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1 Department of Neurology, University of Wisconsin, William S. Middleton Veterans Affairs Hospital, Madison, Wisconsin 53706; and 2 Laboratory of Neurophysiology, Laval University School of Medicine, Quebec City G1K 7P4, Canada
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Lytton, William W., Diego Contreras, Alain Destexhe, and Mircea Steriade. Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. J. Neurophysiol. 77: 1679-1696, 1997. In vivo intracellular recording from cat thalamus and cortex was performed during spontaneous spike-wave seizures characterized by synchronously firing cortical neurons correlated with the electroencephalogram. During these seizures, thalamic reticular (RE) neurons discharged with long spike bursts riding on a depolarization, whereas thalamocortical (TC) neurons were either entrained into the seizures (40%) or were quiescent (60%). During quiescence, TC neurons showed phasic inhibitory postsynaptic potentials (IPSPs) that coincided with paroxysmal depolarizing shifts in the simultaneously recorded cortical neuron. Computer simulations of a reciprocally connected TC-RE pair showed two major modes of TC-RE interaction. In one mode, a mutual oscillation involved direct TC neuron excitation of the RE neuron leading to a burst that fed back an IPSP into the TC neuron, producing a low-threshold spike. In the other, quiescent mode, the TC neuron was subject to stronger coalescing IPSPs. Simulated cortical stimulation could trigger a transition between the two modes. This transition could go in either direction and was dependent on the precise timing of the input. The transition did not always follow the stimulation immediately. A larger, multicolumnar simulation was set up to assess the role of the TC-RE pair in the context of extensive divergence and convergence. The amount of TC neuron spiking generally correlated with the strength of total inhibitory input, but large variations in the amount of spiking could be seen. Evidence for mutual oscillation could be demonstrated by comparing TC neuron firing with that in reciprocally connected RE neurons. An additional mechanism for TC neuron quiescence was assessed with the use of a cooperative model of 
-aminobutyric acid-B (GABAB)-mediated responses. With this model, RE neurons receiving repeated strong excitatory input produced TC neuron quiescence due to burst-duration-associated augmentation of GABAB current. We predict the existence of spatial inhomogeneity in apparently generalized spike-wave seizures, involving a center-surround pattern. In the center, intense cortical and RE neuron activity would be associated with TC neuron quiescence. In the surround, less intense hyperpolarization of TC neurons would allow low-threshold spikes to occur. This surround, an "epileptic penumbra," would be the forefront of the expanding epileptic wave during the process of initial seizure generalization. Therapeutically, we would then predict that agents that reduce TC neuron activity would have a greater effect on seizure onset than on ongoing spike-wave seizures or other thalamic oscillations.
The computer simulations presented here are used to explore possible basic mechanisms underlying an unexpected finding from intracellular recordings in vivo, namely, that an important proportion of thalamocortical (TC) neurons is quiescent during cortically initiated seizures. These seizures consisted of spike-wave (SW) complexes at 2-4 Hz, sometimes associated with faster activities at 10-15 Hz (Steriade and Contreras 1995 Simulations were run on a Sun Sparcstation 10s and Intel Pentium PCs with the use of the NEURON simulator (Hines 1993
More than 500 neurons were recorded intra- and extracellularly in various cortical areas, the rostrolateral district of the RE nucleus, and various dorsal thalamic nuclei (see Steriade and Contreras 1995 Physiology: quiescent TC neurons in vivo
The spontaneous seizures that were recorded were complex mixtures of electrographic patterns including typical SW and polyspike-wave patterns at 2-4 Hz. Seizures were recognized by their abrupt start and termination, by the large increase in the amplitude of the waves, and by a high degree of neuronal synchronization (Fig. 1). During seizures, cortical neurons showed strong depolarizations constituting paroxysmal depolarizing shifts, occurring in close time relation with the spike components of the electroencephalogram (EEG).
Computer model: two modes of oscillation
Thalamic activity in vivo generally features sparse TC activity with relatively greater RE activity. Therefore we explored in detail a computer model that demonstrated the two modes that feature RE activity: the mutual oscillation mode, in which both neuron types fire, and the quiescent mode, in which only the RE fires. These two modes depended primarily on the strength of inhibition from RE to TC.
