INTRODUCTION

Electrical activity is essential for neuronal communication. Over the years, in vivo multielectrode recordings have revealed that the electrical activities of individual neurons are not independent of each other. Instead, neurons tend to fire in a coordinated way within a given neural network. When measured as the electroencephalogram (EEG) or local field potential (LFP) signals, this neural coordination results in complex oscillatory activity patterns, which reflect synchronous synaptic potentials in a local network (Lopes da Silva 1991). Thus, unveiling the physiological mechanisms generating such complex oscillatory neural activity patterns is key to achieving a better understanding of how the brain operates in behaving animals.

The dynamics of the forebrain is not random. Ever since the initial discovery of cerebral electrical activity by Caton (Caton 1875) in rabbits and monkeys, and later in humans by Berger (Berger 1929), different patterns of forebrain activity have been tightly linked to various behavioral and wake-sleep states. Indeed, these distinct patterns of neural activity have become incorporated as part of the criteria of wake-sleep states (Green and Arduini 1954; Rechtschaffen and Kales 1968; Lopes da Silva and van Leeuwen 1969; Timo-Iaria et al. 1970; Moruzzi 1972; Winson 1972; Winson 1974; Gottesmann 1992; Steriade et al. 1993), suggesting that forebrain dynamics fall into several different regimes. This observation is intriguing because the same neural circuit can support several different dynamic regimes, which likely serve distinct roles in information processing and storage. Therefore, a quantitative description of its network dynamics can further reveal how the forebrain underlies so many fundamental functions in mammals.

In this chapter, we first describe the forebrain oscillatory activity patterns associated with different wake-sleep states, and highlight limitations of existing state identification methods. Then, we introduce a novel state-space framework (Gervasoni et al. 2004) that we have employed to quantitatively describe global forebrain dynamics in rodents. Such an analysis revealed several distinct regimes in which the forebrain can operate. These regimes correspond to distinct global brain states and are correlated with the occurrence of major wake-sleep states observed in both rats and mice. In addition, the state-space framework proposed here has allowed us to characterize the gradient dynamics within global brain states, providing a quantitative description of state transition dynamics in rodents. We end this chapter by discussing the underlying driving forces and potential functional roles of global brain states.

FOREBRAIN DYNAMICS IN DIFFERENT WAKE-SLEEP STATES

In mammals, the wake–sleep cycle consists of periodic alternation of three major behavioral states: waking (WK), slow-wave sleep (SWS), and rapid-eye-movement (REM) sleep. In conjunction with prominent changes in the behavior of the animal, these behavioral states are associated with remarkably different forebrain dynamics (Figure 8.1C). During WK, animals interact with their environment either actively or passively to acquire information about their immediate surrounding space. At the same time, cortical activity is dominated by low-amplitude fast oscillations (beta and gamma frequency bands, >20Hz) (Figure 8.1D) (Murthy and Fetz 1992; Steriade et al. 1993; Maloney et al. 1997; Rols et al. 2001). As the animal actively explores the environment, LFP activity displays prominent theta oscillations (5–7 Hz), especially in the hippocampus (Winson 1974; Buzsaki et al. 1990). These oscillations are modulated according to the level of arousal, attention, motor activity, and the presence or absence of incoming stimuli (Murthy and Fetz 1996; Fries et al. 2001; Fell et al. 2003; Buzsaki and Draguhn 2004).

FIGURE 8.1

Local field potentials and behavioral states. (A) Schematic representation of the location of the multielectrode implants on a parasagittal section of a rat brain. The primary somatosensory cortex (Cx), the hippocampus (Hi), the ventromedial posterior (more...)

In contrast to WK, sleep appears as a periodical state of quiescence, in which there is minimal processing of incoming sensory information. The behavioral hallmark of this state could thus be summarized as a suspension of the activities of the waking state. However, sleep is not defined by a homogenous state. At the very least, it can be divided into two distinct states, each named after its main neurophysiological features. As animals fall asleep, slow coherent oscillations emerge in the cerebral cortex in different frequency bands (delta waves 1–4 Hz and spindles 7–14 Hz) (Steriade and McCarley 1990; Steriade et al. 1993) characterizing a first sleep state called slow-wave sleep, or non-REM sleep. These oscillations are organized into complex wave sequences by a very slow oscillation (usually 0.6–1 Hz) (Amzica and Steriade 1995; Contreras and Steriade 1995), and are concomitant with a progressive sensory disconnection (Moruzzi 1972; Steriade and McCarley 1990). As SWS deepens, spindling activities tend to decrease while delta waves become more prominent, with an intensity that correlates with the duration of the preceding awake state (Dijk et al. 1990).

