1Physics Department, University of Ottawa, Ottawa, Ontario K1N 6N5; 2Department of Cell Biology and Anatomy, Neuroscience Research Group, University of Calgary, Calgary, Alberta T2N 4N1; and 3Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada
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ABSTRACT |
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Doiron, Brent,
André Longtin,
Ray W. Turner, and
Leonard Maler.
Model of Gamma Frequency Burst Discharge Generated by Conditional
Backpropagation.
J. Neurophysiol. 86: 1523-1545, 2001.
Pyramidal cells of the electrosensory lateral
line lobe (ELL) of the weakly electric fish Apteronotus
leptorhynchus have been shown to produce oscillatory burst
discharge in the -frequency range (20-80 Hz) in response to
constant depolarizing stimuli. Previous in vitro studies have shown
that these bursts arise through a recurring spike backpropagation from
soma to apical dendrites that is conditional on the frequency of action
potential discharge ("conditional backpropagation"). Spike bursts
are characterized by a progressive decrease in inter-spike intervals
(ISIs), and an increase of dendritic spike duration and the amplitude
of a somatic depolarizing afterpotential (DAP). The bursts are
terminated when a high-frequency somatic spike doublet exceeds the
dendritic spike refractory period, preventing spike backpropagation. We present a detailed multi-compartmental model of an ELL basilar pyramidal cell to simulate somatic and dendritic spike discharge and
test the conditions necessary to produce a burst output. The model
ionic channels are described by modified Hodgkin-Huxley equations and
distributed over both soma and dendrites under the constraint of
available immunocytochemical and electrophysiological data. The
currents modeled are somatic and dendritic sodium and potassium
involved in action potential generation, somatic and proximal apical
dendritic persistent sodium, and KV3.3 and fast transient A-like potassium channels distributed over the entire model
cell. The core model produces realistic somatic and dendritic spikes,
differential spike refractory periods, and a somatic DAP. However, the
core model does not produce oscillatory spike bursts with constant
depolarizing stimuli. We find that a cumulative inactivation of
potassium channels underlying dendritic spike repolarization is a
necessary condition for the model to produce a sustained
-frequency
burst pattern matching experimental results. This cumulative
inactivation accounts for a frequency-dependent broadening of dendritic
spikes and results in a conditional failure of backpropagation when the
intraburst ISI exceeds dendritic spike refractory period, terminating
the burst. These findings implicate ion channels involved in
repolarizing dendritic spikes as being central to the process of
conditional backpropagation and oscillatory burst discharge in this
principal sensory output neuron of the ELL.
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INTRODUCTION |
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The temporal discharge pattern
of central neurons is an important element of signal processing and
information transfer. Cortical neurons have traditionally been grouped
into three broad classes according to their discharge patterns in
response to depolarizing current injection: regular spiking, fast
spiking, and intrinsic bursting (Connors and Gutnick
1990; Connors et al. 1982
; McCormick et
al. 1985
). Both regular and fast spiking cells respond to
depolarizing current with a repetitive discharge of action potentials
but differ in that regular spiking neurons show significant frequency
adaptation in their firing pattern compared with the consistent
discharge frequency of fast spiking cells. However, the discharge
pattern of intrinsic bursting neurons is quite distinct in generating a
phasic burst followed by a tonic discharge of action potentials. Several studies have focused on distinguishing morphological and electrophysiological characteristics of neurons exhibiting these three
patterns of spike output (Franceschetti et al. 1995
;
Jensen et al. 1994
; Mason and Larkman
1990
; Nuñez et al. 1993
; Schwindt et al. 1997
; Williams and Stuart 1999
). A fourth
discharge pattern consisting of rhythmic spike bursts in the
-frequency range (20-80 Hz) has now been identified in cortical as
well as sub-cortical and medullary neurons (Brumburg et al.
2000
; Gray and McCormick 1996
; Lemon and
Turner 2000
; Lo et al. 1998
; Paré
et al. 1995
; Steriade et al. 1998
; Turner
et al. 1994
). This pattern differs from intrinsic bursting
cells by exhibiting a continuous and nonadapting series of spike bursts
during current injection (Gray and McCormick 1996
;
Steriade et al. 1998
; Turner et al.
1994
).
Gamma frequency discharge is thought to be important to several aspects
of signal processing and neuronal synchronization (Gray and
McCormick 1996; Gray and Singer 1989
;
Lisman 1997
; Ribary et al. 1991
),
yet comparatively few studies have examined the mechanisms underlying
burst output at such a high-frequency. Gamma frequency bursting in
hippocampus is known to involve extensive interneuronal synaptic
circuitry (Buzsáki and Chrobak 1995
;
Stanford et al. 1998
; Traub et al. 1998
).
Other studies have revealed that backpropagating dendritic spikes
contribute to burst discharge by generating a depolarizing
afterpotential (DAP) at the soma (Mainen and Sejnowski
1996
; Turner et al. 1994
; Wang
1999
; Williams and Stuart 1999
). The amplitude
of the DAP can be augmented by a persistent sodium current
(INaP) (Brumburg et al.
2000
; Franceschetti et al. 1995
; Wang
1999
) or dendritic Ca2+ current
(Magee and Carruth 1999
; Williams and Stuart
1999
). Alternatively, the amplitude of the DAP can be
influenced by dendritic morphology because the dendrite-to-soma current
flow increases with the relative dendritic to somatic surface area and
decreases with axial resistance (Mainen and Sejnowski
1996
; Quadroni and Knofnel 1994
). Lemon and Turner (2000)
recently described a novel mechanism of
"conditional spike backpropagation" that modulates DAP amplitude
and produces a
-frequency oscillatory burst discharge in pyramidal
neurons of the electrosensory system.
Electrosensory lateral line lobe (ELL) pyramidal cells are principal
output cells in the medulla that respond to AM of electric fields
detected by peripheral electroreceptors (Bastian 1981; Shumway 1989
). Several studies have described
the properties of burst discharge in ELL pyramidal cells
(Bastian and Nguyenkim 2001
; Gabbiani and Metzner
1999
; Gabbiani et al. 1996
; Lemon and Turner 2000
; Metzner et al. 1998
; Rashid
et al. 2001
; Turner and Maler 1999
;
Turner et al. 1994
, 1996
). Signal detection analysis has
shown that ELL pyramidal cells generate burst discharge in relation to
specific signal features, such as up or down strokes in the external
electric field (Gabbiani and Metzner 1999
;
Gabbiani et al. 1996
; Metzner et al.
1998
). Further, significant progress has been made in
identifying how conditional backpropagation generates an oscillatory
pattern of spike bursts in ELL pyramidal cells in vitro. Pyramidal cell
spike bursts are initiated when a Na+ spike
backpropagating over the initial 200 µm of apical dendrites generates
a somatic DAP (Turner et al. 1994
). A
frequency-dependent broadening of dendritic spikes potentiates the DAP
until a high-frequency spike doublet is triggered at the soma
(Lemon and Turner 2000
). The short inter-spike interval
(ISI) of the doublet falls within the dendritic refractory period and
blocks spike backpropagation, removing the dendritic depolarization
that drives the burst. Repetition of this conditional process of
backpropagation groups repetitive spike discharges into bursts in the
-frequency range. A key issue that remains in understanding the
mechanism of ELL burst discharge is the identity of factor(s)
underlying the frequency-dependent broadening of dendritic spikes that
drives burst discharge.
Our present knowledge of spike discharge in ELL pyramidal cells and the
simple mechanism underlying conditional backpropagation provides an
excellent opportunity to model a form of -frequency burst discharge
and test hypotheses about burst generation. This study presents a
detailed compartmental model of an ELL pyramidal cell that is based on
extensive electrophysiological and morphological data. We establish the
distribution and complement of ion channels that are necessary to fit
various aspects of Na+ spike discharge and spike
backpropagation to physiological data. However, the resulting model
neuron fails to reproduce the change in dendritic spike repolarization
and somatic afterpotentials required to induce
-frequency bursting.
Hence we test potential ionic mechanisms that could underlie burst
discharge. Our results show that cumulative inactivation of a dendritic
K+ current is necessary and sufficient to
generate a burst discharge that is remarkably similar to that found in
ELL pyramidal cells in vitro. Some of this work has been previously
reported in abstract form (Doiron et al. 2000
).
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METHODS |
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The compartmental model we use in this investigation builds on
the earlier one introduced in Doiron et al. (2001).
Simulations are performed with the software package NEURON
(Hines and Carnevale 1997
), which uses a central
difference algorithm (Crank-Nicholson) to integrate forward in time.
The time step for all simulations is 0.025 ms, well below the time
scale of the synaptic and ionic responses present in the ELL
(Berman and Maler 1999
; Berman et al.
1997
).
Cell morphology and discretization
Pyramidal cell somata are located within a pyramidal cell body
layer, a distinct lamina in the ELL. Basal and apical dendrites emanate
from the ventral and dorsal aspects of the cell soma, respectively; the
basal dendrites receive electrosensory afferent input while the apical
dendrites receive feedback input (Berman and Maler
1999). There are two classes of pyramidal cells, basilar and
nonbasilar (lacking a basal dendrite), both of which generate
-frequency oscillatory spike bursts that depend on conditional backpropagation into the apical dendrites (Lemon and Turner
2000
; Turner et al. 1994
). The present model is
focused on the activity associated with basilar pyramidal cells to
allow future analysis of the effect of electrosensory afferent input on
burst discharge.
Figure 1 shows our two-dimensional
spatial compartmentalization of a basilar pyramidal neuron based on
detailed spatial measurements of confocal images of a Lucifer
yellow-filled neuron (Berman et al. 1997). The model
contains 153 compartments with lengths ranging from 0.8 to 669.2 µm
and diameters spanning from 0.5 to 11.6 µm. The total model cell
surface area is 65,706 µm2, comparable to other
pyramidal cell models (Koch et al. 1995
). Longer
compartments are further subdivided to guarantee that no isopotential
segment is of length >25 µm, ensuring sufficient computational
precision. This results in a total spatial discretization of the full
model cell into 312 isopotential regions. For simplicity, the initial
segment and soma are represented as a single compartment.