Transition between modes
Given the similar overall inhibitory drive into the TC neuron in the two modes, switching between modes was relatively easy. Simulated cortical stimulation could switch between modes in either direction (Fig. 5). The drive into the RE neuron produced in TC neurons a prolonged IPSP that could be long enough to initiate or maintain the quiescent state (1st 2 stimulations), or deep enough to trigger a low-threshold spike that switched to the mutual state (3rd stimulation). In the latter case, the failure of the RE neuron to develop a full burst in the cycle following the stimulation (Fig. 5,
Degree of quiescence is associated with inhibitory strength
To investigate the generality of the mutual and quiescent modes, we examined other parameter sets. All parameter sets that produced intrinsically oscillatory neurons of both types could produce mutual oscillation. From there, increasing GABAB strength invariably produced TC neuron quiescence. Although GABAB strength was the prime determinant of the degree of quiescence in most parameter sets, GABAA strength could also play a role in cases in which the RE neuron showed prolonged periods of high-frequency regular firing that permitted temporal summation of the relatively brief GABAA IPSPs. We performed further investigations on a parameter set that showed a complex repertoire of intrinsic activity that included multiple burst sizes and variable interburst intervals.
Network simulations
A minimal demonstration of the relevance of the TC-RE pair requires that 1) behavior similar to that seen in the two-neuron network can be seen in a larger network and 2) these similarities reflect comparable physiological relationships between the participating neurons. We simulated a multicolumnar RE neuron-TC neuron network to assess this (Fig. 10A). Activity in the TC neurons ranged from activity similar to that of the two-neuron mutual oscillation (top trace) to complete quiescence (bottom trace). Overall, the activity was similar to that seen with the second parameter set (Fig. 8) despite the much greater complexity of connections, the convergent influence on single TC neurons, and the mutual inhibition between the RE neurons. In general, the degree of activity in a TC neuron correlated with the amount of inhibitory input into that cell (Fig. 10B). However, this relationship was highly variable. This indicated that dynamic factors complemented connection strength in determining mutual oscillation and quiescent episodes.
Synaptic factors could contribute to TC neuron quiescence
A complementary mechanism for TC neuron quiescence was investigated on the basis of a cooperative model of GABAB response. Unlike GABAA currents that appear even with minimal stimulation (Mody et al. 1994 In this paper we have documented a surprisingly extensive TC quiescence associated with SW seizures in vivo. We have considered the implications of this finding in a variety of simple two-neuron networks that highlight the duality of the inhibitory influence from RE to TC. This duality permits the network to produce different states, either quiescent or oscillatory, despite similar patterns of input, and to produce spontaneous or delayed stimulus-associated transitions between states. Additional cooperative effects in inhibitory synapses may also contribute to these transitions.
RE neuron governs oscillatory mode
RE neurons and local thalamic interneurons are the inhibitory elements of the thalamic circuit. Although interneurons might also be involved in thalamic oscillations (Zhu et al. 1995 Parameter variation produces large effects
Relatively minor changes to only 3 of 20 intrinsic parameters produced a vastly different firing pattern (compare Figs. 4 and 8). To get this effect, the T calcium channel density was changed in the TC neuron and RE neuron by 10 and 43%, respectively, and the rate of the RE neuron calcium pump was decreased by 50%. The latter change, largest by percentage, is relatively minor when one considers that this would occur with only a 6.3°C reduction in temperature, assuming a Q10 of 3. Network behavior was particularly sensitive to a change in the calcium pump, because the consequent increase in calcium levels increased the late effects of bursting via coupling to calcium-sensitive potassium channels. This remote effect of bursting promoted the greater irregularity seen with this parameter set. The increase in calcium density in the RE neuron compensated to maintain bursting in the presence of these increased hyperpolarizing forces. The slight increase in TC neuron calcium channel, needed to maintain robust bursting, underlines the interdependence of activity in the two neurons despite the dominance of the RE neuron.
