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The Journal of Neuroscience, October 1, 2002, 22(19):8691-8704
Model of Thalamocortical Slow-Wave Sleep Oscillations and
Transitions to Activated States
Maxim
Bazhenov1,
Igor
Timofeev2,
Mircea
Steriade2, and
Terrence J.
Sejnowski1, 3
1 The Salk Institute, Howard Hughes Medical Institute,
Computational Neurobiology Laboratory, La Jolla, California 92037, 2 Laboratory of Neurophysiology, School of Medicine, Laval
University, Quebec, Canada G1K 7P4, and 3 Department of
Biology, University of California San Diego, La Jolla, California 92093
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ABSTRACT |
During natural slow-wave sleep (SWS) in nonanesthetized cats,
silent (down) states alternate with active (up) states; the down
states are absent during rapid-eye-movement sleep and waking. Oscillations (<1 Hz) in SWS and transformation to an activated awake
state were investigated with intracellular recordings in vivo and with computational models of the corticothalamic
system. Occasional summation of the miniature EPSPs during the
hyperpolarized (silent) phase of SWS oscillation activated the
persistent sodium current and depolarized the membrane of cortical
pyramidal (PY) cells sufficiently for spike generation. In the model,
this triggered the active phase, which was maintained by lateral PY-PY
excitation and persistent sodium current. Progressive depression of the
excitatory interconnections and activation of
Ca2+-dependent K+ current led to
termination of the 20-25 Hz activity after 500-1000 msec. Including
thalamocortical (TC) and thalamic reticular neurons in the model
increased the duration of the active epochs up to 1-1.5 sec and
introduced waning spindle sequences. An increase in acetylcholine
activity, which is associated with activated states, was modeled by the
reduction in the K+ leak current in PY and TC cells
and by a decrease in intracortical PY-PY synaptic conductances. These
changes eliminated the hyperpolarizing phases of network activity and
transformed cortical neurons to tonic firing at 15-20 Hz. During the
transition from SWS to the activated state, the input resistance of
cortical neurons gradually increased and, in a fully activated state,
reached the same or even higher values as during silent phases of SWS
oscillations. The model describes many essential features of SWS and
activated states in the thalamocortical system as well as the
transition between them.
Key words:
slow-wave sleep; waking; thalamus; cortex; sensory input; input resistance; network model
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INTRODUCTION |
When the brain falls asleep, the
spatiotemporal patterns in the waking corticothalamic system (Steriade
et al., 2001 ; Timofeev et al., 2001b) are replaced by low-frequency
synchronous rhythms that are relatively insensitive to incoming signals
(Steriade et al., 1993b). Intracellular and local field potential
recordings in vivo and in vitro have revealed
that spindles (7-14 Hz) are a result of interactions between reticular
(RE) and thalamocortical (TC) neurons in the thalamus (Steriade et al.,
1985, 1993b; von Krosigk et al., 1993). Spindle sequences are initiated
in the thalamic RE nucleus (Steriade et al., 1987; Bazhenov et al.,
1999, 2000) and are terminated through a combination of intrinsic (Bal and McCormick, 1996; Budde et al., 1997; Lüthi et al., 1998) and
network (Timofeev et al., 2001a) mechanisms. Thalamic delta (1-4 Hz)
oscillations can be generated in a single TC cell by the interplay of
intrinsic currents (McCormick and Pape, 1990; Soltesz et al., 1991;
Lytton et al., 1996). Delta and spindle oscillations have been studied
intensively with computational models (Destexhe et al., 1994a, 1996;
Golomb et al., 1994, 1996; Contreras et al., 1996b; Lytton et al.,
1996; Bazhenov et al., 2000).
Less is known about mechanisms underlying the slow (<1 Hz) cortical
oscillation that occurs during SWS in animals and humans (Steriade et
al., 1993b,c; Achermann and Borbely, 1997; Amzica and Steriade, 1997).
The depth-positive phase of slow oscillation observed in the depth
electroencephalogram (EEG) is associated with significant
hyperpolarization of neocortical neurons, whereas the depth-negative
component of the slow oscillation in the depth EEG is related to
relative depolarization and firing of cortical neurons (Contreras and
Steriade, 1995). The survival of slow oscillations after extensive
thalamic lesions (Steriade et al., 1993d) and the absence of slow
oscillations in the thalamus of decorticated cats (Timofeev and
Steriade, 1996) point to an intracortical origin for this rhythm.
Intracellular studies on anesthetized and nonanesthetized cats have
shown that the hyperpolarizing phase of the slow oscillation is
associated with disfacilitation, a temporal absence of synaptic activity (Contreras et al., 1996a; Timofeev et al., 1996, 2001b; Steriade et al., 2001). The long-lasting hyperpolarizations of cortical
neurons are absent when brain cholinergic structures are set into
action (Metherate and Ashe, 1993; Steriade et al., 1993a) or during REM
sleep and waking (Steriade et al., 2001; Timofeev et al., 2001b).
Recent intracellular and local field potential recordings from isolated
cortical slabs in vivo revealed patterns of spontaneous activity lasting 0.5-3 sec and appearing every 20-600 sec (Timofeev et al., 2000a). Intracellular recordings of membrane potentials during
the silent phase of oscillations revealed the presence of small
amplitude depolarizing potentials, but action potentials were never
observed between bursts. The frequency of these miniature events was
reduced immediately after the last burst and increased a few seconds
later. It has been suggested that the random summation of the miniature
EPSPs (minis) during the silent state of the network can
depolarize the membrane potential in any single pyramidal (PY) cell
sufficiently to activate a persistent sodium current, which further
depolarizes the neuron leading to the Na+
spike (Timofeev et al., 2000a). The firing of one or a few cortical neurons could initiate activity in the whole cortical network. Experiments with varying the slab size and scaling analysis of a
cortical model indicated that in a cortical network significantly larger than a small slab, the probability of active state initiation increases and can drive oscillations in the frequency range of SWS
activity (Timofeev et al., 2000a). In the present paper we provide
in vivo data and a model of a corticothalamic system that closely matches activities found during SWS and activated states. Our
modeling study suggests that cortically generated slow oscillations can
interfere with signal processing in thalamocortical systems.
