1The Center for Hearing Sciences and Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland 21205; and 2Division of Otolaryngology-Head and Neck Surgery, Department of Surgery, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7070
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ABSTRACT |
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Kanold, Patrick O. and Paul B. Manis. A Physiologically Based Model of Discharge Pattern Regulation by Transient K+ Currents in Cochlear Nucleus Pyramidal Cells. J. Neurophysiol. 85: 523-538, 2001. Pyramidal cells in the dorsal cochlear nucleus (DCN) show three characteristic discharge patterns in response tones: pauser, buildup, and regular firing. Experimental evidence suggests that a rapidly inactivating K+-current (IKIF) plays a critical role in generating these discharge patterns. To explore the role of IKIF, we used a computational model based on the biophysical data. The model replicated the dependence of the discharge pattern on the magnitude and duration of hyperpolarizing prepulses, and IKIF was necessary to convey this dependence. Phase-plane and perturbation analyses show that responses to depolarization are critically controlled by the amount of inactivation of IKIF. Experimentally, half-inactivation voltage and kinetics of IKIF show wide variability. Varying these parameters in the model revealed that half-inactivation voltage, and activation and inactivation rates, controls the voltage and time dependence of the model cell discharge. This suggests that pyramidal cells can adjust their sensitivity to different temporal patterns of inhibition and excitation by modulating the kinetics of IKIF. Overall, IKIF is a critical conductance controlling the excitability of DCN pyramidal cells.
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INTRODUCTION |
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The set of intrinsic membrane
conductances expressed by a neuron determines how different patterns of
excitation and inhibition are transformed into output spike trains
(Llinas 1988) or in other words, the signal processing
operations that cells perform on the synaptically evoked voltage
waveform. In the auditory system, many neurons show discharge patterns
that appear to be closely regulated by cell-specific patterns of ion
channel expression. Pyramidal cells of the dorsal cochlear nucleus
(DCN) show a variety of different firing patterns to auditory
stimulation in vivo (Godfrey et al. 1975
;
Pfeiffer 1966
; Rhode et al. 1983
). We
demonstrated that the in vivo firing patterns could be replicated in
vitro by varying the pattern of hyperpolarization and depolarization (Manis 1990
). The discharge pattern changes were
consistent with the increased activation of a transient (inactivating)
A-type K+ conductance
(IKI) (Connor and Stevens
1971
) following a hyperpolarization (Manis
1990
). Subsequent modeling studies with generic ionic
conductances have supported this initial hypothesis (Hewitt and
Meddis 1995
; Kim et al. 1994
; Zhao
1993
). Although these models represent a proof of principle and
confirmation of the conceptual model, these models used arbitrarily
defined cell and channel parameters and thus lacked a physiological basis.
Recently we characterized a fast transient potassium current
(IKIF) in vitro in identified DCN
pyramidal cells (Kanold and Manis 1999b). The voltage
and time dependence of conductance was well matched with the voltage
and time dependence of the discharge patterns on prior membrane
hyperpolarization, suggesting that IKIF regulates the voltage-dependent
discharge pattern in DCN pyramidal cells. A conclusive test of the role
of IKIF in generating the discharge
patterns would be to remove the channel from the cell and observe
whether the discharge patterns are altered. Unfortunately due to the
diversity and sequence similarities of K+
channels, few specific antagonists are available, and presently none
are known to be specific for IKIF.
Since we had characterized most outward currents present in DCN
pyramidal cells on a detailed biophysical level (Kanold and Manis 1999b), this information was used to develop a
computational model. Computational models have the advantage that
conductances can be removed from the cell conveniently and the effects
on the simulated discharge can be observed readily. In contrast to
previously published models, the potassium channels in the model are
based on in vitro data. The simulation results show that
IKIF is solely responsible for the
observed voltage-dependent discharge patterns in DCN pyramidal cells.
Moreover, we find that modifications of the voltage and time dependence
of IKIF alter the discharge patterns. The model is consistent with the experimentally observed range of
voltage dependence and channel kinetics and suggests that these may be
adjusted in individual cells to optimize processing of different
patterns of afferent activity.
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METHODS |
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Modeling was performed with programs implemented in C++
(Metrowerks Codewarrior 11) and executed as a MEX-file under MATLAB (version 5.2, The Mathworks, Natick, MA) on a Power Macintosh G3
(Apple, Cupertino, CA). Most results were also confirmed with the same
equations implemented in NEURON, version 4.2 (Hines and Carnevale 1997).
The model pyramidal cell was represented by a single somatic
compartment in which a membrane capacitance
(Cm) is connected in parallel with
voltage- and time-varying ionic conductances. While there is some
evidence that the dendritic trees of DCN pyramidal cells contain active
conductances (Manis and Molitor 1996; Molitor and
Manis 1996
), adding a passive dendritic tree or one with
uniform active conductances did not quantitatively change the results shown here except for a decrease in the input resistance. Thus we
performed all calculations on a point soma model.
The membrane contains five voltage-dependent ionic conductances and a
leak conductance
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(1) |
Kinetic descriptions
The currents were modeled as voltage- and time-dependent
conductances using standard descriptions (Connor et al.
1977; Hodgkin and Huxley 1952
) defined by time-
and voltage-dependent activation and inactivation variables, termed the
gating functions x(V, t). The rate of change of
the gating variables x(V, t) are described by the
first-order differential equation
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(2) |
Fast sodium current (INa)
Because Na+ currents have not been
characterized in DCN pyramidal cells, a simple
INa similar to other
Na+ channels in the literature in central neurons
was implemented (Bernander et al. 1994). The kinetic
equations for INa are given by
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(3) |
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(4) |
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(5) |
Inactivating potassium currents (IKIF and IKIS)
The most prominent outward currents in the somata of DCN
pyramidal cells are the fast and slow inactivating potassium currents IKIF and
IKIS. The kinetic equations for
IKIF and
IKIS were directly derived from the
experimentally determined parameters (Kanold and Manis
1999b)
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
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(11) |
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(12) |
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(13) |
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(14) |
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(15) |
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Noninactivating potassium current (IKNI)
A third potassium current was experimentally observed in both
acutely isolated cells and in patches. This current was a
noninactivating, and behaved according to the following equations
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(16) |
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(17) |
Hyperpolarization activated potassium current (Ih)
Pyramidal cells show a gradual decrease in hyperpolarization
("sag") during long hyperpolarizing pulses (see Kanold and
Manis 1999b; Manis 1990
). In addition, the
membrane time constant is shorter for depolarizations after
hyperpolarizations than for hyperpolarizing steps from the same voltage
(Manis 1990
; unpublished observations). One conductance
that could produce these features is a nonselective
hyperpolarization-activated cation current
(Ih). Therefore a previously published
description of Ih (Destexhe and Babloyantz 1993
; Destexhe et al. 1993
) was
incorporated into the model. Ih
activated below
40 mV and thus contributed slightly to the resting
input resistance. Activation of Ih
reduced the membrane time constant (measured in response to a
depolarization at the end of a 100-ms hyperpolarizing step to
100 mV)
m from 3.2 to 2 ms.
