Laboratoire de Neurophysiologie, Département de Physiologie, Université Laval, Quebec G1K 7P4, Canada
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ABSTRACT |
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Destexhe, Alain and Denis Paré. Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. During wakefulness, neocortical neurons are subjected to an intense synaptic bombardment. To assess the consequences of this background activity for the integrative properties of pyramidal neurons, we constrained biophysical models with in vivo intracellular data obtained in anesthetized cats during periods of intense network activity similar to that observed in the waking state. In pyramidal cells of the parietal cortex (area 5-7), synaptic activity was responsible for an approximately fivefold decrease in input resistance (Rin), a more depolarized membrane potential (Vm), and a marked increase in the amplitude of Vm fluctuations, as determined by comparing the same cells before and after microperfusion of tetrodotoxin (TTX). The model was constrained by measurements of Rin, by the average value and standard deviation of the Vm measured from epochs of intense synaptic activity recorded with KAc or KCl-filled pipettes as well as the values measured in the same cells after TTX. To reproduce all experimental results, the simulated synaptic activity had to be of relatively high frequency (1-5 Hz) at excitatory and inhibitory synapses. In addition, synaptic inputs had to be significantly correlated (correlation coefficient ~0.1) to reproduce the amplitude of Vm fluctuations recorded experimentally. The presence of voltage-dependent K+ currents, estimated from current-voltage relations after TTX, affected these parameters by <10%. The model predicts that the conductance due to synaptic activity is 7-30 times larger than the somatic leak conductance to be consistent with the approximately fivefold change in Rin. The impact of this massive increase in conductance on dendritic attenuation was investigated for passive neurons and neurons with voltage-dependent Na+/K+ currents in soma and dendrites. In passive neurons, correlated synaptic bombardment had a major influence on dendritic attenuation. The electrotonic attenuation of simulated synaptic inputs was enhanced greatly in the presence of synaptic bombardment, with distal synapses having minimal effects at the soma. Similarly, in the presence of dendritic voltage-dependent currents, the convergence of hundreds of synaptic inputs was required to evoke action potentials reliably. In this case, however, dendritic voltage-dependent currents minimized the variability due to input location, with distal apical synapses being as effective as synapses on basal dendrites. In conclusion, this combination of intracellular and computational data suggests that, during low-amplitude fast electroencephalographic activity, neocortical neurons are bombarded continuously by correlated synaptic inputs at high frequency, which significantly affect their integrative properties. A series of predictions are suggested to test this model.
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INTRODUCTION |
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Since the classical view of passive dendritic
integration was proposed for motoneurons 30 years ago (Fatt
1957), the introduction of new experimental techniques such as
intradendritic recordings (Llinás and Nicholson
1971
; Wong et al. 1979
), and visually guided patch-clamp recording (Stuart et al. 1993
; Yuste
and Tank 1996
) has revolutionized this area. These new
approaches revealed that the dendrites of pyramidal neurons are
involved actively in the integration of excitatory postsynaptic
potentials (EPSPs) and that the activation of few synapses has powerful
effects at the soma in brain slices (Markram et al.
1997
; Mason et al. 1991
; Thomson and
Deuchars 1997
). Although remarkably precise data have been
obtained in slices, little is known about the integrative properties of
the same neurons in vivo.
The synaptic connectivity of the neocortex is very dense. Each
pyramidal cell receives 5,000-60,000 synapses (Cragg
1967; DeFelipe and Fariñas 1992
), 70% of
which originate from other cortical neurons (Gruner et al.
1974
; Szentagothai 1965
). Given that neocortical
neurons spontaneously fire at 5-20 Hz in awake animals (Evarts
1964
; Hubel 1959
; Steriade 1978
),
cortical cells must experience tremendous synaptic currents that may
have a significant influence on their integrative properties. This
theme was explored by several modeling studies (Barrett
1975
; Bernander et al. 1991
; Holmes and
Woody 1989
), where it was predicted that synaptic activity may
have a profound impact on dendritic integration. However, despite its
possible importance for understanding neuronal function, the
conductance due to synaptic activity was never measured in awake
animals because of the paramount technical difficulties related to
intracellular recordings in conscious animals.
To circumvent these difficulties, we constrained computational models
of neocortical pyramidal neurons with in vivo intracellular data
obtained in ketamine-xylazine-anesthetized cats before and after local
perfusion of tetrodotoxin (TTX) (Paré et al.
1998b). The interest of this approach derives from the fact
that under ketamine-xylazine anesthesia, cortical neurons oscillate
(<1 Hz) between two states, one where the network is quiescent and
another where it displays a pattern of activity similar to the waking state (Steriade et al. 1993a
,b
) (Fig.
1,A and B). Indeed,
during these active periods (Fig. 1B, underlined epochs), as
in the waking state (Fig. 1A), the electroencephalogram
(EEG) is dominated by waves of low amplitude and high frequencies
(20-60 Hz) and neocortical pyramidal neurons fire spontaneously at
5-20 Hz. Moreover, electrical stimulation of brain stem activating
systems that are believed to maintain the awake state in normal
circumstances elicits periods of desynchronized EEG activity with
similar characteristics under ketamine-xylazine anesthesia
(Steriade et al. 1993a
).
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Thus we estimated the synaptic activity required to account for the differences in neuronal properties observed in vivo during synaptic quiescence (i.e., in the presence of TTX) and during these active periods, here considered as a model of the spontaneous synaptic bombardment occurring in the waking state. The model then was used to infer the impact of this intense synaptic activity on dendritic integration.
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METHODS |
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Intracellular recordings in vivo
We reanalyzed intracellular data obtained from neocortical
pyramidal cells recorded in a previous study (Paré et al.