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MATERIALS AND METHODS |
In vivo recordings
We performed two groups of experiments. In the first, we used
conventional intracellular recordings from neocortical,
thalamocortical, and reticular thalamic neurons in cats anesthetized
with either ketamine-xylazine (10-15 mg/kg and 2-3 mg/kg, i.m.) or
somnotol (35 mg/kg, i.p). The details of these experiments have been
described previously (Timofeev et al., 1996; Timofeev and Steriade,
1997; Steriade et al., 1998). The second group of experiments was
conducted on nonanesthetized, nonparalyzed cats in different states of
vigilance. Details on experimental procedures can be found in Steriade
et al. (2001) and Timofeev et al. (2001b). At the end of experiments, cats were injected intravenously with a lethal dose (50 mg/kg) of sodium thiopental.
Computational model
Intrinsic currents: thalamus. We examined
single-compartment models of TC and RE cells that included voltage- and
calcium-dependent currents described by Hodgkin-Huxley
kinetics:
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(1)
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where Cm = 1 µF/cm2 is the membrane capacitance,
gL is the leakage conductance
(gL = 0.01 mS/cm2 for TC cell and
gL = 0.05 mS/cm2 for RE cell), and
EL is the reversal potential
(EL =  70 mV for TC cell and
EL = 77 mV for RE cell).
Iint is a sum of active
intrinsic currents, and
Isyn is a sum of synaptic
currents. The area of an RE cell was
SRE = 1.43 · 10 4 cm2,
and the area of a TC cell was STC = 2.9 · 104
cm2.
For both RE and TC cells we considered a fast sodium current,
INa, a fast potassium current,
IK (Traub and Miles, 1991), a low-threshold Ca2+ current,
IT [see Huguenard and Prince (1992)
for RE cells and Huguenard and McCormick (1992) for TC cells]), and a
potassium leak current, IKL = gKL(V EKL),
EKL = 95mV. A
hyperpolarization-activated cation current,
Ih(McCormick and Pape, 1990; Destexhe
et al., 1996), was also included in TC cells. The expressions for
voltage- and Ca2+-dependent transition
rates for all currents are given in Bazhenov et al. (1998). The maximal
conductances were gK = 10 mS/cm2,
gNa = 90 mS/cm2,
gT = 2.2 mS/cm2,
gh = 0.017 mS/cm2,
gKL = 00.03
mS/cm2 for TC cells, and
gK = 10 mS/cm2,
gNa = 100 mS/cm2,
gT = 2.3 mS/cm2, and
gKL = 0.005 mS/cm2 for RE cells.
Intrinsic currents: cortex. The cortical PY
cells and interneurons (INs) were two-compartment models with channels
that were modeled by Hodgkin-Huxley kinetics (Mainen and Sejnowski,
1996):
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(2)
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where Cm,
gL are the membrane capacitance and
the leakage conductance of the dendritic compartment,
EL is the reversal potential, VD and
VS are the membrane potentials of
dendritic and axosomatic compartments,
IDint and
ISint are the
sums of active intrinsic currents in axosomatic and dendritic compartments, Isyn is a sum of
synaptic currents, and g is the conductance between axosomatic and dendritic compartments. In this model, the axosomatic compartment has no capacitance to speed up simulations. The soma and
axon initial segment are characterized by high-conductance densities.
When capacitance was included in this compartment, smaller integration
steps were needed to ensure stability of calculation, but model firing
patterns were unaffected (Mainen and Sejnowski, 1996).
The model included the fast Na+ channels,
INa, of a high density in axosomatic
compartment and of a low density in the dendritic compartment. A fast
delayed rectifier potassium K+ current,
IK, was present in the axosomatic
compartment. Persistent sodium current,
INa(p), was included in the axosomatic
and dendritic compartments (Alzheimer et al., 1993; Kay et al., 1998).
A slow voltage-dependent noninactivating
K+ current,
IKm, a slow
Ca2+-dependent
K+ current,
IKCa, a high-threshold
Ca2+ current,
IHVA, and a potassium leak current,
IKL = gKL(V EKL), were included in the dendritic
compartment. The expressions for the voltage- and
Ca2+-dependent transition rates for all
currents are given in Timofeev et al. (2000a). The maximal conductances
and passive properties were Ssoma = 1.0 · 106
cm2, gNa = 3000 mS/cm2,
gK = 200 mS/cm2,
gNa(p) = 0.07 mS/cm2 for axosomatic compartment, and
Cm = 0.75 µF/cm2,
gL = 0.033 mS/cm2,
gKL = 00.0025
mS/cm2,
Sdend = Ssomar,
gHVA = 0.01 mS/cm2,
gNa = 1.5 mS/cm2,
gKCa = 0.3 mS/cm2,
gKm = 0.01 mS/cm2, and
gNa(p) = 0.07 mS/cm2 for dendritic compartment;
EL = 68 mV and
EKL = 95 mV. No
INa(p) was modeled for IN cells. The
resistance between compartments was r = 10 M .
The firing properties of the model in Equation 2 depend on the coupling
conductance between compartments (g = 1/R) and the ratio of dendritic area to axosomatic area
r (Mainen and Sejnowski, 1996). We used a model of a
regular-spiking neuron for PY cells (r = 165) and a
model of a fast spiking neuron for IN cells (r = 50).
Synaptic currents
All synaptic currents were calculated according to:
,](/content/vol22/issue19/fulltext/8691/img004.gif)
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(3)
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where gsyn is the maximal
conductivity, [O](t) is the fraction of open
channels, Esyn is the reversal
potential.
EsynAMPA = 0 mV for AMPA and NMDA receptors,
EsynGABAA = 70 mV for GABAA receptors in RE and PY cells,
EsynGABAA = 80 mV for GABAA receptors in TC cells (Ulrich
and Huguenard, 1997), and
EsynGABAB = 95 mV for GABAB receptors. A simple phenomenological model was used to describe short-term depression of
intracortical excitatory connections (Abbott et al., 1997; Tsodyks and
Markram, 1997; Galarreta and Hestrin, 1998; Timofeev et al., 2000a).
According to this, a maximal synaptic conductance was multiplied to
depression variable, D  1, representing the amount of
available "synaptic resources." D = 1 (1 Di(1 U))exp((t ti)/ ), where U = 0.07 is the fraction of resources used per action potential, = 700 msec the time constant of recovery of the synaptic resources,
Di is the value of D
immediately before the ith event, and
(t ti) is the time
after ith event.
GABAA, NMDA, and AMPA synaptic currents were
modeled by first-order activation schemes (Destexhe et al., 1994b).
