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A. Brain Rhythms
The rhythmic nature of electrical activity in the brain was first discovered in electroencephalographic (EEG) recordings from the scalp by Caton in 1875, and later by Berger in humans (25). They observed that the frequency and amplitude of the oscillations vary widely across different behavioral states. Awake and attentive states are characterized by low-amplitude, high-frequency EEG activity, with significant power in the beta (20-30 Hz) and gamma (30-80 Hz) frequency bands. Large-amplitude alpha rhythms (8-12 Hz) appear mostly in occipital cortex in aroused states with eyes closed and are reduced with eyes open (25). The early stages of sleep are characterized by spindle waves (7-14 Hz), which consist of short bursts of oscillations lasting a few seconds and displaying a typical waxing-and-waning appearance. When sleep deepens, slow-wave complexes, such as delta (1-4 Hz) and slower waves (~1 Hz), progressively dominate the EEG. Slow-wave sleep is interrupted by periods of rapid-eye-movement (REM) sleep, during which the EEG activity has a low amplitude and high frequencies, similar to that during arousal. Finally, the cortex participates in several forms of epileptic seizures, such as the 3-Hz "spike-and-wave" complexes (241).
B. The Building Blocks of EEG Rhythms
The earliest explanation for the EEG rhythmicity was the "circus movement theory" proposed by Rothberger in 1931 (cited in Ref. 38). According to this theory, the rhythms are due to action potentials traveling along chains of interconnected neurons. The period of the rhythmicity corresponded to the time needed for a volley of action potentials to traverse a loop in the chain. Inspired by the circus movement theory, Bishop (28) proposed the concept of "thalamocortical reverberating circuits," in which the rhythmicity was generated by action potentials traveling back and forth between thalamus and cortex. Although the reverberating circuit theory remained prevalent for several years, subsequent experiments demonstrated that the EEG activity is not generated by action potentials (260), invalidating a fundamental premise of the circus movement theory.
An alternative proposal by Bremer (38-40) suggested instead that brain rhythms reflect the autorhythmic properties of cortical neurons and that the EEG is generated by nonpropagated potentials, in analogy with the electrotonic potentials in the spinal cord (33). Bremer (39) also proposed that cortical oscillations should depend on the "excitability cycle" of cortical neurons. He emphasized that cortical neurons are endowed with intrinsic properties that participate in rhythm generation and that brain rhythms should not be described as the passive driving of the cerebral cortex by impulses originating from pacemakers (37, 40). Bremer's proposal for the genesis of EEG rhythmicities rested on four core ideas: 1) the EEG rhythmicity is generated by the oscillatory activity of cortical neurons; 2) the genesis of these oscillations depends on properties intrinsic to cortical neurons; 3) EEG oscillations are generated by the synchronization of oscillatory activity in large assemblies of cortical neurons; and 4) the mechanisms responsible for synchronization are due to intracortical excitatory connections. Most of these assumptions have been validated, and the modern view of EEG genesis is largely based on these principles (see below).
Experiments on motoneurons in the spinal cord (110) provided convincing evidence that the EEG reflects summated postsynaptic potentials. To explain the slow time course of EEG waves, Eccles (110) postulated that distal dendritic potentials, and their slow electrotonic propagation to soma, participate in the genesis of the EEG. This assumption was confirmed by intracellular recordings front cortical neurons, which demonstrated a close correspondence between the EEG and synaptic potentials (68, 69, 184). This view of the genesis of the EEG is still widely held (243).
C. Interaction Between Intrinsic and Synaptic Conductances
Spinal motoneurons integrate synaptic activity and, when a threshold membrane potential is reached, emit an action potential that is followed by a prolonged hyperpolarization (43, 110). This led to an early model of the neuron based on the concept of "integrate and fire" followed by a reset. Early views about activity in other parts of the central nervous system, particularly the cerebral cortex, were strongly influenced by studies of motoneurons, and brain activity was thought to arise by interactions between similar neurons connected in different ways. In this "connectionist" view, the function of a brain area was determined primarily by its pattern of connectivity (110).
