held at different initial holding potentials by
injecting current into the cell (i.e., the holding current). The
duration of holding current before evoking responses assured that any
depolarizing sag due to Ih would reach an
equilibrium, leading to a stable membrane voltage for a sufficient time
to create a stable level of IT inactivation.
Responses, including Ca2+ spikes, then were evoked by
depolarizing current steps on top of the initial holding current, the
steps ranging from 10 to 3,000 pA and having a duration of 200-1,000
ms. After >10 s of holding current, additional current steps were
given on top of the holding current at a rate ranging from 0.1 to 0.3 Hz to ensure a stable initial holding potential before the depolarizing steps.
We adopted a set of minimum requirements to judge an intracellular
recording as acceptable. These included having a resting membrane
potential more negative than
50 mV and action potentials that reached
at least
10 mV; most overshot 0 mV. We routinely monitored and
balanced the bridge during the recordings, and we also measured the
input resistance by determining the slope of the linear portion of the
I-V relationship.
In some experiments for which we had neurobiotin in the recording
electrode, we iontophoresed this dye into the cell with depolarizing
current steps (200-500 pA in steps of 200-400 ms at 0.5-2 Hz for
1-3 min). This was done at the end of electrophysiological recording.
After each such iontophoretic injection, we processed the slice with a
standard protocol to reveal the neurobiotin (Zhan and Troy
1997
) and assess the morphology of the labeled cell with the
light microscope.
Model
Our experimental observations (see RESULTS)
demonstrated that threshold behavior and excitability of
Ca2+ spikes were similar in the presence or absence of TTX
(Hernández-Cruz and Pape 1989
; Jahnsen and
Llinás 1984a
,b
). Thus we chose for our computations 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. Because our main goal
for modeling here is qualitative understanding of threshold and latency
phenomena under current clamp mode, we sought to obtain
semiquantitative agreement, rather than detailed quantitative fits, of
simulated results with experimental data.
Exploratory simulations were performed with the computer program
Cclamp, developed by Huguenard and McCormick (1994)
. The basic behaviors of low-threshold excitability were obtained using the
"IT" case and "blocking" several
voltage-dependent currents until we identified our candidate model.
Thus we developed a minimal model for generation of Ca2+
spikes that mimics our experimental results.
The current balance equation is
|
(1)
|
where IT is the "T type"
low-threshold Ca2+ current, IA is a
transient K+ current, the leakage components
(IK-leak and INa-leak)
are ohmic, and 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 and
IA found in the computer program Cclamp of
Huguenard and McCormick (1994)
and based on their
earlier voltage-clamp data (summarized in McCormick and Huguenard 1992
). The model uses the Goldman-Hodgkin-Katz
formulation for IT as
|
(2)
|
where PT is the maximum permeability of
an open channel (30 cm3/s), 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); F, R, and T are
Faraday's constant, the gas constant, and absolute temperature,
respectively (Hille 1992
). The transient K+
current is given by
|
(3)
|
with the reversal potential VK =
105 mV
and gA = 2 µS unless stated otherwise. The
leakage currents are given by
|
(4)
|
and
|
(5)
|
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
|
(6)
|
where x = mT,
hT, mA, or
hA with
|
(7)
|
The specific parameter values (in millivolts) are
mT =
60.5,
kmT = 6.2,
hT =
84,
khT =
4.03,
mA =
60,
kmA = 8.5,
hA =
78,
khA =
6, and the
"time-constant" functions are
|
(8)
|
|
(9)
|
|
(10)
|
|
(11)
|
|
(12)
|
We adjusted the gating rates to 33.5°C from Cclamp's set
conditions of 23.5°C by using a temperature correction factor,
, of 3.
All computed results shown here were obtained with the above minimal
model using 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.
 |
RESULTS |
Experimental observations
We obtained intracellular recordings in the current clamp mode
from a total of 42 neurons from the cat's lateral geniculate nucleus.
All appeared to be relay cells on the basis of readily evoked
Ca2+ spikes. Also we injected with tracer and recovered a
subset of five of these cells after the recording session, and their
anatomic properties clearly distinguished them as relay cells and not
interneurons (Friedlander et al. 1981
; Guillery
1966
; Sherman and Friedlander 1988
). Detailed
measurements of resting potential and input resistance were made for a
subset of 35 neurons. For these, resting potential was
60.1 ± 4.6 (SD) mV (with a range of
50 to
69 mV). The input resistances
tended to be slightly higher as the cells were hyperpolarized. At rest,
the these values were 31.3 ± 14.7 M
, whereas at 20 mV hyperpolarized to rest, they were 41.5 ± 16.0 M
; this
difference was statistically significant (P < 0.001 on
a paired t-test). Of the 42 cells, 20 were studied
extensively before TTX (0.5-1 µM) was added to the bath to block
sodium channels and thus action potential generation; 15 were studied
briefly before TTX application and then extensively after; and the
remaining 7 cells were studied extensively both before and after TTX application.
Figure 1 illustrates two of the main
phenomena we observed for a typical cell from our sample. The cell in
Fig. 1A was held at the indicated initial membrane potential
at which the voltage-dependent Ca2+ conductance underlying
the low-threshold spike is deinactivated substantially. Figure
1A, top traces, shows the voltage responses to application
of rectangular current injection (indicated below the
traces) in the presence of TTX, which was applied to show evoked
Ca2+ spikes without action potentials. With incremental
10-pA steps of current injection, we saw ohmic responses for smaller
injections until a voltage threshold was reached, at which point that
current injection and all larger ones evoked a Ca2+ spike.
Interestingly, the amplitude of the Ca2+ spike evoked by
the smallest suprathreshold current injection was effectively as large
as all Ca2+ spikes evoked from larger current injections.
The input resistance of this cell was ~60 M
, and thus each
incremental 10-pA current would produce 0.6-mV depolarization. This
means that the full-blown Ca2+ spike was evoked as a nearly
all-or-none event over a range of
1 mV in membrane potential (see
DISCUSSION for further consideration of this nearly
all-or-none behavior). This nearly all-or-none behavior of the
Ca2+ spike is shown more dramatically in the Fig. 1A,
bottom, in which the evoked Ca2+ spikes are
overlapped. These overlapped traces also show that the evoked
suprathreshold responses exhibit three components: an initial ohmic
response (arrow 1), a slow depolarization (arrow 2), and the
Ca2+ spike itself (arrow 3), although the first two phases
are best seen with smaller depolarizing inputs and may be difficult to see with larger ones (see traces 5 and 6 in Fig.
2B). Figure 1, C and D, shows this
same nearly all-or-none behavior for two other geniculate relay cells
with TTX application. Figure 1B shows that a similar effect
was seen in the same cell as shown in Fig. 1A before TTX was
applied. Fewer traces are illustrated in Fig. 1B than in
Fig. 1A for clarity because the evoked action potentials tend to obscure the key features, but when all incremental 10-pA current injection steps are analyzed, the result is exactly as predicted from Fig. 1A with action potentials present.

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Fig. 1.
Activation of low-threshold Ca2+ spikes from relay cells in
an in vitro slice preparation through the cat's lateral geniculate
nucleus. Cells were recorded intracellularly in current-clamp mode.
Membrane potentials shown indicate the initial holding potentials.
A: responses of 1 cell in the presence of 1 µM TTX.