Dependence on postsynaptic voltage for NMDA receptors was 1/(1 + exp((Vpost Vth)/ )), where
Vth = 25 mV, = 12.5 mV
(Traub et al., 1991; Destexhe et al., 1994b; Golomb and Amitai, 1997).
GABAB receptors were modeled by a higher-order
reaction scheme that took into account activation of
K+ channels by G-proteins (Dutar and
Nicoll, 1988; Destexhe et al., 1994b; Destexhe et al., 1996). The
equations for all synaptic currents are given in Bazhenov et al. (1998)
and Timofeev et al. (2000a). The maximal conductances (for each
synapse) were
gAMPA(PYPY) = 0.08-0.15 µS,
gNMDA(PYPY) = 0.01 µS,
gAMPA(PYTC) = 0.08-0.025 µS,
gAMPA(PYRE) = 0.05 µS,
gAMPA(TCPY) = 0.1 µS,
gAMPA(PYIN) = 0.05 µS,
gNMDA(PYIN) = 0.008 µS,
gGABAA(INPY) = 0.05 µS,
gAMPA(TCIN) = 0.1 µS,
gGABAA(RERE) = 0.2 µS,
gGABAA(RETC) = 0.2 µS,
gGABAB(RETC) = 0.04 µS, and
gAMPA(TCRE) = 0.4 µS.
Spontaneous miniature EPSPs and IPSPs followed the same equations
as the regular PSPs, and their arrival times were modeled by Poisson
processes (Stevens, 1993), with time-dependent mean rate
µ1(t) = (2/(1 + exp((t t0)/400)) 1)/100 or
µ2(t) = log((t t0 + 50)/50)/400 (see Fig.
4B), where t0 is a
time instant of the last presynaptic spike (Timofeev et al., 2000a).
The mini amplitude was ~0.75 mV.
Network geometry and stimulation
The cortical model consisted of a one-dimensional two-layer
array of N PY and M = N/4 IN
cells. The thalamocortical model consisted of a one-dimensional
four-layer array of N PY, M = N/4 IN, L = N/2 RE and L = N/2 TC cells (Fig. 1).
N was varied between 20 and 200. In most of
simulations the connection fan-out was ±5 cells for AMPA- and
NMDA-mediated PY-PY synapses; ±1 cell for AMPA- and NMDA-mediated
PY-IN synapses; ±5 cells for GABAA-mediated IN-PY synapses; ±10 cells for AMPA-mediated TC-PY synapses; ±2 cells for AMPA-mediated TC-IN synapses; ±5 cells for AMPA-mediated PY-TC and PY-RE synapses; and ±5 cells for AMPA-,
GABAA-, and GABAB-mediated
synapses between RE and TC cells. Other radii of synaptic
interconnections and N/M/L ratios were
tested to ensure robustness of the results. We also tested the network
including GABAergic synaptic connections between INs. IN-IN coupling
did not have any significant effect on the spatiotemporal patterns of
network activity, and this type of connection was excluded from most of
simulations. Some of the intrinsic parameters of the neurons in the
network were initialized with random variability (Gaussian distribution
with = 5-10%) to ensure the robustness of the results
(Bazhenov et al., 1998).
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Figure 1.
Network geometry. Network model included four
layers of neurons with N PY, M IN, L RE, and L
TC cells. In most simulations we used N = 100, M = 25, and L = 50.
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In simulations with external input, 25% of the TC cells were
stimulated by Poisson-distributed spike trains that were homogeneous across TC cells and the firing rates of which were calculated as
r =  + (0.9 )sin(2 t),
where the average rate was = 25 Hz and = 0.4, 1, and
2.5 Hz.
Computational methods
All simulations described in this paper were performed using the
fourth-order Runge-Kutta [RK(4)] method and in some cases the
embedded Runge-Kutta [RK6(5)] method (Enright et al., 1995) with a
time step of 0.02 msec. Source C++ code was compiled on a Dell
Workstation 420 (1 GHz) using a GCC compiler. A network of 225 cells
took ~20 min of computer time to simulate 1 sec of real time.
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RESULTS |
Intracellular activities of neocortical neurons during three major
states of vigilance
We recorded intracellular activities from >700 cortical neurons
during SWS, REM sleep, and waking in chronically implanted cats. The
major states of vigilance were routinely characterized by recordings of
EEG, electromyogram, and electro-oculogram (Steriade and McCarley,
1990). We distinguished SWS by low-frequency, high-amplitude slow waves
in the EEG, the presence of muscle tone, and the absence of eye
movements. REM sleep was distinguished by activated EEG pattern, REMs,
and the absence of muscle tone. The waking state was identified by
activated EEG, muscle tone accompanied by episodic contractions, and
sporadic eye movements. Intracellular recordings during natural
slow-wave sleep revealed that the distribution of the membrane
potential of neocortical neurons was bimodal (Fig. 2). The depolarizing state of neurons
during SWS corresponded to EEG depth-negativity and periods that
immediately follow the EEG depth-negative wave. Most of the neurons
fired action potentials during the depolarizing state. The
hyperpolarizing state of neurons during SWS corresponded to EEG
depth-positive waves. During REM sleep and the waking state, neurons
displayed a unimodal distribution of the membrane potential centered on
62 mV. In association and sensory cortical areas, regular spiking
neurons stopped firing during ocular saccades in REM sleep (Fig. 2)
because of increased firing of INs (Timofeev et al., 2001b). The waking
state was characterized by tonic firing of neurons and a unimodal
distribution of the membrane potential, similar to that in REM
sleep.
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Figure 2.
Intracellular activity of neocortical neuron
during three major states of vigilance in a chronically implanted,
nonanesthetized cat. High-amplitude and low-frequency field potentials,
intracellular cyclic hyperpolarizing potentials, and stable muscle tone
are distinctive features of SWS. Low-amplitude and high-frequency field
potential oscillations, tonic neuronal firing with small fluctuations
in the membrane potential, rapid eye movements, and muscle atonia are
cardinal features of REM sleep. There is a slight hyperpolarization
during REM-related ocular saccades. Low-amplitude and high-frequency
field potential oscillations, tonic firing with smaller fluctuations in
the membrane potential, and muscle tone with periodic contractions are
characteristics of the waking state. The parts indicated by
arrows are expanded below. At bottom are
histograms of membrane potential distribution during three states of
vigilance. Histograms were constructed by sampling of neuronal activity
at 10 kHz and counting the number of samples with bins of 0.5 mV.