Ih is defined as
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(18) |
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(19) |
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(20) |
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(21) |
Leakage current (IL)
The leakage current representing resistive losses over the
membrane was described by Ohm's law
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(22) |
The reversal potentials for potassium
(VK) and sodium
(VNa) were adjusted to 81.5 mV (as
measured from patches) and 50 mV (as estimated) respectively.
Scaling
In our experiments (Kanold and Manis 1999b),
K+ channel kinetics were measured in outside-out
patches. However, the exact geometry of the patch and hence its area
was unknown, and it is likely based on our observations that the
somatic distribution of channels is uneven. We therefore considered
several factors in setting the magnitudes of conductances. First, the
whole cell capacity Cm was chosen to
match passive membrane properties of acutely isolated whole cells from
rat DCN (Kanold and Manis 1999b
). Isolated DCN cells in
rat pup have narrow fusiform somas >20 µm in length, with
Cm ranging from 12 to 16 pF. These
capacitance values are consistent with a spherical soma of ~20 µm
diam, assuming the standard membrane capacitance density of 1 µF/cm2 (Hille 1992
). We choose
the isolated cells as the target for these simulations because we had
accurate measurements of whole cell currents and input resistances for
this situation. In intact cells in slices, failure to adequately
voltage-clamp dendritic membrane prevented us from obtaining acceptable
estimates for the maximal conductances. The input resistance of the
isolated cells averaged 300 M
, whereas the input resistances of
outside-out patches varied from 3 to 8 G
. Using a scale factor of 30 (~8G
/300M
), we obtained total outward currents at 0 mV of
~5 nA, consistent with our whole cell voltage-clamp data (Fig.
1D). In additional simulations (not shown), we adjusted this
scale factor to mimic an intact cell. The cell capacitance and all
conductances were raised again by a factor of ~20 (to set
Cm to 250 pF, consistent with
Rin = 50 M
and
m = 12 ms), and the input resistance
adjusted via the leak conductance to 50 M
. Although larger currents
were required to obtain equivalent voltage displacements due to the lower input resistance, the results were the same.
The relative conductance ratios of the different outward currents were
derived from the experimental measurements. The conductance of
IKIF
(gKIF) in patches varied from 1.5 to
14 nS and averaged ~5 nS; thus after scaling from patch to whole
cell, gKIF was set to 150 nS. The
measured amplitude of IKIS in patches
is about one-fourth the amplitude of
IKIF (see Kanold and Manis
1999b, Fig. 3), so gKIS was
set to 40 nS. The maximum conductance of gKNI as scaled from patches to whole
cell would be 20 nS. However, this value was too small to rapidly
repolarize action potentials and produce action potentials followed by
undershoots. Setting gKNI to 80 nS
yielded appropriate action potential shapes and physiological action
potential height. We justify this difference on the grounds that
channel densities may be higher in the initial segment of the axon
where action potentials are most likely initiated (Colbert and
Johnston 1996
; Stuart et al. 1997
), whereas our
estimates were from conductances sampled from the soma.
The magnitude of Ih
(gh) was determined from estimates of
the equivalent parallel conductance generated by the sag during the
hyperpolarizing prepulse in current-clamp recordings from slices, which
was 34 nS. This value was then scaled by the relative capacitance of
the isolated cells versus the equivalent capacitance determined from
the m of cells in slices, yielding a whole
cell conductance for gh of 3 nS.
Vh was set to
43 mV (Destexhe
and Babloyantz 1993
; Destexhe et al. 1993
). The
magnitude and time course of the sag produced by this conductance
closely resembled that seen in intracellular recordings from DCN
pyramidal cells.
Voltage-clamp simulations
To confirm the behavior of the model, we compared the size and
voltage dependence of the currents with the experimentally obtained
voltage-clamp data from acutely isolated cells and outside-out membrane
patches. In these voltage-clamp simulations,
gNa is set to zero to eliminate the
contribution of Na+ channels. Activation of the
transient currents was studied using a prepulse protocol similar to the
protocol used experimentally, in which the membrane was held either at
0 or 100 mV to inactivate or deinactivate both transient currents,
respectively. The prepulse was followed by a test step to a varying
voltage. The transient current was inactivated by depolarizing
prepulses (Fig. 1C),and was activated near the resting
potential of
60 mV (Fig. 1D). The size of the transient
current, its kinetics, and its activation voltage is in the range of
the experimental results for acutely isolated cell bodies
(Kanold and Manis 1999b
). Steady-state inactivation was
measured by preceding a depolarizing step with a prepulse to various
voltages (Fig. 1C). The current showed a pronounced transient component after hyperpolarizing prepulses; the amplitude of
the transient current was smaller following depolarizing prepulses. Figure 1E shows the normalized peak transient current as
function of prepulse voltage. Similar to the experimental data
(Kanold and Manis 1999b
, Fig. 4), the inactivation shows
a double Boltzmann shape with half voltages of about
90 and about
40 mV (arrows indicate the estimated midpoints of the 2 inflections).
Setting either gKIS or
gKIF to zero resulted in single
Boltzmann curves (Fig. 1E, dashed lines) that correspond to
the inactivation curves of the unblocked current. Eliminating
IKIF resulted in a single Boltzmann
curve (long dashed line) with a half inactivation of about
40 mV
(vertical thin line), which corresponds to the half inactivation of
IKIS. When
IKIS was removed, a single Boltzmann curve (short dashed line) was observed with a half inactivation of
about
90 mV (vertical thin line), which corresponding to
half-inactivation of IKIF. These
results are similar to those seen with pharmacological block of
IKIS (see Kanold and Manis
1999b
, Fig. 6). When IKIS was
blocked by TEA or 4-aminopyridine (4-AP), the blocked current (determined by subtraction) had half-inactivation at about
40 mV.