Top: original responses. Activation was achieved by
injecting depolarizing rectangular current pulses (indicated
below the traces) starting at 200 pA and incremented in
10-pA steps. Ohmic responses are evoked from smaller currents; the
longest latency Ca2+ spike evoked is from the smallest
suprathreshold current injection, and this latency decreased
monotonically as the amplitude of the current injection was increased.
Bottom: same evoked Ca2+ spikes as shown
top but shifted in time so that they are superimposed.
Numbered arrows indicate 3 different phases of the response to the
current injections: 1 points to the initial, ohmic response; 2 points
to a slower voltage-dependent depolarization; and 3 points to the
Ca2+ spike. Note that the Ca2+ spikes overlap
almost perfectly, indicating their nearly all-or-none nature.
B: same cell as in A before application
of TTX. Top: original recordings; bottom:
traces adjusted in time to overlap the evoked Ca2+ spikes.
Latencies of evoked bursts of action potentials decreased with
increasing amplitudes of current injection. To avoid extensive overlap
in the bottom traces, only 3 burst responses are shown.
C and D: 2 further examples with 1 µM
TTX application as in A. Although numbered arrows are
not shown for these examples, the 3 phases of the evoked response are
clearly visible as in A. Scale marks represent 100 ms
and 10 mV and those in A also apply to
B.
|
|
The second main phenomenon we observed is the dramatic decrease in the
latency of evoked Ca2+ spikes as current injection steps
are increased from the first suprathreshold injection. This is seen
both in the Ca2+ spike latencies (Fig. 1, A,
C, and D) and in the latency of action potentials
riding the crests of the Ca2+ spikes (Fig. 1B).
In both cases, the latency shift exceeds 150 ms. Interestingly, as can
be seen in the overlapped traces of Fig. 1, all Ca2+ spikes
seem to activate from near the same voltage, as if a simple threshold
phenomenon was involved similar to that for an action potential. The
slow depolarization leading to the Ca2+ spike (indicated by
arrow 2 in Fig. 1A) has a lower slope for smaller current
injections, and this is why it takes longer to reach the threshold to
activate the Ca2+ spike with smaller current injections.
Modeling results described in the following text suggest that this
slower depolarization indicated by arrow 2 in Fig. 1A is
caused by activation of IT that is too small to
be regenerative. The outward ohmic current nearly balances the slowly
growing inward IT during this phase of extended
latency. The response becomes regenerative when the threshold is
reached to activate the nearly all-or-none Ca2+ spike.
NEARLY ALL-OR-NONE NATURE OF CA2+ SPIKES.
Figure 2 further illustrates for the same
cell as shown in Fig. 1, A and B, the nearly
all-or-none nature of the Ca2+ spike during TTX
application. Figure 2A shows the peak evoked voltage as a
function of injected current when the cell initially is held at one of
three different initial holding membrane potentials. At a holding
potential of
59 mV (the resting potential for this cell), there is
insufficient deinactivation of the low-threshold Ca2+
conductance for activation of Ca2+ spikes. The result is
that current injection from these holding potentials evokes only an
ohmic response, thereby producing a gradual, smooth increase in evoked
potential with injected current (Fig. 2B, traces
1-3). However, at initial holding potentials of
77 and
87 mV,
at which the Ca2+ conductance is significantly
deinactivated, Ca2+ spikes are evoked by suprathreshold
depolarizing current injections. Thus we see initial ohmic responses
for small current injections until a threshold is reached, at which
point a sudden, dramatic increase in evoked membrane voltage is seen
(as in Fig. 1). This is because Ca2+ spikes are now evoked.
After this threshold is reached, larger current injections have little
effect on the amplitude of the evoked Ca2+ spike (Fig.
2B, traces 4-6). Note also that the Ca2+ spikes
evoked from the
87-mV holding potential are slightly larger. This is
because IT is more deinactivated when the
initial holding potential is
87 mV. Also, a larger current step is
required from
87 mV to get to the activation threshold for
IT so that this response curve is shifted to the
right compared with the curve starting at
77 mV.

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Fig. 2.
Relationship between current injection (400-ms pulses) and the
evoked responses as in Fig. 1A for the same cell in the
presence of 1 µM TTX. A: current injection amplitude
vs. peak evoked voltage defined as the voltage difference between the
peak voltage response and the membrane potential before the current
pulse. Shown are 3 curves representing 3 different initial holding
potentials as shown. Two of the curves ( and
) involved holding potentials ( 77 and 87 mV) that
were sufficiently hyperpolarized that Ca2+ spikes were
evoked once their activation threshold was crossed. Other curve
( and ) involved a holding potential at
rest ( 59 mV) that was too depolarized for generation of
Ca2+ spikes, and thus mainly ohmic responses were seen.
Numbered arrows reflect data points from representative traces in
B. B: representative traces as indicated for generation
of the plots in A. C: current injection vs. amplitude of
evoked response for 11 other cells. Initial holding potentials for
these cells were 80 to 90 mV, ensuring fairly complete
deinactivation of the underlying Ca2+ conductance, and
injected current was in the form of square wave pulses of 400- to
1,000-ms duration.
|
|
The nearly all-or-none activation of the Ca2+ spike is
fairly typical for our population. From initial holding membrane
potentials sufficiently hyperpolarized to deinactivate
IT significantly, every cell of the 22 so
studied with TTX application showed a sudden appearance of the
Ca2+ spike in a single incremental step of current
injection, and thus we never activated a significantly smaller
Ca2+ spike from a just suprathreshold current
injection that became much larger as more current was injected. Only
when the holding potential was more depolarized, so that
IT was more inactivated, did we see evidence of
possibly graded Ca2+ spikes (see also VARIATION OF
CA2+ spike amplitude with
deinactivation level). Of these 22 cells, 11 were studied
with larger incremental current steps of 50 pA before we realized just
how sharp the threshold behavior was for activating the full-blown
Ca2+ spike, so our best examples of this nearly all-or-none
behavior came from the 11 cells studied with incremental current steps near threshold of 10 pA. Figure 2C summarizes the data as in
Fig. 2A for these 11 cells. These 11 examples are all taken
from initial holding potentials of 20-30 mV below rest, in which there
was significant de-inactivation of IT. Every
cell in Fig. 2C showed a simple ohmic response for smaller
current injections interrupted by a sudden rise in voltage to a maximum
value over a single 10-pA current step as the Ca2+ spikes
then were activated. This plot shows the variation in our sample for
the amplitudes of Ca2+ spikes seen and amount of current
injection needed to activate them; variation that is related to, among
other properties, differences in input resistance across cells and
amount of deinactivation of the low-threshold Ca2+
conductance at the initial holding potentials used. Although not shown,
we saw the same nearly all-or-none behavior of Ca2+ spike
activation for all 27 cells studied with no TTX as for the 22 studied
with TTX, and often the same cell was studied before and after TTX application.
Figure 3 shows for the same cell the
analogous feature as illustrated in Fig. 2 but before TTX application.