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Intracellular activities of cortical and thalamocortical neurons
during slow sleep oscillation in anesthetized cats
Intracellular membrane potentials of neocortical and thalamic
neurons were studied in cats anesthetized with ketamine-xylazine by
simultaneous EEG and dual intracellular recordings. Injecting ketamine
and xylazine to mimic this type of anesthesia induced more stereotyped
activity compared with electrophysiological patterns that were found in
naturally sleeping cats (Grenier et al., 2001, their Fig. 13). We
recorded activities of cortical neurons from area 4 and of TC neurons
from the ventrolateral nucleus or the rostrolateral sector of the RE
nucleus. As in previous studies, cortical, thalamocortical, and
reticular thalamic neurons were hyperpolarized during depth-positive
wave of EEG and displayed waning spindles during depth-negative EEG
wave (Contreras and Steriade, 1995; Timofeev and Steriade, 1996). We
emphasize here that although waning spindles were clearly distinguished
in the majority of thalamic neurons during ketamine-xylazine
anesthesia, clear-cut spindles were not as obvious in many neocortical
neurons. Figure 3 provides an example of
dual intracellular recordings from a cortical and a TC neuron during an
EEG depth-negative wave, in which the TC neuron revealed
spindle-related IPSPs sometimes associated with rebound spike bursts,
whereas the firing and subthreshold fluctuations of the membrane
potential of the cortical neuron did not show modulation at spindle
frequency. Intracellular recordings from cortical neurons in naturally
sleeping cats revealed that the vast majority of neurons did not show
intracellular signs of spindles (Timofeev et al., 2000b, 2001b;
Steriade et al., 2001). Indeed, the intrinsic properties of neocortical
neurons in a sleeping (anesthetized) state modify input signals that
might result in desynchronization of the corticothalamic network
(Timofeev et al., 2001a).
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Figure 3.
Sleep spindles in cortical and thalamocortical
neurons during the slow oscillation under ketamine-xylazine
anesthesia. Three traces show depth-EEG from area 4, intracellular
activity from an area 4 cortical neuron, and intracellular activity of
a thalamocortical neuron from the ventrolateral nucleus of the
thalamus. The part indicated by the horizontal bar is
expanded at the bottom. Note that the thalamocortical
neuron does not fire during all cycles of the slow oscillation, and the
cortical neuron does not follow all spike bursts of the thalamocortical
neuron.
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On the basis of these experimental data, we developed a computational
model of the thalamocortical system that closely matched the activities
of cortical and thalamic neurons during slow-wave sleep and its
transition to activated states that correspond to wakefulness or REM sleep.
Spontaneous activity in the isolated cortical network
Poisson processes with time-dependent mean rate were used to model
the arrival times for spontaneous miniature EPSPs at AMPA-mediated synapses between cortical cells (see Materials and Methods) (Timofeev et al., 2000a). Starting from the last Na+
spike during a preceding active period, the rate at each synapse increased rapidly during first few seconds and then grew more slowly as
observed experimentally (Timofeev et al., 2000a). Examples of different
rate functions used in this study are shown in Figure 4B. A random summation
of miniature EPSPs in one of the PY cells in the network could be
sufficient to depolarize this cell to the level of membrane potential
where the persistent Na+ current,
INa(p), is activated.
INa(p) activation was followed then by
a Na+ spike, initiating spread of activity
over the whole network. A single spike in a PY cell was able to
initiate spikes in other neurons that were relatively depolarized by
miniature synaptic events. Network activity was maintained by
INa(p) activation and PY-PY AMPA- and
NMDA-mediated excitatory interconnections. Because a minimal threshold
of synaptic excitation was required to maintain firing, depression of
PY-PY interconnections supplemented by slow activation of the
Ca2+-dependent
K+ current eventually terminated firing,
and the network switched back to the down (silent) state. A
sufficiently high level of IN-mediated inhibition was also required to
ensure transitions to the down state (see below).
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Figure 4.
Patterns of spontaneous activity in the model
network of PY and IN cells. A, On the
left, network size increase from 20 PY-5 IN cells to
100 PY-25 IN cells led to higher frequency of spontaneous bursting and
increased its regularity. On the right, an increase of
the miniature EPSP amplitudes in the network of 20 PY-5 IN cells up to
170% of that on the left had a similar effect as an
increase of network size. B, The shape of the function
describing the mini average rate increase (logarithmic vs exponential)
had little effect on the network dynamics.
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An example of spontaneous activity in the network with 20 PY-4 IN
cells is shown in Figure 4A (left panel,
top). In such a small network the probability that one of
the PY neurons could reach a level of depolarization sufficient for
INa(p) activation was relatively
small, producing a low rate of bursting (25-50 sec intervals between
bursts) and a high variability of interburst intervals. Because the
miniature EPSPs were independent at different synapses and different
cells, as the network size increased the probability that a
Na+ spike would be generated in one of the
neurons increased. Figure 4A (left panel,
middle and bottom) shows examples of networks with 60 PY-15 IN cells and 100 PY-25 IN cells. In the latter case the
network fired more regularly and at a higher frequency of ~0.05 Hz.
An increase of the miniature EPSP amplitude had a similar effect on the
network activity. Figure 4A (right
panel) shows a network with 20 PY-4 IN cells, which fired
quite regularly when the mini amplitude was increased by ~50%.
In a previous analytical model based on experimental data for amplitude
and rate of miniature events, the mini-dependent mechanism drove
periodic network oscillations at frequencies of 0.2-0.5 Hz when the
network size exceeded ~108 neurons
(Timofeev et al., 2000a). This is in the frequency range of SWS
oscillations (Steriade et al., 1993c,d). Computer simulations involving
this many conductance-based model neurons is not yet feasible, so we
increased the amplitude of miniature events by ~50% in our
simulations to obtain SWS-like oscillations in relatively small networks.
Figure 4B shows examples of the membrane potential
for one PY cell from the same network shown in Figure
4A (right panel, bottom) using
different functions for the mean rate of Poisson processes (see
Materials and Methods). The overall patterns of network activation were
virtually identical in both cases, suggesting that the properties of
SWS oscillations are independent of the shape of the rate versus time
curve when the network size or miniature event amplitudes are large enough.