IKIF was TEA and 4-AP resistant and
showed half-inactivation at about
90 mV. The double Boltzmann shape
in the model is not as pronounced as in some of the experimental data
(i.e., see Kanold and Manis 1999b
, Fig. 6), probably
reflecting varying ratios of IKIF and
IKIS in outside-out patches. These
results show that the activation and inactivation of the potassium
currents in the model is similar to the experimental observations.
We also measured the recovery of IKI
from inactivation while varying the length of the hyperpolarizing
prepulse. The amplitude of the transient current was maximal after long
hyperpolarizing steps, whereas it was reduced after short steps. When
the time course of recovery of the peak current (Fig. 1F,
upright triangles) was fitted with a single exponential function over
the range of prepulse durations studied experimentally, the resulting
time constant was 14 ms (Fig. 1F, dashed line). This time
constant is similar to the experimentally observed time constants. We
previously found that the recovery of
IKI was slightly longer than the
dependence of the first spike latency shift on prepulse duration (time
constants of 15-20 vs. 10 ms) (Kanold and Manis 1999b).
In the model, it was apparent that the recovery time course of
IKI was better described with a double
exponential function, with a fast and a slow time constants of 11 and
213 ms (Fig. 1F, solid line), suggesting that removal of
inactivation for the two currents
(IKIF and
IKIS) proceeds with different time
courses. Removing IKIF from the model
resulted in smaller outward transient current and the residual recovery time course was best fit with a single exponential function with a time
constant of 202 ms (Fig. 1F, inverted triangles and solid line), corresponding to the time course of removal of inactivation for
IKIS. These results indicate that the
behavior of the transient currents in the model closely parallels that
of the experimentally studied potassium currents.
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RESULTS |
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The behavior of the point soma model of a DCN pyramidal cell in a
variety of experimental conditions will be investigated and compared
with the experimentally observations reported previously (Kanold
and Manis 1999b). The results are presented in two parts. First, current-clamp simulations will be presented and we show that the
discharge patterns match the experimental observations. Second, we show
how modifications of IKIF voltage
dependence and kinetics within the experimentally observed range alter
the dependence of the discharge pattern on prepulse amplitude and duration.
Spike rate
First, the response of the model to current pulses of varying
amplitudes from rest was examined. The model did not spontaneously fire
action potentials at rest. Depolarizing current injections produced
trains of action potentials (Fig.
2A). The sustained discharge
was very regular, similar to results obtained in vitro (Hirsch
and Oertel 1988; Kanold and Manis 1999b
;
Manis 1990
; Zhang and Oertel 1994
). The
spike frequency increased monotonically and showed some saturation for
large injection currents (Fig. 2B). For small currents, the
firing rate increased with a slope of 1,012 Hz/nA. This slope is about
nine times higher than experimentally measured in slices from guinea
pig (116 Hz/nA) (Manis 1990
), three to nine times higher
than in mice (100-300 Hz/nA) (Zhang and Oertel 1994
),
and four times higher than that in gerbil (258 Hz at 1 nA) (Ding
et al. 1999
). The difference in slopes can be explained by the
higher input resistance of the somatic model as compared with a cell in
slices (300 vs. ~30 M
). Larger model cells with dendritic
compartments or single compartment models with lower input resistances
showed spike rates similar to those in real cells (not shown). For
hyperpolarizing current injections, a "sag" was present in the
response, reflecting activation of Ih,
which is similar to experimental results (Manis 1990
).
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Dependence of the discharge pattern on prepulse voltage
Next, we investigated how the first spike latency (FSL)
and first interspike interval (FISI) depend on the prepulse voltage. In
pyramidal cells, the FSL and FISI are a function of the depth and
duration of hyperpolarization preceding a test depolarization (Kanold and Manis 1999b; Manis 1990
). In
these simulations, we used a 50-ms subthreshold depolarization to
partially inactivate transient currents, as we did experimentally. This
was done to help insure that the state of the channels at the start of
the hyperpolarizing pulse was the same in all cells. The traces in Fig.
3A1 demonstrate the effect of
varying the prepulse amplitudes. For small hyperpolarizations, there
was little change in latency. However, as the hyperpolarization was
increased further, the latency suddenly increased. When the latency
increased, there was a characteristic "hump and sag" of the
membrane potential at the onset (arrowheads in Fig. 3A1). In
Fig. 3B1 the FSL (circles) and FISI (triangles) are plotted
as a function of prepulse voltage. Most of the FSL increases occur when
the prepulse voltage is between
80 and
110 mV. The largest increase
in FSL occurred between
86.3 and
83.3 mV (arrow in Fig.
3B1); this corresponds to the disappearance of the onset
spike (arrowhead in Fig. 3A1). The increase in FSL at this
point is similar to the duration of the FISI, so that the first spike
now occurs approximately where the second spike occurs without prior
hyperpolarization. To estimate the half-voltage for the FSL shift, a
Boltzmann function was fitted to the data (Fig. 3B1, solid
line). The half voltage was
89.3 mV, which is similar to values
obtained experimentally using the same analysis (Kanold and
Manis 1999b
).
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To test the hypothesis that the voltage-dependent FSL shift is due to IKIF, gKIF was set to zero as shown in Fig. 3A2 for the most hyperpolarized prepulse voltage. The FSL was slightly longer than with no prepulse, probably because of the increased passive charging time of the membrane. The shift in FSL with increasing hyperpolarization is small, as shown in Fig. 3B2. These results show that IKIF is necessary for the generation of voltage-dependent discharge patterns.
