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 γ-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). 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.
A major feature in the dynamics of thalamic neurons is the low-threshold Ca2+ spike (LTS) that follows a relatively prolonged hyperpolarization (Jahnsen and Llinas 1984a,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).
The neural activity in epilepsy suggests a high degree of synchrony among populations involved. The extreme activity and adverse outcome seen in status epilepticus may well be manifestations of such high neuronal involvement. Other types of epilepsy are less detrimental. In absence epilepsy, a type of epilepsy that produces SW activity in the thalamus, it is remarkable how rapidly a patient can go from normal cognitive activity to generalized SW complexes and back to cognition, seemingly without skipping a thought. This suggests that many neurons participate in the seizure through inhibition rather than extreme excitation, leaving them in a better position to resume normal function after ictal cessation. Computer simulation studies have demonstrated that apparent widespread population activity may in some cases be surprisingly sparse. In hippocampal simulations, Traub et al. (1987a,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.
In studying a complex system, the appropriate level for meaningful investigation is not known in advance (Lytton and Sejnowski 1992). 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.
In this study we have deliberately avoided the exhaustive reproduction of detailed biophysical data, concentrating instead on exploring dynamics in networks that are capable of generating quiescence in TC neurons. The advantage of this approach is that we were able to explore dynamics in detail to identify critical parameters that suggest general predictions to be tested experimentally. The disadvantage of this simplifying approach is the need to cross-check results among several models. We start with a simple model that proposes a dual role for RE neuron input with the possibility of transitions between two functional modes: the mutual mode, in which the TC neuron fires spike bursts in phase with the RE neuron, and the quiescent mode, in which the TC neuron is prevented from firing by steady hyperpolarization. We cross-check with three other computer models: one emphasizing the generality of the results in a different parameter regime, another demonstrating a different aspect of synaptic dynamics that we believe to be important, and the third showing comparable behavior in a much larger 54-neuron network. No one model has precisely the “right” parameters to make it the Rosetta stone of thalamic physiology. Instead, each simulation is in itself a complex system with emergent behavior that requires “virtual experimentation” and analysis to explain (Wolfram 1984).
Simulations were run on a Sun Sparcstation 10s and Intel Pentium PCs with the use of the NEURON simulator (Hines 1993). Each neuron was represented by a single compartment with a 1,000-μm2 area.
Voltage-sensitive channels included were similar to those used in previous papers (Destexhe et al. 1993). The TC neuron had the following voltage-sensitive channels and typical maximal conductances ḡ (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 × 10−3; slow calcium-dependent potassium channel, 0.005; nonspecific calcium-sensitive cation channel, 3.5 × 10−4. 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 ḡ T in the TC neuron (0.0011), 43% increase in ḡ T in the RE neuron (0.0025), and 50% decrease in the Michaelis-Menten rate of the calcium pump (from 1 × 104 to 5 × 10−5).
The synaptic projection from TC to RE neuron involved α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-d-aspartate (NMDA) components. The connection from RE to TC utilized γ-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: α = 1.1/ms⋅mM, β = 0.19/ms, C dur = 1.1 ms, reversal potential(E rev) = 0 mV, ḡ = 0.002 μS. NMDA: α = 0.072/ms⋅mM, β = 0.0066/ms, C dur = 5.0 ms, E rev = 0 mV, ḡ = 0.0 μS (used for stimulation only). GABAA: α = 0.53/ms⋅mM, β = 0.18/ms, C dur = 1.0 ms, E rev = −90 mV, ḡ = 0.002 μS. GABAB: α = 0.01/ms⋅mM,β = 0.005/ms, C dur = 150 ms, E rev = −95 mV, ḡ = 0.0055 μS.
Cortical stimulation was simulated with the use of a mixed AMPA/NMDA excitation to the RE (ḡ 0.2 and 2 nS, respectively) and AMPA excitation of the TC (ḡ 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. 4 A).