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The proximal apical dendrite is modeled by ten connected compartments
(total length, 200 µm) whose diameter decreases with distance from
the somatic compartment (initial diameter of 11.6 mm, final diameter of
6 µm; see Fig. 1, inset). The dendrite then bifurcates to
give rise to daughter branches of 6 µm diameter, which further
bifurcate with an associated step decrease in diameter, extending a
total distance of ~800 µm in an overlying molecular layer. The
proximal basilar dendrite is modeled as a single compartment of 7.4 µm diameter and 194 µm in length. The distal extent of the dendrite
separates into many compartments that form a bush-like pattern (see
Fig. 1). The lengths of dendrites within the basilar bush range from 3 to 56 µm with diameters as thick as 4 µm to as thin as 0.5 µm. As
the axial resistivity (Ra) and
membrane capacitance per unit area
(Cm) are not precisely known for ELL pyramidal cells, Ra is set to 250 cm and Cm to 0.75 µF/cm2, both realistic values for vertebrate
neurons (Mainen and Sejnowski 1998
). The model cell
temperature is set to 28°C, similar to the natural habitat of the fish.
Model equations
Each ionic current, Ix, is
modeled as a modified Hodgkin/Huxley channel (Hodgkin and Huxley
1952) governed by
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(1.1) |
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(1.2) |
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(1.3) |
Figure 1 introduces the specific ionic currents and indicates their
distribution over the cell. Table 1 gives
the parameters stated in Eq. 1.1-1.3 for each current. In
this study, "proximal dendrite" refers to the initial 200 µm of
the apical dendrite, which is in most pyramidal cells a single
nonbranching shaft over this distance. A detailed analysis of basilar
dendritic electrophysiology is not available, hence few ionic channels
are localized to the basilar dendritic region. The ionic channels
(Ix) influence the potential of each
compartment according to
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(2) |
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RESULTS |
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For each ionic channel incorporated into the model, we first justify the chosen distribution over the cell (Fig. 1) and identify the influence of each conductance on cell membrane potential. Finally, the parameters are fit so that model performance matches known experimental recordings. In the case of insufficient experimental evidence from pyramidal cells, values were taken from experimental or computational results reported for other cells.
Channel distribution and kinetics
PASSIVE CURRENT ILEAK.
Ileak represents the classic leak
channel with voltage-independent conductance and is present in all
compartments. The channel density,
gmax,leak is chosen to establish the
model input resistance as 76.1 M and the passive membrane time
constant as 26.8 ms, similar to values measured in intracellular
recordings of pyramidal cells in vitro (Lemon and Turner
2000
). The leak reversal potential, Erev,leak, is set to
70 mV
(Koch et al. 1995
; Mainen et al. 1995
; Rapp et al. 1996
). Due to the high-density of
K+ currents (see following text) the final
resting membrane potential (RMP) of the core model is
73.3 mV, a
value within the range recorded in pyramidal cells in vitro
(Berman and Maler 1998a
; Turner et al.
1994
).
NA+ AND
K+ CURRENTS.
Previous work has established the distribution pattern of immunolabel
for both Na+ channels and an apteronotid
homologue of the Kv3.3 K+ channel,
AptKv3.3, over the dendritic-somatic axis of pyramidal cells
(Rashid et al. 2001; Turner et al. 1994
).
Electrophysiological studies have further mapped the site for
Na+ spike initiation and conduction over the
soma-dendritic axis (Lemon and Turner 2000
;
Turner et al. 1994
) and identified the kinetic
properties of AptKv3.3 K+ channels in
both native pyramidal cells and when expressed in a heterologous
expression system (Rashid et al. 2001
). Although other
K+ channels are incorporated into the model, our
existing knowledge of the distribution and properties of
Na+ and AptKv3.3
K+ channels are used when possible to constrain
our parameters and improve the representation of action potential
waveforms. We begin by matching the distribution and kinetic properties
of AptKv3.3 channels to experimental data.
IAptKv3.3: high-voltage-activated K+ channel
AptKv3.3 K+ channels are
distributed over ELL pyramidal cell somata as well as apical and basal
dendrites (Rashid et al. 2001). A dendritic distribution
of AptKv3.3 channels is unique in that all previous studies
on Kv3 channels have shown a distribution that is restricted to the
soma, axon, and presynaptic terminals (Perney and Kaczmarek
1997
; Sekirnjak et al. 1997
; Weiser et
al. 1995
). Rashid et al. (2001)
also showed that
AptKv3.3 K+ channels contribute to
spike repolarization in both somatic and apical dendritic membranes.
This role is particularly relevant in dendritic regions where a
reduction in AptKv3.3 current enhances the somatic DAP and
lowers burst threshold.
Figure 2 shows the fit of
AptKv3.3 current in the model to whole cell recordings of
AptKv3.3 K+ current when expressed in
human embryonic kidney (HEK) cells. AptKv3.3 channels
produce an outwardly rectifying current that exhibits a high-threshold
voltage for initial activation (more than 20 mV; Fig. 2, A
and B). Over a 100-ms time frame, step commands produce
little inactivation of AptKv3.3 current in the whole cell
recording configuration (Fig. 2A), although inactivation can
be recorded over longer time frames (Rashid et al.
2001
). As indicated in Table 1, both activation
(mAptKv3.3) and inactivation
(hAptKv3.3) curves are used to
describe IAptKv3.3. The
V1/2 for
mAptKv3.3 is set to 0 mV so as to
produce the high-threshold voltage necessary for activation as shown in
Fig. 2B. A shallow slope of activation, km,AptKv3.3, is required to
produce a gradual rise of IAptKv3.3
with voltage.
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As reported for Kv3 channels in some expression systems,
AptKv3.3 current exhibits an early peak on initial
activation followed by a relaxation to a lower amplitude current for
the duration of a 100-ms step command (Fig. 2A). The origin
of this early peak and relaxation is currently unknown, but it has been
proposed to reflect a transient accumulation of extracellular
K+ when Kv3 channels are expressed at
high-density in expression systems (Rudy et al. 1999).
Since this has not been firmly established, we incorporate inactivation
kinetics (V1/2,h,AptKv3.3, kh,AptKv3.3,
h,AptKv3.3) that allow the model to
reproduce the early transient peak of current (Fig. 2A). An additional characteristic of Kv3 channels is a fast rate of both activation and deactivation (Fig. 2C). The activation time
constant,
m,Kv3.3, is chosen to produce rates
of activation and deactivation that most closely match the experimental
data (Fig. 2C). Because AptKv3.3 channels are
found with high prevalence in the soma and dendrites, they are
incorporated with the above kinetics over the entire axis of the model
cell (Fig. 1). The conductance level is adjusted accordingly to the fit
to experimental data (see following text).
Action potential discharge in ELL pyramidal cells
We first treat somatic and dendritic spike discharge separately to determine the necessary descriptions of the model Na+ and K+ channels required to produce action potential waveforms that match in vitro recordings. Next we focus on the soma-dendritic interaction that gives rise to the DAP that drives burst discharge.
INa,s, IDr,s, and IAptKv3.3: somatic spike
Figure 3A illustrates an
action potential recorded in the soma of pyramidal cells in an in vitro
slice preparation (see also Table 2 for
quantitative comparison of model and experimental somatic action
potential features). As we are interested in first modeling the somatic
spike in the absence of backpropagating spikes, the recording in Fig.
3A was obtained after TTX had been locally applied
to the entire dendritic tree. This effectively blocks all spike
backpropagation and selectively removes the DAP at the soma
(Lemon and Turner 2000). The somatic spike in pyramidal
cells is of large amplitude (typically reaching 20-mV peak voltage) and
very narrow half-width (width at half-maximal amplitude) of ~0.45 ms
(Table 2) (Berman and Maler 1998a
; Turner et al.
1994
). In the absence of a DAP, a fast afterhyperpolarization
(fAHP) that follows the somatic spike is readily apparent (Fig.
3A). A slow Ca2+-sensitive AHP (sAHP)
follows the fAHP but does not contribute directly to the soma-dendritic
interaction that underlies burst discharge (Lemon and Turner
2000
).
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ELL pyramidal cell somatic spikes are generated by TTX-sensitive
Na+ channels (Mathieson and Maler
1988; Turner et al. 1994
), which are modeled
here as a fast activating and inactivating current, INa,s. Rashid et al.
(2001)
established that Kv3 channels contribute to repolarizing
the somatic spike in pyramidal cells. However, local blockade of
somatic Kv3 channels using focal ejections of TEA in vitro only blocks
a fraction of the total repolarization, indicating the additional
involvement of other voltage-dependent K+
channels. Pyramidal cells are known to express large conductance (BK)
Ca2+-activated K+ channels
in both somatic and dendritic membranes (E. Morales and
R. W. Turner, unpublished observations), but they do not appear to
contribute to spike repolarization (Noonan et al. 2000
;
Rashid et al. 2001
). A large fraction of the somatic
spike repolarization is likely mediated by a small conductance
K+ channel (<10 pS) found with high prevalence
in patch recordings (Morales and Turner, unpublished observations).
Although the kinetic properties of this channel have not been
established, whole cell currents in pyramidal cell somata indicate that
it will have properties consistent with a fast activating and
deactivating delayed rectifier-like (Dr) current, referred to here as
IDr,s. We therefore model somatic spike depolarization and repolarization using a combination of INa,s,
IDr,s, and
IAptKv3.3.
INa,s and
IDr,s are confined
to the somatic compartment, which includes both the initial segment and
somatic membrane, and represents the site for Na+
spike initiation in the cell (Turner et al. 1994). The
activation (both INa,s and
IDr,s) and inactivation (only
INa,s) steady-state conductance curve
half voltages, V1/2, and slopes,
k, are similar to values used in previous compartmental
models (Koch et al. 1995
; Mainen et al.
