Laboratory of Neurophysiology, School of Medicine, Laval University, Quebec, Canada G1K 7P4, , 1 Howard Hughes Medical Institute, The Salk Institute, Computational Neurobiology Laboratory, 10010 North Torrey Pines Road, La Jolla, CA 92037 and , 2 Department of Biology, University of California, La Jolla, CA 92093, USA
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Abstract |
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Introduction |
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A key question in an interconnected system is whether increasing its size and connectivity can lead to new properties (Watts and Strogatz, 1998). What causes the presence of spontaneously synchronized activity in the intact cortex, compared to the absence of such activity in slice preparations? Two main factors could explain this difference. The first is the number of interconnected neurons. Even a small increase in the thickness of a cortical slice from 0.4 to 0.5 mm results in a 4- to 5-fold increase in connectivity between pyramidal and non-pyramidal neurons (Thomson et al., 1996
). Secondly, the intrinsic properties of cortical neurons and response patterns remain similar over long-term recordings in constant in vitro conditions (Schwindt et al., 1997
; Gupta et al., 2000
), but they are expressed differently with increased synaptic activity (Steriade, 1997
; Steriade et al., 1998a
) and with changes in the membrane potential (Vm) due to the presence of modulatory systems in vivo (Steriade et al., 1993a
) or application of activating neuro- transmitters in vitro (Wang and McCormick, 1993).
To examine the issue of scaling the size of the network without drastically changing the milieu of the neurons in the network, we developed a new preparation that has advantages of both the in vitro and in vivo preparations. Experimental recordings from small cortical slabs isolated from thalamic and cortical inputs, as well as from a larger isolated gyrus, revealed that activity was sparse and irregular in smaller slabs, but became progressively more similar to the slow oscillations observed in the intact cortical tissue as the size of the slab was increased. In computational models of the cortical network that closely matched the experimental recordings, the initiation event occurred in single cortical neurons driven by spontaneous miniature excitatory postsynaptic activity and spread by recruiting neighboring neurons. Thus, the variability expressed in large-scale activity during sleep states in vivo may reflect events that are initiated in single neurons.
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Material and Methods |
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Experiments were carried out on 35 adult cats anesthetized with ketamine and xylazine (1015 and 23 mg/kg). Under this type of anesthesia, the electrographic pattern consists of a slow oscillation at <1 Hz, mainly 0.60.9 Hz (Steriade et al., 1993c; Amzica and Steriade, 1995a
; Contreras and Steriade, 1995
), very similar to that of the slow oscillation during natural sleep in cats (Steriade et al., 1996
) and humans (Achermann and Borbély, 1997
; Amzica and Steriade, 1997
). The EEG was monitored continuously during the experiments to maintain a deep level of anesthesia and additional doses of anesthetic were given at the slightest tendency toward an activated EEG pattern. In addition, all pressure points and tissues to be incised were infiltrated with lidocaine. The cats were paralyzed with gallamine triethiodide and artificially ventilated to an end-tidal CO2 of 3.53.8%. The heartbeat was monitored and kept constant (90110 beats/min). Body temperature was maintained at 3739°C. Glucose saline (5% glucose, 10 ml i.p.) was given every 34 h during experiments, which lasted for 814 h.
Isolated slabs (Fig. 1) were prepared from areas 5 and 7 of the suprasylvian gyrus in 29 cats. After opening a hole in the parietal bone, a small perforation was made in the dura above a part of the pia that did not contain large vessels. A custom crescent knife was inserted along its curve into the cortex until the tip of the knife appeared ~10 mm frontally under the pia. The knife was then turned by 90° in both right and left directions. The pia was intact except at the place the knife was entered. Such slabs were ~810 mm long (rostro-caudal direction), ~56 mm wide (medio-lateral direction) and ~45 mm deep (Fig. 1a,b
). Slabs showing signs of edema and/or bleeding were not recorded. The completeness of neuronal transections and the boundaries of the slab were verified in every case on 80 µm thionine-stained sections (Fig. 1b
). In six other cats, we isolated the suprasylvian gyrus (Fig. 1c
) by making longitudinal cuts through marginal and ectosylvian gyri. Thereafter, by using an oblique approach we inserted a spatula and undercut the white matter 78 mm below the surface of the suprasylvian gyrus. The size of the isolated gyrus was 30 mm x 20 mm.