Thalamic circuit in a larger network
The existence of circuit components that can be regarded as partially autonomous is of value in providing building blocks for developing and testing notions of large-scale corticothalamic circuitry. The concept of the cortical column has been of great value in simplifying our understanding of the cortex. Our findings suggest how a somewhat different concept of modular organization might also be of value for understanding the thalamus. Such a module would be headed up by one or a few RE neurons that would control a larger set of TC neurons.
Dynamic factors help determine activity
The coexistence of two modes of TC-RE interaction is consistent with a situation in which seemingly minor influences can produce large-scale shifts in activity. Determinants of firing pattern are generally classified as either synaptic or modulatory. Both of these mechanisms are relatively readily dealt with experimentally. A third influence on firing patterns, which we have illustrated here, involves nonlinear dynamics. Relatively simple dynamic influences involve interactions between a postsynaptic potential and the intrinsics of the postsynaptic neuron that allow postsynaptic potentials to have a paradoxical effect (Lytton 1991 Synaptic mechanisms could increase inhibitory tone
A specific synaptic mechanism was also assessed to further explain TC neuron quiescence through burst strength dependency of GABAB responses. It has been proposed that the stronger discharges of thalamic cells following application of bicuculline could result from disinhibition of interneurons projecting to TC cells with GABAB receptors only (Soltesz and Crunelli 1992 Experimental predictions from these studies
The studies' main results that would be experimentally testable are as follows.
Generalized epilepsy and the epileptic penumbra
Our major prediction from both the experiments and modeling presented here is that SW epilepsy may be expected to show inhomogeneities in the epileptic area such that some thalamic territories are more active than others. Paradoxically, the areas of greatest TC neuron activity are not expected to correspond to the hottest epileptic zones. On the contrary, we suggest that the areas that are subject to epileptic overdrive from cortex will be the areas with the highest percentage of thalamic quiescence. This prediction should be experimentally observable with the use of multisite recordings. Clinical correlation might also be obtained with the use of positron emission tomography or functional magnetic resonance imaging.
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
). In that previous study, simultaneous impalements of TC and cortical cells performed during paroxysms developing from sleep patterns showed that a large number (60%) of TC neurons displayed a sustained hyperpolarization during the cortical seizure. These hyperpolarizations were associated with repetitive inhibitory postsynaptic potentials (IPSPs) coincident with paroxysmal depolarizations and spike bursts in cortical cells, and with long (200-300 ms) spike bursts in thalamic reticular (RE) cells (Steriade and Contreras 1995). After seizure cessation, TC neurons returned to resting membrane potential.
,b). This phenomenon has been shown to be due to the T-type Ca2+ channel (Coulter et al. 1989; Crunelli et al. 1989; Hernandez-Cruz and Pape 1989; Suzuki and Rogawski 1989). The T channel can produce intrinsic repetitive bursting in TC neurons (Leresche et al. 1991; McCormick and Pape 1990). Intrinsic bursting also occurs in RE neurons, but the mechanism is somewhat different (Destexhe et al. 1996b; Huguenard and Prince 1992). One minimal circuit that can give rise to coordinated oscillations is a circuit of isolated RE neurons that is effective in producing sleep spindles (Steriade et al. 1987) and whose synchronizing properties have been modeled (Destexhe et al. 1994a,b; Golomb et al. 1994). Corticothalamic projections and connections between TC and RE cells tend to reinforce spindle oscillations (Contreras and Steriade 1996; Destexhe et al. 1993b; Steriade et al. 1972, 1993; von Krosigk et al. 1993; Wang et al. 1995).
,b) have demonstrated that population activity can emerge through the intermittent activation of single neurons whose individual activity was not rhythmic. This resulted from the fact that an individual neuron would be involved in one cycle of an ongoing oscillation and then not involved again for many cycles. Subsequently the same neuron would fire together with a group of neurons that differed from those firing together previously. Therefore this population phenomenon consisted of different populations on different cycles.