From four different initial holding potentials, Fig. 3A
shows the relationship between current injection and the total number
of evoked action potentials. In this analysis, the current injection of
the abscissa refers to the step from the initial holding membrane
potential. In tonic firing mode (initial holding potentials of
47 and
59 mV), there is a gradual, smooth increase in the number of evoked
action potentials with increased current injection once threshold is
reached (Fig. 3B, traces 1-3). However, when the cell is in
burst firing mode (initial holding potentials of
77 and
87 mV), a
more complicated pattern is seen. With small current injections, action
potentials are not evoked until a threshold is reached, at which point
six to seven action potentials suddenly appear. This is because the threshold for Ca2+ spiking has been reached, and the
Ca2+ spikes evoke action potentials. The number of evoked
action potentials plateaus at six to seven for an extensive range of
larger current steps, and then larger current steps begin to increase
the number of action potentials gradually. In Fig. 3B, traces
4 and 5, which illustrate points on the plateau, show
that the evoked response is largely limited to the initial burst of
action potentials associated with the Ca2+ spike.
Trace 6 from Fig. 3B, which is taken from a
larger current injection, shows that these large injections activate
tonic firing after the initial burst. This is because the long current
injection eventually inactivates the low-threshold Ca2+
conductance after the initial burst, and if it is then sufficiently large, tonic firing will ensue.

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Fig. 3.
Relationship between current injection (400-ms pulses) and the evoked
action potential responses for same cell as in Fig. 1B.
A: current injection amplitude vs. total number of action
potentials evoked. Curves with and reflect burst firing, at least initially, whereas the curves with
and reflect tonic firing.
B: representative traces for data points indicated in
A. Note that the small current injection of trace
4 evokes only a single burst, that the larger injection of
trace 5 evokes an initial burst followed after ~70 ms
by a single tonic action potential, and that the even larger injection
of trace 6 evokes an initial burst followed immediately
by sustained tonic firing. C: current injection
amplitude vs. initial firing frequency, which was calculated from the
1st 6 action potentials evoked by the current injection to provide a
clearer comparison of burst vs. tonic firing.
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|
Figure 3A plots total number of action potential evoked by
the long current injection. However, as just noted, responses evoked from holding potentials of
83 and
77 mV can reflect mixed firing modes, burst followed by tonic for larger current injections. Thus the
spike counts indicated in Fig. 3A for larger current injections do not accurately reflect the burst/tonic differences. We
thus calculated the initial evoked frequency evoked by these current
injections by considering the average firing frequency of the initial
six action potentials (Fig. 3C), and this compares only the
initial responses that are purely tonic for the more depolarized
holding potentials and purely burst for the more hyperpolarized ones.
During tonic firing (initial holding potentials of
47 and
59 mV),
the increase in firing frequency is smooth and gradual once threshold
is reached. During burst firing (initial holding potentials of
77 and
83 mV), the initial firing frequency shows a sudden step from zero at
threshold and increases very gradually thereafter.
The plots of Figs. 2 and 3 represent firing versus the amplitude of the
current step injected from the initial holding potential. Figure
4A replots the data from Fig.
3A with the abscissa adjusted to reflect the total current
injected (i.e., initial holding current required for initial holding
potential plus the depolarizing step); Fig. 4, B and
C, shows this relationship for two other representative relay cells. Note that at around threshold levels of current injection, burst firing (Fig. 4,
) occurs at lower levels of injected current than does tonic firing (
). Thus burst firing occurs at a lower membrane potential, which reflects the "low-threshold" nature of
the Ca2+ spike. Furthermore, although not illustrated here,
burst firing commences at a membrane potential that is hyperpolarized
with respect to rest (i.e., negative total injected current), whereas tonic firing begins at a membrane potential that is depolarized with
respect to rest (i.e., positive total injected current), and this was
seen for all other cells studied. Finally, as we have shown earlier,
large current injections always produce tonic firing, even if the
initial response was in burst mode (see Fig. 3). Thus for the larger
current injections that produce tonic firing (>1,200 pA in Fig.
4A), the firing rates are roughly the same regardless of the
all initial holding potentials.

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Fig. 4.
Comparison between burst and tonic firing evoked by current injections
without TTX. Curves with represent burst firing, and
those with represent tonic firing. Unlike the plots in
Fig. 3 in which the abscissas are the amplitude of the depolarizing
pulse from the holding potential, the abscissas in these plots are the
total current injected (i.e., the sum of the current used to move the
cell from rest to the initial holding potential and the depolarizing
current step). A: same data as plotted in Fig.
3A, except that the abscissa is recalculated to reflect
the total current injection. Of particular interest is the range of
near-threshold current injections, which show that burst firing always
can be evoked with less current injection than is the case for tonic
firing. For much larger depolarizing currents, which evoked strong
tonic firing even after an initial burst, the curves largely overlap.
Note that the activating thresholds for burst firing are hyperpolarized
with respect to those for tonic firing. B and
C: data plotted as in A for 2 additional
cells, showing only the range of near-threshold current injections.
Again, bursts are evoked with less current injection than is the case
for tonic firing.
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LATENCY OF LOW-THRESHOLD CA2+ ACTIVATION.
The latency of the evoked Ca2+ spike becomes considerably
shorter with greater current injection (see Fig. 1). This appears to be
related to the rate of rise of the initial depolarizing response before
a near-threshold voltage is reached to initiate the Ca2+
spikes. Figure 5, A and
B, plots the relationship between current injection and
these latencies for the same cell as shown in Fig. 1, A and
B. From both initial holding potentials (
77 and
87 mV)
during TTX application, the latency of Ca2+ spike was
reduced gradually as the current injections increased, from 186 to 25 ms at a holding potential of
77 mV and from 139 to 24 ms at a holding
potential of
87 mV (Fig. 5A). A similar effect is seen
before TTX application when the latency to the first action potential
peak riding the crest of a Ca2+ spike is plotted against
injected current (Fig. 5B). These latencies were reduced
from 143 to 4 ms at a holding potential of
77 mV and from 164 to 7 ms
at a holding potential of
83 mV. The latency reduction was sharp for
initial suprathreshold current injections and became more gradual with
larger current injections.

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Fig. 5.
Relationship between current injection and response latency.
A: effect of current injection on response latency
during 1 µM TTX application for same cell as shown in Fig.
1A. Latency is measured from the initiation of the
depolarizing pulse to the peak of the evoked low-threshold
Ca2+ spike (LTS). Relationships are shown for the 2 initial
holding potentials shown. B: relationships for the same
cell as in A before TTX application for the 2 initial
holding potentials shown before TTX application. Latency was measured
from the start of the current injection to the peak of 1st action
potential of the evoked burst. C: effect of current
injection on response latency of Ca2+ spike for population
of additional 11 cells in the presence of 1 µM TTX.
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Figure 5C shows that the pattern of latency versus injected
current for the same 11 cells illustrated in Fig. 2C. The
maximal latencies we observed to activation of Ca2+ spikes
with just suprathreshold current injections in the presence of TTX was
235 ± 80 ms with a range of 139-425 ms. The activation currents
had to be ~200-400 pA suprathreshold before the latency reduction
became asymptotic. Although not illustrated, the 27 cells studied
without TTX showed the identical pattern, meaning that the latency of
the first spike evoked during burst firing decreased as current
injections increased from threshold to elicit the Ca2+ spike.