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Neuron and Network Models
Each cortical neuron was modeled by two compartments coupled by a 10 M resistance. The ionic currents in the model were taken from a previous study (Mainen and Sejnowski, 1996
), with the addition of a persistent sodium current, INa(p) (Alzheimer et al., 1993
; Kay et al., 1998
) (See Appendix for details). The firing pattern of the compartmental model neuron was controlled by the parameter
, which is the ratio of the surface area of the dendritic compartment to the somatic compartment. For the cortical pyramidal (PY) cells,
= 165 to match the intrinsically bursting responses observed in the majority of pyramidal cells in the slab (Fig. 2
) and
= 50 for interneuron (IN) to obtain regular firing patterns. The addition of a INa(p) to the model increased the bursting of the PY cells compared to the original model (Mainen and Sejnowski, 1996
). In some simulations we varied
around the average value randomly by 1020% to test the effects of variability on the firing patterns of PY and IN cells. Some of the intrinsic parameters (such as the maximal conductances for the INa(p), the high-threshold Ca2+ current and the fast voltage-dependent sodium and potassium currents and resting membrane potentials of the neurons) were initialized around the mean with a random variability of ~10% to ensure robust results. In most of the simulations the synaptic conductances were 0.11 µS for AMPA between PY cells, 0.05 µS for AMPA from PY to IN, and 0.05 µS for GABAA from IN to PY. In some simulations these parameters were varied, as indicated, which affected slightly the duration of active patterns and interburst intervals. The expressions for voltage- and Ca2+-dependent transition rates for all currents are given in the Appendix.
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Spontaneous miniature EPSPs and miniature 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 µ(t) (see below).
Analytical Model
The analytical model for the distribution of interburst intervals is based on the probability of a burst occurring in a single neuron as a function of time since the last burst. Assume that n miniature EPSPs need to occur in a time window t to depolarize the membrane sufficiently to activate the INa(p). Although this assumption is a simplification, it permits the probability distribution function to be calculated analytically with good accuracy. For a Poisson-distributed train of miniature EPSPs the probability to activate the persistent sodium current, and generate a new burst at time instant k
t after the last one is
![]() |
![]() | (1) |
where n is critical number of miniature EPSPs that have to occur inside the time window t to bring a pyramidal cell to the threshold, P<n(s) is the probability of finding less than n miniature events at the time interval [s
t,(s + 1)
t], M is the total number of synapses for one cells, µ(s) is the mean rate of Poisson processes. If f = µ(s)
t M << 1, then
![]() | (2) |
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where P>n(s) is the probability of finding n or more miniature events at the interval [st,(s + 1)
t]. For a network with N pyramidal cells:
![]() | (3) |
The mean firing rate for the HodgkinHuxley model was approximated by either a logarithmic or sigmoid function:
![]() | (4) |
and the in vivo data as fit with the rate function:
![]() | (5) |
Note that for the sigmoid distributions, the rate of minis approaches a constant value. Using the probability distribution function PN(k) above we calculated the mean period T between spontaneous bursting and its standard deviation :
![]() | (6) |
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Results |
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Recordings were made from neocortical neurons in cats under ketaminexylazine anesthesia. Spontaneous and evoked activities were recorded from small cortical slabs, from an isolated gyrus, and from neocortical areas that had intact connections. Isolated slabs (~10 mm x 6 mm) were prepared from association areas 5 and 7 of the suprasylvian gyrus (Fig. 1a,b). In other cats, we isolated the whole suprasylvian gyrus (~20 mm x 10 mm), which extends from the marginal to the ectosylvian gyri (Fig. 1c
).
Data are based on single (n = 95), dual (n = 44) and triple (n = 9) simultaneous intracellular recordings, in conjunction with field potential, from superficial and deep cortical layers. Twenty-four neurons were recorded with QX-314-filled pipettes. The mean Vm of neurons in small cortical slabs was 70.4 ± 0.8 mV and the mean input resistance (Rin) was 48.6 ± 4.7 M (range 30120 M
). Compared to our database of >1000 neocortical neurons recorded from intact neocortical areas, showing a mean Vm of 62 mV and a mean Rin of 22 M
, the neurons in cortical slabs displayed a more negative Vm and a much higher Rin. The more negative Vm and large increase in Rin of neurons recorded from isolated cortical slabs, in which the spontaneous synaptic activity is greatly reduced compared to the intact cortex, corroborate recent experimental and modeling studies comparing the resting properties of neocortical pyramidal neurons during periods with intense synaptic activity in vivo with the properties of pyramidal neurons after microperfusion with TTX or in vitro (Paré et al., 1998
; Destexhe and Paré, 1999
).
Another important difference was that, in slabs, intrinsically bursting (IB) neurons were twice as numerous as in intact cortical areas. These neurons have been described in vitro (Connors et al., 1982; McCormick et al., 1985
) and in vivo (Nuñez et al., 1993
). In our database of in vivo neocortical cells, the proportion of IB neurons was 1520%. In the present series of experiments conducted on isolated slabs, with a more hyperpolarized Vm of cortical neurons and decreased synaptic activity, the IB cells constituted 39% of all neurons (48 of 124). Figure 2a
shows an example of an IB neuron recorded at rest. A depolarizing current pulse (0.5 nA, 0.2 s) resulted in the generation of three high-frequency spike-bursts. A slight DC depolarization of the same neuron converted the burst firing into a regular-spiking (RS) pattern. Similar changes, from IB to RS patterns, were obtained by synaptic activation of increasing strength. High-frequency (100 Hz) pulse-trains at slight intensities (0.12 mA) applied to cortex resulted in bursting responses of IB cells; however, an increased intensity of electrical stimuli (0.75 mA) invariably suppressed the bursting responses and revealed single action potentials (not shown).