1998b). Unpublished intracellular recordings obtained with
K-acetate-filled pipettes (n = 2) also were included in
the analysis. Briefly, intracellular recordings were obtained from
morphologically identified neocortical pyramidal cells in the
suprasylvian gyrus (area 5-7) of cats deeply anesthetized with a
ketamine-xylazine mixture (11 and 2 mg/kg im), paralyzed with gallamine
triethiodide, and artificially ventilated. The level of anesthesia was
determined by continuously monitoring the EEG, and supplemental doses
of ketamine-xylazine (2 and 0.3 mg/kg, respectively, iv) were given to
maintain a synchronized EEG pattern. Lidocaine (2%) was applied to all
skin incisions. End-tidal CO2 concentration was kept at
3.7 ± 0.2% (mean ± SE) and the body temperature was
maintained at 37°C with a heating pad. To ensure recording stability,
the cisterna magna was drained, the cat was suspended, and a bilateral
pneumothorax was performed. Intracellular recording electrodes
consisted of glass capillary tubes pulled to a tip diameter of ~0.5
µm (~30 M
) and filled with K-acetate or KCl (2.5 M). Details
about experimental procedures and cell identification were given
previously (Paré et al. 1998a
,b
). Experiments were
conducted in agreement with ethics guidelines of the Canadian Council
on Animal Care.
TTX microperfusion in vivo
An injection micro-pipette (75 µm tip diameter) was inserted
~2 mm rostral to the recording micropipette to a depth of 1.5 mm. A
solution (Ringer or Ringer + TTX, 50 µM) was pumped continuously through the injection pipette (1-1.5 µl/min) for the duration of the
recording session; the dialyzing solution was changed using a liquid
switch system. The Ringer solution contained (in mM) 126 NaCl, 26 NaHCO3, 3 KCl, 1.2 KH2PO4, 1.6 MgSO4, 2 CaCl2, 5 HEPES, and 15 glucose. The
blockade of synaptic activity by TTX was evidenced by the disappearance
of responses to electrical stimuli applied to the cortex using tungsten
microelectrodes inserted 2 mm caudal to the recording pipette (see
Paré et al. 1997, 1998b
for more details).
Estimation of membrane parameters
Membrane potential (Vm) distributions
were computed from concatenated epochs of intense synaptic activity
totaling ~1 min. The signal was sampled at 5 kHz (for a total of
~300,000 data points), and the positive phase of action potentials
was deleted digitally. The values of these data points (usually 2) were
replaced by that of points immediately preceding the action potentials. No attempt was made to delete spike afterpotentials because they were
distorted by spontaneous synaptic events. The average
Vm (Vm
) and the
standard deviation (
v) were computed from such distributions.
Geometry for computational models
Simulations of cat layer II-III, layer V, and layer VI
neocortical pyramidal cells were based on cellular reconstructions obtained from two previous studies (Contreras et al.
1997; Douglas et al. 1991
). The cellular
geometries were incorporated into the NEURON simulation environment
(Hines and Carnevale 1997
). The dendritic surface was
corrected for spines, assuming that spines represent ~45% of the
dendritic membrane area (DeFelipe and Fariñas 1992
). Surface correction was made by rescaling
Cm and conductances by 1.45 as described
previously (Bush and Sejnowski 1993
; Paré et al. 1998a
). An axon was added, consisting in an initial
segment of 20 µm length and 1 µm diam, followed by 10 segments of
100 µm length and 0.5 µm diam each.
Passive properties
Passive properties were adjusted to experimental recordings in
the absence of synaptic activity: to block synaptic events mediated by
glutamate -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)
and
-aminobutyric acid type-A (GABAA) receptors, the
microperfusion solution contained: Ringer + TTX (50 µM) + 1,2,3,4-tetrahydro-6-nitro2,3-dioxo-benzo[f]quinoxaline-7-sulfon amide
disodium (NBQX, 200 µM) + bicuculline (200 µM). This procedure suppresses all miniature synaptic events, as demonstrated in a previous
study (Paré et al. 1997
).
Fitting of the model to passive responses obtained in such conditions
of absence of synaptic activity was performed using a simplex algorithm
(Press et al. 1986). Fitted parameters were leak
conductance and reversal potential, whereas other passive parameters
were fixed (membrane capacitance of 1 µF/cm2 and axial
resistivity of 250
cm). Other combinations of passive parameters
were also considered, including a supplementary leak in the soma (10 nS) due to electrode impalement, combined with a lower leak conductance
of 0.015 mS cm
2 (Pongracz et al. 1991
;
Spruston and Johnston 1992
) and/or a lower axial
resistivity of 100
cm.
In some simulations, a nonuniform distribution of leak parameters was
used based on estimations in layer V neocortical pyramidal cells
(Stuart and Spruston 1998). As estimated by these
authors, the axial resistance was low (80
cm) and the leak
conductance was low (gleak = 0.019 mS
cm
2) in soma but high (gleak = 0.125 mS cm
2) in distal dendrites.
gleak was given by a sigmoid distribution 1/gleak = 8 + 44/{1 + exp[(x
406)/50]} where x is the
distance to soma. The exact form of this distribution was obtained by
fitting the model to passive responses as described above.
Synaptic inputs
The densities of synapses in different regions of the cell were
estimated from morphological studies of neocortical pyramidal cells
(DeFelipe and Fariñas 1992; Fariñas
and DeFelipe 1991a
,b
; Larkman 1991
;
Mungai 1967
; White 1989
). These densities
(per 100 µm2 of membrane) were as follows: 10-20
GABAergic synapses in soma, 40-80 GABAergic synapses in axon initial
segment, 8-12 GABAergic synapses, and 55-65 glutamatergic (AMPA)
synapses in dendrites.
The kinetics of AMPA and GABAA receptor types were
simulated using two-state kinetic models (Destexhe et al.
1994)
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(1) |
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(2) |
Correlation of release events
In some simulations, N Poisson-distributed random
presynaptic trains of action potentials were generated according to a
correlation coefficient c. The correlation applied to any
pair of presynaptic train, irrespective of the proximity of synapses on
the dendritic tree and correlations were treated independently for
excitatory and inhibitory synapses for simplicity. To generate
correlated presynaptic trains, a set of N2
independent Poisson-distributed random variables was generated and
distributed randomly among the N presynaptic trains. This
procedure was repeated at every integration step such that the
N2 random variables were redistributed constantly among the N presynaptic trains. Correlations
arose from the fact that N2 N and
the ensuing redundancy within the N presynaptic trains.
N2 was chosen such as to generate a correlation of c = 0.05-0.2 calculated from the peak of the
cross-correlation function. Typically, n = 16563 and
N2 = 400 gave a correlation value of
c ~ 0.1.