The data plotted in Fig. 5 reflect activation from long current pulses
of 200-1,000 ms, raising the possibility that long-latency Ca2+ spikes require long current pulses. We used very brief
current pulses (5 ms) to test this on a subset of seven cells, and an example is shown in Fig. 6. Not only are
brief injections of this sort, which temporally are similar to EPSPs,
sufficient to activate Ca2+ spikes, but as with the longer
pulses these activate Ca2+ spikes with a latency that
decreases with increasing amplitude of the injected current. Also, the
Ca2+ spikes are evoked long after the termination of the
current pulses.

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Fig. 6.
Activation of Ca2+ spikes with brief depolarizing pulses
(5-ms duration). Shown are 4 superimposed traces, including responses
to the largest 2 subthreshold injections and to the smallest 2 suprathreshold injections. No TTX was present for these responses.
Ca2+ spikes were evoked well after the cessation of the
current injection, and the latency of the evoked Ca2+
spikes dropped dramatically as the suprathreshold injection was
increased in amplitude.
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VARIATION OF CA2+ SPIKE AMPLITUDE WITH
DEINACTIVATION LEVEL.
The preceding results show that the Ca2+ spike is activated
effectively in a nearly all-or-none manner. Thus with 10-pA current injection steps, a depolarizing input activates only an ohmic response
if subthreshold and a full-blown Ca2+ if suprathreshold. We
cannot rule out the possibility that partial Ca2+ spikes
might have been seen if we used smaller injection increments, but the
fact that we never saw this in any of our cells suggests that the
incremental range of current injections over which partial Ca2+ spikes might be activated is much less than 10 pA and
thus
1 mV of depolarization for a cell with an input resistance of 50 M
. In theory (see DISCUSSION), graded responses may be
expected, although probably with quite a steep dependence on stimulus
amplitude, which is qualitatively what we have seen experimentally.
This implies that the proportion of T channels deinactivated by any
particular initial holding potential limits the maximal amplitude of
the Ca2+ spike realizable from that holding state.
Furthermore as long as this proportion is above a certain value (see
following text), it is more than enough to ensure that a nearly
all-or-none Ca2+ spike is evoked virtually independent of
the amplitude of a suprathreshold depolarizing current injection. This
predicts that the more hyperpolarized the holding potential, the more
that deinactivation will occur, and the larger the Ca2+
spike that will be activated. Figure 2A shows some evidence
for this because the amplitudes of the Ca2+ spikes
activated from
87 mV are larger than those activated from
77 mV.
This is explored more systematically for the same cell in Fig.
7, A-C, studied after TTX
application. In this experiment, current steps were injected into the
cell from a wide range of initial holding potentials. When the initial
holding potential is hyperpolarized enough to permit substantial
deinactivation of IT (i.e.,
93,
79, and
74
mV), the Ca2+ spike is activated in a nearly all-or-none
manner (Fig. 7, A and B). At a slightly more
depolarized initial holding level (i.e.,
72 mV), the evoked response
appears to be graded very slightly. However, the response is very
small, and it is difficult to determine whether it represents the slow
depolarizing phase (arrow 2 in Fig. 1A), the all-or-none
Ca2+ spike (arrow 3 in Fig. 1A), or both. When
the initial membrane holding potential is more depolarized (
59 mV,
which is near rest, and
68 mV), no discernable
IT is evoked and a purely ohmic response occurs.
Figure 7C plots the different holding potentials versus maximum Ca2+ spike amplitude, which is the first
suprathreshold response except for occasional graded responses evoked
from more depolarized holding potentials (see Fig. 7B,
bottom). Thus while depolarizing inputs to these cells activate
Ca2+ spikes in a nearly all-or-none fashion, their
amplitude can be controlled effectively by the level of deinactivation,
which in turn is determined by the level and duration of
hyperpolarization preceding the activating input. Also, very slightly
graded Ca2+ spike amplitudes may be seen for a narrow range
of holding potentials at which IT is
deinactivated less thoroughly (e.g., the
72-mV holding potential
example in Fig. 7, A and B), although even here it is not clear if this response is a full-blown Ca2+ spike
(see preceding text). Figure 7D shows the same relationship as in Fig. 7C for a sample of 10 relay cells.

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Fig. 7.
Effect of deinactivation on Ca2+ spike amplitude.
A: relationship between current injection and peak
evoked response in presence of 1 µM TTX as in Fig. 2. Different
initial holding membrane potentials are shown and were achieved with
constant hyperpolarizing currents. Series of depolarizing current
pulses incremented by 10 pA and with a duration of 300 ms was injected
to evoke ohmic responses (subthreshold currents) or Ca2+
spikes (suprathreshold currents). Curves with represent activation of Ca2+ spikes, and those with
indicate only ohmic responses. B:
representative series of traces from the data plotted in
A for activation of Ca2+ spikes from
different initial holding membrane potentials. Note that for the
relatively depolarized initial holding potential ( 72 mV), graded
amplitudes of response are seen that may or may not involve
Ca2+ spikes (see text for details). C:
relationship between the initial holding membrane potential and the
maximum Ca2+ spike amplitude for same cell as is
illustrated in Fig. 1A. Ordinate represents the
amplitude of the Ca2+ spike evoked from just suprathreshold
current injections. LTS amplitude is defined here as the voltage
difference between the peak of the Ca2+ spike and the level
of the ohmic response remaining 100 ms after the Ca2+
spike ended. , 6 initial membrane potentials from which
the plots in A are taken. D: relationship
between initial holding membrane potential and normalized amplitude of
evoked Ca2+ spike for 11 other relay cells.
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Theoretical observations
Our minimal model with only two voltage-dependent currents,
IT and IA, shows the
basic features of generation of Ca2+ spikes as seen
experimentally (Fig. 8; compare with Figs. 1
and 7). These features include a nearly constant amplitude of the evoked Ca2+ spike for different current steps from a given
holding level, a dramatic effect on latency of the evoked
Ca2+ spikes over a narrow range of suprathreshold current
injection amplitudes, increasing gradation and decreasing amplitude of
the Ca2+ spike with less hyperpolarized holding levels. A
response for a suprathreshold stimulus shows an early small
depolarization (the initial ohmic response, see arrow 1 in Fig.
1A), followed by a phase of slow depolarization (see arrow 2 in Fig. 1A), and finally the Ca2+ spike (see
arrow 3 in Fig. 1A). To evoke a Ca2+ spike from
the model, as in the experimental data, the initial holding membrane
potential must be hyperpolarized adequately so that
IT has been deinactivated sufficiently. Under
these conditions, the peak amplitude of the Ca2+ spike is
nearly independent of the amplitude of the suprathreshold current step.
When the simulation starts with more IT
deinactivation (Fig. 8, A and B), the
Ca2+ spike appears in a nearly all-or-none fashion. If the
holding potential is less hyperpolarized, meaning more of the
IT is inactivated, responsiveness may become
more graded (Fig. 8C). The behavior is thus not strictly all
or none, as becomes apparent when the level of
IT inactivation is relatively high, and this
correlates with the experimental observation that graded responses can
be obtained from relatively depolarized holding potentials (see
trace 3 of Fig. 10; see also DISCUSSION).

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Fig. 8.