What is the impact of spike-bursts, compared to single spikes, on synaptic transmission? The summated postsynaptic response elicited by a spike-burst should be greater than that elicited by a single spike. From single-axon EPSPs studies in vitro, it is known that the pyramid-to-pyramid connections mainly display paired-pulse depression, while pyramid-to-interneurons connections may display either paired-pulse facilitation or depression (Markram, 1997; Thomson, 1997
; Thomson and Deuchars, 1997
; Gupta et al., 2000
). The simultaneously recorded neurons from the in vivo slab (Fig. 2b
) revealed an apparently direct connection from a presynaptic IB neuron to a postsynaptic RS neuron. This was seen in three neuronal pairs. Virtually every spike in the presynaptic neurons elicited a depolarizing response (failure rate 2%), with a latency of 1.2 ± 0.1 ms, measured from the top of the spike to the onset of the EPSP. Direct depolarization of the IB cell resulted in the generation of a high-frequency burst, followed by single-spike firing. In all cases (n = 105), the burst-evoked postsynaptic response in the RS neuron was greater in amplitude than the responses of the same neuron during the tonic firing mode in the presynaptic IB cell (Fig. 2b
) as a result of sublinear temporal summation.
Spontaneous Activities in Isolated Cortical Small Slabs
Field potentials and intracellular recordings from small cortical slabs showed that the network was in a silent state most of the time. In 23 of 29 experiments with small slabs, the field potentials and intracellular recordings revealed the presence of periodic (26 min1) large amplitude depolarizing events (Fig. 3). Similar depolarizing events could be elicited by low-intensity electrical stimulation in all (n = 23) relatively active slabs and in four out of six totally silent slabs (see below, Fig. 6
). In the remaining two slabs, electrical stimulation within the slab resulted in short-lasting EPSPIPSP sequences (up to 0.2 s), without self-sustained oscillations, similar to what usually occurs in the in vitro slice preparation.
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The SDPs in isolation could not depolarize neurons from the resting Vm, i.e. 70 mV, to a level sufficient for spike generation. To produce a significant depolarization, these small signals had to be summated and/or amplified. Several non-exclusive factors may account for such amplification. One of them may be represented by some intrinsic properties of neurons, which are usually masked by ongoing spontaneous activity in the intactcortex preparations, and thus are only revealed during silent states. In fact, neurons recorded from slabs had a propensity to enhance small-amplitude depolarizing inputs (26 out of 32 tested neurons). Short (5 ms), subthreshold current pulses elicited an intracellular response that outlasted the duration of the pulse, whose duration increased by slight DC depolarization (Fig. 4a, stippled areas), above 65 mV, where INa(p) is activated (Crill, 1996
). With suprathreshold stimulation, the spike after- hyperpolarization shunted the prolonged responses. Therefore, as soon as the neuron became involved in the transmission of input signals and could generate spikes, the amplification of small signals was no longer necessary.
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Propagated Responses in Small Cortical Slabs
Multi-site, field potential and intracellular recordings from small slabs revealed that the onset of spontaneous active periods was systematically delayed at neighboring locations, suggesting that the active periods were propagating; however, the exact place of the origin of spontaneous bursts was difficult to assess. It was possible to elicit such bursts by low-intensity electrical stimuli within the slab. In such cases, the origin of active periods was close to the site of stimulation. Triple simultaneous intracellular recordings from one IB and two RS neurons in the area 5 slab (see their electrophysiological identification by depolarizing current pulses in Fig. 6) showed that the stimulus elicited an initially depth-negative field potential and compound depolarizing events in all three neurons, with progressively longer latencies in neurons located farther from the stimulating electrode (Fig. 6
). The onset of the depolarization was used to calculate the velocity of the propagation. Based on multi-site recordings (n = 5), the propagation velocity was in the range 10100 mm/s (mean 43.7 ± 27.8 mm/s).
Models of Cortical Networks
HodgkinHuxley-type compartmental models were used to represent neurons in the cortical model (see Materials and Methods, and Appendix). The parameters of the model neurons were adjusted to mimic the spike bursting patterns observed in recordings from the slabs (Fig. 2c). The synapses between the neurons were based on Markov models of synaptic conductance changes and were also matched to recordings from dual impalements (Fig. 2d
).