Active currents
Active currents were inserted into the soma, dendrites, and axon
with different densities in accordance with available experimental evidence in neocortical and hippocampal pyramidal neurons
(Hoffman et al. 1997; Magee and Johnston
1995
; Magee et al. 1998
; Stuart and
Sakmann 1994
). Active currents were expressed by the generic form
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The voltage-dependent Na+ current was described by
(Traub and Miles 1991)
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The "delayed-rectifier" K+ current was described by
(Traub and Miles 1991)
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A noninactivating K+ current was described by
(Mainen et al. 1995)
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It was reported that some pyramidal cell have a
hyperpolarization-activated current termed Ih
(Spain et al. 1987; Stuart and Spruston
1998
). However, most cells recorded in the present study had no
apparent Ih (see passive responses in Figs. 1
and 2). Occasionally, cells displayed a
pronounced Ih, but these cells were
not included in the present study. This current was therefore not
included in the model.
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All simulations were done using NEURON (Hines and Carnevale
1997) on a Sparc-20 work-station (Sun Microsystems, Mountain
View, CA).
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RESULTS |
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Membrane properties of neocortical pyramidal neurons during active periods
In a previous study (Paré et al. 1998b), the
properties of pyramidal neurons were compared before and after local
TTX application, revealing that differences in background synaptic
activity account for much of the discrepancies between in vivo and in
vitro recordings. Intracellular recordings were performed under
barbiturate and ketamine-xylazine anesthesia, and the input resistance
(Rin) was estimated before and after TTX
application (Paré et al. 1998b
). However, these
properties were never measured specifically during active periods.
Here, we have reexamined and quantified these data by focusing
specifically on active periods occurring under ketamine-xylazine
anesthesia (Fig. 1B, bars). These active periods were
identified as follows: neurons fire at ~5-20 Hz, their membrane potential (Vm) is around
65 to
60 mV, and
the EEG displays low-amplitude waves of fast frequency in the gamma
range. Active periods usually lasted ~0.4-2 s, although periods
lasting up to several seconds occasionally occurred (Steriade et
al. 1993a
).
During active periods, neocortical neurons had a low
Rin, as shown by the relatively small voltage
responses to intracellular current injection (Fig. 1C, top).
Averaging >50 pulses during active periods led to
Rin of 9.2 ± 4.3 M (n = 26), consistent with previous observations (Contreras et al.
1996
).
The total conductance change due to synaptic activity was quantified by
comparing the Rin of the cells during active
periods to that measured after blocking synaptic transmission using
microperfusion of TTX. Under TTX, injection of current pulses led to
larger responses (Fig. 1D) and larger
Rin values (46 ± 8 M; n = 9). This was paralleled by a marked decrease in the amplitude of
Vm fluctuations, as quantified by the standard
deviation of the Vm(
v; Fig.
1E). In nine different cells recorded successively during
active periods and after TTX application,
v was reduced
from 4.0 ± 2.0 mV to 0.4 ± 0.1 mV, respectively (Fig.
1F). Figure 1E also shows that the
Vm dropped significantly to
80 ± 2 mV,
as reported previously (Paré et al. 1998b
). During
active periods, the average Vm
(
Vm
) was
65 ± 2 mV in control
conditions (K-acetate-filled pipettes) and
51 ± 2 mV with
chloride-filled recording pipettes. These conditions correspond to
chloride reversal potentials (ECl) of
73.8 ± 1.6 mV and
52.0 ± 2.9 mV, respectively
(Paré et al. 1998a
).
Normalizing Rin changes with reference to the
Rin measured in the presence of TTX revealed
that in all cells where active periods could be compared with an epoch
of suppressed synaptic activity (n = 9), the
Rin was reduced by approximately the same relative amount (81.4 ± 3.6%; Fig. 1F; data
summarized in Table 1), independently of
absolute values. Similar values were obtained by repeating this
analysis at different Vms, either more
depolarized, by using chloride-filled pipettes (n = 7),
or more hyperpolarized, by steady current injection (1 nA;
n = 2). Taken together, these data show that active
periods are characterized by an about fivefold decrease in
Rin, a significant depolarization of 15-30 mV
depending on the recording conditions;, and a ~10-fold increase in
the amplitude of Vm fluctuations.
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Model of high-frequency release
Computational models of cat neocortical pyramidal cells were used
to estimate the release conditions and conductances necessary to
account for these experimental measurements. A layer VI neocortical pyramidal cell (Fig. 2A) was reconstructed and incorporated
in simulations (see METHODS). As both somatic and dendritic
recordings are critical to constrain, the simulations of synaptic
activity (see following text), passive responses from both types of
recordings (Paré et al. 1997) were used to
constrain the passive parameters of the model. The fitting was
performed such that the same model could fit both somatic and dendritic
recordings obtained in deep pyramidal cells in the absence of synaptic
activity (TTX + synaptic blockers; see METHODS). The same
model could fit both traces (Fig. 2A) with the following
optimal passive parameters: gleak = 0.045 mS cm
2, Cm = 1 µF/cm2, and Ri = 250
cm (see
METHODS). Another fit was performed by forcing
Ri to 100
cm (Cm = 1 µF/cm2 and gleak = 0.039 mS
cm
2). Although the latter set of values were not optimal,
they were used to check for the dependence of the results on axial
resistance. A passive fit also was performed with high membrane
resistance, based on whole cell recordings (Pongracz et al.
1991
; Spruston and Johnston 1992
), and a somatic
shunt due to electrode impalement. In this case, the parameters were as
follows: 10 nS somatic shunt, gleak = 0.0155 mS
cm
2, Cm = 1 µF/cm2,
and Ri was of either 250 or 100
cm. A
nonuniform leak conductance, low in soma and a high in distal dendrites
(Stuart and Spruston 1998
), also was tested (see
METHODS). No further effort was made to optimize passive
parameters as models and experiments were based on different cellular
morphologies. This fitting procedure ensured that the model had an
Rin and a time constant consistent with both
somatic and dendritic recordings free of synaptic activity.
The next step was to simulate TTX-resistant miniature synaptic
potentials occurring in the same neurons. These miniature events were
characterized in somatic and dendritic intracellular recordings after
microperfusion of TTX in vivo (Paré et al. 1997)
(Fig. 2B, left). To simulate them, a plausible range of
parameters was determined based on in vivo experimental constraints.