Simulated membrane potential time courses showing responses to
depolarizing current steps for minimal model of relay cell without
action potential currents but with the K+ "leak"
conductance and IA present. Three different
initial holding membrane potentials are shown. Below the
voltage traces is shown the time course of the 400-ms current
injection. In all cases, as in the experimental data, the minimum
suprathreshold current injection evoked the Ca2+ spike with
the longest latency, and this latency reduced to asymptotic levels as
the amplitude of current injections increased (see Figs. 1, 2, 8, and
9). Current injections are given as Ip = Ip, o + j* Ip;j = 1,2. A: initial holding potential of 90 mV,
corresponding to holding current of 258 pA with
Ip, o = 48 pA and
Ip = 10 pA. , relative
peak values of IT (using the holding
membrane potential as a reference line) and their times of occurrence.
B: initial holding potential of 85 mV, corresponding
to holding current of 220 pA with Ip, o = 20 pA and Ip = 16.7 pA. C:
initial holding potential of 80 mV, corresponding to holding current
of 188 pA with Ip, o = 10 pA and
Ip = 12 pA. Response amplitude diminishes
as holding potential increases to less negative levels
(A-C), as in experimental data from Figs. 11 and 12. Range of latencies is largest and gradation of response amplitude is
smallest for the most negative holding potential (A).
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DISSECTING THE MODEL'S CA2+ SPIKE.
To understand the effect of just suprathreshold activating currents on
the latency of Ca2+ spikes, we have dissected
in Fig. 9 the time course of the response in
Fig. 8A to the minimum suprathreshold current injection,
which evoked the longest-latency Ca2+ spike. Also shown is
the time course of hT (- - -), which is the
fraction of channels not inactivated: the larger is
hT, the more IT is
deinactivated, and as expected depolarization during the
Ca2+ spike causes hT to drop with a
time scale of tens of milliseconds. Figure 9B shows the
interplay between the different currents during this response. The
early depolarization originates from the combination of injected
current and leakage current (Ileak
Iapp;
-
), which is initially inward.
This current approaches zero at around
83 mV, and the membrane would
come to rest there if no other currents were involved. However,
IT (
), beginning from near zero at the
(deactivated) holding state, continues to grow slowly. Although the
leakage and injected current combination becomes outward, this is more
than offset by the slowly growing IT, which is
inward. Until relatively late in the response, these components remain
small and nearly cancel each other. Thus while the net current (
) is
depolarizing during period of slow depolarization before initiation of
the Ca2+ spike, its time course is not monotonic. It jumps
up, then decreases to a minimum, becoming quite small and thereby
stalling the depolarization. IT and membrane
voltage continue to grow slowly together until the membrane voltage
enters the regime for regenerative activation of
IT. The nonlinear voltage dependent gating of
IT determines the voltage range in which the
sharply rising upstroke of the Ca2+ spike occurs.

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Fig. 9.
Time courses of variables and individual ionic currents during a
simulated response of a Ca2+ spike as in Fig. 8. Response
shown is to a just-suprathreshold current injection (97 pA), so the
Ca2+ spike has a long latency. Initial holding membrane
potential is 95 mV achieved with a holding current of 300 pA.
A: time courses of membrane voltage (V,
) and inactivation variable (hT, - - -)
to a depolarizing current pulse starting at 100 ms. Ordinate reflects
relative values for V and hT.
Membrane potential initially relaxes with a membrane time constant (of
~30 ms) to a more slowly rising phase before the Ca2+
spike begins abruptly. Some inactivation of
IT occurs (hT
decreases) during the initial depolarization before the initiation of
the Ca2+ spike, and the inactivation then proceeds rapidly
during the upstroke of the Ca2+ spike. B:
membrane currents during response shown in A; inward
currents are plotted down. IT ( )
grows slowly and then very fast to initiate the Ca2+ spike.
IA (- - -) makes little contribution until
the Ca2+ spike begins. Combined stimulating and leakage
currents (Iapp and
Ileak, respectively; - ) is initially
inward then becomes outward, opposing IT.
Sum of currents with negative sign ( ) is proportional to
dV/dt, and it thus has a local flat
minimum during period before the Ca2+ spike is initiated.
Horizontal corresponds to 0 current.
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Several additional features in Fig. 9 are noteworthy. First,
during a long-latency activation of a Ca2+ spike, a
considerable degree of inactivation of IT may
occur before the Ca2+ spike is initiated (see
hT in Fig. 9A). Because the time
constant of hT is voltage dependent and large in the
100-
to
70-mV range, less inactivation occurs with shorter latencies for
initiation of the Ca2+ spike. Second, the level of
IA is insignificant throughout all of the
response before activation of the Ca2+ spike and therefore
plays only a minor role in determining the latency of the
Ca2+ spike. Third, the reduction in
hT before activation of the Ca2+
spike suggests that a smaller IT is generated
when the latency is longer (i.e., from just suprathreshold current
injections). The triangular data points in Fig. 8A indicate
the relative peak values of IT (and times of
occurrence) for the spikes, showing the decrease with longer latency.
Nevertheless, the case in Fig. 9A illustrates that a sizable
Ca2+ spike proceeds even if hT drops below the
50% level. Finally, in passing, we note that IT
peaks and is inactivated almost completely before the peak of the
Ca2+ spike occurs.
Although IA is not the determining factor for
the latency of evoked Ca2+ spikes in our model, it does
control the amplitude of these spikes. It is the only nonlinear,
voltage-dependent, outward current in this minimal model. In thalamic
relay cells, other K+ currents also contribute to limiting
the Ca2+ spike amplitude (Huguenard and McCormick
1992
). Correspondingly, we have used the model to show that
other K+ currents acting alone also could restrict the
Ca2+ spike amplitude (not shown). However, other active
K+ currents, without IA present,
affect the low-threshold spike rising phase differently. With
IA, the rise is less rapid and the
depolarization peak is rounded. Without IA, the
other K+ currents limit amplitude abruptly by interrupting
a very rapid upstroke, leaving a cornered leading edge, sometimes with
a tiny overshoot (not shown). The other K+ currents that we
considered have higher thresholds (like the delayed rectifier) or are
activated by Ca2+ and so must follow after the recruitment
of IT. They only can play a role after the
upstroke of the Ca2+ spike is well underway, unlike
IA, which begins acting in the subthreshold
regime. These other candidates do not influence the latency effects
that we have seen.
We have focused here on IA for amplitude control
because of the above observations and because we wanted to explore its
effect on response latency, an often-implicated role for
IA (McCormick 1991
;
Rogawski 1985
; Storm 1988
). From Fig.
9B, where IA affects latency to peak
only slightly, we predict, and Fig.
10A confirms, that similar long
latencies and threshold behaviors occur when IA
is blocked. Furthermore, Fig. 10B shows that changing the
effectiveness of IA by changing its inactivation
time constant has virtually no effect on the latencies of
Ca2+ spikes. IA, however, does
affect the amplitude of the Ca2+ spikes because no
IA permits the largest Ca2+ spikes
(Fig. 10A), and increasing the inactivation time for
IA reduces the amplitude of these
Ca2+ spikes (Fig. 10B). In any case, we conclude
that the properties of IT alone can account for
the observed latency effect.

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Fig. 10.
Simulated membrane potential time courses showing responses to
depolarizing current steps as in Fig. 8 showing effects of
IA. Initial membrane potential is 91.7 mV,
which is achieved with a holding current of 272 pA. A:
simulations with all voltage-dependent K+ currents
suppressed, including IA. As in the
experimental data shown in Fig. 1, the responses to subthreshold
current steps are ohmic and to suprathreshold steps are
Ca2+ spikes. Increasing the suprathreshold current
injections significantly reduces the latency of the evoked
Ca2+ spike with little effect on its amplitude.