In models of interconnected PY and IN cells (see Materials and Methods), the probability of spontaneous miniature EPSPs at each synapse started from zero probability at the last Na+ spike in the presynaptic PY cell, increased during the first few seconds and more slowly reached an asymptote (see Fig. 3). Figure 7a
shows one PY neuron that was randomly selected from the network of 2 x N PY-IN neurons, where N was varied from 50 to 2000. When the summation of the miniature EPSPs in one of the PY cells depolarized this cell sufficiently to activate the INa(p) and to initiate a Na+ action potential, the activity spread through the network and was maintained by lateral PYPY excitation and INa(p) (Fig. 7b
). A similar mechanism for propagation has been previously described (Golomb and Amitai, 1997
); however, this network model only had excitatory neurons and only a single burst lasting ~50 ms was studied. In our model, a weak depression of the excitatory interconnections and activation of the Ca2+-dependent K+ current led to the termination of activity after a few hundred milliseconds. A similar effect could be achieved by slow inactivation of INa(p) (Fleidervish and Gutnick, 1996
), which, however, was not taken into account in the model. Because any PY neuron could be an initiator of the spontaneous activity and because these events are independent, the total probability of initiation in the network increased with N, the number of cells in the network (see below). As a consequence, there was a strong variability in the time intervals between patterns of activity in the small network of 2 x 50 PYIN cells. In larger networks, the increased number of foci where the activity could be initiated resulted in an increase in the frequency of active periods and less variability in their occurrence (Fig. 7a
). Note that the probability of spike initiation was smaller for the boundary PY cells, which received a reduced number of intact synapses, so that the active periods were usually initiated far from the network boundaries (see Fig. 7b
). To test the effects of miniature EPSP size, their amplitude was increased by either 50% (top trace in Fig. 7c
) or 100% (lower trace in Fig. 7c
). These modifications significantly increased the frequency of spontaneous bursting and in the latter case produced almost periodic oscillations at ~0.5 Hz. This activity is similar to the slow oscillations recorded in vivo during slow wave sleep (Steriade et al., 1993c
).
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The relatively low frequency of active states recorded in small isolated slabs, compared to the cortically generated slow oscillation (Steriade et al., 1993c; Contreras and Steriade, 1995
), could be due to the relatively small number of neurons in the slab. If so, then an increase in the number of cortical cells in the isolated network may increase and stabilize the frequency of oscillations. To test this hypothesis, we recorded from the isolated suprasylvian gyrus (see Fig. 1c
and Materials and Methods). A summary of the results obtained in these experiments (n = 6) is presented in Figure 8
. Field potential recordings from the intact cortex revealed the presence of the cortically generated slow oscillation, accompanied by spindles of thalamic origin (Steriade et al., 1993c
; Contreras and Steriade, 1995
), in simultaneous recordings from seven cortical sites (Fig. 8a
). Following the isolation of the suprasylvian gyrus, recording electrodes were placed into the same cortical sites. The frequency of recorded slow activity was similar to the frequency of the slow oscillation, but spindles were absent because thalamocortical projections were interrupted (Fig. 8b
). An example of intracellular activity recorded from the isolated gyrus is shown in Figure 8c
. Neurons were hyperpolarized during the depth-positive component of the field potential and were depolarized, and fired action potentials, during the depthnegative field potentials, as found in intact cortex.
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Discussion |
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The greatly increased incidence of IB neurons may be ascribed to the reduction in synaptic activity within small slabs. One of the documented properties of IB neurons is their transformation to an RS-type pattern by synaptic activation and depolarization during brainstem-induced arousal (Steriade et al., 1993a), mainly due to the activation of metabotropic glutamate and cholinergic receptors (Wang and McCormick, 1993). In recent intracellular recordings during natural states of vigilance in behaving cats, the incidence of IB neurons was <5% (Steriade et al., 1999
), consistent with the hypothesis proposed above.
Whereas action potentials were absent between the largeamplitude depolarizing events, separated by very long periods of neuronal silence, SDPs (probably minis) occurred at high frequencies. In recent studies conducted in vivo and in cultures, the TTX-resistant minis were found to be sensitive to GABAA or AMPA antagonists (Paré et al., 1997) and were implicated in the maintenance of dendritic spines (McKinney et al., 1999
). The spontaneously occurring SDPs and the non-linear amplification of small amplitude signals contribute to the generation of large depolarizing events, occasionally superimposed by action potentials, as shown here in isolated slabs. It is likely that the depolarization of neuronal soma by subthreshold current pulses (see Fig. 4
) activates INa(p), which occurs ~10 mV more negative than the transient Na+ current (Stafstrom et al., 1982
, 1985
; Thomson et al., 1988
). The AHP following the action potentials results in a large conductance increase that significantly decreases the slow regenerative INa(p) (Schwindt et al., 1988
). As soon as action potentials are generated, and even more so with spike-bursts generated by IB neurons, the non-linear amplification is shunted by AHPs and feedback synaptic activity. Computer simulations support the hypothesis that intrinsic currents amplify small incoming signals during the silent periods.