Studies on invertebrates during the 1970s revealed that neurons are endowed with complex intrinsic firing properties that depart from the traditional integrate-and-fire model (2, 55-57, 176). Further evidence against the integrate-and-fire view came from studies of small invertebrate ganglia showing that connectivity was insufficient by itself to specify function (126, 274) and that the modulation of intrinsic properties needed to be taken into account (146). The generality of these results was confirmed in intracellular recordings from vertebrate slice preparations (6, 171, 172, 204-207), which revealed that central neurons also have complex intrinsic properties (202).
The nonlinear interactions between ionic conductances are complex. Computational models can make a significant contribution in linking the microscopic properties of ion channels and cellular behavior. This approach was used by Hodgkin and Huxley (157) to understand the genesis of action potentials, and essentially the same approach has been used in modeling studies to understand the complex behavior of central neurons. Perhaps the best characterized neurons in the vertebrate brain are those in the thalamus, which we review here (see sect. II).
In addition to having complex intrinsic properties, neurons also interact in various ways, including chemical synaptic transmission, electrical coupling through gap junctions, and ephaptic interactions through electric fields. Whole cell and patch-clamp recording techniques (264) have been used to investigate the detailed mechanisms underlying the conductances of ionic channels involved in synaptic transmission. An extraordinarily rich variety of dynamic properties of synaptic interactions between central neurons has been uncovered on a wide range of time scales. Many neurotransmitters and receptor types have been identified in the thalamocortical system (222), each of which confers characteristic temporal properties to synaptic interactions. The properties of the main receptor types mediating synaptic interactions are now well understood.
It is now well accepted that rhythmicity arises from both intrinsic and synaptic properties (106b, 310, 312). Some neurons generate oscillations through intrinsic properties and interact with other types of neurons through multiple types of synaptic receptors. These complex interactions generate large-scale coherent oscillations. Understanding how the interactions between ionic conductances can generate rhythms is difficult, and computational models can help in exploring the underlying mechanisms. This review shows how this approach has been used to understand how the interplay between intrinsic and synaptic conductances generate oscillations at the network level (see sect. III).
D. Thalamocortical Loops
We focus here on two types of rhythms: spindle oscillations and absence seizures, both of which are generated in the thalamocortical system schematized in Figure 1. Sensory inputs from visual, auditory, and somatosensory receptors do not reach the cerebral cortex directly, but synapse first on thalamocortical (TC) relay cells in specific regions of the thalamus. These relay cells in turn project to their respective area in primary sensory cortex. These topographically organized forward projections are matched by feedback projections from layer 6 of cortex to the corresponding afferent thalamic nucleus (174,278).
[FIGURE 1 OMITTED]
Within the thalamus, there are reciprocal connections between TC and thalamic reticular (RE) neurons. The RE cells are GABAergic and send their projections exclusively to relay nuclei, but they also receive excitatory collaterals from both ascending (thalamocortical) and descending (corticothalamic) fibers. Thalamocortical loops therefore include both bidirectional excitatory interactions between the cortex and thalamus and inhibition through the collaterals of ascending and descending fibers to GABAergic neurons. These inhibitory interactions are needed to explain the large-scale synchrony of thalamocortical oscillations (see sect. IV).
Several types of brain rhythms originate in the thalamocortical system. Spindle waves are by far the best understood type of rhythmicity in this system, in part because they can be enhanced by anesthetics such as barbiturates (8, 81). The thalamic origin of spindles was first suggested by Bishop (28), who observed the suppression of rhythmic activity in the cortex after sectioning connections with the thalamus and was confirmed in experiments on decorticated animals (3, 234). The cellular events underlying this rhythmic activity have been identified in vivo (305, 310) and in isolated thalamic slices in vitro (346). The biophysical mechanisms underlying spindle rhythmicity were uncovered in slice preparations, particularly the voltage-dependent conductances and receptor types involved. Theories for the genesis and termination of spindle oscillations need to be rigorously tested.