For the large network simulations (Figs. 10 and 11), intrinsic parameters were identical to the original parameter set. Each of nine columns was headed by a single RE neuron that controlled 5 TC neurons for a total of 54 cells. Within a column, reciprocal connectivity was complete. Between columns, connectivity probability from TC neuron to RE neuron and from RE neuron to TC neuron were equal. Different densities were assayed. The simulations shown used densities of 0.67 for the immediate neighboring column and 0.34 for the following column in either direction with wraparound. REs were always connected to neighboring RE neurons and were connected with a probability of 0.5 to RE neurons two columns distant. Synaptic strengths of inputs to the TC neuron were randomized uniformly (GABAA: 0.3 ± 0.2 nS, GABAB:0.3 ± 0.2 nS). Inputs to the RE neuron were not randomized (GABAA: 0.3 nS, AMPA: 0.5 nS). All synaptic delays were taken to be 0.5 ms.
For the two-neuron network, 6 s of simulated time took 3 min to run on a 100-MHz Pentium or a Sparcstation 10 running Solaris 2.4.
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). 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.
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).
RE neurons discharged relatively long bursts (150–300 ms) in relation to the EEG spikes (Figs. 2 B1 and 3). Many of these prolonged bursts were modulated at 10 Hz or were made up of multiple smaller bursts at 10 Hz (3rd burst in Fig. 3 B). RE neuron bursts appeared to be riding a depolarization, presumably due primarily to cortical driving (Fig. 3). Active TC neurons presumably also contributed to these compound excitatory postsynaptic potentials.
TC neurons showed two types of behavior: 1) 40% of TC neurons were entrained into the seizures and discharged high-frequency spike bursts concomitant with the EEG spikes (see Steriade and Contreras 1995); 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. 2 A, 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).
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.
With weaker inhibition, a mutual oscillation was produced in which a burst in each modeled neuron was matched by one in the other (Fig. 4 A). This resulted because the TC-RE excitatory drive was sufficient to produce a nearly immediate burst in the RE neuron. The RE burst produced a mixed GABAA and GABAB IPSP in the TC, sufficient to deinactivate the T channel and produce a subsequent low-threshold spike, completing the cycle (Fig. 4, middle inset). The frequency of oscillation was primarily determined by the duration of the complex IPSP. The intrinsic oscillatory frequency of the TC neuron also played a role with IPSPs of brief duration (Lytton et al. 1996).
Close inspection of the RE neuron oscillation showed the oscillation to be of a “period 2” or higher type, meaning that two or more distinct periods took place before the pattern repeated. These two periods were seen readily in the RE neuron trace: a burst (1st period) and a subsequent subthreshold depolarizing hump (2nd period) that can be seen between each burst (Fig. 4, ↓). 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. 4 B.
In the other mode, which we will call the quiescent mode, drive from RE to TC continuously hyperpolarized the TC neuron (Fig. 4 B). This mode was favored by increasing the conductance of GABAB. The RE neuron showed repetitive single-spike LTS-based bursting at a higher frequency determined by interactions between the depolarizing nonspecific calcium-sensitive cation channel and T calcium channel and the hyperpolarizing slow calcium-dependent potassium channel, as demonstrated previously (Avanzini et al. 1989; 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).
The fact that RE neuron bursting was relatively rapid was more important than the strength of the inhibition in preventing activity in the TC neuron. If this frequency were slower, the TC neuron would have time for I T to deinactivate and generate a low-threshold spike. In fact, the higher bursting frequency of the RE neuron in the quiescent mode was associated with a reduced burst duration, and thus a reduced IPSP. The reduction in burst length to a single spike was due to the short interburst interval available to produce RE neuron T channel deinactivation and to the absence of coincident TC neuron drive. Thus overall inhibition in the quiescent mode was no greater than that in the mutual mode. Timing altered the behavior.
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, ↓) permitted the development of a TC neuron burst, leading to the mutual mode.