The activity in the slab propagated with a velocity that was in a range similar to that previously reported from studies on cell cultures prepared from the cortex of embryonic rats (Maeda et al., 1995) and in disinhibited slices (Chagnac-Amitai and Connors, 1989
). EPSPs reaching the neurons at a relatively hyperpolarized level do not elicit spikes but activate INa(p), which may lead to spike generation delayed by 3050 ms from the EPSP onset. Under these conditions, only a few synapses are needed to delay the response by hundreds of milliseconds, as in Figure 4
. Thus, during the silent states of the isolated slabs as well as during the prolonged hyperpolarizations characterizing the state of sleep or anesthesia, the SDPs, delayed spiking and mutual facilitatory connections are responsible for the propagation at the onset of active periods. This propagation may also be mediated by the abundant intracortical connections within the cat suprasylvian gyrus, as shown both morphologically (Avendaño et al., 1988
) and electrophysiologically (Amzica and Steriade, 1995b
). Similar horizontal projections of pyramidal axons, spanning up to 8 mm, are found in the visual cortex (Gilbert, 1992
) as well as in other areas. The coherent membrane potential fluctuations recorded from neocortical neurons during the slow (<1 Hz) oscillation (Amzica and Steriade, 1995a
,b
) and other activities (Lampl et al., 1999
) are mediated by the same intracortical connections because these slow rhythms survive thalamectomy (Steriade et al., 1993c
).
Although large depolarizations were commonly found spontaneously or could be elicited by stimulating the slab, spontaneous slow oscillations were absent in small slabs; however, slow oscillations were present in larger isolated cortical territories, covering a full gyrus. Thus, the occurrence and maintenance of spontaneous oscillations may require a minimal number of neurons. Assuming a columnar density of ~160 000 neurons/mm2 in neocortex, >10 x 106 neurons (for a slab of 6 mm x 10 mm size) and >50 x 106 neurons (for an isolated gyrus of 30 mm x 20 mm size) were needed. The analytical model for the occurrence of spontaneous activity (see Materials and Methods) predicted that the frequency of spontaneous oscillations should be stabilized near the frequency level of slow cortical oscillations for networks containing more than ~100 x 106 neurons (see Fig. 9b). In network models of thalamic reticular neurons, the propensity for self-sustained oscillations also depended critically on the number of synapses in the network (Bazhenov et al., 1999
). Thus, there may be a general principle regarding the minimum size of network connectivity needed to achieve spontaneous, large-scale coherent activity in thalamocortical systems. In the model, this size depended on many parameters such as the average number of synapses on one cell and the probability and the amplitude of miniature EPSPs for each synapse, which need to be more accurately estimated from direct measurements (Murthy et al., 2000
).
In the above scenario, slow wave activity is driven by the spontaneously occurring coincidence of small depolarizing events, such as miniature excitatory postsynaptic potentials, or minis. Spontaneous miniature synaptic activity is caused by action-potential-independent release of transmitter vesicles and is regulated at the level of single synapses (Salin and Prince, 1996; Paré et al., 1997
). The frequency of spontaneous miniature synaptic events increases with the probability of evoked release in cortical neurons (Prange and Murphy, 1999
). Thus, the synapses with the highest probability of release (Murthy et al., 1997
) should make the largest contribution to initiating an action potential in a neuron. Glutamate application at synapses between hippocampal neurons produces long-term potentiation of the frequency of spontaneous miniature synaptic currents (Malgaroli and Tsien, 1992
), which suggests that the synapses with the highest rates of spontaneous miniature synaptic currents are the most likely to have been recently potentiated. During sleep the initiation of spikes could therefore occur in neurons with the largest number of recently potentiated synapses. If these spontaneously occurring minis are amplified by the intrinsic currents in dendrites, it may not take a large number of coincident events to initiate a spike. The spiking neuron would further need to recruit additional neurons connected to it; the ones nearest to threshold would be those depolarized as a consequence of minis, so that the recruited network would preferentially include cells that had been recently potentiated. Other factors that would influence recruitment include multiple synaptic boutons (Markram et al., 1997
), spike bursting, which may itself further potentiate recently activated afferent synapses by virtue of the burst in the postsynaptic cell (Paulsen and Sejnowski, 2000
), and efferent synapses that were recently potentiated. This interpretation is consistent with the observation that unilateral somatosensory stimulation prior to sleep in humans increases the power of low-frequency oscillations, but only on the side of the cortex that received stimulation (Kattler et al., 1994
).
The model shows how a single neuron could recruit an avalanche of activity in a selected subset of a previously silent recurrent network of cortical neurons and serve as the nucleus for the spread of activity to neighboring cortical territory. This sequence of events should start from a basal state of inactivity, when the silent cortex is primed for the type of sharp wave activity that has been observed in the hippocampus (Buzsáki, 1986). Thus, the slow oscillations characteristic of the cortex during sleep may be an emergent property of large corticothalamic systems that, surprisingly, may be triggered by activity originating in single neurons. One of the predictions of this model is that the frequency of slow oscillations should be temperature dependent, since the rate of miniature synaptic activity (Barrett et al., 1978
), and hence the probability of reaching threshold, should increase with temperature. The temperature dependence of the frequency of slow oscillations observed in hibernating hamsters is compatible with this prediction (Deboer, 1998
).
The relatively simple cortical network models examined here may not include features of the cerebral cortex needed to fully understand the genesis of slow cortical oscillations. Other explanations may also be compatible with the experimental data; nonetheless, the data and models form a consistent picture and further experimental studies are needed to test the predictions and refine the proposed mechanisms.