B: simulations similar to A, except that
IA is present with a varying inactivation
time constant (see Eq. 11). Numbered arrows indicate
simulations with the normal time constant (1), twice the time constant
(2), and 10 times the time constant (10). These changes in
IA affect the amplitude but not the latency
of the evoked Ca2+ spikes. Thus the latency effect in this
model does not depend on IA.
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The simulation in Fig. 10A of a pure Ca2+
spike, with IT and leakage as the only intrinsic
currents, enables us to examine further the threshold properties of
activating a full-blown Ca2+ spike. Here we see that the
Ca2+ spike has a characteristic take-off from a critical
voltage range, and this may be considered a quasithreshold like that of
the action potential (see also Fig. 1). Another way to see this is with
phase plane plots that show the response trajectory projected onto a plane of two dynamic variables. Figure
11A shows the responses from
Fig. 10A plotted as curves of
C*dV/dt, where C is
membrane capacitance and C*dV/dt is
ionic plus injected current versus voltage (V). Because
t is the parameter along a trajectory, the need to translate
curves in time to compare transient responses (as done in Fig. 1) is
obviated. Flow along the trajectories is clockwise (arrows in Fig.
11A), starting at the holding state to the far left. During
the period before the Ca2+ spike is evoked, the trajectory
is flat and lies just above the zero current axis. The triangular
portion of the curves represent the upstrokes of the Ca2+
spikes, and the upper apex coincides with the maximum rate of rise. The
peaks of the Ca2+ spikes occur where the trajectory crosses
the zero-current axis, at the right corner. The recovery phase of the
low-threshold Ca2+ conductance corresponds to when the
trajectory lies below the zero-current axis. The fact that these
several trajectories for different stimuli nearly superimpose during
their early rising phases (lower left side of the triangles) shows the
common mechanism of activation of a full-blown Ca2+ spike
within in a critical and limited voltage range, producing the
appearance of a quasithreshold for membrane voltage. The underlying mechanism, which is a fast, voltage-gated amplification of
IT, also may be visualized from these phase
planes. Figure 11B shows a selected example of a
Ca2+ spike evoked with a long latency, redrawn from Fig.
11A, together with the component currents. The overall
membrane potential is represented by the solid curve, and the open
circles along it represent equally spaced, 5-ms increments to
illustrate motion along the trajectory (i.e., faster where the
are
farther apart). Here, one sees that the upstroke portion of the
Ca2+ spike, especially the early phase, is accounted for by
the dynamics of IT, which is shown by the curve
with short dashes. This trajectory explicitly shows us the nonlinear
relationship of IT to voltage during a
Ca2+ spike. Regenerative growth of
IT drives the acceleration in voltage, where
dV/dt is increasing. Although this triangular
portion is reminiscent of the instantaneous current-voltage
(I-V) relation for IT (with
inactivation, hT, held fixed) the two are not
identical because here hT is changing with time.
In contrast to the nonlinear behavior of IT, the
remaining current is linear with respect to voltage, as seen by the
lower curve (
-
) in Fig. 11B.

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Fig. 11.
Trajectories of Ca2+ spikes in the voltage-current phase
plane. Shown are responses of a reduced model having
IT and Ileak but
without IA to various current injection
steps from an initial holding membrane potential of 91.5 mV.
A: series of curves of membrane voltage vs. membrane
current, the latter calculated from
C*dV/dt, where
C is capacitance, each curve has a clockwise motion
(arrows) with time as a parameter. Initial holding state is at the
far left. B: single curve ( ) redrawn from
A. Shown for comparison are the current-voltage
trajectories of the individual components of the total current, which
are IT (- - ) and
Ileak Iapp
( - ); these currents are plotted with reversed sign. At each
voltage, the sum of components equals
C*dV/dt. Note that the
rapid phase of the upstroke is nearly equal to the regenerative
IT. , equal time increments
(5 ms) along the trajectory of the Ca2+ spike; their wide
spacing during the upstroke indicates that it is very rapid.
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DISCUSSION |
We have systematically examined certain features of activation of
the Ca2+ spike in geniculate relay cells, using a
combination of current-clamp recording with an in vitro slice
preparation and computational modeling. Much of the previous
quantitative experimental work directed at the Ca2+ spike
and the underlying IT has been done in vitro
with voltage-clamp recording, often in acutely dissociated cells
(Coulter et al. 1989
; Hernández-Cruz and
Pape 1989
). This body of work has enabled the development of
theoretical models for Ca2+ spike generation. The models
have been shown to mimic some general aspects of Ca2+ spike
excitability, but there is only a limited set of experimental observations from current-clamp recording that is available for more
thorough comparisons. Our primary goal was to provide a more systematic
quantitative characterization of threshold, amplitude, and latency
properties for Ca2+ spike activation in relay cells. We
also sought to test if our experimental observations from current-clamp
recording are consistent with the voltage-clamp data by using a minimal
computational model to simulate current-clamp results from
voltage-clamp data. Furthermore we use the model to gain insight into
the threshold behavior of Ca2+ spike generation.
Our main observations with this approach are fivefold. 1)
The Ca2+ spike, when triggered, is nearly all or none, and
it in turn evokes a number of action potentials that ride its crest.
2) The process of activating IT
consists of a slowly depolarizing phase that, if sufficiently strong,
activates a later, very fast, depolarization, which is the
Ca2+ spike. 3) The initial slow phase of
IT activation has a variable slope that is
determined at least partly by the amplitude of initial depolarization,
and this, in turn, determines the latency of the nearly all-or-none
Ca2+ spike. 4) Although the size of the
depolarizing input affects the latency of the evoked Ca2+
spike, it has little effect on its amplitude, the spike is evoked in a
nearly all-or-none manner. Instead, the amplitude of the Ca2+ spike is controlled in current-clamp recording by the
extent of membrane hyperpolarization from which the Ca2+
spike is evoked. This hyperpolarization affects the degree of deinactivation of IT and thus the availability
of IT for activation of the Ca2+
spike. 5) Finally, the main observations we have made in our electrophysiological recordings can be simulated from our computational model cell, and the modeling suggests explanations for some of the
phenomena we have observed for activation of Ca2+ spikes.
Amplitude of the Ca2+ spike
Voltage-clamp studies of IT show that the
activation range is fairly extensive, meaning that the underlying
conductance grows in a sigmoid fashion over a voltage range of 10-15
mV (Coulter et al. 1989
; Crunelli et al.
1989
; Hernández-Cruz and Pape 1989
). In
the model, kmT equals 7.4 mV. Furthermore the
activation time constant is based on voltage-clamp measurements at room
temperature, whereas our experiments were carried out much closer to
body temperature, and warmer conditions increase the rate of
activation. In any case, activation of IT causes
rapid depolarization if the membrane voltage is not clamped. Thus in
normal conditions (i.e., no voltage clamp), a small depolarizing input
may evoke a small initial IT, which will cause
further depolarization that increases the IT in
a positive feedback process. Our data indicate that this regenerative process, which is analogous to an autocatalytic chemical reaction (see
also Coulter et al. 1989
; Crunelli et al.