Dependence of the discharge pattern on prepulse duration
We next examined the effect of changing the duration of the hyperpolarizing prepulse on the FSL. Figure 4A shows four traces with varying prepulse durations. Increasing the length of the prepulse from 3.0 to 9.2 ms increased the FSL from 6.2 to 10.0 ms. However, lengthening the prepulse further to 10.8 ms increased the FSL to 23.7 ms. Note that the first spike occurs at a latency just slightly longer than the second spike for a prepulse duration of 9.2 ms, indicating that the onset spike has been deleted (arrowhead). The voltage showed a hump and sag in place of the deleted onset spike. The cell fires now with a buildup pattern. Further increases in the prepulse duration lead to a further increase in FSL. The FSL increased linearly for short prepulses (Fig. 4B1), probably due to passive charging of the membrane, and then abruptly transitioned to a long FSL pattern. Note the small concurrent changes in FISI at the transition point (open triangles).
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The shift in FSL with prepulse duration was fitted with a single
exponential function (Fig. 4B1, solid line), with a time constant of 9 ms, similar to that seen experimentally (Kanold and Manis 1999b). Removal of
IKIF abolished most of the dependence of the FSL on the prepulse duration (Fig. 4B2, filled
circles). A small residual linear FSL shift was present after the
removal of IKIF for short pulses. This
shift is also seen with IKIF (Fig. 4B1) and is probably due to passive charging of the
membrane. The FSL decreases for long hyperpolarizing steps, an effect
likely due to the activation of Ih,
which lowers the membrane time constant during repolarization. These
results suggest that increased availability of
IKIF is directly responsible for the
increase in FSL with longer hyperpolarizing steps. They also
suggest that Ih may play a modulatory role in this process.
Transitions between discharge patterns
To this point, it has been demonstrated that the model showed a
regular or buildup pattern after hyperpolarizing prepulses, depending
on the prepulse amplitude. Pyramidal cells can show a regular, buildup,
or pauser pattern or transition between these patterns depending on the
levels of hyperpolarization and depolarization (see Kanold and
Manis 1999b; Manis 1990
). The transition from a
buildup to a pauser pattern usually occurs when the depolarization is
made larger.
Figure 5 shows the response of the model
to several prepulse levels while testing with larger depolarizing
currents (200 instead of 100 pA). Now the model responds with an
increased FISI, but a short FSL, following hyperpolarized pulses (Fig.
5A1, ). This is the hallmark of the pauser pattern. The
increase in FISI largely occurs between
80 and
110 mV, with an
estimated half voltage of
99 mV (Fig. 5B), similar to the
range observed in vitro (Kanold and Manis 1999b
). Pauser
responses were abolished when IKIF was removed from the model (not shown). The model also changed firing pattern from regular to pauser as the length of the hyperpolarizing pulse was increased (Fig. 5, C and D); however,
the transition in this case is more gradual than that shown in Fig. 4.
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Intermediate amplitude (150 pA) depolarizing steps caused the model to
show all three discharge patterns when varying the prepulse
hyperpolarization (Fig. 6, A
and C). For small hyperpolarizations, the model showed a
regular discharge pattern, whereas increasing the amount of
hyperpolarization caused a switch to a pauser pattern (arrow in Fig.
6A1). With further hyperpolarization, the onset spike failed
(arrowhead) and the model fired with a buildup pattern. The transition
between pauser and buildup pattern is visible as a large increase in
FSL and an associated decrease in FISI (Fig. 6B). Similar
transitions between firing patterns were seen in vitro (Kanold
and Manis 1999b; Manis 1990
). The model also
changed firing pattern from regular to pauser to buildup as the length of the hyperpolarizing pulse was increased (Fig. 6, C and
D).
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To summarize, the model can show all three discharge patterns: regular, buildup, and pauser. Which pattern is produced depends on the levels of prehyperpolarization and on the magnitude of the test depolarization. The voltage and time dependence of these patterns is similar to that seen in cells in brain slices, including the sharp transitions between firing modes that are seen with small changes in stimulation conditions. It appears that IKIF controls these discharge patterns since when it is removed from the model, the cell only fires regularly regardless of the stimulus conditions.
Influence of the half-inactivation voltage of IKIF on discharge pattern
If IKIF controls the
discharge patterns of the cells, then the voltage dependence of the FSL
and the inactivation of IKIF should be
related. Indeed, a wide range of half-inactivation voltages of
IKIF
(VKIF) and half-voltages of the FSL
shift (VFSL) were observed
experimentally (Kanold and Manis 1999b). To directly test this hypothesis, VKIF was varied
from its control value of
89.6 mV to values ranging from
99.6 to
64.6 mV. Figure 7A shows the
results of parametric simulations in which both the prepulse amplitude
and VKIF were varied. The plot shows
contour lines of the FSL during these trials; regions associated with
particular discharge modes are indicated on the graph. For small
hyperpolarizations and negative VKIF,
no increase in FSL is seen; the cell always fires in a regular pattern.
However, increasing the hyperpolarization to near
100 mV results in a
large increase in FSL, corresponding to the buildup pattern. When
VKIF is made more positive, then the
region of rapid FSL increase occurred at less hyperpolarized prepulse
levels. For example, when VKIF is
64.6 mV, the cell fires with a buildup response for prepulses just
below the resting potential. For these conditions (100-pA depolarizing
test pulse), the FISI shows little change for any combination of
prepulse voltage. To explore the association between half-inactivation
and FSL voltage dependence, the half-voltage of the Boltzmann fit to
the prepulse voltage dependence for each value of
VKIF was computed as shown in Fig.
3B1. These data almost fell on a line with a slope of 1 (Fig. 7B,
), suggesting that the region of the main
latency shift and the half-inactivation voltage of
IKIF are strongly correlated. We also
analyzed the model using 200-pA depolarizations, where cells show a
transition from regular to pausing patterns. The results were similar
in that the FISI was strongly correlated with
VKIF (not shown).
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Next we investigated how variations of the half-inactivation voltage of
IKIF
(VKIF) affect the dependence of the
FSL on prepulse duration. Figure 7, C and D,
shows the dependence of FSL and FISI on prepulse duration over a range
of VKIF. For a given combination of
hyperpolarization and depolarization, the FSL is somewhat independent of VKIF, except for long pulses where
the latency shift depends on both pulse duration and
VKIF (Fig. 7C). In the same
simulations, the FISI increased significantly when
VKIF was less negative for prepulse
durations where a short FISI was produced under control conditions
(Fig. 7D). For example, varying the prepulse duration with
VKIF = 64.5 mV yields a regular
response for very short prepulses, pauser responses for prepulses
between 4 and ~12 ms, and buildup responses for longer prepulses.