Absence seizures also originate in the thalamocortical system. Because they are generalized and involve large-scale synchrony, Jasper and Kershman (173) suggested that they may have foci in thalamic nuclei that widely project to cortex. This hypothesis was supported by chronic recordings during absence seizures in humans, showing that signs of a seizure were observed first in the thalamus before appearing in the cortex (360; but see Ref. 240). Experimental models of absence seizures, such as the penicillin model in cats (256), showed that although the thalamus is critical for generating seizures, it was not sufficient to explain all of their properties. Seizures can be obtained from injection of convulsants limited to cerebral cortex, but not when the same drugs are injected into the thalamus (130, 258, 302). It is now clear that both the thalamus and the cortex are necessary partners in these experimental models of absence seizures, but the exact mechanisms are unknown (74, 129). Computational models can help identify the critical parameters involved in the genesis of pathological behavior, as well as suggest ways to resolve apparently inconsistent experimental observations, as explored in section IV.
Despite progress in understanding how the EEG is generated, the possible significance of brain oscillations for the large-scale organization of information processing in the brain remains a mystery. After summarizing current knowledge of the mechanisms that generate spindle oscillations, absence seizures, and other types of thalamocortical oscillations, we explore possible functions for these rhythms (see sect. IVC) suggested by the computational models.
II. SINGLE-CELL PACEMAKERS: OSCILLATIONS AND BURSTS EMERGING FROM THE INTERPLAY OF INTRINSIC CONDUCTANCES IN SINGLE NEURONS
We first review how interactions between conductances within a single cell can generate phenomena like bursting or intrinsic oscillations, and how these properties are tuned by calcium and neuromodulators. We examine these mechanisms through computational models constrained by experimental data.
A. Thalamic Relay Cells
1. Rebound bursts in thalamic relay cells
In addition to relaying sensory input to cortex, TC neurons have intrinsic properties that allow them to generate activity endogenously. Following inhibition, these cells can under some circumstances produce bursts of action potentials, called a "low-threshold spike" (LTS) or "postinhibitory rebound." The importance of the rebound response of TC cells was first established by Andersen and Eccles (9), who called it "postanodal exaltation." It was later characterized in vitro by Llinas and Jahnsen (209) and in vivo by Deschenes et al. (84) and has become generally known as the "rebound burst" or LTS. Andersen and Eccles (9) were the first to show that TC cells display bursts of action potentials tightly correlated with the offset of inhibitory postsynaptic potentials (IPSPs).
In vitro studies (209, 171) demonstrated that TC cells possess two different firing modes. In the "tonic" mode, near the resting membrane potential (approximately--60 mV), the relay neuron fires trains of action potentials at a frequency proportional to the amplitude of the injected current (Fig. 2A, left panel). This is similar to the response of many other neurons and is explained by the voltage-dependent [Na.sup.+] and [K.sup.+] currents that generate action potentials. In contrast, at hyperpolarized membrane potentials, thalamic neurons can enter a "burst mode" (Fig. 2A, right panel), firing high-frequency bursts of action potentials (~300 Hz) at the offset of hyperpolarizing current injection. A burst can also occur following a strong IPSP, which provides hyperpolarization and return to rest similar to the conditions simulated by current injection. The response of a neuron to a depolarizing current injection depends on its previous state, producing a steady low-frequency firing rate if injected at a depolarized level, but eliciting a burst followed by a long afterhyperpolarization if injected in a sufficiently hyperpolarized state.