1995
; Rapp et al. 1996
). Spike threshold occurs at Vthres >
60 mV, a value close to that
reported for pyramidal cell spike threshold in vitro (Berman and
Maler 1998a
).
Previous compartmental models of mammalian neurons typically
incorporate action potential half-widths of 1-2 ms (de Schutter and Bower 1994; Koch et al. 1995
; Mainen
et al. 1995
; Rapp et al. 1996
). Given the
comparatively narrow half-width of ELL pyramidal cell spikes (Table 2),
we choose relatively short INa,s and
IDr,s time constants of activation and
inactivation,
m and
h
(Table 1), and gmax,Na,s is set to 1.8 S/cm2. To compensate the
Na+ conductance and achieve proper
repolarization, gmax,Dr,s is set to a
value of 0.7 S/cm2. We note that the model
density of Na, s and Dr, s channels are comparable to that used in the
spike initiation zone of other compartmental models (de Schutter
and Bower 1994
; Koch et al. 1995
; Mainen
et al. 1995
; Rapp et al. 1996
). Figure
3B shows somatic action potentials with
INa,s alone (trace 1) and both
INa,s and IDr,s (trace 2) inserted in the model.
The reduction in spike half-width and amplitude when
IDr,s is present allows the model somatic spike to better approximate experimental recordings (compare Fig. 3, A and B).
In considering the role of AptKv3.3 K+
current, we find that AptKv3.3 channels alone could account
for only a fraction of the total somatic spike repolarization. Figure
3C compares the somatic action potential with no
IDr,s or
IAptKv3.3-mediated repolarization
(trace 1) to one with only IAptKv3.3
current (trace 2). A reduction of spike width by
IAptKv3.3 during the initial falling
phase of the action potential with a minimal reduction in peak voltage
matches the results of earlier modeling studies that considered the
role of Kv3.1 K+ channels in spike repolarization
(Perney and Kaczmarek 1997; Wang et al.
1998
). As shown in Fig. 3C (trace 4), spike
repolarization is most closely modeled when
IDr,s and
IAptKv3.3 are both present at the
soma, with AptKv3.3 conductance set to 6.5 S/cm2 (Rashid et al. 2001
).
Removing AptKv3.3 conductance slightly reduces the rate of
spike repolarization without significantly affecting action potential
amplitude. Such an effect on spike repolarization by
AptKv3.3 is also consistent with pharmacological tests in
vitro (Rashid et al. 2001
).
INa,d, IDr,d, and IAptKv3.3: dendritic spike
Many central neurons are known to be capable of actively
backpropagating Na+ spikes from the soma and over
the majority of the dendritic tree (Stuart et al. 1997b;
Turner et al. 1991
, 1994
; Williams and Stuart 1999
; see Häusser et al. 2000
for review).
Patch-clamp recordings in hippocampal pyramidal cells further indicate
that Na+ channels are distributed with a
relatively uniform density over the entire dendritic tree (Magee
and Johnston 1995
); a distribution that has been used in other
modeling studies (Mainen et al. 1995
; Rapp et al.
1996
). We have previously determined that
Na+ channel immunolabel in ELL pyramidal cells is
uniformly distributed in the cell body region but exhibits a distinct
punctate distribution over the proximal 200 µm of apical dendrites
(Turner et al. 1994
). This distribution correlated with
the distance over which TTX-sensitive spike discharge was recorded,
suggesting that the immunolabel correspond to Na+
channels involved in spike generation. Electrophysiological recordings further established that Na+ spikes are initiated
in the somatic region but backpropagate over only ~200 µm of the
dendritic tree that can extend as far as 800 µm (Maler
1979
; Turner et al. 1994
). In this respect,
spike backpropagation in ELL pyramidal cell dendrites falls between the
active conduction of Na+ spikes seen over the
entire axis of cortical neuron dendrites and the passive decay of
Na+ spikes seen over the proximal dendrites of
cerebellar Purkinje cells (Häusser et al. 2000
;
Hoffman et al. 1997
; Stuart and Häusser 1994
; Stuart et al. 1997a
).
Figure 3D shows an ELL pyramidal cell dendritic spike
recorded ~150 µm from the soma. The dendritic spike half-width is
substantially larger than that of the somatic spike, with the total
duration approaching as much as 12 ms in recordings ~200 µm from
the soma. Recordings in the slice preparation further indicate that
even proximal dendritic spikes (50 µm) exhibit a sharp decrease in the rate of rise and rate of repolarization with respect to somatic spikes. This difference in rate of repolarization leads to a
substantial delay in the peak latency of dendritic versus somatic
spikes with a rapid increase in this difference beyond ~100 µm
(Turner et al. 1994). Modeling this rapid change in
spike characteristics in proximal dendrites requires a specific set of
parameters for both dendritic Na+ and
K+ conductances.
Given the immunocytochemical data (Turner et al. 1994),
the distribution of dendritic Na+ channels is
confined to five punctate zones of 5 µm in length (200 µm2 area) along the proximal apical dendrite
that are assigned a high Na+ channel density
(Fig. 1). The distance between active dendritic zones also increases
with distance from the soma. Specifically, active
INa,d zones 1-3 are separated by 15 µm of passive dendrite, while zones 3-5 are separated by 60 µm of
passive dendrite. Lacking a cytochemical localization of
IDr,d K+
channels in dendrites, we co-localized these channels to the five
active dendritic zones. As stated in the preceding text, AptKv3.3 channels are incorporated over the entire
soma-dendritic axis, although with varying levels of conductance for
somatic, proximal apical dendritic, and distal apical and basal
dendritic compartments.
We first attempted to equate the kinetic parameters of Na, d and Dr, d
channels to those of somatic Na, s and Dr, s, respectively, but with
reduced channel densities to produce a lower amplitude dendritic spike,
as done in previous studies (Mainen et al. 1995; Traub et al. 1994
). However, this led to dendritic
spikes with too short of a half-width and delay time to peak
incompatible with intracellular dendritic recordings. A first attempt
at correcting this discrepancy was raising the model axial resistance,
thereby reducing the passive cable propagation of the spike along the dendrite. However, to obtain model agreement with experimental data,
Ra had to be set outside acceptable
norms by a factor of 10 (Mainen and Sejnowski
1998
). This approach was problematic and hence abandoned.
Recently differences in ion channel kinetics have been observed for
dendritic Na+ and K+
channels as compared with those at the soma, indicating precedence for
applying differential kinetic properties to somatic versus dendritic
ion channels (Colbert et al. 1997; Hoffman et al.
1997
; Jung et al. 1997
). Since a similar level
of analysis is not yet available for ELL pyramidal cells, we explored a
broad range of kinetic parameters describing both
INa,d and
IDr,d. More successful modeling of
experimental results is achieved by increasing the steady-state
conductance curve slope, k, and time constant,
, for both
the activation and inactivation of
INa,d and
IDr,d as compared with their somatic
counterparts. Simulations using only INa,d and
IDr,d then begin to reproduce the
delay in dendritic spike peak as well as the increase in spike
half-width, the longer rate of rise, and the slower rate of
repolarization when compared with the somatic spike (Fig.
3B). By comparison, modeling the dendritic spike with only
INa,d and
IAptKv3.3, does not achieve a
sufficient rate of spike repolarization (Fig. 3F, trace 1 vs. 2). By combining IDr,d with
IAptKv3.3 set to a density of 1 S/cm2 in the proximal apical dendrite and a lower
density of 0.5 S/cm2 in other dendritic
compartments a good fit to experimental data is obtained (cf. Fig. 3,
D and F, trace 4). Note that incorporation of
AptKv3.3 current also reduces dendritic spike amplitude
(Fig. 3F; trace 4). This result is consistent with
experimental data indicating a slight increase in dendritic spike
amplitude following local ejections of 1 mM TEA to block dendritic
AptKv3 channels (Rashid et al. 2001
).
Soma-dendritic interactions underlying the DAP
Figure 4 illustrates the effects of
combining active somatic and dendritic compartments on spike waveforms.
Previous intracellular recordings have indicated substantial
differences in the duration and peak response of somatic versus
dendritic spike waveforms (Fig. 4A). Both experimental
recordings in Fig. 4A were obtained in intact slices with
full backpropagation of spikes into dendrites. Under these conditions,
the somatic spike is followed by a clear DAP that superimposes on the
somatic fAHP (Fig. 4A). The DAP is due to the dendritic fast
sodium currents, INa,d, which boost the backpropagating action potential to elevated voltages in the dendrite, and promotes return electrotonic current flow during the
longer duration dendritic spike (Turner et al. 1994).
When the model includes active spike discharge in both somatic and dendritic compartments, it successfully reproduces a DAP at the soma
that is offset by the fAHP (Fig. 4B). If the
gmax of all INa,d currents is set to zero, in
effect removing the active zones from the apical dendrite, the
influence of the DAP at the soma is lost, uncovering a clear fAHP at
the soma. Only a low-amplitude passive reflection of the somatic spike
occurs in the apical dendrites (Fig. 4C), as recorded in
vitro when TTX is focally applied to the dendrites to block active
spike backpropagation (Turner et al. 1994
).
|
Spike backpropagation and refractory period
Figure 4D plots how the fitted kinetics of
INa,d and
IDr,d affect the backpropagation of
action potentials initiated at the soma. Shown is the peak voltage of
the response measured at a select number of compartments for both
active propagation (gmax,Na,d = 0.6 S/cm2) and passive electronic
conduction (gmax,Na,d = 0 S/cm2) in the dendritic compartments. In the
proximal apical dendrite (<200 µm), the five active
INa,d sites incorporated into the
model boost the peak of the backpropagating action potential over that measured during passive conduction. In the mid-distal dendrite (>200
µm), the peak voltage decays exponentially in both cases because no
active inward currents are believed to boost the voltage beyond this
distance (Turner et al. 1994). This decrease in spike amplitude near 200 µm also qualitatively mimics the properties of
backpropagating spikes as measured through laminar profile field
potential analysis (Turner et al. 1994
).