). To some, the very goal of reductionism in complex systems may seem misguided. Experimentally, however, the reductionistic approach to corticothalamic networks has proven extremely successful, pinpointing essential elements determining oscillatory activity (Steriade et al. 1993). In the present paper we isolate a rather simple circuit, namely the TC-RE reciprocal interaction, and also describe the influence of corticothalamic volleys. The two-neuron TC-RE model has limitations because it omits the intra-RE connections that have been described morphologically (Deschenes et al. 1985; Yen et al. 1985), electrophysiologically (Bal and McCormick 1993; Huguenard and Prince 1994; Ulrich and Huguenard 1996), and in computer network models (Destexhe et al. 1994a; Golomb et al. 1994). Therefore we reassessed the TC-RE interaction in the context of a larger model that includes these and other connections. Because RE neurons are GABAergic, reciprocally connected to TC neurons, and highly active during both wake and sleep states as well as in various experimental models of thalamic oscillations (Steriade et al. 1986), it seems likely that they are a major source of hyperpolarizing postsynaptic potentials in TC neurons. Indeed, after disconnection from RE inputs, prolonged, rhythmic, spindle-related TC neuron IPSPs show dramatically reduced duration and rhythmicity (Steriade et al. 1985). We therefore posit that, at intermediate strengths, these hyperpolarizing potentials could serve to prime LTSs in TC neurons, whereas at higher strengths these hyperpolarizations would render TC neurons inactive. Thus the RE neuron input would be required for TC activity in one setting while precluding activity in another setting.
).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
). Each neuron was represented by a single compartment with a 1,000-µm2 area.
). The TC neuron had the following voltage-sensitive channels and typical maximal conductances 
(in mS/cm2) fast sodium conductance, 0.03; delayed rectifier conductance, 0.002; T channel conductance, 0.001; H conductance, 1.2 × 10
4. In the RE neuron the values were (in mS/cm2) fast sodium conductance, 0.1; delayed rectifier conductance, 0.01; T channel conductance, 1.75 × 103; slow calcium-dependent potassium channel, 0.005; nonspecific calcium-sensitive cation channel, 3.5 × 104. Calcium removal in both neuron types was effected by a previously described calcium pump (Destexhe et al. 1993). The parameter adjustments required to go to the second parameter set used for Figs. 8 and 9 were as follows (in mS/cm2): 10% increase in T in the TC neuron (0.0011), 43% increase in T in the RE neuron (0.0025), and 50% decrease in the Michaelis-Menten rate of the calcium pump (from 1 × 104 to 5 × 105).
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FIG. 8.
Increasing inhibitory strength favors quiescent mode. Each pair of traces shows RE neuron activity at top and TC neuron activity at bottom. Total GABAergic strength increases from A to D. A and B can be classified as a mutual mode oscillation, whereas D is quiescent mode. C shows that mutual activity can give way to quiescence. Arrows in B: 3-burst RE motif similar to that seen in D.
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FIG. 9.
Cortical resetting similar to Fig. 6 with the use of alternate parameter set. Only TC neuron activity is shown; filled circles show time of cortical stimulation. With no stimulation (top trace), TC neuron shows a 2-s quiescent period. Second and 4th traces: quiescent period moved forward with cortical stimulation. Third trace: quiescent period little changed. Fifth trace: elimination of the quiescent period with stimulation.
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) components. The connection from RE to TC utilized -aminobutyric acid-A (GABAA) and GABAB components. All synapses were parameterized with the use of the two-state model previously described (Destexhe et al. 1994c; Lytton 1996). Parameters were as follows. AMPA: = 1.1/ms·mM, 
= 0.19/ms, Cdur = 1.1 ms, reversal potential(Erev) = 0 mV, = 0.002 µS. NMDA: = 0.072/ms·mM, = 0.0066/ms, Cdur = 5.0 ms, Erev = 0 mV, = 0.0 µS (used for stimulation only). GABAA: = 0.53/ms·mM, = 0.18/ms, Cdur = 1.0 ms, Erev = 
90 mV, = 0.002 µS. GABAB: = 0.01/ms·mM, = 0.005/ms, Cdur = 150 ms, Erev = 95 mV, = 0.0055 µS.
0.2 and 2 nS, respectively) and AMPA excitation of the TC ( 2 nS). In Fig. 12, cortical stimulation was simulated with repetitive AMPAergic activation of the RE neuron alone. In this model, a different GABAB model was used, with inclusion of cooperativity in the activation kinetics (Destexhe and Sejnowski 1995). Details of the simulation method in this figure are given in Destexhe et al. (1996). Most oscillations were initiated with a brief hyperpolarizing pulse in the TC neuron (Fig. 4A).