[FIGURE 2 OMITTED]
The ionic mechanism underlying the "low-threshold" behavior of thalamic neurons is a slow, low-threshold [Ca.sup.2+] current (171, 172), which was characterized in voltage-clamp experiments (67, 71, 148, 319). This current is carried by low-voltage activated [Ca.sup.2+] channels described previously (49,50) and later called "T-type" [Ca.sup.2+] channels (242). Cloning of the T-type channels revealed several distinct subunits, which may account for functional difference according to the type of subunit assembling the channel (192). Like the [Na.sup.+] current described by Hodgkin and Huxley (157), the T current ([I.sub.T]) of thalamic neurons is transient and shows activation followed by inactivation. However, the voltage range over which [I.sub.T] activates is close to the resting potential, in contrast to the [Na.sup.+] current, which activates at more depolarized levels. The kinetics of [I.sub.T] are considerably slower than the [Na.sup.+] current. A voltage-clamp characterization of the [I.sub.T] in thalamic cells performed in dissociated TC cells by Huguenard and Prince (163) provided the quantitative data on the kinetics of activation and inactivation of this current used in the computational models below.
2. Models of the rebound burst and the role of dendrites
Hodgkin and Huxley (157) introduced computational models to determine whether the ionic mechanisms identified in their voltage-clamp measurements were sufficient to account for the generation of the action potential. The same approach was taken to study the genesis of bursting behavior. Hodgkin-Huxley-type models of TC neurons were first introduced by McMullen and Ly (230) and Rose and Hindmarsh (262) based on the experiments of Jahnsen and Llinas (171). The more recent characterization of the [I.sub.T] by voltage-clamp methods (see above) provided precise measurements for the time constructs and steady-state values of activation and inactivation processes. Several Hodgkin-Huxley-type models based on voltage-clamp data replicate the rebound-burst properties of TC cells (95, 96, 106, 162, 214, 225, 332, 352, 356). The most salient features of the rebound burst can be reproduced by single-compartment models containing [Na.sup.+], [K.sup.+], and T-type currents described by Hodgkin-Huxley-type kinetics (Fig. 2B). Simplified "integrate-fire and burst" models have also successfully reproduced the most salient features of TC cells bursts (284). However, to reproduce all the features of the rebound burst in TC cells, the [I.sub.T] must be concentrated in the dendrites, where a large number of synaptic terminals are located (174, 197).
Imaging experiments clearly show dendritic calcium signals during bursts in TC cells (238, 373), consistent with results from current-clamp and voltage-clamp experiments (106, 371). The dendritic localization of the [I.sub.T] was shown by direct measurements of channel activity in dendrites (361). To estimate the [I.sub.T] density in dendrites, a TC neuron was recorded in slices of the ventrobasal thalamus (163), stained with biocytin, and reconstructed using a computerized camera lucida (106). Two sets of data were used to constrain the amount of calcium current in dendrites. First, recordings of the [I.sub.T] were made from dissociated TC cells (163), which lack most of the dendritic structure and are electrotonically compact, therefore minimizing voltage-clamp errors. These recordings were then compared with voltage-clamp measurements of the [I.sub.T] in intact TC cells, which were ~5-14 times larger than in dissociated cells (106).
Models based on the reconstructed dendritic morphology of TC cells were used to explore the consequences of varying the density of the current in the different dendritic and somatic regions (106). The low amplitude of [I.sub.T] in dissociated cells could be reconciled with the high-amplitude currents observed in intact cells if the concentration of T-type calcium channels was 4.5-7.6 times higher in the dendrites than in the soma (106). The same density gradient of calcium channels in the model also reproduced the bursts of spikes evoked in the current-clamp protocols (106). Similar findings were reported in another modeling study (12), which predicted that the dendrites of TC cells must contain the [I.sub.T] (in addition to delayed-rectifier [K.sup.+] current [I.sub.Kd]). This was needed for the model to generate tonic or burst firing with the correct voltage-dependent behavior and oscillations (12).
The predicted high densities of T-type calcium channels in the dendrites of TC cells were confirmed by direct measurements of channel activity using cell-attached recordings (361). The density was, however, not uniform, but was concentrated mostly in stem dendrites up to 40 [micro]m from the soma, while distal dendrites had low T-channel densities. The results based on this type of distribution were equivalent to those based on the distribution of [I.sub.T] density discussed above. (1) Thus it is essential that most of the T channels are dendritic, but how they are distributed within the dendrites is not critical. A similar conclusion about dendritic currents was reached in a model of delta oscillations in TC cells (113).