Spatiotemporal properties of SWS oscillations
In the model, each pattern of activity started from a spike in one
of the PY cells and then spread over the network. Figure 5A shows two-dimensional (2-D)
plots of PY activity in the network with 100 PY-25 IN cells. The
spatiotemporal patterns depended on the coupling strengths between PY
cells and between PY and IN cells. Generally, an increase of the
maximal conductance between PY neurons increased the duration of active
phases. An increase of maximal conductances between PY and IN cells or
IN and PY cells had more complex effects. The example in Figure
5A shows that an increase of the AMPA-mediated conductance
from PY to IN cells increased the regularity of SWS oscillations. This
occurred because strengthening PY to IN connections enhanced inhibitory
feedback and made possible earlier and more reliable termination of the active states. This effect was similar to a direct increase of the
GABAA-mediated conductance from IN to PY cells
(data not shown). However, an excessive increase of GABAergic coupling
between IN and PY cells also significantly reduced the duration of the
active states. When GABAA-mediated conductances
from IN to PY cells were blocked, the active phase lasted continuously.
Introducing GABAergic inhibitory connections between INs had little
effect and was generally similar to reducing
GABAA-mediated conductance from IN to PY cells (data not shown). This effect of IN-IN coupling was further reduced when the reversal potential for GABAA synapses in
INs was depolarized relative to the IN resting potential (Paré et
al., 2000). IN cells generally showed patterns of activity that were
similar to those in PY cells (see Fig. 7). Thus, silent (down) states were not maintained by GABAA IPSPs but reflected
disfacilitation in the cortical network.
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Figure 5.
Effect of PY-PY and PY-IN conductances on
spontaneous waves propagation. A, Reduction of the
maximal conductances for PY-IN synapses decreased the regularity of
spontaneous patterns. B, Velocity of propagation (in
cells per second) versus maximal conductances for PY-PY and PY-IN
synapses.
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Spiking patterns propagated through the network with a
velocity that depended on the maximal conductances for synaptic
interconnections, as illustrated in Figure 5B. An increase
of the excitatory conductance between PY cells in the network with
fixed radii of synaptic interconnections increased the propagation
velocity; changes of maximal conductance between PY and IN cells had
the opposite effect. This phenomenon has been reported previously in
the theoretical study of the network of excitatory and inhibitory
cortical neurons (Golomb and Ermentrout, 2001, 2002).
SWS oscillations in the thalamocortical network
To explore the properties of SWS oscillation in a thalamocortical
network, we simulated networks with 100 PY-25 IN-50 RE-50 TC cells
(Fig. 1). Although thalamic RE and TC cells were not necessary to
maintain SWS oscillations in the model, their presence changed
spatiotemporal patterns of SWS activity. Figure
6 shows 2-D spatiotemporal plots of PY
and TC networks during SWS oscillations. Each active phase was
initiated in one of the cortical PY cells and then spread over the
thalamocortical network. Figure 6 shows that isolated spikes occurred
in many PY cells during silent phases of SWS oscillations. These spikes
were not able to induce postsynaptic response unless the postsynaptic
cell itself was sufficiently depolarized by random mini
summation. PY cells fired at a higher frequency during the
initial phase of the depolarized state and at a reduced firing rate
after 200-300 msec (Fig. 7). The IN cell shown in Figure 7 (bottom) fired before the PY cell because
it received direct excitatory input from one of the PY neurons that fired earlier in the cycle as indicated by the local field potential trace. In TC cells, activity patterns always started from
hyperpolarization because the immediate effect of PY spiking was a
burst of spikes in RE cells (Fig. 7). This hyperpolarization was
followed by deinactivation of low-threshold
Ca2+ current,
IT, and rebound low-threshold spike.
Only a few TC cells fired Na+ spikes in
the second cycle; in many cases TC cells showed a few cycles of
subthreshold ~10 Hz oscillations followed by a few cycles with
low-threshold spikes crowned by action potentials. This pattern is a
signature of waning spindle oscillations usually observed during active
phases of SWS (Timofeev and Steriade, 1996). The main factor
contributing to spindle termination in this model was powerful and
nonsynchronous AMPA-mediated PY  RE input depolarizing RE
cells that inactivated IT and
terminated rebound oscillations in the RE-TC circuit (Fig. 7) [see
also Timofeev et al. (2001a)].
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Figure 6.
Two-dimensional plots of spontaneous activity in
the thalamocortical network. One hundred PY-25 IN-50 RE-50 TC cells
were simulated. Two active periods are expanded below. It shows that
each pattern of activity was randomly initiated at different foci of
the network.
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Figure 7.
Membrane potential traces of individual PY,
IN, RE, and TC cells from the network in Figure
6. Spontaneous firing in the PY-IN network initiated waning spindles
in the RE-TC network. The spindles in TC cells usually started with
two to three cycles of subthreshold (no spikes) oscillations mediated
by inhibitory input from RE neurons.
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AMPA-mediated input from TC to PY cells induced additional
depolarization, increasing the duration of cortical active phases up to
1-1.5 sec (compare Figs. 5A and 6). In some cases, thalamic spindles
outlasted cortical activity, which also reduced the duration of
corresponding down states in the cortical network; TC-mediated EPSPs
arriving at the top of mini-induced depolarization in PY cells could
initiate new active patterns after ~0.5 sec or less. Thus, compared
with the isolated cortical network, SWS sleep oscillations in the full
thalamocortical model were characterized by prolonged active (up)
states and reduced silent (down) states. This prediction is consistent
with recordings from cortical slice preparations in which SWS
oscillations are characterized by prolonged down and relatively short
up states (Sanchez-Vives and McCormick, 2000).
Transition from SWS oscillations to activated state
Activation of neuromodulatory systems controls the transition from
sleep to activated states (Steriade and McCarley, 1990). An increase in
the level of acetylcholine release associated with activation of
nicotinic and muscarinic receptors depolarizes cortical pyramidal cells
and thalamic relay cells both in awake states and during REM sleep.
This effect is achieved mainly by blocking resting potassium
conductances in these cells (McCormick, 1992). We modeled the effect of
cholinergic excitation by blocking potassium leak current in PY and TC
cells. Figure 8A1 shows
examples of PY, RE, and TC cells from the network 100 PY-25 IN-50
RE-50 TC cells in which IKleak
current was completely blocked in PY and TC cells. Cortical
depolarization eliminated the silent phases of SWS oscillation, and PY
cells fired continuously in the frequency range of 30-40 Hz. RE and TC
cells received tonic excitation from cortex and were silent.
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Figure 8.