Then, a search within this parameter range was performed to find an
optimal set that was consistent with all constraints. These constraints were the densities of synapses in different regions of the cell, as
derived from morphological studies of neocortical pyramidal cells
(DeFelipe and Fariñas 1992
; Fariñas
and DeFelipe 1991a
,b
; Larkman 1991
;
Mungai 1967
; White 1989
) (see
METHODS); the quantal conductance at AMPA and
GABAA synapses, as determined by whole cell recordings of
neocortical neurons (Markram et al. 1997
; Salin and Prince 1996
; Stern et al. 1992
); the value
of
v during miniature events after TTX application in
vivo (~0.4 mV for somatic recordings and 0.6-1.6 mV for dendritic
recordings) (Paré et al. 1997
); the change in
Rin due to miniature events, as determined in
vivo (~8-12% in soma and 30-50% in dendrites) (Paré et al.
1997
); and the distribution of mini amplitudes and frequency, as
obtained from in vivo somatic and dendritic recordings (Fig. 2B,
insets).
An extensive search in this parameter range was performed and a narrow
region was found to satisfy the above constraints. The optimal values
found were a density of 20 GABAergic synapses per 100 µm2
in the soma, 60 GABAergic synapses per 100 µm2 in the
initial segment, 10 GABAergic synapses and 60 glutamatergic (AMPA) synapses per 100 µm2 in the dendrites; a
rate of spontaneous release (assumed uniform for all synapses) of
0.009-0.012 Hz; and quantal conductances of 1,000-1,500 pS for
glutamatergic and 400-800 pS for GABAergic synapses. In these
conditions, simulated miniature events were consistent with experiments
(Fig. 2B, right), with v of 0.3-0.4 mV in
soma and 0.7-1.4 mV in dendrites, and Rin
changes of 8-11% in soma and 25-37% in dendrites.
To simulate the intense synaptic activity occurring during active
periods, we hypothesized that miniature events and active periods are
generated by the same population of synapses with different conditions
of release for GABAergic and glutamatergic synapses. The preceding
model of miniature events was used to simulate active periods by
increasing the release frequency at all synaptic terminals.
Poisson-distributed release was simulated with identical release
frequency for all excitatory synapses
(fe) as well as for inhibitory synapses
(fi). The release frequencies fe and fi affected the
Rin and average Vm
(Vm
) (Fig.
3A). These aspects were
constrained by the following experimental measurements (see preceding
section): the Rin change produced by TTX should be ~80%; the Vm should be around
80 mV
without synaptic activity; the Vm should be
about
65 mV during active periods (ECl =
75 mV); and the Vm should be around
51 mV during
active periods recorded with chloride-filled electrodes
(ECl =
55 mV). Here again an extensive search
in this parameter space was performed, and several combinations of
excitatory and inhibitory release frequencies could reproduce correct
values for the Rin decreases and
Vm differences between active periods and after
TTX (Fig. 3A). The optimal values of release frequencies
were fe = 1 Hz (range 0.5-3 Hz) for excitatory
synapses and fi = 5.5 Hz (range 4-8 Hz) for
inhibitory synapses.
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An additional constraint was the large Vm
fluctuations experimentally observed during active periods, as
quantified by v (see preceding section). As shown in
Fig. 3B (
,
,
,
), increasing the release
frequency of excitatory or inhibitory synapses produced the correct
Rin change but always gave too small values of
v. High release frequencies led to membrane fluctuations
of small amplitude, due to the large number of summating random events (Fig. 3B4). Variations within 50-200% of the optimal value
of different parameters, such as synapse densities, synaptic
conductances, frequency of release, leak conductance, and axial
resistance, could yield approximately correct
Rin changes and correct
Vm but failed to account for values of
v observed during active periods (Fig. 3C,
×).
One additional assumption had to be made to reproduce
Vm fluctuations comparable to those occurring in
vivo. In the cortex, action potential-dependent release is clearly not
independent at different synapses, as single axons usually establish
several contacts in pyramidal cells (Markram et al.
1997; Thomson and Deuchars 1997
). More
importantly, the presence of oscillatory amplitude fluctuations in the
EEG (see Fig. 1, A and B) implies correlated
activity in the network. A correlation therefore was included in the
release of different synapses (see METHODS). For the sake
of simplicity, the correlation was irrespective of the proximity of
synapses on the dendritic tree and correlations were treated
independently for excitatory and inhibitory synapses. Figure
3D shows simulations of random synaptic bombardment similar to Fig. 3B4 but using different correlation coefficients.
The horizontal alignment of the open symbols in Fig. 3D5
shows that the degree of correlation had a negligible effect on the
Rin because the same amount of inputs occurred
on average. However, the degree of correlation affected the standard
deviation of the signal. Several combinations of excitatory and
inhibitory correlations, within the range of 0.05-0.1, gave rise to
Vm fluctuations with comparable
v
as those observed experimentally during active periods (Fig.
3D5; compare with Fig. 1F; see also Table 1).
Introducing correlations among excitatory or inhibitory inputs alone
showed that excitatory correlations were most effective in reproducing the Vm fluctuations (Fig. 3D5,
).
To check if these results were affected by voltage-dependent currents,
we estimated the voltage-dependent currents present in cortical cells
from their current-voltage (I-V) relationship. The
I-V curve of a representative neocortical cell after TTX
microperfusion is shown in Fig.
4A. The I-V curve
was approximately linear at Vms more
hyperpolarized than 60 mV but displayed an important outward
rectification at more depolarized potentials similar to in vitro
observations (Stafstrom et al. 1982
). The
Rin was of ~57.3 M
at values around rest
(about
75 mV) and 30.3 M
at more depolarized
Vm (greater than
60 mV), which represents a
relative Rin change of 47%. This cell had the
strongest outward rectification in six cells measured after TTX
(relative Rin change of 30 ± 11%, n = 6).
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In the model, this type of I-V relation was simulated by including two voltage-dependent K+ currents, IKd and IM (see METHODS). In the presence of these two currents, the model displayed a comparable rectification as the cell showing the strongest rectification in experiments under TTX (Fig. 4B; the straight lines indicate the same linear fits as in A for comparison).
The constraining procedure described above then was used to estimate
the release conditions in the presence of voltage-dependent currents.
First, the model including IKd and
IM was fit to passive traces obtained in the
absence of synaptic activity to estimate the leak conductance and leak
reversal (similar to Fig. 2A). Second, the release rate
required to account for the v and
Rin change produced by miniature events was
estimated as in Fig. 2B. Third, we estimated the release
rates that could best reproduce the Rin,
Vm
and
v (see Fig. 3).