Thus the prepulse duration necessary to initiate the transition from
regular to pauser, and from pauser to buildup, depends on the value of
VKIF.
These simulations suggest that cells with different half-inactivation voltages for IKIF will respond with different discharge patterns to the same stimulus. We suggest that the variability of the voltage dependence of the discharge patterns seen experimentally reflects the underlying variability of VKIF. Moreover, if a cell can adjust VKIF, then it can dynamically alter its response to a particular stimulus.
Influence of the kinetics of IKIF on discharge pattern
Because voltage dependence of the FSL and the inactivation of
IKIF were related, we investigated how
the kinetics of IKIF influence the
discharge pattern. The kinetics of
IKIF vary over a wide range
(Kanold and Manis 1999b), and activation and
inactivation rates appear to be correlated for individual cells.
Therefore in the next set of simulations, we varied the base value of
the activation time constant (
mF) from its
control value of 0.5 ms to values up to 4 ms (this corresponds to a
simple additive shift of the
-V curves). To maintain the
experimentally observed correlation between
act and the inactivation time constant
(
hF), we also changed the base value of
hF according to the formula
hF = 7.1 + 5.8*
mF
(Kanold and Manis 1999b
). Figure 8,
A and B, shows the effect of changing the kinetics of
IKIF on the FSL and FISI as the
prepulse amplitude was varied. The parameters corresponding to the
traces shown in Fig. 5A1 are indicated (- - - and
).
Increasing
mF and
hF
caused an increase in the FSL shift for large hyperpolarizations (Fig.
8A). However, for intermediate hyperpolarizations between about
85 and
90 mV, large increases in FISI were seen when the time
constants were increased (Fig. 8B). Thus the cell now
responded in a pauser pattern instead of a buildup pattern. The plots
of FSL and FISI are complimentary, indicating that there are discrete transitions between firing patterns for specific prepulse conditions, as
mF/
hF are varied.
When we superimpose the contours that defined the borders of the
increased FSL or increased FISI pattern (Fig. 8C), the
resulting responses of the cell showed three discrete areas. First,
there is an area where both FSL and FISI are short (labeled
"regular"). Second, there is an area where FSL is long and FISI is
short (labeled "buildup"). Finally, there is an area where FISI is
long and the FSL is short (labeled "pauser"). The shaded region
indicates the transition zone between the pauser and buildup firing
patterns. The prepulse voltages for this transition zone are directly
related (but not completely monotonically) to the time constants of
activation and inactivation. In general, increasing the time constants
caused a shift of the pauser/buildup transition to more hyperpolarized
potentials.
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Varying the kinetics of IKIF had a
similar effect on the discharge pattern changes induced by varying
prepulse duration (Fig. 8, D and E). Again, the
regions of pauser and buildup responses are complementary. When
mF and
hF are
increased, the cell fires with a pauser pattern for prepulse durations
that generate a buildup pattern under control conditions (Fig.
8F). The prepulse duration at which the pauser/buildup
transition occurred increases monotonically as
mF and
hF are increased.
These results show that the cells firing pattern to prepulses of
particular amplitude or duration depends on the time constants of
activation and inactivation of IKIF.
In conjunction with the results of the previous section, it appears
that cells have two independent mechanisms by which they can control
their firing patterns: adjustment of
VKIF or of the rates
mF and
hF.
Phaseplane analysis
The results presented in the preceding text strongly suggest that
the availability of IKIF, as
controlled by its inactivation gating variable
(hF), is the crucial variable
controlling the discharge pattern. To evaluate the association between
the inactivation of IKIF and the
discharge pattern, especially around the transition between regular and
buildup patterns, a phaseplane analysis was performed using the model
under standard conditions of VKIF and mF/
hF. Figure
9A1 shows the voltage traces
used for the analysis. The thin trace was obtained with a
hyperpolarizing prepulse of 9.2 ms (generating a regular discharge
pattern), and the thick trace was obtained with a 10.8-ms prepulse
(generating a buildup discharge pattern). The traces have been aligned
at the onset of the test depolarization. Figure 9A2 shows
the time course of the inactivation gating parameter of
IKIF
(hF). During the 9.2-ms hyperpolarizing pulse, hF increases
from its steady-state value at rest of 0.012 to 0.164 at the onset of
depolarization (thin line). A prepulse of 10.8 ms resulted in an
increase of hF to 0.225 at the onset
of depolarization (thick line). As the cell was depolarized,
hF increased to a maximum of 0.203 and
0.266, respectively. These results suggested that a critical amount of IKIF had to be deinactivated to cause
discharge pattern transitions and that this amount was between 16.4 and
22.5% of the maximal IKIF.
|
The trajectory of hF during the voltage excursion is presented with phaseplane plots during the hyperpolarization, the rising phase of the membrane voltage, and the first few spikes in Fig. 9B1. hF increased during the hyperpolarization. The transition between the two discharge patterns is visible as a divergence in the trajectory (arrow) between the 9.2 ms (thin line) and 10.8 ms (thick line) condition. For the same traces, the activation of IKIF (mF) showed a much smaller dependence on prepulse duration (Fig. 9B2).
To test whether the amount of inactivation of IKIF is crucial in determining firing pattern, a perturbation analysis was performed. Figure 9C illustrates the effect of perturbations of hF from the resting value of 0.012 to values between 0.1 and 0.3 coincident with the onset of depolarization (no hyperpolarization is applied in these simulations). Figure 9D shows the resulting FSL (filled circles) and FISI (open triangles) for the different values of hF. The unfilled circles correspond to the voltage traces in Fig. 9C. Increasing hF from 0.1 up to 0.21 resulted in a small increase in FSL. At a value of hF of 0.22 (vertical dashed line), a large increase in FSL was seen (arrow), which coincided with a decreased FISI. The large changes in FSL observed with a small increase in hF to 22% are suggestive of a bifurcation. However, only a mathematical analysis of the equilibrium points of the system can definitively demonstrate a bifurcation. Nonetheless these results indicate that the critical time at which the cell shifts into a long latency firing mode is determined by the amount of IKIF available at the moment of depolarization, i.e., by the amount of inactivation that has been removed during the hyperpolarization.