Effects of synaptic conductances and potassium
leak current on network activity. Decrease of potassium leak current in
PY and TC cells transformed SWS oscillations into
persistent firing at frequency depending on PY-PY synaptic
conductance. A, In the presence of the strong
RE-TC-RE coupling the RE-TC network generated spontaneous
spindles even during continuous firing in the PY-IN network.
A1,
gPYPY = 0.15 µS, gRETC = 0.2 µS,
gTCRE = 0.4 µS. A2,
gPYPY = 0.09 µS, gRETC = 0.2 µS,
gTCRE = 0.4 µS. A3,
gPYPY = 0.09 µS, gRETC = 0.1 µS,
gTCRE = 0.2 µS. B, Input resistance of PY cells and frequency of
spontaneous firing versus maximal conductances for AMPA-mediated PY-PY
synapses (gKL = 0, gRETC = 0.1 µS, gTCRE = 0.2 µS) and potassium leak channels
(gPYPY = 0.08 µS,
gRETC = 0.1 µS, and
gTCRE = 0.2 µS).
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The application of the cholinergic agonist muscarine depresses
intracortical EPSPs by ~35-40%; GABAB
receptor agonist application has a similar effect (Gil et al., 1997).
This suggests that in states of arousal when forebrain activity is
high, intracortical synapses are relatively depressed via presynaptic
GABAB and muscarinic receptors (Gil et al.,
1997). To model this, AMPA-mediated synaptic conductances between PY
cells were reduced (Fig. 8A2). One effect was a
reduction of the cortical firing rate to ~20-25 Hz. Reduction of
depolarizing input from cortex in turn affected the firing patterns of
RE and TC cells. The membrane potential of RE cells became
hyperpolarized when the corticothalamic drive was reduced, which
partially deinactivated RE IT
channels. This led to persistent activity in frequency range of 10-15
Hz in the RE-TC circuit through the mechanisms similar to those
responsible for spindles (Fig. 8A2). Because this
activity depended on the synaptic coupling between RE and TC cells, we
reduced GABAA- and AMPA-mediated conductances between thalamic neurons. This eliminated persistent firing of RE and
TC cells; the cortical firing rate was further reduced to 15-20 Hz
(Fig. 8A3). Note that now RE cells occasionally fired spikes that were not able, however, to initiate sustained activity in
the RE-TC circuit. The frequency of cortical firing as a function of
maximal conductance for AMPA-mediated PY-PY synapses is plotted in
Figure 8B (top). For low values of PY-PY
coupling, cortical PY cells fired at frequencies of 15-20 Hz in the
frequency range of spontaneous cortical activity recorded in
vivo (Steriade et al., 2001).
Input resistance of PY cells
Changes of the maximal conductances for the
K+ leak current and the PY-PY synaptic
current can change the input resistance of PY neurons. We
systematically varied gKleak and
gPYPY in PY cells starting from the network state shown in Figure
8A3. As AMPA-mediated
gPYPY increased, the input resistance quickly decreased from ~200 M for
gPYPY = 0.08 µS to ~150 M for
gPYPY = 0.16 µS (Fig. 8B). The frequency of spontaneous
firing increased from ~14 to ~40 Hz. An increase of the maximal
conductance for the K+ leak current had a
similar effect: the input resistance was reduced to ~170 M when
gKleak increased from 0 to 3 µS/cm2 (Fig. 8B,
bottom). These results suggest that modifications of intrinsic and synaptic properties of cortical cells during the sleep-wake transition can affect their input resistance.
To model the transition from SWS oscillations to an activated state in
the thalamocortical network, both the K+
leak conductances in PY and TC cells and the PY-PY synaptic current were changed simultaneously. Figure
9A shows examples of activity in one PY cell at different stages of transition. The transition to an
activated state was characterized by an increased duration of the
epochs when neurons fired continuously; the silent (down) states
appeared less frequently and finally disappeared. To show changes in
the frequency domain, we plotted integrated (in different frequency
bands) values of the power spectrum (Fig. 9B) at different transitional stages. There was a dramatic decrease in power in the
frequency band below 2 Hz indicating the disappearance of low-frequency
periodic switches between up and down states. At higher frequencies the
changes were not as significant, except for an increase in power in the
10-20 Hz band, which reflected a reduction of the firing rate in the
activated state compared with active (up) states of SWS
oscillations.
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Figure 9.
Transition from SWS oscillation to activated state
in the thalamocortical network model. A, Decrease of the
maximal conductances for potassium leak current in PY and TC cells and
synaptic conductance between PY neurons eliminated silent phases in the
cortical network activity. The firing became persistent and its
frequency stabilized at ~17 Hz. SWS state:
gPYPY = 0.15 µS, gRETC = 0.2 µS,
gTCRE = 0.4 µS, gKL = 0.3 µS/cm2; activated state:
gPYPY = 0.08 µS, gRETC = 0.1 µS,
gTCRE = 0.2 µS, gKL = 0. B,
Integrated power in different frequency bands (as indicated in this
figure) during transition to activated state. C, The
input resistance of PY cells increased from ~110 M (during up
phases of SWS oscillations) to ~190 M (during activated state),
thus reaching the level of the input resistance during silent
(Down) phases of SWS.
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Figure 9C shows the input resistance of PY cells at
different stages of transition to an activated state. There was a
significant difference in the input resistances between silent and
active states of SWS oscillations (Fig. 9C,
left). As parameters changed, not only did the down states
disappear but also the input resistance in the activated states
increased. In a fully activated network the input resistance reached
(or even exceeded) the level measured during silent states of SWS
oscillations (Fig. 9C, right). Note the jump in
the input resistance value after the silent (down) states became
irregular (Fig. 9C, middle). During SWS
oscillations the firing rate of PY cells was higher right after onset
of an active state and was reduced at the end, which affected the input resistance. Input resistance values plotted in Figure 9C
were averaged over 30 individual measurements similar to our previous study (Steriade et al., 2001). When down states became irregular and
rare, there were fewer measurements near the onset of the active states
where input resistance was reduced because of the higher firing rate.