To test the accuracy of fit of channel parameters for
INa,s, INa,d,
IDr,s, and
IDr,d, we measure the refractory
period of both somatic and dendritic spikes (Fig.
5, A and B). The
simulation protocol is equivalent to the condition-test (C-T) interval
experiment used by Lemon and Turner (2000). In the
model, this consists of first injecting a brief somatic current pulse
sufficient to induce a single somatic spike that backpropagates into
the dendrites. A second identical current pulse is then applied at a
variable time interval following the first pulse to identify relative
and absolute refractory periods. At sufficiently long test intervals (Fig. 5, A and B, 8 ms) the second pulse evokes
full somatic and dendritic spikes, both identical to the condition
responses. At the soma, a reduction in the C-T interval to ~4 ms
results in a select blockade of the DAP without significant effect on
the somatic spike (Fig. 5A). Somatic spike amplitude remains
essentially stable for C-T intervals above 2.5 ms, although C-T
intervals below this slightly reduce spike amplitude, given that
INa,s has not completely recovered
from inactivation. An absolute somatic refractory period is evident at
a C-T interval of 1.5 ms (Fig. 5A). The effects of a similar
series of C-T intervals monitored 200 µm from the soma reveals a
relative refractory period for dendritic spikes between 4 and 6 ms, as
reflected by a gradual decline in spike amplitude. This reduction in
amplitude ends at C-T intervals between 2.0 and 3.0 ms (Fig.
5B), with subsequent failure of the small potential evoked
at C-T intervals of ~1.5 ms.
|
Each of these properties qualitatively match experimental results in
pyramidal cells of an absolute somatic refractory period at ~2 ms, a
relative dendritic refractory period between 5 and 7 ms and an absolute
dendritic refractory period between 3 and 4 ms (Lemon and Turner
2000). Furthermore a selective block of the somatic DAP over
the same range of C-T intervals that reduce dendritic spike amplitude
is also a characteristic observed in intact pyramidal cells
(Turner et al. 1994
).
INaPdetermining RMP, nonlinear EPSP boosting, and
latency to first spike shifts
A TTX-sensitive and persistent Na+ current
(INaP) (French et al.
1990) has been recorded at both the somatic and dendritic level
of ELL pyramidal cells (Berman et al. 2001
;
Turner et al. 1994
). Blocking this current with focal
ejections of TTX in vitro results in a clear hyperpolarizing shift in
cell resting membrane potential (RMP) and an increase in the latency to
discharge a spike at the soma (Turner et al. 1994
).
There is also a prominent voltage-dependent late component to the
dendritic and somatic excitatory postsynaptic potential (EPSP) evoked
by stimulation of descending tractus stratum fibrosum (tSF) inputs that
terminate in the proximal dendritic region (Berman and Maler
1998c
; Berman et al. 1997
). Recent work
indicates that focal ejection of TTX at the soma selectively blocks
this late component of the tSF-evoked EPSP (Berman et al.
2001
). Each of these results identifies an important
contribution by INaP in determining
the resting membrane potential (RMP) of the cell, in boosting the tSF
synaptic depolarization, and in setting the latency to spike discharge.
We determine the model NaP channel parameters through a detailed match
to these constraints.
NaP channels are modeled in both the soma and proximal apical dendrite
as suggested by experimental and modeling studies of ELL pyramidal
cells (Fig. 1) (Berman and Maler 1998c; Turner et al. 1994
). In the absence of definitive knowledge of the
distribution of dendritic NaP channels, a uniform distribution of NaP
channels over the entire proximal apical dendrite is chosen. Local TTX applications in vitro produce quantitatively similar shifts in RMP at
both the somatic and dendritic level of pyramidal cells (Turner
et al. 1994
). We hence choose a relative factor of 3.5 for the
ratio of total somatic/dendritic NaP channel density to account for the
greater proximal apical dendritic surface area. This produces
approximately equal net INaP current
from both soma and dendrite in response to similar depolarizations.
To set the NaP channel activation parameters,
V1/2 and k, we consider its
effects on the model cell RMP. To do so, we apply a small constant
depolarizing somatic current injection to the model
(Iapp < 100 pA), which is
insufficient to cause spiking. After a transient period of
depolarization, the model membrane voltage settles to a steady-state
value, which we label as the "effective" RMP. The shape of the
increase in RMP as Iapp increases will
be determined by the specific NaP distribution. Figure
6A plots
this final equilibrium somatic voltage (t >200 ms) as a function of Iapp with NaP present in
various compartments (see figure legend for description). For small
currents (Iapp < 50 pA), the rise in
RMP is linear (Ohm's law) because at these potentials (Vm < 70 mV) NaP is not
significantly activated. However, for larger applied currents
(Iapp > 60 pA) yielding higher RMP
values (Vm >
70 mV), a significant
nonlinear RMP increase occurs when NaP is present (trace 1, Fig.
6A). This effect requires a steep subthreshold voltage
dependency of activation that forces the half activation of
INaP,
V1/2,m,NaP, to be set to
58.5 mV and the activation slope parameter,
km,NaP, to be low, 6 mV. This agrees
with the experimental effects of TTX application on pyramidal cell RMP
in vitro (Berman and Maler 1998c
; Turner et al.
1994
) and with experimentally determined
V1/2 (
56.92 mV) and k
(9.09) voltages for NaP in rat and cat thalamocortical neurons
(Parri and Crunelli 1998
). The quantitative agreement
with experiment is achieved by adjusting
gmax,NaP. However, since
f-I characteristics (see Fig. 8) are compromised with a
significant modification of gmax,NaP,
the fit is balanced to produce a realistic RMP, and proper
f-I relationship for the model cell.
|
As illustrated in Fig. 6A, restricting the NaP distribution
to either somatic or dendritic membranes (traces 2 and 3) reveals the
nonlinear effect of NaP density in determining the RMP (for Iapp > 80 pA the difference
between traces 1 and 4 is larger than the sum of the differences
between traces 2 and 3 with 4). The nonlinear effect will be treated
when we analyze the role of NaP in EPSP boosting (see following text).
The near exact quantitative agreement of traces 2 and 3 in Fig.
6A indicate that the effect of NaP on the RMP is not
site-specific between soma and proximal dendrite. This is expected
since the net NaP currents of both somatic and dendritic membranes are
set to be equal (see preceding text). The parameters that model the
steady-state characterization of the NaP,
V1/2,m,NaP, and
km,NaP, are now set; however, the dynamics of the INaP current,
determined by m,NaP, remains to be addressed.
INaP currents have been shown to boost
the amplitude of subthreshold EPSPs in cortical pyramidal cells
(Andreasen and Lambert 1999; Lipowsky et al.
1996
; Schwindt and Crill 1995
; Stafstrom et al. 1985
; Stuart and Sakmann 1995
); there is
recent evidence in ELL pyramidal cells for a similar effect
(Berman and Maler 1998c
; Berman et al.
2001
). To set the time constant of NaP activation,
m,NaP, we consider the EPSP boosting
properties of the model INaP. The
inset in Fig. 6B shows somatic recordings of a
distally evoked EPSP under control and somatic TTX conditions. The
boost provided by TTX-sensitive currents begins with the fast rising phase of the EPSP, suggesting that NaP channels activate quickly (Fig.
6B; compare the inset control trace to the TTX
trace). To match the data, the model
m,NaP is
set to a small value (
= 0.3 ms). This fast activation
coincides with the treatment of INaP in other
ionic models (Lipowsky et al. 1996
; Wang
1999
). Figure 6B shows the model somatic voltage
response due to dendritic EPSP activation under the same various NaP
distributions considered in Fig. 6A. The EPSP boost observed
with all distributions shows that the subthreshold boost of the EPSP by
INaP is substantial and that indeed
the boost begins with the rising edge of the potential, thereby
matching experimental data.
The nonlinear nature of INaP boosting of EPSPs is apparent in Fig. 6B when we compare EPSP amplitudes when NaP is present in both the somatic and proximal apical dendritic compartments (trace 1) to NaP distributions in only in the somatic (trace 2) or dendritic (trace 3) compartments. Figure 6B shows approximately a 3-mV boost of the model EPSP amplitude when comparing the control case to complete NaP removal (trace 1 as compared with 4). However, with only somatic or dendritic NaP distribution (trace 2 or 3), a boost of <1 mV at the peak of the EPSP is observed. A linear increase in the degree of EPSP enhancement would require that the effects of traces 2 and 3 summate algebraically to produce trace 1. The nonlinear boosting is a result of the steep sigmoidal voltage activation of NaP (plot not shown).
It has been experimentally shown in thalamocortical neurons that
INaP activation reduces the latency to
spike in response to depolarizing current (Parri and Crunelli
1998). We hence further test the fit of NaP parameters by
considering the model cell's latency to discharge a spike on membrane
depolarization. Figure 6C plots the model latency to first
spike as a function of applied somatic suprathreshold depolarizing
current under all four NaP conditions described in Fig. 6 (A
and B). All traces show that just above the rheobase current
(minimum current required to induce spiking) the latency to first spike
is long, yet as the input current is increased, the latency decays to
shorter values. Comparing the various NaP conditions reveals that
increasing INaP reduces the rheobase
current of the cell, with a full 0.71-nA shift occurring between the
condition in which all somatic and dendritic NaP removed (trace 4) as
compared with the condition in which
INaP is distributed over the both
somatic and dendritic membranes (trace 1). As a result of the rheobase
shift, Fig. 6C shows the latency to first spike at
Iapp = 0.81 nA with all NaP removed to
be 62.4 ms as compared with the control latency of 4.3 ms at the same current.