Influence of Ih
Ih had been included in the model to provide a substrate for the observed differences in membrane charging time constants to hyperpolarizing and depolarizing steps and to account for the observed sag in the response to hyperpolarized pulses. So far the influence of Ih on the discharge patterns was unclear. Therefore Ih was removed from the model and the voltage and time dependence of the discharge patterns were investigated. Since Ih is partially available at rest, it was necessary to adjust the leak conductance gL to 3 nS to keep the input resistance at rest the same as in all prior simulations.
Figure 10A shows the
discharge patterns with different prepulse amplitudes. Increasing the
amount of hyperpolarization increased the FSL. The model showed a
firing pattern transition between 83.6 and
86.8 mV (Fig.
10A1). The increase in FSL with prepulse amplitude was
fitted with a Boltzmann function with a half-voltage of
91.0 mV (Fig.
10B). Thus the removal of
Ih shifted the voltage dependence of
the transition by about
2 mV (compare with Fig. 3). The retention of
the hump and sag at the onset of the depolarizing step suggests that
the hump and sag is not due to slow deactivation of
Ih.
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Lengthening the prepulse increased the FSL (Fig. 10C). The
sharp transition between discharge pattern occurred between prepulses of 9.2 and 10.8 ms (Fig. 10C1), visible as steep increase in
latency with increasing prepulse duration (Fig. 10D). The
prepulse duration at which the discharge pattern transition occurs is
unchanged (compare with Fig. 4). However, the recovery time constant
was slightly increased to 12.4 ms (Fig. 10D, ).
Together these results suggest that although Ih is not responsible for discharge pattern transitions, it can modulate the bifurcation-generating mechanism since its activation during hyperpolarizing steps both decreases the membrane time constant and reduces the hyperpolarization. Thus cells with a larger amount of Ih are likely to show discharge pattern transitions with smaller hyperpolarizations and at shorter prepulse duration. However, during long hyperpolarized steps, Ih causes a reduction in hyperpolarization and a decrease in the membrane time constant. Under these conditions, pauser responses are seen with depolarizations that would yield buildup responses without Ih. For example, the reduction in FSL for long prepulses in Fig. 7C is not present when Ih is removed (not shown).
Influence on action potential shape
One hallmark of the activity of
IKI in other systems is the narrowing
of action potentials following hyperpolarizations or action potential
widening after firing of successive action potentials (Gean and
Shinnick-Gallagher 1989; Ma and Koester 1995
,
1996
). Therefore the effects of hyperpolarized prepulses on the
shape of the first action potential in the pauser pattern
were investigated.
Four parameters of the first action potential during a
depolarization were characterized. The first two parameters are the maximum rising and falling slope of the spike, whereas the second two
parameters are the rising and falling action potential half-widths. Figure 11 shows the four parameters as
a function of prepulse voltage, comparing the control condition ()
and the effect of the removal of IKIF
(
) on these four parameters. Under control conditions, the maximum
rising slope of the first spike is reduced from control for prepulses
negative to rest (Fig. 11A), indicating slowed charging of
the membrane. The decrease in rising slope saturated at about
110 mV.
The maximum falling slope increased for more hyperpolarized prepulses
(Fig. 11B), indicating faster repolarization. The rising half-width was only slightly reduced by hyperpolarized prepulses (Fig.
11C), whereas the falling action potential half-width was strongly reduced in the presence of hyperpolarizing prepulses (Fig.
11D), consistent with a faster repolarization. The total action potential width was reduced from 0.78 to 0.63 ms at
115 mV, a
decrease of ~20%. Hyperpolarizations to
80 mV, which is in the
range reached by inhibitory postsynaptic potentials (IPSPs), reduced
the width of the action potential by ~4%. Removal of
IKIF abolished the effects of the
hyperpolarizing prepulse (Fig. 11,
). Removal of
IKIF did not alter spike shape after
depolarizations from rest, which is expected because at rest most
IKIF is inactivated. From Fig. 11, it
is evident that IKIF affects the
repolarization phase more strongly than the depolarization phase. These
simulations demonstrate that small excursions of the membrane potential
from rest before a depolarization can modify action potential shape if
IKIF is present in a cell.
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DISCUSSION |
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This model captures the different discharge patterns of DCN pyramidal cells observed in vitro as well as the sharp, stimulus dependent transitions between the patterns. Similar to the experimentally observed behavior, the model shows that a single cell, depending on the pattern of hyperpolarization and depolarization, can generate all three patterns. Furthermore the model demonstrates that modifying the voltage- and time-dependent behavior of a single conductance can play a critical role in generating diversity in the discharge patterns.
Previous models
Previous computational models of DCN pyramidal cells using generic
channel parameters (Hewitt and Meddis 1995; Kim
et al. 1994
; Zhao 1993
) replicated some response
characteristics of DCN pyramidal cells, supporting the hypothesis that
a transient potassium conductance could explain the different discharge
patterns (Manis 1990
). However, they required ad hoc,
although experimentally informed, assumptions about the voltage and
time dependence of the underlying ion channels. In each of these
models, the absolute density of different conductances and the ratios
between the magnitudes of the conductances appear to be far from
experimentally observed values. In contrast to the previous models, the
model presented in this paper is based on detailed physiological data
and consequently should more accurately represent actual cellular
dynamics. This model reproduced several salient behaviors of DCN
pyramidal cells and showed clearly the intimate association of
IKIF and the discharge patterns. The
model also predicts how modulation of
IKIF should affect discharge patterns.
One issue that arises is whether IKIF
can be sufficiently de-inactivated under normal conditions to lead to
the discharge pattern changes we have modeled here. The simulation
results shown seem to suggest that rather large hyperpolarizations are
necessary to remove inactivation of
IKIF. In all of the simulations shown here, a small subthreshold depolarizing pulse was delivered prior to
hyperpolarization. This pulse itself inactivates
IKIF and shifts the voltage dependence
of the discharge patterns in a hyperpolarizing direction. We
specifically used this protocol to simulate the experimental situation
employed previously (Kanold and Manis 1999b). However,
we have found that IPSPs evoked by parallel fiber stimulation are
sufficient to move the cells from one discharge mode to another (Kanold and Manis 1999a
) and that inactivation is
further removed by short trains of IPSPs. Simulations with this model
without the depolarizing step further support the increased
availability of IKIF near the resting potential.