1989
), underlies the generation of Ca2+ spikes
because they seem to be activated in a nearly all-or-none manner (see
Figs. 1-3 and 8, A and B). This means that, when
the cell is in burst mode, it responds to suprathreshold depolarizing inputs with Ca2+ spikes that vary little in amplitude or
shape, although as noted below, their latency can be quite variable.
These features of amplitude, sharpness of threshold, and latency for
Ca2+ spike activation are not readily evident from the
gating properties generated from voltage-clamp studies, but when these
data are used to model IT activation in
current-clamp recording, nearly all-or-none behavior is seen. Our
current-clamp experiments coupled with the modeling help to further
synthesize these voltage-clamp data into understanding Ca2+
spike excitability in relay cells, and this also complements previous
current-clamp studies.
Although the size of an activating input has little effect on the
amplitude of the evoked Ca2+ spike, the level of preceding
hyperpolarization certainly does. This hyperpolarization level
determines the magnitude of IT deinactivation available at the time when a stimulus is delivered, thereby influencing significantly the amplitude of the Ca2+ spike if the input
is suprathreshold. We conclude from these observations that the
amount of deinactivation rather than the activating input controls the
amplitude of the Ca2+ spike. Interestingly, in the model,
the amount of IT recruited depends not only on
the extent of hyperpolarization before IT activation but also on the depolarizing input (see Figs. 8A
and 11A). Because IT inactivates
somewhat during the slow depolarization phase, the extent of this
inactivation is greater for longer latencies of Ca2+ spike
activation. Even though the peak of the conductance associated with
IT may drop substantially with increasing
latency, the computed voltage peak of the Ca2+ spike is
diminished only slightly (see further for discussion). This is because
the relationship between conductance and voltage response is nonlinear
and sublinear for large conductance inputs, so that, for example,
halving the conductance does not half the peak voltage.
The amplitude of the Ca2+ spike is also limited by active
K+ currents. We have not explored the effects of these
other currents in detail, although we expect that, for our experiments
with TTX, the high-threshold currents like the delayed rectifier are
far less activated than they might otherwise be. Our modeling results suggest that IA, which also operates in the
low-voltage regime where IT is activated,
contributes significantly to limiting the amplitude of the
Ca2+ spike. Further study on the properties and spatial
localizations of IA and other K+
conductances is merited to characterize more fully their role in burst
mode firing in relay cells.
There is now ample data from lightly anesthetized and awake animals
that thalamic relay cells firing in burst mode effectively transmit
peripheral information to cortex (Guido and Weyand 1995
; Sherman 1996
). These nearly all-or-none amplitude
properties of the Ca2+ spike thus have important
implications for how information is relayed through the lateral
geniculate nucleus and, presumably, through other thalamic nuclei as
well. Suppose that the amplitude of the Ca2+ spike is
monotonically related to the number of action potentials in the evoked
burst. This implies that a relay cell in burst mode will respond to
suprathreshold EPSPs with little relationship between the amplitude of
the EPSP and the number of action potentials in the burst. For a given
level of hyperpolarization preceding the EPSP and thus a given level of
IT deinactivation, essentially all
suprathreshold EPSPs will evoke the same amplitude of response. Even if
the deinactivation level of the IT varies during
burst firing because of fluctuations in membrane potential, the nearly all-or-none nature of the evoked Ca2+ spike means that no
clear relationship will be present between the input EPSP amplitude and
the evoked response. When the same relay cell responds in tonic mode,
larger suprathreshold EPSPs will evoke more action potentials (see Fig.
4A). However, within a narrow range of initial membrane
potentials for which IT is less deinactivated,
the evoked response, which may or may not involve a Ca2+
spike, may be very slightly graded (Fig. 7) and related in amplitude to
the amplitude of the EPSP. Unless burst firing was somehow limited to
this small range of initial membrane potentials and reduced levels of
IT deinactivation, which seems unlikely but must
be empirically tested in behaving animals, burst firing would reflect
poorly the stimulus amplitude.
In the visual system, we can imagine how this would relate to the
response of geniculate relay cells to varying contrasts because larger
contrasts evoke stronger responses in retinal inputs to these relay
cells (e.g., Troy and Enroth-Cugell 1993
), and this, in
turn, leads to larger EPSPs. With the cell in burst mode, it would be
unable to encode these varying contrasts in its response to cortex,
because all suprathreshold contrasts would evoke the all-or-none burst.
However, in tonic mode, the relay cell would be able to inform cortex
about a large range of contrasts. In this regard, we predict that tonic
firing would represent contrast in a much more linear fashion than
would burst firing. There is support for this from receptive field
studies of cells in the cat's lateral geniculate nucleus because there
is considerably more response linearity in tonic than in burst firing
(Guido et al. 1992
, 1995
; Sherman 1996
).
Also, the conclusion that burst firing is largely like an on-off
switch
there is no response at all for subthreshold stimuli and a
nearly fixed response for all suprathreshold stimuli
while tonic
firing involves graded responses would suggest that a burst response
would more clearly signal the presence of or change in a stimulus than
would tonic firing. This, too, has been shown with in vivo studies
because burst firing is better for signaling the detection of a novel
or changed stimulus than is tonic firing (Guido et al.
1995
; Sherman 1996
).
Although our data indicate that burst firing would produce a similar
response for a wide range of amplitudes of activating ESPSs, this
happens only when the amount of deinactivation, or hT, is the same. Our data also indicate that the
amount of deinactivation does have an effect on the size of the
Ca2+ spike (Fig. 7). However, over a large range of initial
membrane potentials, the effect is small. There is thus little effect
on the number of action potentials activated (Fig. 3) and thus the signal relayed to cortex. During in vivo recording in both anesthetized and awake preparations (Guido and Weyand 1995
;
Guido et al. 1992
), geniculate relay cells switch
between burst and tonic firing, presumably under the control of inputs
from cortex and brain stem that modulate membrane potential and thus
the level of deinactivation (Lu et al. 1993
;
McCormick 1992
; Sherman 1996
;
Sherman and Guillery 1996
). Thus for the cell to begin
firing in burst mode, there must first be a prolonged
hyperpolarization, which may occur passively from the withdrawal of
excitatory inputs or actively from inhibitory inputs, and the strength
in terms of amplitude and duration of this hyperpolarization sets the
extent of deinactivation. This, then, controls the amplitude of the
burst response to the subsequent activating input to the relay cell. If
the hyperpolarizing process that deinactivates these relay cells is
fairly consistent in the behaving animal, leading to uniform
deinactivation, then the response relayed to cortex in burst mode
always would be fairly constant regardless of the stimulus; if this
deinactivating process is variable, then so would responses in burst
mode. At present, there are no published data on the variability in the
amplitude of burst responses, nor do we understand these deinactivation
processes well enough to predict this.
Latency of the Ca2+ spike
Although the intensity of the activating input has little
effect on the amplitude of the burst response, it does affect the response latency, at least for smaller suprathreshold inputs (Figs. 8,
C and D, and 9). The latency dependence comes
from the interaction between the initial ohmic response and the
voltage-dependent gating of IT. According to
voltage-clamp data, the activation gating of IT
is sigmoidal, rising exponentially with voltage from zero to its half
activation around
60 mV, with a "width" parameter of 6.2 mV.