Figure 6C also indicates that the nonlinear effects of INaP already seen on the RMP and EPSP amplitude are even more dramatic on both the rheobase current and latency shift. Partial removal of NaP (traces 2 and 3) only shifts the rheobase and the latency to first spike by slight amounts from the control case (trace 1) when compared with the dramatic shifts observed with a block of both somatic and dendritic INaP (trace 4). The quantitative agreement between latency shifts observed when either somatic or dendritic NaP are removed shows that there is no spatial differences of NaP effects on rheobase current or latency as expected by the spatially balanced net ionic current.
Finally, we compare the model spike latency characteristics with
experimental measurements from ELL pyramidal cell latency to spike
(Berman and Maler 1998b). In ELL pyramidal cells, the transition from long to short latencies to spike does indeed occur over
a small depolarizing current interval (~0.1 nA), as in the model
control case (trace 1, Fig. 6C). The model results show a
power law decay (spike latency ~ 1/
). This could not be fit with a
power law as in the model results. The model latency decay occurred
with all INaP parameter sets explored;
however, the given fitted parameters (Table 1) produced the best
approximation to experimental latency shifts. The discrepancy between
the experimental and model latency decay is presently unexplained.
IAlatency to first spike from hyperpolarized
potentials
Previous studies of ELL pyramidal cell electrophysiology
(Berman and Maler 1998b; Mathieson and Maler
1988
) have suggested the existence of a transient outward
current similar to
IA (Connor and Stevens 1971
). Both studies observed an increase in spike latency if a depolarization was preceded by membrane hyperpolarization, an effect previously attributed to the activity of an
IA current (Connor and Stevens
1971
; McCormick 1991
). At this time, patch-clamp recordings have not conclusively shown the possible contribution of an
IA current at the somatic or dendritic
level of pyramidal cells (Turner, unpublished observations). Our
attempts to simulate the experiments performed in Mathieson and
Maler (1988)
now show that to reproduce the observed effects of
membrane potential on the latency to spike discharge, a low density of
IA-like K+
current must be introduced into the model cell.
Because patch-clamp recordings in pyramidal cells have not yet isolated
transiently activating and inactivating channels consistent with a
traditional A-type K+ current, the choice of
channel distribution over the model cell must be postulated. A previous
compartmental model has shown that altering the distribution of
IA channels over a cell gives only small deviations in observed IA
character, with the exception of cells with large axial resistance
(~2,000 cm) (Sanchez et al. 1998
). Our model neuron
axial resistance (250
cm) is much lower, and hence any chosen
channel distribution should not significantly affect cell output.
Considering this result, we distribute
IA uniformly over the whole cell (Fig.
1).
The half voltages for the steady-state conductance curves for
IA currents are set to
V1/2,m,A = 75 mV and
V1/2,h,A =
85 mV and the curve slope
factors to km,A = 4 mV and
kh,A =
2 mV. Other models of
IA (Huguenard and
McCormick 1992
; Johnston and Miao-Sin Wu 1997
;
Sanchez et al. 1998
) show
IA window currents at more depolarized
levels ranging over a larger voltage interval. However, in the absence
of definitive IA characterization in
ELL pyramidal cells, we choose to fit the activation/inactivation parameters to ensure that IA does not
affect the model RMP yet that inactivation could be removed with
moderate hyperpolarization (in correspondence with the results of
Mathieson and Maler 1988
).
m,A
is set to 10 ms to have sufficiently rapid A-type
K+ channel activation (Johnston and
Miao-Sin Wu 1997
). However, the time constant of
IA inactivation,
h,A, is chosen to be 100 ms to produce an
appropriate latency to first spike and a subsequent transient increase
in spike frequency over the first 200 ms (Doiron et al.
2001
).
Figure 7A shows the model cell
response without IA present
(gmax,IA = 0) to a depolarizing
somatic current injection of 0.6 nA. The model cell is at a resting
potential of 73 mV prior to the stimulus. A repetitive firing pattern
results with a latency to first spike of 6.05 ms (stimulus onset is at
t = 0) and ISI of 9.5 ms. Figure 7B repeats
this simulation but with a 50-ms prestimulus hyperpolarization of
11
mV induced via
0.2-nA current injection. Again, repetitive firing
occurs, yet with a slightly longer latency to first spike of 12.1 ms
followed by a repeating ISI of ~9.5 ms. These results qualitatively
match those obtained by Mathieson and Maler (1988)
when
1 mM 4-aminopyridine (4-AP, a known IA
channel blocker) was bath applied to ELL pyramidal cells in vitro.
However, under control conditions, a substantially longer latency to
first spike was observed in ELL recordings when a prestimulus
hyperpolarization preceded depolarization (Mathieson and Maler
1988
). Furthermore when depolarizing current is applied from a
hyperpolarized level, the first ISI is long and then subsequent ISIs
slowly shorten (an increase in cell firing rate) in the first 200 ms of
the stimulus, presumably due to IA
inactivation.
|
Figure 7, C and D, illustrates simulation
protocols identical to those shown in A and B,
respectively, yet with IA channels distributed across the model cell.
gmax,IA is fit to match the experimental findings of Matheison and Maler (1988) with
a final assigned value of gmax,IA = 1.2 mS/cm2. At a resting potential of
73 mV,
IA is substantially inactivated so
that depolarizing the somatic compartment via a 0.6-nA current injection results in a latency to first spike and subsequent ISI shift
that is nearly identical to the results obtained when
IA is not incorporated into the model
(cf. Fig. 7, A and C). However, with a
prestimulus hyperpolarization, the same net current injection produces
a latency to first spike of 78.5 ms, an increase of 66.3 ms as compared
with spike discharge without a prestimulus hyperpolarization (Fig.
7D). In addition, in the presence of
IA the ISI begins at 14.4 ms and
reduces to 10 ms after 200 ms of depolarization, successfully reproducing the gradual increase in spike frequency observed in pyramidal cells (not shown). Smaller depolarizations
(Iapp < 0.6 nA) following equivalent
prestimulus hyperpolarizations (Iapp =
0.2 nA) induce larger differences in latencies to first spike for
cases without IA. Similarly, larger
depolarizations (Iapp > 0.6 nA) give
smaller latency shifts. These results are also qualitatively similar to
the ELL experimental results of Matheison and Maler
(1988)
.
Since gmax,x represents the maximal channel conductance of current Ix in the compartment of interest, it provides an indirect value for the expected channel density of the channel in that compartment. It is therefore interesting to note that comparing the model currents IAptKv3.3 to IA shows that gmax,AptKv3.3 is three orders of magnitude larger than gmax,A when spike discharge properties are properly reproduced. If this is an accurate representation of the situation in pyramidal cells, the high-density of AptKv3.3 could have masked evidence of an IA in patch-clamp recordings.
IKA, IKBsomatic K+
currents
Somatic K+ currents in ELL pyramidal cells have only recently been subjected to voltage-clamp analysis and cannot be fitted as stringently as currents discussed in previous sections. However, without a proper treatment of somatic K+, both the model f-I relationship and spike frequency adaptation disagree with experimental results. In this section, we introduce two somatic K+ currents, IKA and IKB, to improve model performance in these areas.
Whole cell recordings in ELL pyramidal cell somata indicate a prominent
expression of Ca2+-dependent large conductance
(BK) K+ channels (Morales and Turner, unpublished
observations). The effect of these channels is modeled by a
voltage-dependent current, IKA,
because of the uncertainties on the location and magnitude of
Ca2+ influx in pyramidal cells. The dynamics is
similar to that of IAptKv3.3, given
the fast rate of BK activation and deactivation in ELL pyramidal cells
(Morales and Turner, unpublished observations). Specifically, a fast
activation time constant (small m,KA) is chosen for IKA dynamics, and the
current is set to be high threshold in its initial activation (small
km,KA and depolarized
V1/2,m,KA, see Table 1).
Whole cell recordings reveal that iberiotoxin-sensitive BK
K+ channels contribute ~75% of the somatic
K+ current (Morales and Turner, unpublished
observations). Consequently the gmax
of IKA is adjusted to first establish
the BK simulated current to a level approximately triple that of
somatic IAptKV3.3 at voltages >0 mV
(results not shown). Because of its fast activation and the lack of
inactivation, IKA overlaps the sAHP
following a somatic spike and hence significantly affects the model
f-I relationship. Thus in addition, the channel density,
gmax,KA, is set so that f-I
characteristics of the model more closely approximate ELL pyramidal
cells (see Fig. 8). The f-I
curves show a rheobase current of 0.1 nA with a saturating rise in
spike frequency as current increases. This is equivalent to measured
f-I curves from ELL pyramidal cells in control situations
(Berman and Maler 1998b; Lemon and Turner
2000
).
|
Spike frequency adaptation during long current pulses (Mathesion
and Maler 1988) has been reported in some ELL pyramidal cells, although it is typically not prominent. The original version of our
model incorporated a slow, noninactivating K+
current termed IKB to provide correct
frequency adaptation under constant depolarizing current (Doiron
et al. 2001
). The kinetic parameters of this current are not
modified from the original model, where comparisons between
experimental and model frequency adaptation are presented.
In summary, the core pyramidal cell model includes 10 ionic currents, each described by separate Hodgkin/Huxley dynamics. Model AptKv3.3 currents match HEK cell experiments that isolate and describe properties of this current. The model cell gives the correct shape and refractory properties for both somatic and dendritic spikes and the generation of a DAP at the soma by the backpropagating spike. The model somatic and dendritic NaP channels produce the correct shifts in RMP, boosting of EPSPs, and reduction in spike latencies from rest, as observed in experimental recordings in vitro. A-type K+ channels are included so as to give correct latency to spike from hyperpolarized potentials. Finally, the model shows correct passive and f-I characteristics as determined from intracellular recordings.