Evidence that IKIF is responsible for discharge pattern changes
Removal of IKIF abolishes the dependence of the FSL shift on the presence of hyperpolarizing prepulses, providing strong evidence that IKIF is responsible for the discharge pattern changes. The voltage-dependent behavior is very robust with respect to the kinetics of IKIF and does not depend on a singular point in the parameter space. As such, these discharge patterns are a general consequence of the presence of IKIF in a neuron. An additional membrane mechanism that might be involved in generating these discharge patterns is Ih. However, removing Ih resulted in a relatively modest change in the behavior of the model, suggesting that this conductance likely plays only a modulatory role in regulating discharge patterns.
The model suggests that the sharp discharge pattern transitions seen experimentally are caused by the availability of a critical amount of outward current carried by IKIF that can oppose the inward current at depolarization onset. The underlying mechanism of the transition (the availability of IKIF) is a continuous process, whereas the presence of a spike in the response is a discrete event. The hump and sag response seen at the onset of the buildup pattern is partially a remnant of the absent onset spike (caused by initial activation of Na+ currents) and partially mediated by delayed activation of IKIF and IKIS. If IKIF and IKIS activate more rapidly, then the hump and sag are absent. Experimentally, a strong hump and sag is frequently seen, which might be due to rapid membrane charging or to a larger amount of available IKIF at rest. It should be noted that the passive membrane time constants used in the model are on the lower end of the experimentally observed range. Thus it is also possible that an additional inward current (e.g., carried by sodium or calcium ions) is involved in this behavior in pyramidal cells.
Regulation of discharge patterns by IKIF
The inactivation kinetics of IKIF
employed in this model were based on means from experimental
measurements. The voltage dependence of the FSL in the model matched
the mean of the experimentally observed results for buildup cells.
However, our experimental measurements revealed a range of kinetics
(Kanold and Manis 1999b), which in turn could correspond
to a range of firing behaviors. Some cells could easily fire in all
three patterns, whereas others fired preferentially in a pauser or
buildup modes (unpublished observations). The simulations show that
variation of the half-inactivation of
IKIF
(VKIF) can change the half-voltage of
the FSL shift, spanning the experimentally observed range. The
half-voltage of the FISI shift for the pauser pattern is always
negative to the half-voltage for the buildup pattern; this matches our
experimental results. VKIF and the
half-voltage of the FSL shift show a strong correlation, whereas the
dependence of the FISI in the pauser mode on channel kinetics is
somewhat more complex.
The fact that the model showed all types of responses with parameter
variations within the physiological range suggests that regulation of
IKIF might account for the variations
in the observed discharge patterns. For example, the model generated
pauser responses when depolarized from slightly below rest but only
when VKIF was shifted toward positive
values. Pauser responses differ from buildup responses in the
occurrence of an onset spike before the outward currents turn on. Using
stronger depolarization with prepulse levels that generate buildup
responses can elicit pauser responses under some conditions. Similarly,
the FSL in the buildup response depends on the interaction between the
channel kinetics and the hyperpolarizing inputs. The stimulus space
boundary for generating a pause (long FISI) or transitioning to a long
FSL can be shifted by adjusting VKIF
or mF/
hF and thus the
availability and rate of activation of
IKIF at the onset of depolarization.
Evidently by adjusting these parameters, a neuron can change the
relationship between the discharge pattern and stimulus conditions.
There is emerging evidence that individual neurons may adjust the
operating points of their ion channels in response to their activity or
the activity of their afferents (Aizenman and Linden 2000; Desai et al. 1999
; Golowasch et al.
1999
; LeMasson et al. 1993
; Stemmler and
Koch 1999
; Turrigiano et al. 1996
). This is an
important concept since it potentially adds to the diversity and
dynamics of information processing mechanisms available to neurons.
Although the most commonly considered feedback mechanism is
intracellular calcium, sensing the spiking activity of the cell over
various time scale(s) (Liu et al. 1998
; Shin et
al. 1999
), other mechanisms undoubtedly exist. If cells adjust
their channel expression or channel function, then the intrinsic
discharge patterns of a cell may be quantitatively unique depending on
the cell's stimulus and activity history (Jaeger and
Bower 1999
); individual cells may be "tuned" to
have increased or decreased sensitivity to particular regimes of
spatiotemporal patterns of synaptic input.
We previously postulated that rapidly inactivating
IKIF currents in the DCN arise from
channels composed of Kv4.2 and possibly Kv4.3, based on both kinetics and pharmacology
(Kanold and Manis 1999b). Kv4.2
specifically is highly expressed in the cochlear nucleus, including in
pyramidal cells (Fitzakerley et al. 2000
). The
Kv4 family of channels has been shown to
associate with a family of potassium-channel interacting proteins
(KChIP) (An et al. 2000
). These proteins contain four
E-F hand domains that bind calcium and that ultimately impart a calcium
regulation of the channels. When associated with
Kv4 channels, KChIP subunits can modulate
inactivation time constants and the rate of recovery from inactivation
as well as the activation voltage dependence. Thus in principle,
calcium acting through an auxiliary subunit is one way to modulate
these channels. Kv4.2 channels can also be
modulated by protein kinase C (PKC), several isoforms of which are
abundant in DCN neurons, including pyramidal cells (Garcia and
Harlan 1997
; Garcia et al. 1993
; Saito et
al. 1988
). The effect of PKC activation is a rapidly
developing, dose-dependent and pharmacologically specific decrease in
the total outward current through Kv4.2 channels
without any effect on the voltage or time dependence of the current in
expression systems (Nakamura et al. 1997
) and with
a modest reduction of the availability of the conductance in intact
systems (Hoffman and Johnston 1998
). cAMP-dependent protein kinase (PKA) can likewise phosphorylate
Kv4.2 (Anderson et al. 2000
) and
has effects similar to PKC on native channels (Hoffman and
Johnston 1998
), decreasing total available current at a given
voltage. Both PKC and PKA can shift the voltage dependence of
inactivation
8 mV. However, the effects of PKC and PKA on the
inactivation rates are not as large as those produced by association with Ca2+-bound KChIP, suggesting that channel
availability and kinetics may be modulated somewhat independently.