The presence of voltage-dependent currents produced smallbut
detectable
changes in the optimal release conditions. For example, the
same Rin change,
Vm
and
v as the passive model with
fe = 1 Hz and fi = 5.5 Hz
was obtained with fe = 0.92 Hz and
fi = 5.0 Hz (8-9% lower) in a model containing
IKd and IM. Both models gave nearly identical
v values for the same value of
correlation. A similar constraining procedure also was performed using
a nonuniform leak distribution with high leak conductances in distal
dendrites (see METHODS), in addition to
IKd and IM, and nearly
identical results were obtained (not shown). We therefore conclude that leak and voltage-dependent K+ currents have a small
contribution to the Rin and
v of
active periods, which are mostly determined by synaptic activity.
Impact of synaptic activity on integrative properties
The experimental evidence for a ~80% decrease in
Rin due to synaptic bombardment betrays a
massive opening of ion channels. In the model, the total conductance
due to synaptic activity was 7-10 times larger than the leak
conductance. In conditions of high membrane resistance based on whole
cell recordings (Pongracz et al. 1991; Spruston
and Johnston 1992
), the conductance due to synaptic activity
was 20-30 times larger than the dendritic leak conductance.
The impact of this massive increase in conductance on dendritic
attenuation was investigated by comparing the effect of current injection in active periods and synaptic quiescence (Fig.
5). In the absence of synaptic activity
(Fig. 5B, smooth traces), somatic current injection (Fig.
5B, left) elicited large voltage responses in dendrites, and
reciprocally (Fig. 5B, right), showing a moderate
electrotonic attenuation. By contrast, during simulated active periods
(Fig. 5B, noisy traces), voltage responses to identical current injections were reduced markedly, betraying a greatly enhanced
electrotonic attenuation. In these conditions, the relative amplitude
of the deflection induced by the same amount of current with and
without synaptic activity, as well as the difference in time constant,
were in agreement with experimental observations (compare Fig.
5B, Soma, with Fig. 1, C and D). The
effect of synaptic bombardment on the time constant was also in
agreement with previous models (Bernander et al. 1991;
Holmes and Woody 1989
; Koch et al. 1996
).
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Dendritic attenuation was characterized further by computing somatodendritic profiles of Vm with steady current injection in the soma: in the absence of synaptic activity (Fig. 5C, Quiet), the decay of Vm after somatic current injection was characterized by space constants of 515-930 µm, depending on the dendritic branch considered, whereas the space constant was reduced by about fivefold (105-181 µm) during simulated active periods (Fig. 5C, Active).
To estimate the convergence of synaptic inputs necessary to evoke a
significant somatic depolarization during active periods, a constant
density of excitatory synapses was stimulated synchronously in
"proximal" and "distal" regions of dendrites (as indicated in Fig. 6A). In the absence of
synaptic activity, simulated EPSPs had large amplitudes (12.6 mV for
proximal and 6.0 mV for distal; Fig. 6B, Quiet). By
contrast, during simulated active periods, the same stimuli gave rise
to EPSPs that were barely distinguishable from spontaneous
Vm fluctuations (Fig. 6B, Active).
The average EPSP amplitude was 5.4 mV for proximal and 1.16 mV for
distal stimuli (Fig. 6B, Active, avg), showing that EPSPs
are attenuated by a factor of 2.3-5.2 in this case, with the maximal
attenuation occurring for distal EPSPs. Figure 6C shows the
effect of increasing the number of synchronously activated synapses. In
quiescent conditions, <50 synapses on basal dendrites were sufficient
to evoke a 10-mV depolarization at the soma (Quiet, proximal), and the
activation of ~100 distal synapses was needed to achieve a similar
depolarization (Quiet, distal). During simulated active periods, >100
basal dendritic synapses were necessary to reliably evoke a 10-mV
somatic depolarization (Active, proximal), whereas the synchronous
excitation of 415 distal synapses only evoked depolarization of a few
millivolts (Active, distal).
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To determine whether these results are dependent on the specific
morphology of the studied cell, four different cellular geometries were
compared, ranging from small layer II-III cells to large layer V
pyramidal cells (Fig. 7A). In
experiments, the absolute Rin values varied from
cell to cell. However, the relative Rin change
produced by TTX was similar in all cells recorded. Similarly, in the
model, the absolute Rin values depended on the
cellular geometry: using identical passive parameters, the
Rin values of the four neurons shown in Fig.
7A ranged from 23 to 94 M. However, high-frequency
release conditions had a similar impact on their membrane properties.
Using identical synaptic densities, synaptic conductances, and release
conditions as detailed above led to a decrease in
Rin of ~80% for all cells (Fig.
7B). Vm fluctuations also depended
critically on the degree of correlation between the release of
different synapses. Uncorrelated events produced too small
v (Fig. 7B, ×), whereas a correlation of 0.1 could reproduce both the Rin change and
v (Fig. 7B,
). The value of
v was correlated with cell size (not shown), and the
variability of
v values was relatively high compared
with that of Rin decreases. The effect of
synaptic activity on dendritic attenuation was also independent of the
cell geometry: the space constant was reduced by about fivefold in all
four cells (not shown). Moreover, for the two layer V neurons,
stimulating several hundreds of synapses at a distance of >800 µm
from the soma had undetectable effects during active periods (Fig.
7C). This result was also reproduced using low axial
resistivities (Fig. 7C, dashed lines).
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These results show that intense synaptic activity has a drastic effect
on the attenuation of distal synaptic inputs. However, voltage-dependent currents in dendrites may amplify EPSPs (Cook and Johnston 1997) or trigger dendritic spikes that propagate toward the soma (Stuart et al. 1997
). Therefore the
attenuation of EPSPs must be reexamined in models that include active
dendritic currents.
Firing properties during active periods
The response of the simulated neuron to depolarizing current
pulses was tested in the presence of voltage-dependent Na+
currents, in addition to IKd and
IM. In the absence of synaptic activity (Fig.