The phase of the stimulation was important in determining its ability to alter the oscillation pattern (Fig. 6). Stimulation did not always effect the change immediately, but could instead effect the transition several cycles later.
Transitions between modes also occurred spontaneously in the absence of stimulation (Fig. 7). Phase plane representations helped us further analyze these transitions. Studying trajectories of all possible pairs of state variables revealed that this spontaneous transition was primarily associated with shifts in the intrinsic state variables of the RE neuron, without substantial alteration in the entrained activity of the TC neuron. Here again, RE neuron activity determined the oscillation mode. RE neuron T channel activation and inactivation showed the clearest evidence of systematic alteration leading up to the transition. Figure 7 A shows an initial mutual oscillation mode that spontaneously gave way to the quiescent mode. Eight bursts preceding the transition are shown. Individual cycles are labeled as a key to the phase planes in Fig. 7 B. Inspection of the voltage trace alone suggested that the initial mutual mode in the RE neuron would be an approximately period 2 oscillation, because the voltage appeared to go through two dissimilar cycles, burst and subthreshold excitation, before repeating. (This would not be precisely period 2 because the individual bursts and interbursts were not identical.) However, inspection of the T channel activation/inactivation (m T/h T) phase plane of Fig. 7 Ba revealed that the subcycles labeled 1 and 2 were quite distinct. Therefore what appeared to be an approximate period 2 oscillation was in fact closer to an approximate period 4 oscillation.
The alternating bursts illustrated in Fig. 7, Bb and Bc, were similar, although burst b showed a slight progressive increase in T channel inactivation on subsequent cycles. Burst c showed no systematic shift. These shifts were slight, with all individual bursts being similar to one another. The alternating interbursts, labeled 1 and 2 in Fig. 7 Ba, showed a voltage amplitude difference most clearly seen in Fig. 7 C. The interburst labeled 1 had a sequence comparable with that of the burst in Bc, showing no clear progression with time. The interburst labeled 2, by contrast, gradually shrank on subsequent cycles before disappearing entirely at the onset of the quiescent mode. The quiescent mode lacked interburst depolarizations and was therefore represented as open loops rather than full orbits in the phase plane (3). Nonetheless, the amplitude and location classes them with the orbit labeled 1. The duration of transit labeled 3 is substantially less than that labeled 1 because it does not go through the full loop, the depolarizing hump having become a full burst. In summary, the quiescent transition represents an elimination through collapse of one interburst orbit with a continuation in abbreviated form of the alternating interburst orbit.
The above phase plane diagrams are based on m and h variables that are not observable experimentally. Figure 7 C illustrates the same interburst orbits (1 and 2 in Fig. 7 Ba) in a phase plane of intracellular calcium and voltage, which are experimentally measurable. The inner and outer loops could still be distinguished, although they were not as clearly separated as they were in the m T/h T plane. Additionally, the gradual collapse of the inner orbit, although also visible, was difficult to see in this cross section.
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.
Figure 8 illustrates the range of activity obtained by increasing the strength of inhibitory input into the TC neuron. Each pair shows the activity in the RE neuron (top traces) and TC neuron (bottom traces). A complex mutual mode oscillation was seen, with regular TC neuron bursting coexisting with irregular RE neuron bursting interspersed with runs of rapid spiking (Fig. 8 A). The regularity of TC neuron bursting suggested that the TC neuron was leading the oscillation in this case, with the RE neuron showing either a burst or brief spike train in response to each TC neuron burst. Increased inhibition produced a more complex mutual oscillation (Fig. 8 B) in which TC neuron bursting occurred at a subharmonic of that seen above. Although the TC neuron regularity demonstrated an important role of TC neuron intrinsic properties in this oscillation, the RE neuron was playing a larger role here in determining the TC neuron interburst interval. In particular, a three-burst RE neuron motif (Fig. 8 B, arrows), associated here with a longer TC neuron interburst interval, was identical in form to the burst groups seen in quiescent mode (Fig. 8 D). A further increase in inhibition (Fig. 8 C) demonstrated that the mutual mode could spontaneously make the transition into a quiescent mode, as seen with the previous parameter set (Fig. 7 A). Sufficient inhibition yielded a quiescent mode oscillation (Fig. 8 D). As with other parameter sets, the RE neuron bursting pattern was less complex with TC neuron feedback absent.