Together, these results raise the likely possibility that
Kv4.2 and/or Kv4.3 are
targets of modulation by either calcium or protein kinases in pyramidal cells.
Another implication of our modeling results is that a morphologically
defined class of cells can show diverse discharge patterns due to
differences in the specific properties of intrinsic conductances. Since
the specific functional properties in part depend on posttranslational modifications of the ion channels (as discussed in the preceding text),
it follows that the discharge patterns may not be strictly correlated
with the overall pattern of ion channel expression. Consequently the
association of a particular discharge pattern observed in vivo with a
particular cell type, as is sometimes assumed to be the case, becomes
somewhat problematic as noted previously in the cochlear nucleus
(Ding et al. 1999; Rhode et al. 1983
;
Rouiller and Ryugo 1984
). Ultimately identical patterns of excitatory and inhibitory input may generate a characteristic response in each cell that depends on the cells history and function. However, the possible repertoire of discharge patterns that can be
generated will be limited by the specific types of channels expressed
in a cell and their spatial pattern of insertion in the cell membrane.
Changes in action potential shape
The presence of IKIF in the cell
reduced the duration of the first action potential following
hyperpolarizing prepulses. This is similar to results in rat amygdala
neurons where IKI causes a narrowing
of the first action potential following a depolarization from a
hyperpolarized potential by 14% (Gean and Shinnick-Gallagher 1989). Action potential widening can lead to increased
Ca2+ influx; this, in terminals, leads to altered
neurotransmitter release (Augustine 1990
; Bourque
1991
; Coates and Bulloch 1985
; Eliot et
al. 1993
; Giese et al. 1998
; Gillette et
al. 1980
; Jackson et al. 1991
; Lin and
Faber 1988
; Mudge et al. 1979
). At the squid giant synapse, a 30% increase in presynaptic action potential width
increased total presynaptic calcium influx by 230% (Augustine 1990
). Therefore depending on the specific set of
Ca2+ conductances, it is possible that action
potential narrowing due to preceding hyperpolarization (i.e., IPSPs)
can cause a significant decrease in Ca2+ influx
for backpropagating action potentials, which are present in pyramidal
cells (Manis and Molitor 1996
).
Ca2+ influx via backpropagating action potentials
can lead to altered cellular excitability (Aizenman and Linden
2000) or changes in synaptic strength (Markram et al.
1997
). Hence modulation of the first action potential in the
response may affect its ability to induce such changes, e.g., for brief
stimuli. Recent studies showed impaired associative memory and learning
after removal of K+ channels and that this effect
might be due to altered Ca2+ influx caused by
spike broadening (Giese et al. 1998
; Meiri et al.
1997
). Thus the presence of
IKIF in DCN pyramidal cells can potentially influence the synaptic and integrative properties of these
cells following hyperpolarization and might ultimately contribute to
other short- and long-term changes in cell function.
Functional implications
The pyramidal cells receive inhibitory input from at least three
distinct sources. A significant source of hyperpolarization is
inhibitory input from DCN cartwheel cells (Davis and Young 1997; Davis et al. 1996
; Zhang and Oertel
1994
) that is of relatively long duration (10-30 ms). Input to
the cartwheel cells arises from parallel fibers that carry both
auditory and nonauditory input [e.g., somatosensory input from the
pinna (Kanold and Young 1998
; Young et al.
1995
)]. If hyperpolarization from these cells deinactivates
IKIF, then
IKIF may play an important role in the integration of auditory and nonauditory information as it allows prior
nonauditory input to modify the acoustically evoked response. Consequently the response of DCN pyramidal cells to auditory stimuli can be highly dependent on nonauditory context. Another important inhibitory input arises from the vertical or tuberculoventral cells
(Brawer et al. 1974
; Lorente de No 1933
;
Rhode 1999
; Zhang and Oertel 1993
), which
are thought to play a critical role in the generation of the acoustic
responses of the pyramidal cells. Based on the interpretation of
cross-correlation analyses (Voigt and Young 1980
) and
current-source density analysis (Manis and Brownell
1983
), these cells presumably provide brief IPSPs to the
pyramidal cells. Presumably individual IPSPs from these cells would be
less effective than the slow cartwheel cell IPSPs in deinactivating
IKIF because of their brief time
course, but this could be overcome by summation over time and by
convergence. A third source of inhibition is the wideband inhibitory
input. This input is necessary to explain the response maps of
pyramidal and vertical cells (Davis and Young 2000
; Nelken and
Young 1994
; Spirou and Young 1991
; Spirou
et al. 1999
) and is postulated to arise from the onset-C cells
of the VCN (Doucet and Ryugo 1997
; Jiang et al.
1996
; Smith and Rhode 1989
). The temporal
properties of inhibition produced by this input are not known. In
principle, either of these latter inputs could effectively utilize
IKIF to alter the firing patterns of
pyramidal cells depending on the spectro-temporal structure of the
acoustic input (for example, see Palombi et al. 1994
;
Parham and Kim 1993
).
The dependence of the discharge pattern on the historical combination of hyperpolarization and depolarization as reflected in the inactivation and activation of IKIF suggests a simple mechanism of encoding temporal information by a population of cells. Cells expressing IKIF with different inactivation characteristics, yet receiving identical patterns of synaptic input, would respond to a common temporal sequence of activity with different firing patterns. Across a population of such cells, the driving activity will be encoded in the relative latencies and interspike intervals. This timing, as regulated by IKIF, would then carry a code for the recent history of activity in inhibitory, as well as excitatory, inputs to the cell.
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ACKNOWLEDGMENTS |
---|
We thank E. D. Young and D. O. Kim for insightful discussions during this project.
This work was supported by National Institute on Deafness and Other Communication Disorders Grant R01 DC-00425 to P. B. Manis.
Present address of P. O. Kanold: Harvard Medical School, Dept. of Neurobiology, Goldenson Bldg. 405, 220 Longwood Ave., Boston, MA 02115.
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FOOTNOTES |
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Address for reprint requests: P. B. Manis, Div. of Otolaryngology-Head and Neck Surgery, Dept. Surgery, 610 Burnett-Womack Bldg., CB#7070, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7070 (E-mail: pmanis{at}med.unc.edu).
Received 6 July 2000; accepted in final form 23 October 2000.
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REFERENCES |
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