After a certain time spent in SWS, a second sleep state ensues, characterized in humans by dreaming and conspicuous REM. Appropriately, this state has been named REM sleep (Aserinsky and Kleitman 1953; Dement and Kleitman 1957). During REM sleep, the cortical activity is quite similar to that observed during WK (Winson 1974; Borbely et al. 1984). That means that, for instance, in rats prominent gamma oscillations (Maloney et al. 1997; Gross and Gotman 1999) and theta oscillations (Vanderwolf 1969) are observed during this sleep state.

Although cortical activity of REM sleep is remarkably similar to that of WK, the functional sensory disconnection of the cortex reaches a maximum and motor output is actively suppressed (Dement and Kleitman 1957; Jouvet et al. 1959; Jouvet 1962). This has motivated some authors to propose an alternative nomenclature for REM sleep, calling it either activated (Aserinsky and Kleitman 1953) or paradoxical sleep (Jouvet 1962).

STATE-SPACE FRAMEWORK REVEALS GLOBAL BRAIN STATES

Five years ago, we set out to develop a novel framework to quantitatively describe the type of global forebrain dynamics that defines distinct awake-sleep states. This novel approach was based primarily on analyzing the spectral information of LFPs. To avoid the limitations of the state-coding algorithms originating from predefining a set of categorically different states, we took the alternative approach. This involved representing the LFP spectral information with continuous-scale spectral features. Our assumption at the time was that if appropriate spectral features were chosen, one would be able to not only reveal global dynamic states generated by the forebrain, but also provide highly quantitative descriptions of the transition processes involved in switching from one state to another. Furthermore, because behavioral states are known to be associated with different forebrain dynamics, the spectral features we chose should also be able to separate the major behavioral states generated by our subjects (rats and mice). Such a framework could further address questions such as: how many distinct brain states really exist? Are these dynamic states different categorically or part of a continuous spectrum? Do state transitions follow stereotypical sequences?

In the next section we describe the approach that allowed us to implement the novel state-space framework required to address these broad issues (Gervasoni et al. 2004).

2-D State Space

To reveal the stable neuronal dynamic regimes of forebrain networks, we focused on investigating the spectral content of forebrain LFP activity. LFPs were represented in the frequency domain as power spectrogram (Figure 8.1D), with the amplitude of each frequency bin calculated every second of the data record. Consistent with our understanding of spectral patterns in different wake-sleep states, the spectrogram showed more theta and gamma oscillation power during WK and REM, and more delta and spindle oscillations during SWS.

The grouping of frequency bins into frequency bands indicated that different frequency bins were not independent of each other. The implication is that if covarying frequency bins were appropriately combined, the spectrogram could be represented with much fewer variables, while still preserving most of the information. In the literature of statistical pattern recognition (Webb 2002), this is equivalent to a dimension reduction problem, i.e., representing a high-dimensional data set (in our case, many frequency bins) with only a few variables (spectral features).

One commonly used dimension reduction technique is principal component analysis (PCA), which searches for linear combinations of original variables in the high-dimensional data set, called principal components (PC), that explain the maximal amount of variability of the original data. Successive PCs contain orthogonal combinations of original variables, and are sorted by the amount of variability each PC explains. Thus, most of the information of the high-dimensional data set could be represented by the first few PCs that account for most of the variability. When PCA was applied to the spectrogram, the first two PCs (Figure 8.2A, left panel) typically explained 70–80% of the total variability of the LFP spectrogram.^* The spectral combinations of the first two PCs were similar in shape when calculated from different forebrain LFPs.

FIGURE 8.2

(See color insert following page 140.) Construction of state-space map. (A) Left panel, spectral features (PC1 and PC2) obtained by applying PCA to the spectrogram of individual forebrain LFPs in one rat. Right panel, difference of the average amplitude (more...)

A different dimension reduction strategy, such as linear discriminant analysis, relies on the knowledge of underlying categories and searches for features that best differentiate these classes. In our case, we were interested in finding spectral features that at least can separate the three major wake-sleep states. Assuming multidimensional normal distribution of spectral amplitudes within each class, the discriminant features correspond to the difference of the average spectrum between wake-sleep states. As illustrated in Figure 8.2A (right panel), the main spectral difference between SWS and WK states is in the slow frequency oscillations (<20 Hz), whereas the spectrums of WK and REM mainly differ in the delta (1–4 Hz) and theta (5–9 Hz) oscillations in opposite directions.