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FIG. 12.
Mutual oscillation and quiescent mode produced with the use of frequency-sensitive GABAB synapse model with varying strength of simulated cortical stimulation of RE neuron through -amino3 - h y d r o x y - 5 - m e t h y l - 4 - i s o x a z o l e p r o p i o n i cacid (AMPA) receptors. A: 10-Hz stimulation at low intensity (1 spike per cortical stimulation) produced the mutual oscillation. The TC neuron followed the stimulation at a subharmonic of 5 Hz. B: same frequency stimulation at stronger intensity (3 spikes per stimulus) produced the quiescent oscillation. IPSPs occurring at 10 Hz coalesced so that no TC neuron rebound was seen.
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FIG. 4.
Mutual and quiescent oscillations in the 2-neuron network. Dashed lines: resting membrane potential. A: mutual oscillation between RE neuron and TC neuron. Bursting occurs nearly in phase because the excitatory input from the TC neuron is sufficient to cause an almost immediate burst in the RE neuron. Note the subthreshold depolarizing hump ( 
) between each burst. Middle inset shows that the TC neuron burst produced immediate excitation of the RE neuron, causing it to fire (scale: 100 ms, 5 mV). The RE neuron hyperpolarizes the TC neuron, facilitating a subsequent low-threshold spike. Right inset shows the 3-spike RE burst in this mode. B: quiescent oscillation involves tonic inhibition of the TC neurons by the intrinsically bursting RE neurons. Right inset shows the single spike RE burst.
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FIG. 10.
Different degrees of involvement of individual TC neurons in ongoing activity in the large columnar network. A: some neurons appear to be involved in ongoing mutual oscillation (top 2 traces), whereas others burst much less frequently or are entirely silent (bottom trace). B: number of spikes during 8 s in the multicolumnar network as a function of the strength of -aminobutyric acid-A (GABAA), GABAB, or summed GABAA + GABAB input into each TC neuron. Although the number of spikes declines with increasing inhibitory strength, very different spike numbers can be found with neurons seeing similar inhibition.
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FIG. 11.
Relation of TC neuron to RE neuron activity during transient synchronous activity in a large columnar network. TC neuron shown at bottom projects to each of the 3 RE neurons shown. Dashed extension of TC spike: TC activity generally stimulates activity in each of the RE neurons in a manner suggestive of the mutual oscillation mode. Histogram at top: binned activity in the TC neurons. Filled circles: precise spike time of each neuron. Open circles: spike times for the TC neuron shown in bottom trace.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). Of these, 124 neurons were entrained in spontaneous seizures. In computer simulation, ~600 models were evaluated. Four parameter sets were explored in detail out of many that were assayed.
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FIG. 1.
Spontaneous seizure in intracellularly recorded cortical and thalamocortical (TC) neurons under ketamine-xylazine anesthesia. Cortical cell from motor cortex, together with the surface and depth electroencephalogram (EEG) from the vicinity, was recorded simultaneously with a TC neuron from the ventrolateral (VL) nucleus. The spontaneous development from the slow sleep oscillation into a polyspike-wave epilepsy pattern was reflected as high-amplitude negative polyspikes in the depth EEG that reversed polarity at the surface. Cortical cell showed paroxysmal depolarizing shifts of up to 30 mV related to the depth EEG negative deflections and TC neuron showed repetitive inhibitory postsynaptic potentials (IPSPs) at 10 Hz. Polyspikes recurred at 2-3 Hz. During the seizure the TC neuron remained quiescent with the exception of a brief (0.65 s) period of silent EEG that was accompanied by TC neuron depolarization and firing of single spikes (see detail 2).
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FIG. 2.