ELL pyramidal cell bursting
Figure 9A shows the
model's repetitive discharge properties (nonburst activity) in
response to depolarizing somatic current injection. However, the lack
of a transition to -burst discharge suggests that there are missing
elements in the model. We should note that electrophysiological work to
date has reported no evidence for a low-threshold "T"-type
Ca2+ current or
Ih in ELL pyramidal cells, two
currents known to underlie burst discharge in many cell types
(Huguenard 1996
; Pape 1996
). Rather,
burst discharge in ELL pyramidal cells comes about through a
progressive shift in the interaction between soma and dendrite during
repetitive discharge (Lemon and Turner 2000
). In the
following sections, we alter the kinetic properties of specific ion
channels to test their ability to generate burst discharge in the core model. We first introduce a well-studied bursting mechanism involving slow activating K+ channels (Chay and
Keizer 1983
) in the hopes of achieving bursting. Burst
discharge in the model does occur but fails to qualitatively reproduce
several burst properties in somatic and dendritic recordings of ELL
pyramidal neurons. We then insert various potential burst mechanisms
into the ionic description of the model. It will be shown that a slow,
cumulative, inactivation of a dendritic K+
current coupled with the longer refractory period of the dendritic spike as compared to the somatic spike is required to reproduce ELL
pyramidal cell
-bursting.
|
Standard burst mechanism: slow activating K+ current
Reduced dynamical burst models show a characteristic ability to
switch between stable oscillatory discharge (burst) and quiescent rest
voltage (inter-burst) (see Izhikevich 2000;
Rinzel 1987
; Wang and Rinzel 1995
; for a
review of dynamical bursting models). What is required to switch
between these states is a slow dynamical variable. In most previous
compartmental models of intrinsic bursting, this slow variable is a
Ca2+ and/or voltage-dependent
K+ channel,
K(Ca) (Chay and Keizer
1983
; Mainen and Sejnowski 1996
; Pinsky
and Rinzel 1994
; Rhodes and Gray 1994
;
Traub et al. 1994
; Wang 1999
; to name but
a few). The mechanism involves increases in intracellular
Ca2+ due to repetitive firing. This causes a slow
activation of K(Ca), thereby
hyperpolarizing the cell. The hyperpolarization by
K(Ca) first acts as a voltage shunt,
increasing the ISIs at the tail of a burst. When
K(Ca) is sufficiently activated, spike
discharge stops completely, and the burst terminates. At hyperpolarized levels, K(Ca) deactivates, and spiking
(bursting) may once again occur, given sufficient depolarization. This
gives a characteristic burst pattern, with an increasing ISI during the
length of the burst. This pattern has been observed in both experiment
(Gray and McCormick 1996
) and models that use
K(Ca) (Wang 1999
).
Burst discharge in ELL pyramidal cells is insensitive to the
Ca2+ channel blocker Cd2+
(Rashid et al. 2001), and hence
K(Ca) is presumably not implicated in
the burst mechanism. Yet a slow, increasing K+
current that terminates the burst is still a potential mechanism. Rather than hypothesize a new ionic K+ channel,
we modify the existing somatic IKA to
produce the desired effects. Specifically, Fig. 9 shows the model
somatic voltage under constant somatic current injection after the
activation time constant
m,KA is increased
from 1 ms (Fig. 9A) to 50 ms (Fig. 9B). Bursting
occurs, yet with a burst frequency of ~5 Hz, whereas pyramidal
neurons exhibit typical burst frequencies in the
range (20-80 Hz)
(Lemon and Turner 2000
). To rectify the discrepancy,
m,KA is reduced to 10 ms with the
corresponding spike train shown in Fig. 9C. The burst
frequency now approaches experimental values, but the spike pattern
within a burst disagrees with experimental data. We elaborate on the
discrepancies in the following text.
Figure 9 (D and E) illustrates the somatic
and dendritic (200 µm) responses during a single burst from the train
shown in Fig. 9C. During a burst, the model somatic voltage
shows the existence of multiple spike doublets (2 spikes at
>200-Hz frequency), while the dendritic voltage shows
multiple spike failures (Fig. 9, D and
E). Both somatic and dendritic bursts show no growing
depolarization during the burst as evident from the lack of both an
increasing DAP at the soma and spike summation in the dendrite.
Dendritic spike broadening is not observed during the length of a
burst, and the somatic spike train is followed by a large DAP that
fails to elicit a spike due to a large KA conductance at the end of the
burst. Finally, Fig. 9D shows an increasing
inter-doublet interval during a burst. This result is similar to other
bursting models incorporating a slow activating
K+ current (Rhodes and Gray 1994;
Wang 1999
) but does not match the properties of burst
discharge in ELL pyramidal cells (Lemon and Turner
2000
). Therefore these discrepancies indicate that a slow
activating K+ current is inadequate to model the
burst discharge that incorporates conditional backpropagation in ELL
pyramidal neurons.
ELL burst mechanism
To produce an output that more closely simulates pyramidal cell
burst discharge, we concentrate on methods in which a decreasing ISI
pattern during a burst can be realized in the model. The duration of an
ISI is determined by the amount of somatic depolarization that produces
the next spike in a spike train. Hence changes in ISIs must be linked
to changes in the amount of depolarization during a spike train. In the
present study, somatic depolarization is determined from two sources: a
constant applied current Iapp and a
dendritic component activated by spike backpropagation that generates
the DAP. Because Iapp is constant, the
ISI decrease observed during a burst should be correlated with
increases in the DAP as shown by Lemon and Turner
(2000). Four possible alternatives for DAP increase present
themselves. First, cumulative inactivation of dendritic fast
Na+ current could broaden dendritic spikes
indirectly by diminishing the activation of dendritic repolarizing
currents (IDr,d and
IAptKv3.3). The broadening of the
dendritic spike could lead to DAP growth at the soma. Second, a slowly
activating inward current could increase the dendritic depolarization
during repetitive discharge and hence augment the somatic DAP. Third, a
cumulative inactivation of a dendritic K+ current
involved in dendritic spike repolarization would increase dendritic
spike duration during a burst and increase the DAP. The fourth
potential mechanism is a cumulative decrease in
K+ currents underlying AHPs at the soma that
would allow the DAP to become progressively more effective in
depolarizing somatic membrane. However, this mechanism has been ruled
out because somatic AHPs are entirely stable in amplitude at the
frequencies of spike discharge encountered during burst discharge
(Lemon and Turner 2000
). We consider each of the
remaining alternatives in the following text.
Slow inactivation of dendritic Na+ channels
Patch-clamp recordings in hippocampal pyramidal cells have shown
that the amplitude of dendritic spikes are reduced substantially during
repetitive discharge (Colbert et al. 1997;
Golding and Spruston 1998
; Jung et al.
1997
; Mickus et al. 1999
). The reduction in
dendritic spike amplitude saturates during long stimulus trains, giving
a final steady-state potential height. Jung et al.
(1997)
and Colbert et al. (1997)
have identified
the cause to be a slow inactivation of dendritic
Na+ channels. This process may also contribute to
a decrease in dendritic spike amplitude in ELL pyramidal cells observed
during antidromic spike trains (Lemon and Turner 2000
).
As stated in the preceding text, a slow inactivation of dendritic
Na+ channels could contribute to burst discharge
by reducing the activation of K+ currents that
repolarize the dendritic spike (IDr,d
and IAptKv3.3 in the model).
Mickus et al. (1999) presented a detailed kinetic model
of INa,d inactivation that considers
two separate inactivation states variables: fast and slow. Slow
inactivation is the state variable that cumulatively grows from spike
to spike, producing spike attenuation during repetitive discharge. To
incorporate this concept into the model Hodgkin-Huxley framework, we
propose to modify the existing INa,d
description through the addition of a second inactivation state
variable pNa,d designed to represent a
slow inactivation according to
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Colbert et al. (1997) and Jung et al.
(1997)
both reported that full recovery of
Na+ channel inactivation occurred in the order of
seconds. This time scale is to long reproduce ELL pyramidal cell spike
bursts because significant INa,d
recovery needs to occur within the inter-burst interval, which is
10-15 ms (Lemon and Turner 2000
). However, simply
setting
p,Na,d so that recovery from
Na+ channel inactivation occurs on a 15-ms time
scale also results in significant recovery from inactivation during
repetitive spike discharge, removing the decrease in spike amplitude
during the burst. Recovery from slow inactivation of dendritic
Na+ channels after a stimulus train has been
shown to be accelerated through membrane hyperpolarization
(Mickus et al. 1999
). This is ideal for allowing only
significant inactivation recovery of dendritic
Na+ in the inter-burst interval, which occurs in
proximal apical dendrites at potentials up to
10 mV lower than
intra-burst subthreshold potentials (Lemon and Turner
2000
). We therefore extend the description of
p,Na,d to include voltage dependence as
originally modeled by Hodgkin and Huxley (1952)
. Rather
than using the
and
rate formalism, we simply assumed a
sigmoidal relation between
p,Na,d and
Vm
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(5) |
Figure 10A shows the
response of the model dendritic compartment (200 µm) to two 50-ms
step somatic depolarizations of 1 nA, separated by 15 ms to simulate
the occurrence of a burst AHP. Spike amplitude during both trains of
backpropagating model spikes show attenuation similar in both magnitude
and time scale to that observed in recordings of bursting ELL pyramidal
cell proximal apical dendrites (Lemon and Turner 2000).
The model dendritic spikes do indeed show a full recovery from slow
inactivation during a 15-ms pause between depolarizations (Fig.
10A). This indicates that the inclusion of voltage
dependence of
p,Na,d produces a recovery from
Na+ channel inactivation that would be necessary
to sustain bursting. Nevertheless Fig. 10B shows that under
constant somatic depolarization, only rapid dendritic spike
attenuation, which saturates at a fixed amplitude, and not burst
discharge is observed. This pattern is identical to the attenuation and
saturation of dendritic spike amplitude observed in rat CA1 pyramidal
cells during antidromic repetitive stimulation (Colbert et al.