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Notes |
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Address correspondence to Professor M. Steriade, Laval University, School of Medicine, Laboratory of Neurophysiology, Quebec, Canada G1K 7P4. Email: mircea.steriade{at}phs.ulaval.ca.
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Appendix |
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![]() | (A1) |
![]() |
where Cm is the membrane capacitance and gL is the leakage conductance of the dendritic compartment, EL is the reversal potential, VD and VS are the membrane potentials of the dendritic and axo-somatic compartments, ID and IS are the sums of active intrinsic currents in axo-somatic and dendritic compartments, Isyn is a sum of synaptic currents and g is the conductance between axo-somatic and dendritic compartments. The area of an axo-somatic compartment was 106 cm2 for both PY and IN cells and the ratio between areas of the dendritic and axo-somatic compartments was = 165 for PY cells and
= 50 for IN cells. The model included a high density of the fast Na+ channels, INa, in axo-somatic compartment and a low density in the dendritic compartment. A fast potassium K+ current, IK, and persistent Na+ current, INa(p), were present in the axo-somatic compartment. A slow, voltage-dependent K+ current, IKm, a slow, Ca2+-dependent K+ current, IK(Ca), a high-threshold Ca2+ current, ICa, and a persistent Na+ current, INa(p), were included in the dendritic compartment. The passive parameters were Cm = 0.75 µF/cm2 , gL = 0.033 mS/cm2 , EL = 70 mV, g = 10 M
.
Intrinsic Currents
The ionic currents are described by the equation:
![]() | (A2) |
where the maximal conductances are gNa = 3000 mS/cm2, gK = 200 mS/cm2, gNa(p) = 0.060.07 mS/cm2 for axo-somatic compartment; gNa = 1.5 mS/cm2 , gKm = 0.01 mS/cm2, gNa(p) = 0.060.07 mS/cm2, gK(Ca) = 0.3 mS/cm2, gCa = 0.010.015 mS/cm2 for dendritic compartment. For all cells ENa = 50 mV, EK = -95 mV, ECa = 140 mV.
The gating variables m(t), h(t) for all of the ionic currents follow:
![]() | (A3) |
INa(p):
IK(Ca):
IKm:
ICa:
IK:
INa: .
For each cell the Ca2+ dynamic were described by a simple first-order model:
![]() | (A4) |
where [Ca] = 2.4 x 104 mM is the equilibrium intracellular Ca2+ concentration, A = 2 x 104 mM cm2/(ms µA) and
= 160 ms.
Synaptic Currents
GABAA and AMPA synaptic currents are given by
![]() | (A5) |
where gsyn is the maximal conductance and E is a depression variable. The reversal potential is EAMPA = 0 mV for AMPA receptors and EGABAA = 70 mV for GABAA receptors. The fraction of open channels [O] is calculated according to the kinetic equation
![]() | (A6) |
where (x) is the Heaviside function, t0 is the time instant of receptor activation. The parameters for the neurotransmitter pulse were amplitude A = 0.5 and duration tmax = 0.3 ms. The rate constants,
and ß, were
= 10 ms and ß = 0.25 ms for GABAA synapses and
= 0.94 ms and ß = 0.18 ms for AMPA synapses. E was calculated according to the interactive scheme (Tsodyks and Markram, 1997
):
![]() | (A7) |
where t is the time interval between nth and (n+1)th spike,
= 700 ms is the time constant of recovery of the synaptic resources and USE is the fractional decrease of synaptic resources after an action potential which was varied between 0.07 and 0.15.
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References |
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Alzheimer C, Schwindt PC, Crill WE (1993) Modal gating of Na+ channels as a mechanism of persistent Na+ current in pyramidal neurons from rat and cat sensorimotor cortex. J Neurosci 13:660673.[Abstract]
Amzica F, Steriade M (1995a) Short- and long-range neuronal synchronization of the slow (<1 Hz) cortical oscillation. J Neurophysiol 73:2038.
Amzica F, Steriade M (1995b) Disconnection of intracortical synaptic linkages disrupts synchronization of a slow oscillation. J Neurosci 15:46584677.[Abstract]
Amzica F, Steriade M (1997) The K-complex: its slow (<1 Hz) rhythmicity and relation with delta waves. Neurology 49:952959.[Abstract]
Andrade, R. (1991) Blockade of neurotransmitter-activated K+ conductance by QX-314 in the rat hippocampus. Eur J Pharmacol 199:25962.[ISI][Medline]
Avendaño C, Rausell E, Perez-Aguilar D, Isorna S (1988) Organization of the association cortical afferent connections of area 5: a retrograde tracer study in the cat. J Comp Neurol 278:133.[ISI][Medline]
Avoli M (1986) Inhibitory potentials in neurons of the deep layers of the in vitro neocortical slice. Brain Res 370:165170.[ISI][Medline]
Barrett EF, Barrett JN, Botz D, Chang DB, Mahaffey D (1978) Temperature-sensitive aspects of evoked and spontaneous transmitter release at the frog neuromuscular junction. J Physiol 279:25373[Abstract]
Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (1998) Computational models of thalamocortical augmenting responses. J Neurosci 18:64446465.
Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (1999) Self-sustained rhythmic activity in the thalamic reticular nucleus mediated by depolarizing GABAA receptor potentials. Nature Neurosci 2:168174.[ISI][Medline]
Burns BD (1950) Some properties of the cat's isolated cerebral cortex. J Physiol 111:5068.[ISI]
Buzsáki G (1986) Hippocampal sharp waves: their origin and significance. Brain Res 398:242252.[ISI][Medline]
Chagnac-Amitai Y, Connors BW (1989) Horizontal spread of synchronized activity in neocortex and its control by GABA-mediated inhibition. J Neurophysiol 61:747758.
Connors BW, Gutnick MJ, Prince DA (1982) Electrophysiological properties of neocortical neurons in vitro. J Neurophysiol 48:13021320.
Connors BW, Malenka RC, Silva LR (1988) Two inhibitory postsynaptic potentials, and GABAA and GABAB receptor-mediated responses in neocortex of rat and cat. J Physiol 406:443368.[Abstract]
Contreras D, Steriade M (1995) Cellular basis of EEG slow rhythms: a study of dynamic corticothalamic relationships. J Neurosci 15:604622.[Abstract]
Crill W. E. (1996) Persistent sodium current in mammalian central neurons. Annu Rev Physiol 58: 34962.[ISI][Medline]
Deboer T (1998) Brain temperature dependent changes in the electroencephalogram power spectrum of humans and animals. J Sleep Res 7:254262.[ISI][Medline]
Destexhe A, Paré D (1999) Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81:15311542.
Echlin FA, Arnett V, Zoll J (1952) Paroxysmal high voltage discharges from isolated and partially isolated human and animal cerebral cortex. Electroenceph Clin Neurophysiol 4:147164.[ISI]
Fatt P, Katz B (1952) Spontaneous subthreshold activity at motor nerve endings. J Physiol 117:109128.[ISI]
Fleidervish IA, Gutnick MJ (1996) Kinetics of slow inactivation of persistent sodium current in layer V neurons of mouse neocortical slices. J Neurophysiol 76:21252130.
Galarreta M, Hestrin S (1998) Frequency-dependent synaptic depression and the balance of excitation and inhibition in the neocortex. Nature Neurosci 1:587594.[ISI][Medline]
Gilbert CD (1992) Horizontal integration and cortical dynamics. Neuron 9:113.[ISI][Medline]
Golomb D, Amitai Y (1997) Propagating neuronal discharges in neocortical slices: computational and experimental study. J Neurophysiol 78:11991211.
Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:109113.
Gupta A, Wang, Y, Markram H (2000) Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science 287:273278
Hille B (1977) Local anesthetics: hydrophilic and hydrophobic pathways for the drug-receptor reaction. J Gen Physiol 69:497515.[Abstract]
Kay AR, Sugimori M, Llinás R (1998) Kinetic and stochastic properties of a persistent sodium current in mature guinea pig cerebellar Purkinje cells. J Neurophysiol 80:11671179.
Kattler H, Dijk DJ, Borbély AA (1994) Effect of unilateral somatosensory stimulation prior to sleep on the sleep EEG in humans. J Sleep Res 3:159164.[ISI][Medline]
Lampl I, Reichova I, Ferster D (1999) Synchronous membrane potential fluctuations in neurons of the cat visual cortex. Neuron 22:361374.[ISI][Medline]
Llinás R, Ribary U (1993) Coherent 40-Hz oscillation characterizes dream state in humans. Proc Natl Acad Sci USA 90:20782081.
Maeda E, Robinson HPC, Kawana A (1995) The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons. J Neurosci 15:68346845.[ISI][Medline]
Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363366.[ISI][Medline]
Malgaroli A, Tsien RW (1992) Glutamate-induced long-term potentiation of the frequency of miniature synaptic currents in cultured hippocampal neurons. Nature 357:134139.[ISI][Medline]
Markram H (1997) A network of tufted layer 5 pyramidal neurons. Cereb Cortex 7:523533.
Markram H, Lubke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213215.
McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J Neurophysiol 54:782806.
McKinney RA, Capgna M, Dürr R, Gähwiler BH, Thompson SM (1999) Miniature synaptic events maintain dendritic spines via AMPA receptor activation. Nature Neurosci 2:4449.[ISI][Medline]
Murthy VN, Sejnowski TJ Stevens CF (1997) Heterogeneous release properties of visualized individual hippocampal synapses. Neuron 18:599612.[ISI][Medline]
Murthy VN, Sejnowski TJ, Stevens C (2000) Dynamics of dendritic calcium transients evoked by quantal release at excitatory hippocampal synapses. Proc Natl Acad Sci USA 97:901906.