Simulated cortical stimulation of the mutual oscillation with this parameter set also showed the ability to change it over to the quiescent mode (Fig. 9). The first trace shows a brief period of quiescent mode starting about halfway through the period shown. Stimulation at various phases could advance the quiescent period (2nd and 4th traces), delay it (5th trace), or leave it virtually unchanged (3rd trace). Stimulation could also precipitate a transition in the opposite direction, from quiescence to mutual oscillation (not shown).
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. 10 A). 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. 10 B). However, this relationship was highly variable. This indicated that dynamic factors complemented connection strength in determining mutual oscillation and quiescent episodes.
Observations of mutually connected TC-RE pairs demonstrated that RE neuron firing usually followed TC neuron firing after a brief interval (Fig. 11). Thus the relationship between reciprocally connected neurons was comparable with that which we observed with the two-neuron network (Fig. 4). Other RE neuron bursts were due to other converging TC neurons or to intrinsic activity of the RE neuron. Although intra-RE inhibition had significant effects on the overall oscillation, it did not eliminate the relationship between reciprocally connected cell pairs.
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), 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).
With this synaptic model, RE neuron excitatory discharges at ∼10 Hz could still produce both mutual and quiescent oscillation (Fig. 12). The 10-Hz frequency in this model was driven by simulated cortical stimulation to the RE neuron. Similar oscillatory patterns were obtained if both TC neuron and RE neuron were both stimulated, as long as the TC neuron IPSP was dominant. With relatively low-intensity cortical stimulation, the strength of the RE neuron burst was not sufficient to produce much GABAB activation. The IPSP was sufficiently strong to produce a TC neuron LTS, however, leading to the mutual oscillation mode (Fig. 12 A). With stronger cortical stimulation, more prolonged RE neuron burst discharges evoked a more prominent GABAB current in the TC neuron (Fig. 12 B). This current was sustained because of the high stimulation frequency compared with its slow decay. This clamped the TC neurons at a hyperpolarized membrane potential and produced the quiescent mode.
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), 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.
The relatively high rate of activity of RE neurons compared with TC neurons during SW oscillations (Steriade and Contreras 1995) 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.
In vivo, the extent and pattern of RE neuron activity may be more a reflection of cortical drive into the RE neuron than a manifestation of intrinsic activity. This drive, however irregular, would interact with the RE neuron's active conductances to produce the final spike pattern in a way that is still unknown. Quiescence would still be determined by the pattern of RE neuron activity.
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.
The sensitivity of behavior to relatively minor parameter alterations might lead one to despair of ever getting the right parameters. However, both sets might well be within the range of parameters that could coexist across the population of neurons, perhaps regulated by conditions related to bursting, as suggested by previous researchers (Lemasson et al. 1993).
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.
Our exploration of a larger network served to demonstrate that the TC-RE circuit would keep the characteristics described for the two-cell model when immersed in a larger network. Convergence onto the TC neuron generally increases the chances of being in the quiescent state because of the influence of many more IPSPs coming from these many RE neurons, whereas mutual inhibition among RE neurons tends to reduce RE firing and promote TC neuron activity. These additional connections disrupted the consistency of the reciprocal relation between a single TC neuron and a single RE neuron, because IPSPs from other RE neurons could disrupt a low-threshold spike that otherwise would have formed (Fig. 11). Convergence onto the RE neuron was less detrimental to the mutual oscillation because excitatory activation follows almost immediately and is not subject to interference from converging TC projections.
Our columnar network is similar to previous models of synchronized oscillations and propagating properties in thalamic networks (Destexhe et al. 1996; 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.
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; 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).