External stimulation
It is generally assumed that during SWS the thalamus partially
blocks sensory input to the cerebral cortex (Steriade et al., 1993b;
Timofeev et al., 1996). We used our model to explore the ability of a
thalamocortical network to transmit prethalamic input up to the level
of PY cells during SWS oscillations and in an activated state. To model
prethalamic stimulation, 25% of TC cells in the model were stimulated
by external AMPA synapses with Poisson-distributed spike trains with a
mean rate 25 Hz modulated by sinusoidal function at different
frequencies: 0.4, 1, and 2.5 Hz (see Materials and Methods). Figure
10 shows running spike histograms
(RSHs) for input spike trains and spike trains in TC and PY cells. RSHs
for TC and PY cells were averaged over 25% of the population; TC cells receiving external stimulation and their target/postsynaptic PY neurons
were used to calculate averages. In the activated state, the
prethalamic stimulus appeared at a cortical level as modulation of
background activity. Responses of cortical PY cells correlated well
with the input signal at all tested frequencies (Fig. 10A). This is also illustrated at Figure
11A, in which normalized
power spectra of the RSHs are plotted. At all frequencies the peaks in
the power spectra for input signals and thalamic and cortical activities coincided. When the same input was applied to the network in
the SWS state, the cortical response was a superposition of the input
signal and an intrinsic oscillation (Fig. 10B). The power spectra for PY neurons innervated by fibers from those TC cells that
received input signals were generally shifted to the frequency range
1.5-2.5 Hz, (Fig. 11B), compared with PY cells located
remotely from direct stimulation. The durations of the silent (down)
phases were reduced in PY neurons located postsynaptically to TC cells receiving external input, which changed the overall frequency of SWS
oscillations in these neurons. At 2.5 Hz (Fig. 11B) and higher (data not shown), the power spectra of cortical oscillations contained peaks corresponding to the frequency of stimulation. The
maximum of the cross-correlation function between input RSH and PY
responses also increased. Thus, during SWS, external inputs at higher
frequencies were transferred more accurately, because the local
subpopulation of PY cells fired almost continuously (Fig.
12).
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Figure 10.
Cortical response during thalamic stimulation.
Twenty-five percent of the TC cells were stimulated by
Poisson-distributed spike trains; those rates were modulated at 0.4, 1, and 2.5 Hz. A, Activated state. B, SWS
state. For each graph, the bottom panel
shows an RSH of the input spike trains; the middle panel
shows an RSH averaged over all TC cells receiving input (25% of TC
population); the top panel shows an RSH averaged over PY
cells receiving afferents from those TC neurons that were stimulated
(25% of the total PY population). The ability of the thalamocortical
network to transmit sensory input was reduced in the SWS state.
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Figure 11.
Precision of PY responses during thalamic
stimulation. Power spectra of RSHs from Figure 10 and
cross-correlations between input RSHs and PY responses are shown.
A, Activated state. B, SWS state. During
SWS oscillations the low-frequency input was masked by intrinsic
network oscillations more severely than input at higher
frequencies.
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Figure 12.
Cortical activity at different distances from the
stimulation site. Two PY neurons from the PY-IN-RE-TC network are
shown. The cell receiving excitatory drive from the thalamus shows
almost persistent firing (bottom panel), while a
remotely located cell displays "normal" SWS activity (top
panel).
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DISCUSSION |
Cortical SWS oscillations are low-frequency (0.3-1 Hz) rhythms
dominating cortical activity during natural sleep and under some types
of anesthesia (Steriade et al., 1993b,c,d). During SWS the
entire thalamocortical network switches periodically between up and
down states. The down state is characterized by disfacilitation, a
state-specific withdrawal of synaptic activity leading to synaptic silence, whereas the up state is characterized by spiking in the frequency range of 20-30 Hz. SWS activity exhibits remarkable synchrony between different cortical areas (Amzica and Steriade, 1995a,b) and between cortex and thalamus (Contreras and Steriade, 1995). A recent study of SWS oscillation during natural sleep indicates
that silent (down) states are not associated with IPSPs but rather are
the result of activating intrinsic (presumably potassium) currents in
cortical neurons and global disfacilitation (Timofeev et al., 2001b).
Cortical inhibitory interneurons follow the same pattern of activity as
excitatory cells; they are silent during down states of SWS
oscillations (Steriade et al., 2001; Timofeev et al., 2001b). Thus, the
whole thalamocortical network is silent (inactive) during down states
of SWS oscillations, which raises a question about the mechanisms
leading to reinitiation of activity at the onset of each active phase.
One possible mechanism for recovery of active states during SWS could
be the dynamics of some intrinsic currents in cortical neurons such as
the hyperpolarization-activated cation current, Ih, similar to the way that dynamics
of the low-threshold Ca2+ current and
Ih in thalamic relay cells can
organize their oscillations in the delta frequency range (McCormick and
Pape, 1990; Soltesz et al., 1991; Lytton et al., 1996). Recently, it
was shown using a cortical slice preparation that in a relatively high
concentration (3.5 mM) of extracellular
K+, cortical slices can oscillate in the
frequency range of slow sleep oscillations (Sanchez-Vives and
McCormick, 2000). This activity was usually initiated in layer 5 and
propagated over the whole slice. Although these results do not exclude
the possibility of intracellular mechanisms for SWS oscillations, it is
not clear how the specific conditions in those slice preparations
affected the excitability of cortical neurons and the temporal patterns of their activity.
The approach taken here was to critically test whether SWS oscillations
can be maintained by intrinsic mechanisms in an isolated part of the
cortical network in vivo. These experiments used a cortical
slab preparation: a 10 × 6 mm slab of cortex that was synaptically isolated from the rest of the cortical network but kept
with a natural blood supply (Timofeev et al., 2000a). Although neurons
outside the slab demonstrated "normal" SWS oscillations, activity
in the small slab consisted of small depolarizing potentials, presumably spike-independent minis (Fatt and Katz, 1952), interrupted by bursts of high-amplitude depolarizing events. These bursts lasted
0.5-3 sec, appeared at very low frequencies (2-6
min1), and were composed of EPSPs and
IPSPs (Timofeev et al., 2000b). Miniature EPSPs observed during silent
periods had a mean amplitude of 0.54 mV; their incidence decreased
significantly immediately after a burst and recovered during the
following 3-4 sec (Timofeev et al., 2000a). When a whole gyrus was
isolated, its activity was similar to normal SWS activity. This
suggests that the relatively low frequency of bursting in the isolated
slab could be caused by the relatively small number of neurons in the
slab compared with a gyrus or the intact cortex, thus pointing to
network mechanisms for SWS oscillations. To test this hypothesis, the
mean and SD of interburst intervals were estimated analytically as a
function of number of neurons in a network (Timofeev et al., 2000a).