The localization of dendritic calcium currents in dendrites has several functional consequences. First, the presence of the calcium current at the same sites as inhibitory synapses is likely to enhance the rebound responses of TC cells (106c). Second, the shunting effects of tonic excitatory cortical synapses and inhibitory synapses on burst generation would be more effective if the [I.sub.T] were dendritic (106). As a consequence, the activity of corticothalamic synapses can counteract bursting, and rapidly switch the TC neuron from the burst mode (cortical synapses silent) to the tonic mode (sustained cortical drive). Local dendritic interactions thus allow corticothalamic feedback to potentially control the state of thalamic neurons on a millisecond time scale compared with conventional neuromodulatory mechanisms, which operate over hundreds of milliseconds (222).
3. Bursts in awake animals
The TC cells in the thalamus generate powerful synchronized bursts of action potentials during sleep; in comparison, the activity in alert animals is dominated by single-spike (tonic) firing (201, 309). There is, however, evidence for the presence of bursts in the thalamus of awake animals (142, 143, 278). These thalamic bursts may represent a special type of information in alert states, such as novelty detection (278). However, the occurrence of bursts is rare in the thalamus of aroused animals and may instead signify that the animal is drowsy (296); this possibility is supported by observations that thalamic bursts are negatively correlated with attention (357).
The occurrence of bursts as a rebound to inhibition during oscillatory states similar to sleep oscillations (9, 305, 312) has been intensively studied with computational models (reviewed in Ref. 106b), but bursts following excitatory inputs have not been as well studied (106c). Excitatory stimulation by sensory synapses was modeled by a constant density of glutamatergic (AMPA) synapses on proximal TC dendrites (174, 197), up to 40 [micro]m from the soma. The threshold for action potential generation was estimated by increasing the conductance of this synapse and, as expected, when the cell was hyperpolarized (less than -65 mV), the synaptic stimulus could evoke bursts of action potentials. At more depolarized resting values (more than -65 mV), excitatory stimuli evoked tonic firing. In control conditions, the region of membrane potential corresponding to the burst mode was large, and the minimal excitatory postsynaptic potential (EPSP) amplitude to evoke a burst was about 0.035 [micro]S (106c), which represents ~230-350 simultaneously releasing glutamatergic synapses, based on an estimated quantal amplitude of 100-150 pS (246, 247). Models therefore predict that an excitatory stimulus should efficiently evoke bursts only when the TC cell is in the right range of membrane potentials.
In contrast, when the membrane of model TC cells was more leaky, as occurs during tonic activity of the network in vivo, the burst region narrowed, and there was a large range of stimulus amplitudes for which the only possible spike output was the tonic mode (106c). Under these conditions, the minimal EPSP amplitude needed to evoke bursts was ~0.09 [micro]S, which corresponds to ~600-900 simultaneously releasing synapses. In the visual thalamus, the evoked conductance from a single retinal afferent is 0.6-3.4 nS (1.7 nS on average), which represents from 4 to 27 quantal events (246). This suggests that the simultaneous release of all terminal sites from 8 to 87 retinal axons are required to evoke bursts in relay cells (front 22 to 220 under in vivo conditions). However, one morphological study reported that a single retinal axon can make a large number of synaptic terminals onto the same relay neuron, forming a significant proportion of all of its retinal synapses (145). It is therefore possible that the convergence of a relatively small number of afferent axons could evoke bursts, which would support the notion that bursts are easily triggered by afferent excitatory synapses. More precise measurements of the number of synaptic terminals from single axons are needed to determine the convergence of afferent activity needed to trigger bursts in relay cells.
Models of TC neurons based on reconstructed morphologies and dendritic [I.sub.T] therefore suggest that sensory-initiated bursts are possible, but they require a large convergence of excitatory stimuli and are more likely to occur under conditions of low activity. This is consistent with the view that in burst mode the thalamus strongly filters afferent information (223). This also supports the view that bursts may be a "wake-up call" signal during drowsiness or inattentive states (278), although it is not clear how the cortex would distinguish these "wake-up" bursts from bursts occurring spontaneously (or in an oscillation) during states of low vigilance.