Spontaneous polyspike-wave seizures are reflected by repetitive IPSPs and quiescent membrane potential in a large proportion of TC neurons. A: example of a VL TC neuron at rest, recorded simultaneously with the depth EEG from the precruciate motor cortex, showing no rebound bursts during the 2-Hz polyspike-wave seizure. Fast IPSPs at 10 Hz ( 
), related to EEG polyspikes, characterized the activity of this TC neuron during the seizure. B: depth EEG from the precruciate cortex was recorded together with an extracellularly recorded thalamic reticular (RE) neuron from the rostrolateral sector and an intracellularly recorded VL TC neuron. Depth EEG polyspikes at 2 Hz were associated with RE neuron bursts lasting 150-300 ms, and repeated IPSPs in TC neurons that on 2 occasions led to a low-threshold spike (LTS) in isolation with no sodium spikes (
). A burst from the RE neuron is expanded at right (*).
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FIG. 3.
Seizures in a single animal showed marked similarities between events (A and B). Motor cortical and VL TC neuron were recorded simultaneously, together with the depth and surface EEG from motor cortex, during spontaneous 2-Hz polyspike-wave seizures. Although RE neurons were recorded later rather than simultaneously, seizure stereotypy was so pronounced that the bursts aligned perfectly. Prolonged bursting in RE neurons was due to strong, rhythmic excitatory postsynaptic potentials from cortex or from active TC neurons. This was related to repetitive IPSPs in TC neurons that generated TC neuron quiescence during the seizures.
); 2) 60% of TC neurons were quiescent during the seizure and exhibited an almost continuous synaptic bombardment. These synaptic potentials mainly consisted of IPSPs (Fig. 1, details 1 and 2, ). Excitatory postsynaptic potentials of cortical origin were also seen. Occasionally the TC neuron could "escape" from the prolonged synaptic bombardment and generate a low-threshold spike without superimposed fast sodium action potentials (Rush and Rinzel 1994). Hyperpolarization of TC neurons was a mixture of sustained, tonic hyperpolarization of 10-15 mV (Fig. 2A, after the right angle arrow) and phasic hyperpolarizations recurring at ~10 Hz ( in Figs. 1 and 2). These phasic IPSPs coincided with paroxysmal depolarizing shifts in the cortical neuron (Fig. 1).
).
). This brief depolarization represented T channel current that fell short of the threshold needed to trigger sodium spikes. The failure to form a burst could be traced back to residual inactivation from the preceding large, partially TC-driven burst. The subthreshold depolarization, although not large enough to produce a full burst, was sufficient to further inactivate the T channel. Therefore another delay, comparable with that occurring between the burst and this subthreshold depolarization, occurred before the neuron would burst again. During this delay, T channel deinactivation increased to the point where a full burst could be generated on the following cycle. This gave a frequency that was half of what it would be had these subthreshold depolarizations resulted in bursts, and approximately half of that seen with the oscillation shown in Fig. 4B.
; Bal and McCormick 1993; Destexhe et al. 1994c). TC neuron silence was due both to the frequency and the size of the RE neuron bursts. The smaller bursts were associated with smaller IPSPs, albeit still of sufficient size to generate an LTS. The higher interburst frequency did not leave sufficient time for this LTS to develop however. In vivo, still faster bursting appears to be caused by cortical driving rather than by intrinsic mechanisms (Steriade and Contreras 1995).
) permitted the development of a TC neuron burst, leading to the mutual mode.
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FIG. 5.
Repeated cortical stimulation ( 
) can repeatedly switch oscillation mode. The 1st stimulation switches from mutual to quiescent mode; the 2nd is ineffectual; the 3rd switches back to mutual, and the 4th yet again to quiescent. The failure of the RE neuron to reach threshold after the 3rd stimulation () permits the shift to the mutual mode.
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FIG. 6.
TC neuron activity with cortical stimulation ( ) at different phases in the cycle initiates quiescent mode at different intervals. Only the TC neuron activity is shown. First and 5th traces: stimulation producing no alteration in the ongoing mutual oscillation. Second, 3rd, and 4th traces: onset of quiescent mode after 3, 2, and 7 cycles, respectively. Dashed line: time of next cycle without stimulation.
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FIG. 7.