Conductance has an even steeper rise with voltage because, in
Hodgkin-Huxley-like descriptions, it depends on some power (2 in our
model) of the activation variable, mT, for the
conductance of IT. The activation gating is
fast, but the activation level is so small (i.e., deactivated) in this
low-voltage regime (even with inactivation removed) that when the ohmic
depolarization enables recruitment of IT to
begin, the growth of membrane voltage is very slow. For subthreshold
inputs, the ohmic component (leakage plus injected current) becomes
outward and dominates the weak IT. Strong
suprathreshold inputs mean that the voltage is more quickly brought
into the range where the autocatalytic growth of
IT occurs, and latency is short (as in Fig.
12). Over a narrow range of just
suprathreshold depolarization, the competition between the ohmic and
small inward IT means slow growth of membrane
voltage until the nonlinear exponential rise of
IT wins over the linear voltage dependence of
leakage current. The latency is enhanced further because during the
slow depolarization before initiation of the Ca2+ spike,
IT can inactivate somewhat (as seen in Fig. 9).
A complementary account of these latency effects in a relay cell model
is offered by Rose and Hindmarsh (1989)
using the
instantaneous I-V relation and phase plane concepts. Our
explanations of latency do not invoke any opposing active
K+ currents, such as IA. We have
demonstrated in our model with IA blocked or
with its inactivation slowed (see Fig. 10) that the long latency seen
for just suprathreshold inputs is a property solely of
IT.
The implication of this seems obvious: the timing of responses relayed
to cortex in burst mode must be very unreliable for near threshold
stimuli. One prediction is that a cell firing in burst mode to low
contrast stimuli would respond with a highly variable and long latency,
but responses to high contrasts would show shorter latencies with less
variation. How this latency behavior of burst firing for geniculate
relay cells affects visual processing needs to be explored further. For
instance, it is well known that it takes less time in psychophysical
experiments to detect stimuli expected to evoke greater firing in
retinal inputs, such as brighter stimuli (Alpern 1954
;
Lennie 1981
; Wilson and Lit 1981
) or
stimuli with higher contrast (Harwerth and Levi 1978
),
and perhaps this property of burst firing contributes to this phenomenon.
Theoretical considerations on firing threshold for
Ca2+ spikes
FitzHugh (1960
, 1969
) described two basic types of
threshold behaviors in excitable membranes. A quasithreshold phenomenon is characterized by a finite latency and a continuous dependence of
response amplitude on stimulus strength. In contrast, a singular-point threshold phenomenon exhibits infinite latency and a discontinuous stimulus-response curve. The latter type is associated with a steady-state current-voltage relation that is N-shaped as elaborated by
Rinzel and Ermentrout (1989)
. The standard
Hodgkin-Huxley model has the former type of excitability as does our
minimal model. Comparison of these theoretical notions and our
experimental data suggest that the relay cells that we observed also
had the quasithreshold behavior, although with a very steep
stimulus-response dependence. This means that one should in principle
be able to evoke, using finely tuned stimuli, graded responses. Because
of these rigorous distinctions we have throughout the paper referred to
the relay cell's responsiveness as "nearly" all or none. If the
continuous nature of the response amplitude is in question, it can
sometimes be exposed by adjusting other stimulus or environmental
parameters, such as the holding level of hyperpolarization for relay
cells (as we have done in Fig. 11) or, for example, temperature in the Hodgkin-Huxley model and space-clamped squid giant axon (Cole et
al. 1970
; FitzHugh 1966
).
Although our model is based on voltage-clamp data, it is idealized: for
example, the cable properties of relay cells are ignored. Although
relay cells are relatively compact electrotonically, we expect that
some aspects of Ca2+ spike generation are affected by the
spatial distribution of T channels underlying IT
and those for other intrinsic currents, as well as ionotropic and
metabotropic receptors activated by various synaptic inputs. This
deserves study. There is good evidence that much of
IT is of dendritic origin (Destexhe et
al. 1998
; Munsch et al. 1997
; Zhou et al.
1997
). One expects that the membrane voltage versus current
curves to be right-shifted if somatic inputs are delivered and
IT is distally (i.e., largely dendritically) distributed (see Destexhe et al. 1998
). Perhaps the
additional time needed for recruitment when IT
is remote might contribute to longer latencies as well.
It also would be useful to explore further with compartmental modeling
the extent of IT recruitment that underlies
variable latency responses. Our single compartment model shows reduced IT for longer latency responses (Fig.
8A and implied by Fig. 11 because
dV/dt is mostly due to IT
during the upstroke of the Ca2+ spike). If significant
Ca2+ entry is associated with burst mode the ability to
grade, this entry could have functional significance. However, we see
little suggestion of a graded IT in our
experimental results (as interpreted in our experimental
dV/dt vs. V plots, which have not been
shown). It will be interesting to learn, with future modeling studies, why this is not seen. Perhaps the segregation of
IT to distal sites away from our stimulating
electrode ensures more autonomous burst responses and thus could
explain as well the extreme lack of response amplitude dependence on
stimulus in our experiments as compared with modest dependence in the theory.
Conclusions
We have shown that activation of the Ca2+ spike
behaves qualitatively like that of conventional
Na+/K+ action potentials, with a quasithreshold
for voltage, a nearly all-or-none appearance, and a variable latency
around threshold that drops precipitously with increasing intensity of
activation. The major features of our experimental observations from
current-clamp recording are supported by simulations in a reduced model
based on voltage-clamp data. These properties of geniculate relay
cells, which presumably extend generally to thalamic relay cells, have important implications for relay of information through thalamus to cortex.
One implication is that the relay of information during burst firing
should be highly variable in time with near threshold stimuli but
become much more stable with stronger activating inputs. Our results
also suggest that when relay cells fire in burst mode as a result of
being activated from hyperpolarized levels by their driving inputs, the
response relayed to cortex is either zero, if the driving input is
subthreshold, or a burst that is largely invariant in amplitude over a
wide range of suprathreshold inputs. This contrasts sharply with
tonic responsiveness when relay cells fire as a result of being
activated from depolarized levels by their driving inputs: here the
response relayed to cortex is graded over a large range of input
intensities. Thus a relay cell during burst firing is geared to signal
rather dramatically the presence of or sudden change in its driving
inputs (e.g., a novel visual stimulus in the receptive field of a
geniculate relay cell), whereas during tonic firing it would more
readily signal continuous changes in its driving inputs. This notion is
consistent with a previous suggestion from receptive field studies that
tonic firing of geniculate cells provides a more linear relay better
adapted to analyzing a stimulus faithfully, whereas burst firing
provides better stimulus detectability (Guido et al.
1995
; Sherman 1996
).
 |
ACKNOWLEDGMENTS |
We are grateful to A. Houweling and T. Ozaki for sharing their
NEURON scripts for the Huguenard-McCormick model.
This work was supported by National Eye Institute Grant EY-03038 and a
postdoctoral research fellowship to X. J. Zhan from Fight for
Sight, research division of Prevent Blindness America.
 |
FOOTNOTES |
Address for reprint requests: S. M. Sherman, Dept. of
Neurobiology, State University of New York, Stony Brook, NY 11794-5230.
The costs of publication of this article were defrayed in part by the
payment of page charges. The article must therefore be hereby marked
"advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 24 August 1998; accepted in final form 11 January 1999.
 |
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