Nuñez A, Amzica F, Steriade M (1993) Electrophysiology of cat association cortical cells in vivo: intrinsic properties and synaptic responses. J Neurophysiol 70:418430.
Paré D, Lebel E, Lang EJ (1997) Differential impact of miniature synaptic potentials on the somata and dendrites of pyramidal neurons in vivo. J Neurophysiol 78:17351739.
Paré D, Shink E, Gaudreau H, Destexhe A, Lang EJ (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical neurons in vivo. J Neurophysiol 79:14501460.
Paulsen, O and Sejnowski TJ (2000) Natural patterns of activity and long-term synaptic plasticity. Curr Opin Neurobiol 10:172179.[ISI][Medline]
Prange O, Murphy TH (1999) Correlation of miniature synaptic activity and evoked release probability in cultures of cortical neurons. J Neurosci 19:64276438.
Redman S (1990). Quantal analysis of synaptic potentials in neurons of the central nervous system. Physiol Rev 70:165198.
Salin PA, Prince DA (1996) Spontaneous GABAA receptor-mediated inhibitory currents in adult rat somatosensory cortex. J Neurophysiol 75:15731588.
Schwindt PC, Spain WJ, Crill WE (1988) Influence of anomalous rectifier activation on afterhyperpolarization of neurons from cat sensorimotor cortex in vitro. J Neurophysiol 59:468481.
Schwindt PC, O'Brien JA, Crill WE (1997) Quantitative analysis of firing properties of pyramidal neurons from layer 5 of rat sensorimotor cortex. J Neurophysiol 77:24842498.
Stafstrom CE, Schwindt PC, Crill WE (1982) Negative slope conductance due to a persistent subthreshold sodium current in cat neocortical neurons in vitro. Brain Res. 236:221226.[ISI][Medline]
Stafstrom CE, Schwindt PC, Flatman JA, Crill WE (1984) Properties of subthreshold response and action potential recorded in layer V neurons from cat sensorimotor cortex in vitro. J Neurophysiol 52:244263.
Stafstrom CE, Schwindt PC, Chubb MC, Crill WE (1985) Properties of persistent sodium conductance and calcium conductance of layer V neurons from cat sensorimotor cortex in vitro. J Neurophysiol 53:153170.
Steriade M (1997) Synchronized activities in coupled oscillators in the cerebral cortex and thalamus at different levels of vigilance. Cereb Cortex 7:583604.[Abstract]
Steriade M, Amzica F, Nuñez A (1993a) Cholinergic and noradrenergic modulation of the slow (~0.3 Hz) oscillation in neocortical cells. J Neurophysiol 70:13851400.
Steriade M, McCormick DA, Sejnowski TJ (1993b) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679685.[ISI][Medline]
Steriade M, Nuñez A, Amzica F (1993c) Intracellular analysis of relations between the slow (<1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram. J Neurosci 13:32663283.[Abstract]
Steriade M, Amzica F, Contreras D (1996) Synchronization of fast (3040 Hz) spontaneous cortical rhythms during brain activation. J Neurosci 16:392417.[Abstract]
Steriade M, Timofeev I, Dürmüller N, Grenier F (1998a) Dynamic properties of corticothalamic neurons and local cortical interneurons generating fast rhythmic (3040 Hz) spike bursts. J Neurophysiol 79:483490.
Steriade M, Timofeev I, Grenier F, Dürmüller N (1998b) Role of thalamic and cortical neurons in augmenting responses and self-sustained activity: dual intracellular recordings in vivo. J Neurosci 18:64256443.
Steriade M, Timofeev I, Grenier F (1999) Intracellular activity of various neocortical cell-classes during the natural wake-sleep cycle. Soc Neurosci Abstr 25:1661.
Stevens CF (1993) Quantal release of neurotransmitter and long-term potentiation. Cell 72:5563.[ISI][Medline]
Thomson AM (1997) Activity-dependent properties of synaptic transmission at two classes of connections made by rat neocortical pyramidal axons in vitro. J Physiol 502:131147.[Abstract]
Thomson AM, Deuchars J (1997) Synaptic interactions in neocortical local circuits: dual intracellular recordings in vitro. Cereb Cortex 7:510522.[Abstract]
Thomson AM, Girdlesone D, West DC (1988) Voltage-dependent currents prolong single-axon postsynaptic potentials in layer III pyramidal neurons in rat neocortical slices. J Neurophysiol 60:18961907.
Thomson AM, West DC, Hahn J, Deuchars J (1996) Single axon IPSPs elicited in pyramidal cells by three classes of interneurones in slices of rat neocortex. J Physiol 496:81102.[Abstract]
Tsodyks MV, Markram H (1997) The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94:719723.
Wang Z, Cormick DA (1993) Control of firing mode of corticotectal and corticopontine layer V burst-generating neurons by norepinephrine, acetylcholine and 1S,3R-ACPD. J Neurosci 13:21992216.[Abstract]
Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393:440442.[ISI][Medline]