Figures 5, 6, and 9 show how changes in the timing of a simulated cortical input can either influence activity immediately, after a variable amount of time, or not at all. The means by which an input can have temporally remote effects is explored in our phase-plane analysis of Fig. 7. A single input, in this case a simple hyperpolarization of the TC neuron, has distant effects. Our analysis demonstrated a complex progression primarily affecting the T channel. This progression took place within the context of an approximate period 4 oscillation. The phrase period 4 indicates a return to the same spot in phase space every fourth orbit. Because the progression of a dynamic system is completely determined by its position in phase space, a return would mean that the system would continue on to repeat exactly the same orbit every fourth time. In this case, the system we are analyzing is not engaged in a continuous oscillation but is instead a nonstationary system making a transition to a different type of oscillation. The system can be described as “approximately period 4” because it comes close to the same orbit every fourth time around. The specific orbit that seemed most indicative of an ongoing change was that labeled 2 in Fig. 7 Ba. This orbit became gradually smaller as a reduction in the size of the interburst depolarizing transient was associated with less initial activation and inactivation of the T channel. This alteration eventually reached a point where the net T channel activation was insufficient to generate the large RE neuron burst associated with the mutual oscillation.
True causality cannot be established in a dynamic system because state variables are linked continuously. However, this analysis did establish a critical role for the T channel in this transition. This ion channel would presumably be the most sensitive target at which a pharmacological agent could impede or augment this transition.
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; 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).
As presented here, this model of GABAB responses could also contribute to TC neuron quiescence. In Fig. 12, 10-Hz oscillations in RE neurons were not intrinsic but were generated by weak stimulation at 10 Hz. This in turn evoked GABAA-dominated IPSPs in the TC neuron to entrained it as well (Fig. 12 A). Stronger-intensity cortical stimulation at the same frequency could force the thalamic circuit into the quiescent mode (Fig. 12 B), because the more prolonged RE neuron discharges evoked a stronger GABAB IPSP in the TC neuron.
Experimental predictions from these studies
The studies' main results that would be experimentally testable are as follows.
1) We demonstrated that RE neuron activity was temporally associated with TC neuron activity in the mutual mode and that RE neuron activity was more regular during quiescent mode. We predict that cross-correlograms of RE neuron and TC neuron spike trains would show a peak at 2–3 ms, demonstrating the monosynaptic influence of the TC neuron. This has already been shown in part (Shosaku 1986). We additionally predict a significantly more powerful dominant frequency in the power spectrum of RE neuron activity associated with quiescent TC neurons.
2) The switch between modes by cortical shocks could be tested directly in vivo. We predict that single shocks would not only produce a single LTS in the TC neuron but also produce a significant alteration in the probability of firing for a 500-ms window following the shock. Observation of this long window would be necessary given the delayed mode switching that we observed.
3) Increasing GABAB strength with application of agonists such as baclofen in vivo would increase the duration of TC neuron quiescent periods and the percentage of neurons that show quiescence. This prediction is consistent with the effect that presynaptic GABAB inhibition has in decreasing intra-RE neuron inhibition, leading to enhanced inhibition in TC neurons (Ulrich and Huguenard 1996). Increasing GABAA strength with benzodiazepines would not be efficacious in producing increased quiescence.
4) Our major prediction concerns the spatiotemporal pattern of seizure activity associated with quiescence in TC neurons. This prediction is discussed in detail below.
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.
Additionally, we predict that SW epilepsy spreads through a process involving a focus and a neighboring epileptic penumbra (Dichter and Spencer 1969). 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).
“Spread of generalized epilepsy” would appear to be an oxymoron, because generalized epilepsy is defined electroencephalographically by its simultaneous appearance across the scalp. However, it has long been appreciated that actual synchrony of occurrence would only be possible in the presence of an external synchronizing agent such as the shock of electroconvulsive therapy or the sudden immersion of the brain in penicillin (Fisher and Prince 1977a,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).
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.
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.