4. Intrinsic oscillations in thalamic relay cells
In addition to displaying burst and tonic modes, TC cells can also generate sustained oscillations. In experiments performed in cats in vivo, TC cells generated oscillations in the delta frequency range (0.5-4 Hz) after removal of the cortex (73). Oscillations in the same frequency range were also observed in TC cells in vitro (190, 191, 226). These intrinsic slow oscillations consisted of rebound bursts recurring periodically and have been also called "pacemaker oscillations" (190, 191). These slow oscillations were resistant to tetrodotoxin, suggesting that they were generated by mechanisms intrinsic to the TC cell.
The intrinsic delta oscillations depend on the membrane potential (226). Oscillations were only possible if TC cells were maintained at relatively hyperpolarized potentials, within the range of the burst mode, suggesting that the [I.sub.T] actively participated in its generation. Another property, illustrated in Figure 3A, is that these oscillations disappeared following blockade of another current, called [I.sub.h] (226) with [Cs.sup.+]. [I.sub.h] is a mixed [Na.sup.+]/[K.sup.+] cation current responsible for anomalous rectification in TC cells (253). In voltage-clamp, [I.sub.h] is activated by hyperpolarization in the subthreshold range of potentials (226, 290). These data indicate that intrinsic oscillations in TC cells are generated by an interplay between [I.sub.T] and [I.sub.h].
[FIGURE 3 OMITTED]
5. Models of the conductance interplay to generate intrinsic oscillations
Several computational models have shown that the interaction between [I.sub.h] and [I.sub.T] can account for the genesis of low-frequency oscillations in TC cells (91, 95, 96, 214, 217, 225, 332, 352). In addition to [I.sub.T] (see above), these models included Hodgkin-Huxley-type models of [I.sub.h] based on voltage-clamp data obtained in TC cells. Several types of models have been used for this current, beginning with simple one-variable models based on a single activation gate (96, 214, 217, 225, 332, 352). This class of models only has one gate and cannot account for the observation that the [I.sub.h] activates slowly, with a time constant greater than 1 s at 36[degrees]C (226, 290), but deactivates faster (114, 125, 175, 335, 340). A model with a dual gating process, combining fast and slow activation gates, can reproduce the voltage-clamp behavior of [I.sub.h] in detail (91, 95).
Although both types of models of [I.sub.h] gave rise to slow oscillations when [I.sub.h] is combined with [I.sub.T], the double-activation model generated more complex oscillatory patterns, such as waxing-and-waning oscillations (see below). Figure 3B illustrates the oscillations generated by a single-compartment model of a TC cell comprising [I.sub.T] and [I.sub.h], as well as [I.sub.Na]/[I.sub.K] responsible for action potentials. Examination of [I.sub.T] and [I.sub.h] conductances during the oscillation revealed that the activation of [I.sub.h] depolarizes the membrane slowly until a LTS is generated by activation of [I.sub.T]. During the depolarization provided by the LTS, [I.sub.h] deactivates, and together with the termination of the LTS the membrane becomes hyperpolarized. This hyperpolarization allows [I.sub.T] to deinactivate to prepare for the next LTS, and as [I.sub.h] slowly activates, the cycle restarts. The same mechanism has been explored, with minor variations, in several modeling studies that used different models of [I.sub.T] and [I.sub.h] (91, 95, 96, 152, 214, 217, 225, 332, 352), suggesting that the interplay between [I.sub.T] and [I.sub.h] is a highly robust way to generate slow oscillations. This conclusion is also supported by a dynamic-clamp study showing that delta oscillations are lost in TC cells if [I.sub.h] is blocked, but can be restored by injection of a computer-generated [I.sub.h] conductance (161).