8A), the model displayed
pronounced spike frequency adaptation due to IM,
similar to "regular spiking" pyramidal cells in vitro
(Connors et al. 1982). However, spike frequency
adaptation was not apparent in the presence of correlated synaptic
activity (Fig. 8B), probably due to the very small
conductance of IM compared with synaptic
conductances. Nevertheless, the presence of IM
affected the firing behavior of the cell, as suppressing this current
enhanced the excitability of the cell (Fig. 8B, No
IM). This is consistent with the increase of
excitability demonstrated in neocortical slices (McCormick and
Prince 1986
) after suppression of IM by application of acetylcholine.
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In the presence of Na+ and K+
voltage-dependent currents, simulated active periods generated
"spontaneous" firing at an average rate that depended on the
action potential threshold, which was affected by Na+
current densities. Setting the threshold at about 55 mV in soma, based on our experiments, led to a sustained firing rate of ~10 Hz
(Fig. 9A), with all other
features consistent with the model described earlier. In particular,
the Rin reductions and values of
v produced by synaptic activity were affected minimally
by the presence of voltage-dependent currents (Table 1). However, this
was only valid for Rin calculated in the linear
region of the I-V relation (less than
60 mV; see Fig. 4).
Thus at Vms more negative than
60 mV, the
membrane parameters are essentially determined by background synaptic
currents with a minimal contribution from intrinsic voltage-dependent
currents.
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In these conditions, the firing rate of the cell was sensitive to
the release frequency: a threefold increase in release frequencies led
to a proportional increase in firing rate (from ~10 to ~30 Hz; Fig.
9B, - - -). Indeed, if all release frequencies were
increased by a given factor, the firing rate increased by about the
same factor (Fig. 9C, ). This shows that, within this
range of release frequencies, the average firing rate of the cell
reflects the average firing rate of its afferents. However, this
relationship was broken if the release frequency was changed only at
excitatory synapses: doubling the excitatory release frequency with no
change in inhibition tripled the firing rate (Fig. 9C,
).
Surprisingly, in Fig. 9B there was only a 12%
Rin difference between the 10 and 30 Hz
conditions, although the release frequency was threefold higher. This
is due to the saturation effect of the Rin
change as a function of release frequency (Fig. 3A1). This
property may explain the observation that visually evoked responses are
not paralleled by substantial Rin changes in
area 17 neurons (Berman et al. 1991).
Sharp events of lower amplitude than action potentials are also visible
in Fig. 9, A and B. These events are likely to be dendritic spikes that did not reach action potential threshold in the
soma/axon region, similar to the fast prepotentials described by
Spencer and Kandel (1961). Similar events were reported
in intracellular recordings of neocortical pyramidal cells in vivo (Deschênes 1981
).
Integrative properties during active periods
The dendritic attenuation of EPSPs was examined in the presence of
voltage-dependent Na+ and K+ dendritic
conductances. Using the same stimulation paradigm as in Fig.
6B, proximal or distal synapses reliably fired the model cell in quiescent conditions (Fig.
10A, Quiet). The stimulation of distal synapses elicited dendritic action potentials that propagated toward the soma in agreement with a previous model (Paré
et al. 1998a). During active periods (Fig. 10A,
Active), proximal or distal stimuli did not trigger spikes reliably
although the clustering of action potentials near the time of the
stimulation (*) shows that EPSPs affected the firing probability. The
evoked response, averaged from 1,000 sweeps under intense synaptic
activity (Fig. 10A, Active, avg), showed similar amplitude
for proximal or distal inputs. Average responses did not reveal any
spiky waveform, indicating that action potentials were not precisely
timed with the EPSP in both cases.
|
It is interesting to note that, in Fig. 10A, distal stimuli evoked action potential clustering, whereas proximal stimuli did not, despite the fact that a larger number of proximal synapses were activated. Distal stimuli evoked dendritic action potentials, some of which reached the soma and led to the observed cluster. Increasing the number of simultaneously activated excitatory synapses enhanced spike clustering for both proximal and distal stimuli (Fig. 10B, *). This also was evidenced by the spiky components in the average EPSP (Fig. 10B, Active, avg). Comparison of responses evoked by different numbers of activated synapses (Fig. 10C) shows that the convergence of several hundred excitatory synapses was necessary to evoke spikes reliably during intense synaptic activity. It is remarkable that with active dendrites, similar conditions of convergence were required for proximal or distal inputs, in sharp contrast to the case with passive dendrites, in which there was a marked difference between proximal and distal inputs (Fig. 6C).
The magnitude of the currents active at rest may influence these
results. In particular, the significant rectification present at levels
more depolarized than 60 mV (Fig. 4A) may affect the attenuation of depolarizing events. To investigate this aspect, we
estimated the conditions of synaptic convergence using different distributions of leak conductances. Although suppressing the
IM conductance enhanced the excitability of the
cell (see preceding text), it did not affect the convergence
requirements in conditions of intense synaptic activity (compare Fig.
11, A and B).
Using a different set of passive parameters based on whole cell
recordings, with a low axial resistance and a high membrane resistivity
(Pongracz et al. 1991
; Spruston and Johnston
1992
), also gave similar results (Fig. 11C). Using a
nonuniform distribution of leak conductance with strong leak in distal
dendrites (Stuart and Spruston 1998
) (see
METHODS) also led to similar convergence requirements (Fig. 11D). In addition, we tested a 10 nS electrode shunt in soma
with a larger membrane resistivity in dendrites and obtained nearly identical results (not shown).
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These results show that under conditions of intense synaptic activity, synaptic currents account for most of the cell's input conductance, whereas intrinsic leak and voltage-dependent conductances have a comparatively small contribution. It also shows that hundreds of synaptic inputs are required to fire the neuron reliably, and that this requirement seems independent of the location of the synaptic inputs.
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DISCUSSION |
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The present study provides the first quantitative characterization of the membrane properties of neocortical pyramidal cells in conditions of network activity similar to those observed during the waking state. Intracellular recordings and biophysical models indicated that synaptic activity produces a massive conductance change that is about five times larger than the conductances already present in the cell in the absence of synaptic activity. The model shows that this conductance increase has a major impact on the electrotonic attenuation of EPSPs along the dendritic tree. As this finding might have important implications for understanding how cortical cells process information, we first consider possible pitfalls of our experimental and modeling procedures and then discuss the significance of these findings.
Possible sources of error
A first possible source of error is that the ~80% decrease in Rin produced by synaptic activity was observed under anesthesia and a different value might characterize the waking brain. However, the fact that cells fire at similar rates during active periods of ketamine-xylazine anesthesia and during wakefulness indicates that both must be characterized by a similar pattern of synaptic bombardment. This view also is supported by the similar spectral composition of the EEG in these two states.