Analysis of spontaneous transition from mutual to quiescent mode with bursting viewed in the RE neuron T channel m/h plane. A: RE neuron voltage trace (top) and TC neuron voltage trace (bottom, truncated) show 8 bursts of mutual activity followed by switch into the quiescent state. Letters next to portions of each cycle give the key for the phase planes below. Interburst intervals are labeled a are depicted in Ba; the number indicates which cycle (1, outer; 2, inner). Alternating bursts labeled b and c are shown in Bb and Bc. Initial oscillation appears to be approximately period 2 with burst alternating with an interburst depolarization. B: apparent approximate period 2 oscillation illustrated to be period 4: 4 cycles occur before the cycle repeats. In each phase plane, abscissa gives the value of mT (T channel activation), ordinate the value of hT (T channel inactivation). All trajectories run clockwise. Interbursts (1 and 2) alternated between large cycles (1) and small cycles (2). Burst in Bb showed a progression of gradually increasing hT, whereas burst in Bc was more coherent and showed no regular shift. The inner loop labeled 2 gradually collapsed to terminate the oscillation. The subsequent interburst (3) was similar in extent to the cycle labeled 1. Sequential cycles are indicated in the following order: thin solid line, thick dashed line, thin dashed line, thick solid line. C: inner and outer interburst cycles seen in the voltage-calcium plane corresponded to Ba, 2 and 1, respectively. The collapse of the inner cycle is not as clear as in Ba, 2, however.
), GABAB-mediated responses require high stimulation intensities to be evoked, as seen in both hippocampal (Davies et al. 1990; Dutar and Nicoll 1988) and thalamic slices (Huguenard and Prince 1994; Sánchez-Vives et al. 1995). The synaptic model used in this simulation utilized cooperativity in the activation of GABAB-mediated current to produce this effect (Destexhe and Sejnowski 1995).
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
), the RE neuron appears to play a major role in several preparations (Steriade et al. 1985, 1987; von Krosigk et al. 1993). Therefore it is natural to consider it the primary candidate for producing an ongoing hyperpolarization leading to TC quiescence.
) suggests a concept of RE neuron dominance in these oscillations. The RE neuron control of oscillation mode shown in this paper reinforces this notion. In the first model shown, rapid RE neuron bursting produced the quiescent mode by reinforcing TC neuron hyperpolarization before the TC neuron was able to burst. Less frequent RE neuron bursting produced the mutual mode, in which TC neuron bursting fed back and helped determine the frequency of the RE neuron. In the cooperative GABAB model, it was the number of spikes in the RE burst that controlled TC activity by providing a prolonged activation of GABAB currents.
).
; Golomb et al. 1996). However, the present model had a restricted longitudinal extent and did not include topographic axonal projections between TC and RE cells, which are prerequisites for propagating phenomena. A common conclusion emphasized by these models was the critical role for the RE nucleus in controlling the type of oscillation exhibited by the thalamic network. In the present paper we document further this critical role by showing that RE neuron activity can also determine patterns of oscillatory activity with quiescent TC neurons.
; Lytton and Sejnowski 1991). More complex dynamic interactions involve subtle changes in timing and cumulative shifts in hidden variables (Fig. 7). In a milieu that is inherently chaotic by virtue of its size and complexity, these may be very hard to explore in simulations and nearly impossible to explore experimentally (Hirsch and Baird 1995).
; Wallenstein 1994). In a previous study, we proposed an alternative explanation based on burst strength dependency of GABAB responses (Destexhe and Sejnowski 1995). The transformation of 9- to 11-Hz spindle oscillations into 3- to 4-Hz oscillations of higher synchrony in thalamic networks (Kim et al. 1995) could also be reproduced by this model (Destexhe et al. 1996).
). We additionally predict a significantly more powerful dominant frequency in the power spectrum of RE neuron activity associated with quiescent TC neurons.
). Increasing GABAA strength with benzodiazepines would not be efficacious in producing increased quiescence.