1997
; Jung et al. 1997
). It is also important to
note that significant broadening of model dendritic spikes does not
occur under these conditions, and an ISI of 8 ms is sustained during
repetitive discharge (Fig. 10B). Further adjustment of model
INa,d parameters does not
qualitatively change these results. These simulations indicate that a
cumulative inactivation of Na, d and the associated decrease in spike
amplitude is not sufficient to produce burst discharge in the core
model. Although this mechanism may contribute to the processes
underlying dendritic spike failure in the intact cell, we remove slow
inactivation of Na, d from subsequent simulations to simplify the
analysis.
|
Slow activation of INaP
Recent experimental studies have suggested that
INaP contributes
substantially to the depolarization that drives burst discharge in
several mammalian neurons (Azouz et al. 1996;
Brumburg et al. 2000
; Franceschetti et al.
1995
; Magee and Carruth 1999
). In ELL pyramidal
cells, we find that INaP kinetics that
lead to appropriate shifts in RMP and EPSP amplitude are not able to
promote burst discharge. To identify the potential for
INaP to contribute to burst discharge
in Apteronotus pyramidal cells, a slow activating component
to the typical fast activating INaP is
hypothesized. If such a component was added to the model description,
then NaP could cumulatively grow during a burst, thereby broadening
dendritic spikes. This would produce a slow growth in DAP amplitude, a
reduction in spike latency to discharge, and a shortening in ISI
through a burst. We modify the existing description of
INaP in both somatic and dendritic
compartments by creating a second activation variable, qNaP, in the NaP current equation
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(6) |
|
As reported previously, these results indicate that
INaP is capable of contributing to
burst discharge in the -frequency range (Wang 1999
).
However, in ELL pyramidal cells, this current is unable to promote
burst discharge without the addition of a slow activation rate into
INaP channel kinetics. The failure to produce multiple spike bursts even with the slow activation time constant may be a result of the steeply nonlinear positive feedback incorporated into NaP (Fig. 6). Therefore we remove the slow activation of NaP introduced in this section from all subsequent analyses.
Cumulative inactivation of dendritic K+ channels
Previous studies have shown that a cumulative inactivation of
K+ channels is essential for producing a
frequency-dependent spike broadening (Aldrich et al.
1979; Ma and Koester 1995
; Shao
et al. 1999
). Direct experimental evidence for the existence of
a cumulatively inactivating K+ channel within ELL
pyramidal cell dendrites has yet to be established. Nonetheless the
assumption is indirectly supported by the dendritic spike broadening
observed during bursting (Lemon and Turner 2000
) (Fig.
13). Instead of inserting a separate K+ channel
into the model, we choose to modify the dendritic
K+ channel, Dr, d, so that it inactivates
substantially over the length of a burst yet remains constant during an
individual action potential.
The core model Dr, d kinetics include only fast activation, represented
by the state variable mDr,d. To
incorporate cumulative inactivation within the model, we introduce a
second state variable hDr,d,
representing inactivation, inserted into the current equation for Dr, d
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(7) |
Figure 12 (A and B) illustrates the effects of incorporating cumulative inactivation of Dr, d into the core model according to Eq. 7. The qualitative change from nonbursting to bursting behavior is evident. Direct comparisons to experimental data are presented in the following text. Figure 12C plots the state variable hDr,d from the same simulation as in Fig. 12B. The slow increase of inactivation (hDr,d decreases) occurs over the length of each individual burst. At burst termination, inactivation is removed quickly (hDr,d increases) due to the large hyperpolarization associated with a burst AHP (bAHP), and slow inactivation begins again with the next burst. Because of the addition of this second state variable, hDr,d, which oscillates between values of 0.3 and 0.1 during bursting, gmax,Dr,d is increased from 0.2 to 0.65 S/cm2 to compensate. This ensures that the current IDr,d remains comparable between nonbursting and bursting models.
|
Figure 13 compares in detail the
characteristics of burst discharge in ELL pyramidal cells to burst
simulations when a cumulative inactivation of
IDr,d is incorporated into the model.
Shown are somatic and dendritic recordings of a single spike burst with the equivalent simulation results at the same scale below. Comparing the somatic recording and simulation (Fig. 13, A and
B) reveals that the model successfully reproduces a
progressive increase in the DAP, a reduction in ISI during the burst,
and a high-frequency spike doublet that is followed by a
large-amplitude burst AHP; all characteristic and key elements in the
process of conditional spike backpropagation (Lemon and Turner
2000). Note that potentiation of the DAP in the model occurs at
the same initial intra-burst ISI as pyramidal cells, with a matching
decrease in ISI over the course of a six-spike burst. The final burst
frequency in both experiment and simulation is 25 Hz (not shown),
within the expected range of oscillatory burst frequency near burst
threshold (Lemon and Turner 2000
). At the dendritic
level (Fig. 13, C and D), the model now
reproduces a progressive frequency-dependent spike broadening that
underlies a temporal summation of dendritic spikes (Fig. 13,
C and D, insets). This temporal summation leads
to the further development of a depolarizing envelope that contributes
to potentiation of the DAP at the soma. The dendritic simulation also
correctly replicates the conditional failure of spike backpropagation
when a spike doublet is generated at the soma as indicated by a
passively reflected partial spike response at the end of the simulated
burst (Fig. 13D). Finally, the hyperpolarization produced by
the bAHP is sufficient to promote recovery from
IDr,d inactivation (Fig. 12C), essentially resetting the duration of dendritic spikes
to allow the cell to repeat this process and generate the next burst.
|
One discrepancy between the dendritic simulation and experimental recordings is the lack of dendritic spike attenuation in the model output (Fig. 13D). Although the ionic mechanism underlying this process in pyramidal cells is unknown, it may involve a slow inactivation of dendritic Na+ channels as modeled in Fig. 10. However, the results of Fig. 13 clearly indicate that it is not essential to reproducing the major features of burst discharge. Hence, for simplicity, it is not incorporated into the model at this time.
It should be noted that the voltage and time dependencies of
IDr,d inactivation,
hDr,d, are chosen so as to best
reproduce the experimental data. In fact, several characteristics of
burst output depend strongly on the kinetic properties of
IDr,d inactivation. Specifically,
reduction of Dr,d 2 ms removes all burst
output from the simulations, indicating that
IDr,d inactivation must be cumulative
to achieve burst discharge. Setting
Dr,d to
values above 2 ms does not prevent bursting but rather modifies burst frequency, with
Dr,d >10 ms producing
oscillatory burst discharge outside the
-frequency range (<20 Hz).
Realistic modifications of
kh,Dr,d do not
qualitatively change burst output in the model. However, increases or
decreases of V1/2,h,Dr,d
outside the voltage range attained by dendritic spikes (below
80 or
above
20 mV) blocks burst discharge. This again emphasizes the
importance of the properties of backpropagating dendritic spikes in
activating and inactivating IDr,d
channels to bring about burst discharge.
Dissection of the burst mechanism
We investigated the role of several potential ionic mechanisms to
simulate ELL pyramidal cell -frequency burst discharge. We could not
match experimental results for
-frequency burst output by
introducing a slow activation of somatic K+
conductance, a slow inactivation of Na, d channels, or a slow activation of NaP, indicating that these conditions are not by themselves sufficient components of the burst mechanism. In contrast, introducing a cumulative inactivation of dendritic
K+ current was very successful in producing a
realistic burst output, suggesting that this mechanism is an essential
factor in pyramidal cell
bursting. We now dissect the complete
burst mechanism into the main ionic currents that underlie its
evolution and termination.
We first elicit a single burst by somatic depolarization, shown in Fig.
14A complete with spike
doublet and bAHP; all subsequent analysis will pertain to this burst.
Figure 14B plots the time series of the channel conductance
gDr,d from the apical dendritic compartment 200 µm from the soma (last active zone) over the duration of the burst. Recall that gDr,d = gmax,Dr,d · mDr,dhDr,d,
where mDr,d and
hDr,d are the respective activation
and cumulative inactivation parameters of the dendritic
K+ channel. Figure 14B shows the
conductance of Dr, d tracking each spike in the burst as it activates
and deactivates quickly (the activation time constant
m,Dr,d = 0.9 ms). A cumulative inactivation is
clear from the attenuation of gDr,d
that occurs during the burst. This attenuation leads to dendritic spike
broadening and a temporal summation of dendritic spikes that produces a
slow depolarizing envelope (Fig. 13). The combination of an increase in
dendritic spike duration and a slow depolarizing envelope allows the
DAP at the soma to increase from spike to spike during the burst. The
increase in the DAP further depolarizes the soma to reduce the ISI as
the burst evolves. Thus cumulative inactivation of a dendritic
K+ channels is sufficient in itself to account
for each of the key properties of spike discharge that characterize
burst generation in pyramidal cells (Lemon and Turner
2000
). Another factor that merits further consideration in
future electrophysiological studies is the kinetic properties of
INaP that might contribute to the dendritic depolarization observed during repetitive discharge.
|
The termination of the burst is quite separate from the mechanism
driving spike discharge. Figure 14C plots
gNa,d, the dendritic Na+ conductance 200 µm from the soma during the
length of the burst. Recall that the conductance is given by
gNa,d = gmax,Na,d and mNa,dhNa,d.
Here gNa,d decreases slightly with
each spike in the burst but exhibits a pronounced decrease on the
generation of a spike doublet at the end of the spike train (Fig.
14C). This corresponds to a failure of spike backpropagation
when the high frequency of the spike doublet exceeds the dendritic
refractory period as reflected by the significant drop in
gNa,d on the final spike. In contrast,
doublet frequencies of firing can easily be sustained by the somatic
conductance gNa,s (not shown),
allowing two full somatic spikes to be generated (Fig. 14A).
When the dendritic spike fails to activate, the DAP is selectively
removed at the somatic level, uncovering a large bAHP that signifies
the end of a spike burst (Fig. 14A). To test the
significance of the dendritic refractory period for burst generation,
we performed additional simulations where
INa,d was replaced by
INa,s, thereby establishing equivalent
dendritic and somatic refractory periods. Spike bursts do not occur in
these simulations with only repetitive discharge observed for all
levels of depolarizing somatic current injection. Hence the longer
refractory period of the dendrite as compared with the soma is
necessary for burst termination as proposed by Lemon and Turner
(2000).