6. Waxing-and-waning oscillations
The slow intrinsic oscillations generated by TC cells can be modulated by different factors. Cat TC cells studied in a low-[Mg.sup.2+] medium in vitro displayed either a resting state, sustained slow oscillations, or intermittent "waxing-and-waning" oscillations (190, 191) (second trace in Fig. 3A). The latter consisted of an alternation between periods of oscillation (0.5-3.2 Hz), lasting 1-28 s, with periods of silence, lasting 5-25 s, during which the membrane progressively hyperpolarized. The waxing-and-waning envelope was resistant to tetrodotoxin (191), suggesting mechanisms intrinsic to the TC neuron. In analogy with the waxing and waning of spindles observed in vivo, they have also been called "spindlelike oscillations" (190, 191). However, in vivo spindles oscillate at a higher frequency (7-14 Hz) and depend on interactions with neurons of the thalamic reticular nucleus (see sect. IIIC), which distinguishes them from the waxing-and-waning oscillations intrinsic to TC cells.
The pharmacology of intrinsic waxing-and-waning oscillations was investigated by Soltesz et al. (290), who found that they were dependent on [I.sub.h]. Slow delta-like oscillations and waxing-and-waning oscillations can be observed in the same TC cell by altering [I.sub.h] (290) (Fig. 3A). Increasing the amplitude of [I.sub.h] by norepinephrine can transform delta-like oscillations into waxing-and-waning oscillations; application of [Cs.sup.+], an [I.sub.h] blocker, transforms the depolarized state into waxing-and-waning oscillations, the delta-like oscillations, and finally a hyperpolarized resting state (290) (Fig. 3A). In addition, the intrinsic waxing-and-waning oscillations can be transformed into sustained slow delta-like oscillations by applying a depolarizing current (190, 191).
7. Models of waxing-and-waning oscillations
Several ionic mechanisms for generating waxing-and-waning oscillations have been suggested. The first model (95) was inspired by experiments on the [I.sub.h] current in heart cells demonstrating regulation of [I.sub.h], by intracellular [Ca.sup.2+] (144). The steady-state activation of [I.sub.h] is dependent on the intracellular [Ca.sup.2+] concentration ([[[Ca.sup.2+]].sub.i]), shifting toward more positive membrane potentials with increasing [[[Ca.sup.2+]].sub.i] (144). Because calmodulin and protein kinase C were not involved in the [Ca.sup.2+] modulation of [I.sub.h], [Ca.sup.2+] may affect the [I.sub.h] channels directly (144), with the binding of [Ca.sup.2+] increasing the conductance of [I.sub.h], or indirectly through the production of cAMP (213). Different variants of calcium-dependent regulation of [I.sub.h] have been proposed (72, 85, 222).
The modulation of [I.sub.h] by [Ca.sup.2+] was studied in several bursting models of the TC cells. The simplest model was based on the assumption that [Ca.sup.2+] bind directly to the open state of the channel, thereby "locking" [I.sub.h] into the open configuration and shifting its voltage dependence as observed experimentally (95). Calcium upregulation was also proposed to occur according to a model in which the calcium indirectly affects the [I.sub.h] channel through an intermediate messenger, which itself binds to the open state of [I.sub.h] channels (96). Another ionic mechanism for waning has been proposed (350) based on activity-dependent adenosine production, which affects the voltage dependence of [I.sub.h] but in the opposite direction (244). Waxing-and-waning oscillations were also modeled by the interaction between [I.sub.T], [I.sub.h], and a slow potassium current (91,152).