). At the focus, intense cortical and RE neuron activity would produce relative TC neuron quiescence as stated above. In the penumbra, RE neuron divergence would produce less intense hyperpolarization in TC neurons, allowing LTSs and the appearance of the mutual oscillation. This center-surround organization should be apparent with an active center in cortex and a corresponding quiescent center in thalamus. Such inhomogeneities might be transiently present on seizure initiation as one or more foci quickly coalesce and synchronize in a process of generalization. The rapidity of this process would make it hard to detect. Inhomogeneities would also occur in the established seizure either as a result of the dynamic properties that we have shown or in response to local accumulation of extracellular modulators such as adenosine or potassium. Indeed, preliminary data support the existence of such center-surround activity in thalamus (Contreras and Steriade, unpublished results).
,b; Gloor 1979). A generalized epilepsy of spontaneous occurrence must start in one or several places and subsequently spread and synchronize, as has been demonstrated in an animal model of SW epilepsy (Steriade and Amzica 1994). Our hypothesis suggests that this process of progressive synchronization might involve the rapid spread of an epileptic penumbra of bursting TC neurons, followed by a period of relative TC neuron quiescence in the established seizure. This distinction between seizure onset and the established seizure would have therapeutic implications. Agents such as ethosuximide, which depress the TC neuron T channel, would be expected to suppress seizure initiation and spread while having relatively less effect on established epileptic and nonepileptic oscillations (Kellaway et al. 1990).
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ACKNOWLEDGEMENTS |
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This research was supported by the Office of Research and Development, Medical Research Service of the Department of Veterans Affairs, and by the National Institute of Neurological Disease and Stroke. D. Contreras, A. Destexhe, and M. Steriade were supported by grants from the Medical Research Council of Canada, Human Frontier Science Program, and the Savoy Foundation.
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FOOTNOTES |
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Address for reprint requests: W. W. Lytton, Dept. of Neurology, University of Wisconsin, William S. Middleton Veterans Affairs Hospital, 1300 University Ave., MSC 1720, Madison, WI 53706.
Received 20 September 1996; accepted in final form 6 December 1996.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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a program for simulation of nerve equations.
In: Neural Systems: Analysis and Modeling,
edited by
and F. Eeckman
. Norwell, MA: Kluwer, 1993, p. 127-136This article has been cited by other articles:
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 A. DESTEXHE and T. J. SEJNOWSKI Interactions Between Membrane Conductances Underlying Thalamocortical Slow-Wave Oscillations Physiol Rev, October 1, 2003; 83(4): 1401 - 1453. [Abstract] [Full Text] [PDF]
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M. Steriade Impact of Network Activities on Neuronal Properties in Corticothalamic Systems J Neurophysiol, July 1, 2001; 86(1): 1 - 39. [Abstract] [Full Text] [PDF]
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 M. Steriade The GABAergic reticular nucleus: A preferential target of corticothalamic projections PNAS, March 16, 2001; (2001) 71051998. [Full Text]
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M. Steriade and F. Amzica Intracellular Study of Excitability in the Seizure-Prone Neocortex In Vivo J Neurophysiol, December 1, 1999; 82(6): 3108 - 3122. [Abstract] [Full Text] [PDF]
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 A. Destexhe Spike-and-Wave Oscillations Based on the Properties of GABAB Receptors J. Neurosci., November 1, 1998; 18(21): 9099 - 9111. [Abstract] [Full Text] [PDF]
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M. Steriade and D. Contreras Spike-Wave Complexes and Fast Components of Cortically Generated Seizures. I. Role of Neocortex and Thalamus J Neurophysiol, September 1, 1998; 80(3): 1439 - 1455. [Abstract] [Full Text] [PDF]
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D. Neckelmann, F. Amzica, and M. Steriade Spike-Wave Complexes and Fast Components of Cortically Generated Seizures. III. Synchronizing Mechanisms J Neurophysiol, September 1, 1998; 80(3): 1480 - 1494. [Abstract] [Full Text] [PDF]
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I. Timofeev, F. Grenier, and M. Steriade Spike-Wave Complexes and Fast Components of Cortically Generated Seizures. IV. Paroxysmal Fast Runs in Cortical and Thalamic Neurons J Neurophysiol, September 1, 1998; 80(3): 1495 - 1513. [Abstract] [Full Text] [PDF]
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M. Steriade The GABAergic reticular nucleus: A preferential target of corticothalamic projections PNAS, March 27, 2001; 98(7): 3625 - 3627. [Full Text] [PDF]
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