The ionic basis of the bAHP has not been fully determined, but the
initial early phase of this response is insensitive to both TEA and
Cd2+, eliminating many candidate
K+ currents in pyramidal cells that could
actively contribute to the bAHP (Noonan et al. 2000).
However, we should note that the large hyperpolarization of the model
bAHP is also due to slight summation of the somatic
IKA (
KA = 1 ms) that occurs only at doublet frequencies (data not shown). Although
this effect enhances burst termination, elimination of
IKA does not prevent bursting in the model.
Figure 14D presents the cumulative inactivation of gDr,d and the sudden failure of gNa,d as a function of spike number of the burst presented in Fig. 14A. This superimposes the results of Fig. 14, B and C, and considers the evolution and termination of the burst as events driven by action potentials. Figure 14E schematically summarizes the burst mechanism by considering the end effect of IDr,d and INa,d in shaping the soma-dendritic interaction. Their action results in a cumulative DAP growth and eventually a sharp DAP failure that is the manifestation of the burst mechanism presented in Fig. 14, B-D, at the level of membrane voltage.
The currents IA and IKB were included for all bursting simulations. However, the presence of these channels is not required for model bursting (data not shown). This is clear because IA requires hyperpolarization to remove inactivation and therefore was inactivated at the depolarized membrane potentials required for bursting. IKB has a time course in the order seconds and can be approximated as static on the short time scale of bursting.
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DISCUSSION |
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Importance of a realistic model of ELL pyramidal cells
Recently the ELL has been the focus of numerous investigations
into the role of bursting in sensory information processing (Gabbiani and Metzner 1999; Gabbiani et al.
1996
; Metzner et al. 1998
). Feedforward
information transfer is currently under study in the ELL through
modeling of P-afferent dynamics and coding (Chacron et al.
2000
; Kreiman et al. 2000
; Nelson et al.
1997
; Ratnam and Nelson 2000
;
Wessel et al. 1996
). Studies of synaptic feedback to the
ELL involve both experimental and computational work (Berman and
Maler 1998a
-c
; 1999
; Berman et al. 1997
;
Doiron et al. 2001
; Nelson 1994
). In fact
recent experimental work has suggested that feedback activity modulates
bursting behavior in ELL pyramidal cells (Bastian and Nguyenkim
2001
). The subtle nature of these issues points to the
usefulness of a detailed and realistic compartmental model for creating
and testing hypotheses concerning burst mechanisms and their regulation
by feedforward and feedback synaptic input.
ELL burst mechanism
Our results suggest the following necessary and sufficient conditions for ELL pyramidal cell bursting. First, there must be a dendritic Na+ current to support spike backpropagation into the proximal apical dendrites, yielding a DAP at the soma. Second, there must be a (proposed) cumulative inactivation of a K+ conductance involved in dendritic spike repolarization. This inactivation effectively results in a dendritic spike broadening during repetitive discharge that is known to potentiate DAP amplitude at the soma. Finally there must be a longer spike refractory period in the dendrites compared with the soma, causing backpropagation to be conditional on the somatic spike discharge frequency, which terminates a burst at sufficiently high discharge rates.
AptKv3.3 as a possible candidate for Dr, d
In the present study, we assigned kinetic properties to the Dr, d
channel that allow it to be activated by dendritic spikes and to
exhibit cumulative inactivation during repetitive spike discharge by
virtue of a relatively low V1/2 for
inactivation. It is important to note that the Dr, d channel is a
hypothetical channel subtype inserted in the model to allow for proper
simulation of the dendritic spike response. The question remains as to
which, if any, dendritic channel in intact ELL pyramidal cells matches the description of Dr, d. One potential current is AptKv3.3,
which is located with high prevalence over the entire axis of pyramidal cells (Rashid et al. 2001). Indeed, pharmacological
blockade of dendritic AptKv3 channels has been shown to
decrease dendritic spike repolarization and lower the threshold for
burst discharge (Rashid et al. 2001
). The possibility
therefore exists that dendritic AptKv3.3
K+ channels may serve a similar capacity as the
Dr, d channels in the current model.
We modeled IAptKv3.3 according to the
kinetic properties inherent to whole cell currents when
AptKv3.3 channels are transiently expressed in HEK cells
(Rashid et al. 2001). These currents share several
properties with Dr, d channels, including fast activation and
deactivation kinetics. The major difference is the
V1/2 of activation:
V1/2,m,Dr,d =
40 mV and
V1/2,m,AptKv3.3 = 0 mV.
We found that burst discharge can still be produced in the model if
V1/2,m,Dr,d is raised no higher than
20 mV with corresponding adjustments to channel density to offset the
smaller degree of current activation. However, with
V1/2,m,Dr,d >
20 mV, the model
could not produce bursting with realistic values of
gmax,Dr,d. Similarly,
AptKv3.3 as modeled in the cell could not produce bursting
with a V1/2 of 0 mV, even if a
cumulative inactivation similar to Dr, d was introduced (results not
shown). We have recently begun to characterize an additional slow
inactivation process in AptKv3.3 channels that has not been
incorporated into the present model. Recent work further indicates that
the V1/2 for AptKv3.3 slow
inactivation can exhibit a leftward (negative) shift in the outside-out
as compared with whole cell recording configuration (Morales and
Turner, unpublished observations). This suggests that
AptKv3.3 kinetics are subject to second-messenger regulation
as previously shown for other Kv3 channel subtypes (Atzori et
al. 2000
; Covarrubias et al. 1994
; Moreno
et al. 1995
; Velasco et al. 1998
). The potential
therefore exists for a selective modulation of dendritic
AptKv3.3 kinetics that would allow this channel to exhibit a
cumulative inactivation during repetitive spike discharge. Further
experimental work will be needed to determine the exact
voltage-dependence and regulation of somatic versus dendritic
AptKv3.3 channels to test this hypothesis.
Relation to in vivo bursting
A recent quantitative analysis of burst discharge in ELL pyramidal
cells has shown that the ISIs during spontaneous bursts recorded in
vivo remain relatively constant, and often lack a terminating spike
doublet; results that differ from the burst mechanism routinely
recorded in vitro (Bastian and Nguyenkim 2001). At
present the discrepancy between the bursts that are driven by
current-evoked depolarizations in vitro and baseline discharge recorded
in vivo is not clear. There are many differences between the state of
pyramidal cells in vivo versus in vitro: the resting membrane potential
of pyramidal cells in vivo is closer to spike threshold (J. Bastian,
personal communication), the input resistance of pyramidal cells is
likely to be far lower in vivo because of synaptic bombardment
(Bernander et al. 1991
; Paré et al.
1998
; Bastian, personal communication), stimulation in vitro is
via constant current injection, whereas in vivo the primary stimulus is
a stochastic synaptic input to dendrites, and in vivo studies contain
network effects which in vitro studies necessarily lack. Further
exploration with the model ionic channel parameters, to modify these
features, as well introducing simulated synaptic input, may bridge the
gap between in vivo and in vitro results. However, more detailed
experimental analysis is required before any modeling attempt is to be
made along these lines.
Application of ELL burst model to mammalian chattering cells
Sustained -frequency bursting, or chattering behavior, has been
observed in mammalian cortical neurons (Brumburg et al.
2000
; Gray and McCormick 1996
;
Llinás et al. 1991
) and corticothalamic neurons
(Steriade et al. 1998
). Wang (1999)
produced a "chattering" behavior in a two-compartment neuron model
that incorporates a similar "ping-pong" reciprocal interaction
between the cell soma and dendrites we have described in ELL pyramidal
cells. The evolution and termination of the burst in Wang's model
relies on a cumulative activation of
K(Ca). This produces a characteristic
increase of intra-burst ISIs and a prominent DAP in the inter-burst
interval (Wang 1999
). We have shown (Fig. 9) that this
mechanism is not able to produce realistic ELL pyramidal cell bursts
because it fails to reproduce a decrease in intra-burst ISIs, the slow
somatic depolarization that increases the DAP, and the lack of a DAP at burst termination as observed with pyramidal cells in vitro
(Lemon and Turner 2000
). Our proposed mechanism
successfully reproduces all the preceding criteria. Brumburg et
al. (2000)
report the cumulative reduction of spike fAHPs as a
burst evolves in supragranular cortical neurons. This result also
cannot be reproduced by cumulative activation of
K(Ca) in our model, as used in
Wang (1999)
or in other detailed IB neuron compartmental
models (Mainen and Sejnowski 1996
; Pinsky and
Rinzel 1994
; Rhodes and Gray 1994
; Traub
et al. 1994
). Brumberg et al. (2000)
hypothesize
that the mechanism underlying
-burst discharge in mammalian visual
cortex could be either a slow increase of a Na+
current or a slow decrease of a K+ current. Our
modeling of ELL pyramidal cells reveals that cumulative inactivation of
a dendritic K+ current can play a key role in
generating burst discharge, a result that may have wide applicability
to cells discharging in the
-frequency range.
The NEURON codes for our ELL pyramidal cell model are freely available at http://www.science.uottawa.ca/phy/grad/doiron/
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ACKNOWLEDGMENTS |
---|
The authors thank N. Berman, E. Morales, N. Lemon, and L. Noonan for the generous use of data. Many useful discussions with M. Chacron, C. Laing, and J. Lewis were greatly appreciated during the writing of the manuscript. R. W. Turner is an Alberta Heritage Foundation for Medical Research Senior Scholar.
This research was supported by operating grants from National Science and Engineering Research Council (B. Doiron and A. Longtin) and Canadian Institute for Health Research (L. Maler and R. W. Turner).
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FOOTNOTES |
---|
Address for reprint requests: B. Doiron, Physics Dept., University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada (E-mail: bdoiron{at}science.uottawa.ca).
Received 18 January 2001; accepted in final form 10 May 2001.
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REFERENCES |
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