Two factors might have led us to underestimate the decrease in
Rin produced by spontaneous synaptic activity.
First, NMDA receptors are antagonized by ketamine, and these channels
must reduce further the Rin of cortical cells
during the waking state. Second, TTX microperfusion may not have been
completely effective in blocking all synapses (although evoked EPSPs
were suppressed) (Paré et al. 1997, 1998b
), therefore
contributing to an additional underestimation of the real
Rin change. Ideally, the same analysis should be
performed in awake animals, which raises a number of technical difficulties.
Another possible source of error is that the contribution of neuromodulatory currents to the Rin change was not investigated. Most likely, TTX application not only suppresses fast (ionotropic) synaptic activity but also neuromodulatory (metabotropic) influences. Future studies should address this aspect using microperfusion of ionotropic synaptic blockers (NBQX, 2-amino-5-phosphonopentanoic acid, and bicuculline) to estimate the respective contribution of ionotropic and metabotropic activity to the Rin change.
A source of error often raised for sharp-electrode recordings is
that the impalement damages the cell. Experimental and modeling evidence suggests that cell damage had a negligible effect on the
relative Rin changes measured experimentally.
First, blocking spontaneous synaptic activity in vivo using TTX leads
to Rin values that are similar to those seen in
vitro using the same type of electrodes (Paré et al.
1998b). Second, we report here low Rin values during intense synaptic activity and much larger
Rin values after TTX application. These data
clearly show that the low Rin of neocortical
cells in vivo is not due to cell damage but is attributable to action
potential-dependent factors. The marked difference in
Vm before and after TTX also shows that the
depolarized Vm of neocortical cells in vivo is
also a consequence of synaptic activity.
The model supports these conclusions by showing that synaptic activity
can account for the changes in Rin,
Vm, and v. Given that the change
in Rin attributable to synaptic activity was
estimated experimentally in the same cells before and after TTX, it is
reasonable to assume that the same electrode shunt was present in both
conditions. This shunt was included implicitly in the model when
adjusting its passive properties (Fig. 2A). It also was
included explicitly in the model, in combination with higher membrane
resistivity, and similar results were obtained. Given that dendritic
attenuation is determined essentially by dendritically located
conductances, it is not surprising that a simulated electrode shunt in
the soma had a minimal effect here.
Another possible source of error is the contribution of
voltage-dependent currents that are activated indirectly by synaptic events. In pyramidal neurons, the most numerous ion channels are synaptic: in hippocampal pyramidal cell's dendrites, Na+
and K+ currents total ~100-200 pS/µm2
(Magee and Johnston 1995; Magee et al.
1998
) while AMPA receptors amount to ~700
pS/µm2 (assuming 0.6 spines per µm2, 1 release site per spine and a quantal conductance of 1,200 pS). The
present analysis was based on relatively hyperpolarized Vm (less than
55 mV), as cells were around
80 mV under TTX and in the range of
70 to
55 mV during active
periods, with rare excursions above
55 mV (see Fig. 1F).
In this range of membrane potential, only a small fraction of
voltage-dependent channels should be open, whereas a large fraction of
ionotropic receptor channels seem to be activated in the conditions
studied here. The current-voltage relation was indeed approximately
linear in the Vm range below
60 mV (Fig.
4A), suggesting that the Rin change estimated in this region of Vm is essentially
due to synaptic currents. In addition, simulations indicate that
voltage-dependent K+ currents contribute <10% of the
measured Rin change, even though the model was
fit to the cell showing the strongest rectification in our database
(Fig. 4). Nevertheless, a significant rectification is present at
levels more depolarized than
55 mV (Fig. 4A) and should
affect the attenuation of depolarizing events. Together, these data
indicate that, for Vms lower than
60 mV, the
conductance due to synaptic activity accounts for most of the
Rin change observed. Further models and
experiments are required to investigate if these conclusions are also
valid for neurons possessing a prominent Ih
(Stuart and Spruston 1998
) or prominent calcium and
calcium-dependent currents, which may play a role in shaping large
depolarizing events.
The lack of constraints is another possible source of error for models.
Here, the model was constrained by experimental observations obtained
in three conditions of synaptic activity recorded in the same
population of cells: absence of synaptic activity (TTX + synaptic
blockers), miniature synaptic events (TTX) and intense synaptic
activity. For each of these states, the Rin,
Vm, and v were calculated, thus
providing severe constraints for the model. Indeed, a relatively narrow
range of synaptic density, conductance, and release frequency could
account for these measurements. However, some parameters were not well
constrained. First, there are few or no data available on a possible
nonuniform distribution of synaptic densities, reversal potential, rate
of release, correlation of release, as well as the nature,
distribution, and kinetics of voltage-dependent currents. These
different possibilities should be addressed by future studies as data
become available. Second, the axial resistance
Ri could not be constrained. This parameter is
usually estimated in the range of 200-300
cm (Rall et al. 1992
), but a recent study suggested lower values (Stuart
and Spruston 1998
). We have tried simulations using
Ri of 250 or 100
cm and nearly identical
results were obtained (Figs. 7C and 11C).
A final source of error is that the models were not simulating the
cellular geometries of the recorded neurons. The fact that similar
results were obtained using different cellular geometries (Fig. 7)
indicates that the exact dendritic morphology was not critical here.
However, the dendritic morphology influenced the value of
v for equivalent changes in Rin
(Fig. 7B). Future studies should use cellular
reconstructions of the recorded cells, allowing more precise
simulations of passive properties and of the impact of synaptic currents.
Release conditions at cortical synapses
In the suprasylvian cortex of awake cats, neurons display
"idle" firing rates of ~10 Hz but the rate increases to 20-60
Hz when cells respond to sensory stimuli (Kalaska 1996).
In the model, a ~10-Hz firing rate was obtained with release
frequencies of 0.5-3 Hz for excitatory synapses and 4-8 Hz for
inhibitory synapses. These values are significantly below the reported
average firing rate of cortical neurons in this state, suggesting that
the release probability of excitatory synapses is significantly less
than unity (0.025-0.6). Indeed, in vitro studies indicate a
significant decrease in release probability at steady state
(Thomson et al. 1993
). It should be noted, however, that
the estimation of release frequency is dependent of the synaptic
density: a twice lower density would require a doubled release
frequency to reproduce equivalent results. The present densities were
matching the density of spines in rat neocortical dendrites (0.6 spine
per µm2 in Larkman 1991
). It is possible
that the spine density is lower or higher in cats in which case our
estimates of release probability should be revised.