All models generated waxing-and-waning oscillations, but only those based on the upregulation of [I.sub.h] by [Ca.sup.2+] reproduced the slow periodicity, the slow oscillation frequency, and the progressive hyperpolarization of the membrane during the silent period. Moreover, the [Ca.sup.2+]-dependent models also displayed the correct coexistence of oscillatory and resting states in TC cells, as shown in Figure 3Bi. For fixed [I.sub.T] conductance, increasing [I.sub.h] conductance led successively to slow oscillations in the delta range (1-4 Hz), then to waxing-and-waning slow oscillations and, finally, to the relay resting state, consistent with in vitro studies (290) (compare with Fig. 3A). According to this mechanism for waxing-and-waning oscillation (Fig. 3Bii), calcium enters through [I.sub.T] channels on each burst, resulting in an increase of [Ca.sup.2+] (or [Ca.sup.2+]-bound messenger) and a gradual increase of [I.sub.h] channels in the open state ([O.sub.L]). This produces a progressive afterdepolarization (ADP) following each burst until the cell ceases to oscillate (Fig. 3Bii). The membrane then progressively hyperpolarizes during the silent period, as [I.sub.h] channels unbind the messenger.
The presence of this ADP was observed during waxing-and-waning oscillations in cat TC cells maintained in low magnesium in vitro (191), as well as in ferret thalamic slices (19). It is possible to artificially induce this ADP by evoking repetitive burst discharges in TC cells (19). The ADP is responsible for a marked diminution of input resistance in successive responses (19). These features were observed in a model based on the upregulation of [I.sub.h] by [Ca.sup.2+] (96).
Recent experiments provide direct evidence for the [Ca.sup.2+]-dependent regulation of [I.sub.h] channels predicted in modeling studies. Although [Ca.sup.2+] does not directly modulate [I.sub.h] channels in thalamic neurons (44), experiments with caged [Ca.sup.2+] in thalamic neurons have demonstrated an indirect calcium-dependent modulation of [I.sub.h] (212), with cAMP acting as the intermediate messenger (213).
B. Thalamic Reticular Neurons
1. Rebound bursts in thalamic reticular cells
RE neurons recorded in awake animals fire tonically, but during slow-wave sleep the activity of these cells changes to rhythmic firing of bursts (307). A typical burst of action potentials in an RE cell during natural sleep shows an accelerando-decelerando pattern of action potentials (Fig. 4A). In intracellular recordings, both modes of firing in RE cells could be elicited, depending on the membrane potential. Depolarizing current pulses from -68 mV produced tonic firing, whereas the same pulse delivered at more hyperpolarized levels elicited a burst. The burst in a model RE cell shows a slowly rising phase and is broader than in TC cells, and there is always an accelerando-decelerando pattern of sodium spikes, typical of RE cells recorded from anesthetized, naturally sleeping animals as well as in animals under different anesthetics (59, 107, 237, 307) (Fig. 4A).
[FIGURE 4 OMITTED]
The rebound burst of RE cells studied hl vitro (14, 17), like that of TC cells, is mediated by a low-threshold [Ca.sup.2+] current. However, the characterization of the T-type [Ca.sup.2+] current in RE cells by voltage-clamp methods revealed marked differences with the [I.sub.T] of TC cells. In RE cells, the kinetics were slower and the activation was less steep and more depolarized than that found in TC cells (163). This current was named "slow [I.sub.T]", or [I.sub.Ts]. In some preparations, however, the [I.sub.T] of RE cells appears to be similar to that of TC cells (333). Nevertheless, the observation of two distinct types of T channels is consistent with the differences observed after reconstitution of cloned T channels, which displayed different voltage dependence and kinetics and regional distribution (321). In particular, thalamic relay and reticular neurons express different T-channel subtypes (321), consistent with the electrophysiological differences found between TC and RE neurons (163).
2. Models of the rebound burst in RE cells and the role of dendrites
The properties of burst generation in RE cells were examined in Hodgkin and Huxley (157) types of models derived from voltage-clamp measurements. Early models (90, 355) used a [I.sub.T] similar to that found in TC cells, based on the data available at that time (14, 208, 228). More recent characterization of the kinetics of the [I.sub.T] in RE cells (163) has led to more accurate models of [I.sub.Ts] in these cells (97, 348).
Although single-compartment Hodgkin-Huxley type models were able to account for the genesis of bursts in RE cells, not all features of these bursts were found. For example, the slowly rising phase of the burst, …