For a slab the estimated mean was ~24 ± 21 sec; the mean
decreased with the size of the network and reached 4.9 ± 2.3 sec
for a network the size of a gyrus. Thus, cortical SWS oscillations
could arise from the same mechanisms as spontaneous slab activity in
the limit of a very large neuronal population.
In computer simulations of Hodgkin-Huxley-type model neurons, an
increase in the mini rate or amplitude had a similar effect on the
frequency of spontaneous bursting as an increase of the network size.
In this study, we used a relatively small thalamocortical network
comprising a few hundred neurons and a higher mini rate and amplitude
to explore properties of SWS activity. On each cycle of oscillation, an
active phase was started in one or a few PY neurons driven by the
spontaneously occurring coincidence of miniature ESPSs. Mini-evoked
depolarization led to INa(p)
activation and a burst of spikes. Once started, the activity propagated
with a velocity that depended on the maximal conductances of the
inhibitory and excitatory synapses between PY and IN cells. In a
network model including only cortical PY and IN cells, each pattern of activity lasted 0.5-1 sec and was terminated by synaptic depression and activation of IK(Ca). A
sufficiently high level of inhibitory feedback was required to maintain
transitions to the down state. Duration of active phases depended on
the presence of NMDA receptors between PY cells. When NMDA currents
were blocked, only short bursts lasting <0.5 sec were obtained.
Thalamic relay cells have intrinsic properties that generate slow (<1
Hz) oscillations (Hughes et al., 2002). Intrinsic slow oscillations in
TC neurons can be synchronized by corticothalamic input (Timofeev and
Steriade, 1996) and contribute to enhancing and shaping the slow sleep
rhythm. In the full thalamocortical model, the active phases of SWS
oscillations usually lasted longer (1-1.5 sec), partially maintained
by the depolarizing drive from TC neurons.
Transition to activated states
The transition from slow-wave sleep to REM sleep or waking
is controlled by activation of neuromodulatory systems (Steriade and
McCarley, 1990). Acetylcholine increases during the transition to both
REM sleep and waking, whereas noradrenaline and serotonin are increased
during waking only (for review, see Steriade et al., 1997). To
model the activation of these neuromodulatory systems, K+ leak currents were blocked in PY and TC
cells in the model (McCormick, 1992). This depolarized the neurons and
eliminated the silent (down) states of SWS oscillations, and the
neurons fired continuously. To ensure realistically low frequencies of
spontaneous activity in an activated state, maximal conductances for
AMPA-mediated synapses between PY neurons in the model had to be
reduced by ~40%. This is consistent with experimental findings that
application of muscarine or a low concentration of acetylcholine
depressed intracortical EPSPs both in vitro (Gil et al.,
1997) and in vivo (Oldford et al., 2000). We then tested the
ability of the thalamocortical network model to process prethalamic
sensory input. In an activated state the network precisely transformed
the input (rate-modulated Poisson spike train) into responses from
cortical PY cells. During SWS oscillations the cortical response was
masked by intrinsic activity, especially at low frequencies of
stimulation. Surprisingly, at higher frequencies signal transmission
was improved because the local groups of PY neurons fired almost
continuously during stimulation. This result can explain the blockage
of slow EEG rhythms and the appearance of fast oscillations (20-40 Hz)
restricted to the motor cortex in experiments with high-frequency
stimulation of interpositus and dentate cerebellar nuclei in
vivo (Steriade, 1995).
The transition to an activated state is associated with an
increase in the input resistance of cortical cells in vivo
(Steriade et al., 2001). In the network model there was also a
significant difference between the input resistances of PY cells in the
down (silent) and up (active) states during SWS oscillations. This difference was explained primary by a high level of synaptic activity during active phases of SWS. The input resistance gradually increased during the transition from SWS to an activated state, eventually reaching the same or a higher level as during silent phases of the SWS
oscillations. Both reduction of K+ leak
and AMPA-mediated synaptic conductances in cortical neurons contributed
to this shift in the passive properties of neurons during waking.
Conclusion and model predictions
The present model provides, for the first time, a complete and
realistic mechanism for generating cortical slow-wave sleep rhythms. In
the proposed scenario of slow-wave sleep, the "re-excitation" of
the cortical network on each cycle of oscillation is driven by the
spontaneously occurring coincidence of miniature EPSPs. This mechanism
was previously proposed to explain spontaneous active states in the
isolated cortical slab (Timofeev et al., 2000a) and was used here to
explain periodic transitions between silent and active states of slow
sleep oscillations. In large neocortical networks there may be many
independent foci where activity could be initiated almost
simultaneously. The model requires more than a single spike in a PY
cell to induce the active (up) state, and many PY cells fired isolated
spikes during silent phases of SWS oscillations (Fig. 6). These spikes
were unable to induce postsynaptic response unless the postsynaptic
cell was itself sufficiently depolarized by random mini summation.
Thus, in a large cortical network, several events (a spike in one PY
cell and a sufficiently high depolarization in a few other cells) must occur simultaneously to initiate an active state. The model predicts that the persistent Na+ current is
important in initiating transitions from silent (down) to active (up)
states and that the Ca2+-dependent
K+ current as well as synaptic depression and IN-mediated
inhibition are important in terminating active phases.
The model explains the transition from SWS to activated states (such as
REM sleep or waking). It predicts that this transition is accomplished
by changing both the passive properties of cortical neurons and the
nonlinear map of prethalamic signals to cortical responses in a
frequency-dependent matter. Some of these predictions were confirmed
recently in in vivo studies with naturally awake and
sleeping cats (Steriade et al., 2001; Timofeev et al., 2001b).
Recent studies have reported that slow-wave sleep may be essential for
memory consolidation and memory formation (Gais et al., 2000; Stickgold
et al., 2000). The cellular mechanisms underlying sleep-related memory
consolidation including synaptic plasticity and cellular conditioning
(Timofeev et al., 2002) can be further integrated into the model.
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FOOTNOTES |
Received April 5, 2002; revised July 1, 2002; accepted July 3, 2002.
This research was supported by National Institutes of Health Grant
NS40522, the Human Frontier Science Program, and the Canadian Institutes of Health Research (Grant MOP-37862). I.T. is a scholar of
Fonds de la Recherche en Santé du Québec.
Correspondence should be addressed to Dr. Maxim Bazhenov, The Salk
Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037. E-mail:
bazhenov{at}salk.edu.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