Nevertheless, these release conditions could reproduce the depolarized Vm and the reduced Rin evidenced by in vivo experiments. This seemed independent of the exact details of dendritic morphology and cell size (Fig. 7), suggesting that different cells in the neocortex experience similar release conditions during active periods. The model therefore predicts that these changes are generic and are typical of the state of cortical neurons during intense network activity.
In addition to high-frequency release conditions, it was necessary to
include a significant correlation among release events to account for
experimental measurements. No correlation was necessary to reproduce
the characteristics of miniature synaptic potentials, as expected if
these events arise from spontaneous release occurring independently at
each terminal. On the other hand, an average correlation of ~0.1 was
necessary to account for the Vm fluctuations observed during active periods. This is consistent with the average correlation of 0.12 measured between pairs of neurons in the cerebral cortex of behaving monkeys (Zohary et al. 1994). The
model suggests that this factor, together with the high-frequency
release conditions, is sufficient to account for the membrane
properties of neocortical cells during active periods. Our results are
compatible with the view that during active periods, neocortical cells
display weakly correlated discharges (c ~ 0.1)
(Zohary et al. 1994
) occurring at high firing rates (~5-20 Hz)
(Evarts 1964
; Hubel 1959
; Steriade 1978
).
Implication for dendritic integration
According to cable theory (Rall 1995), dendritic
attenuation depends on the membrane conductance. Because our
experiments provide evidence for a massive increase of the total
membrane conductance during active periods, they predict a major effect on dendritic attenuation, but the exact magnitude of this effect is
unknown. The model, constrained by Rin,
Vm
, and
v before and after
TTX, revealed drastic effects on dendritic attenuation and that a large
number of convergent dendritic synaptic inputs are required to affect
the voltage at the soma. By simulating synchronous excitatory synaptic
events, it was estimated that the synchronous activation of 80-150
synapses on basal dendrites was necessary for the cell to reach action
potential threshold (
55 mV), whereas
415 synapses simulated in
distal branches evoked insufficient somatic depolarization (Fig.
6C) or no depolarization at all (Fig. 7C). These
simulations show that, because of passive dendritic attenuation, it is
difficult for EPSPs arising at distal sites to have a significant
effect on the soma if passive properties had to be considered solely.
A very different picture was seen in the presence of dendritic
Na+ and K+ currents. During intense background
synaptic activity, the convergence of hundreds of coincident synaptic
inputs was required to evoke spiking reliably (Fig. 10,
A-C), similar to the convergence requirements determined with passive dendrites (Fig. 6). However, by contrast with
the tremendous attenuation of distal inputs in a passive neuron (Fig.
7C), with active dendrites, the number of synapses required
to evoke spiking reliably was approximately the same for proximal and
distal stimulation (Fig. 10C). This shows that integrative
properties cannot be simply deduced from passive dendritic attenuation.
Low-amplitude EPSPs experienced tremendous attenuation because they
were subthreshold for the activation of voltage-dependent currents.
However, the synchronized stimulation of hundreds of excitatory
synapses evoked dendritic action potentials that propagated toward the
soma and had an equivalent effect on the firing probability irrespective of their distance from the soma. Active dendrites therefore diminish the variability of the response due to the location
of inputs, in agreement with a previous proposition (Cook and
Johnston 1997).
The fact that a large number of synchronous synaptic events are
required to evoke spiking reliably could suggest that pyramidal cells
act like coincidence detectors, as proposed previously
(Bernander et al. 1991). However, Fig. 9B
also shows that the cell reliably responds to the average firing rate
of its afferents. Therefore our experiments and models cannot
distinguish between these two possibilities. Rather, our results
suggest that, in conditions of intense synaptic activity, pyramidal
cells respond reliably only when a very large number of synapses change
their release frequency or timing, therefore detecting changes in large
populations of neurons.
Predictions
The first prediction of this model is that neurons intracellularly
recorded in the suprasylvian cortex during the awake state should have
markedly reduced Rin (by a 5-fold factor, see
preceding text). This could be tested by performing intracellular
recordings in awake animals together with local application of TTX.
Although these experiments presently represent a real technical
challenge, it is likely that improvements in intracellular recording
techniques will make it feasible in the near future.
The second prediction is that a large number of synapses must be activated to influence significantly the probability of action potential generation in neocortical pyramidal neurons in active states. This could be tested using intracellular recordings in ketamine-xylazine anesthesia in a first step and subsequently in awake animals if possible. The convergence criteria could be estimated by using local iontophoresis of increasing amounts of glutamate. The effect on action potentials could be evaluated using similar averaging procedures as shown here. Performing the same experiment under TTX may be used to provide a control of the amplitude/conductance of the evoked EPSPs in the absence of synaptic activity.
The third prediction of the model is that during active periods, similar convergence criteria should be observed for the activation of proximal versus distal synapses. This could be tested using similar paradigms as above by comparing the effect of local glutamate application in deep versus superficial layers of the cortex. The threshold amount of glutamate should be independent of the depth of application.
In conclusion, experiments and models indicate that intense network activity similar to the waking state consists in weakly correlated high-frequency release conditions responsible for a major increase of conductance in pyramidal neurons. The model further indicates that hundreds of highly correlated inputs are required to discharge the cell reliably (Fig. 10C). We suggest that intense network activity maintains pyramidal cells in an idle state during which they are ready to respond rapidly to brief changes of correlation within hundreds of their synaptic inputs. A change of correlation, or synchrony, seems to be the most efficient manner to carry information in these conditions, which supports a possible role for synchronized oscillations in cortical information processing.
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ACKNOWLEDGMENTS |
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This research was supported by the Medical Research Council of Canada and the Natural Science and Engineering Research Council of Canada.
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FOOTNOTES |
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Address for reprint requests: A. Destexhe, Dépt. de Physiologie, Faculté de Médecine, Université Laval, Québec G1K 7P4, Canada.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 10 August 1998; accepted in final form 20 November 1998.
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REFERENCES |
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