The spectral features obtained from these two different approaches were qualitatively similar (Figure 8.2A), indicating that these two features preserved most of the information about LFP spectrograms and at the same time could differentiate behavioral states. Based on these features, we developed a 2-D state-space framework to represent the LFP spectral information (Figure 8.2B). While focusing on the same frequency bands revealed by these spectral features, we chose to represent them in the form of spectral amplitude ratios: x-axis 0–4.5/0–9 Hz and y-axis 0–20/0–55 Hz. These ratios were designed such that the numerator frequency band was always contained in the denominator frequency band, so that the ratios were bounded in the [0, 1] range. These ratios provided the advantage of within-animal normalization that does not depend on the absolute amplitude of LFP signals, and were therefore easier to interpret and compare across animals. These two spectral features were calculated for each second of LFP data, plotted as a point in the 2-D state space. Contiguous points in the state space can be joined to form state trajectories, which provide temporal dynamic information on how spectral patterns evolve through time. Moreover, the speed of spectral evolution can be quantified as the spatial distance between temporally adjacent points on the same trajectory, or trajectory speed.

Global Brain States

Initially, the 2-D state space revealed at least three well-defined clusters in each animal (Figure 8.3). The presence of clusters indicated that the forebrain dynamics preferentially spent time in those dynamic patterns. These clusters correspond to stable dynamic regimes of the forebrain network, i.e., the main global brain states observed in mammals. The demonstration of clearly separated clusters indicates that the three global brain states are categorically different dynamic regimes. To further confirm this result, we calculated the average trajectory speed on each part of the state space (Figure 8.3C). Regions of the state space where spectral features changed slowly coincided with the three main clusters, whereas regions of fast spectral changes corresponded to transitional zones between major clustfers. This result confirmed that clusters represent stable forebrain dynamic regimes: when the forebrain dynamics entered one of the three attractor states, the system was quite stable and moved little. On the other hand, points between clusters represent transitions between global brain states.

FIGURE 8.3

(See color insert following page 140.) Global brain states. (A) Scatter plots of the 2-D state space, color-coded for behaviorally coded states. Each dot corresponds to a 1 s window from which the amplitude ratios were calculated. For all animals, 48 (more...)

GLOBAL BRAIN STATES: THE NEURAL CORRELATES OF WAKE-SLEEP STATES

As these spectral features were also optimized to distinguish between the three major behavioral states, it is important to evaluate how global brain states correspond to behaviorally coded wake-sleep states. When behavioral states were color-coded onto the state space, the three main clusters grossly corresponded to the three major wake-sleep states (Figure 8.3A). The SWS cluster occupied the upper-right quadrant because the prominent slow oscillations (0–20 Hz) lead to a high value on the y-axis, and the prominent delta oscillations (1– 4 Hz) lead to a high value on the x-axis. Both REM and WK clusters had smaller values on the y-axis compared to the SWS cluster. REM cluster was located to the left of the WK cluster because the highly prominent theta oscillations (5–9 Hz) during REM lead to smaller values on the x-axis. Although a considerable degree of interanimal variability is to be expected when recording from outbred laboratory animals, we found remarkable similarity across the state space obtained for different animals.^* In all animals we investigated, the relative positions of the three major clusters were highly conserved.

State-Coding Algorithm

For a quantitative comparison between the state-space framework and behavioral state coding, we developed an algorithm to convert the continuous-scale state-space representation into discrete global brain states focusing on the three main clusters (Figure 8.4). The spirit of this algorithm was to take advantage of the well-separated clusters and the temporal information inherent in the state space, as opposed to treating each time point as an independent sample. Because we have demonstrated that the three major clusters were stable attractor states in the state space, we considered all short trajectories (less than 20 s) leaving and reentering a given cluster boundary without touching the boundaries of other clusters as random fluctuations of the same cluster. The system was considered to be moving toward a different state only after the trajectory leaves the cluster boundary for an extended period of time. Thus, points outside the initial cluster boundaries could also be assigned to the major states, depending on their temporal continuity with adjacent clusters. Data points not coded as any of the major states (15–20%) were labeled state transitions (Figure 8.4).

FIGURE 8.4

Automatic state-coding algorithm. Comparison of automatic state-coding with behavioral states in two rats. Upper panel, contour maps show cluster boundaries (red contour) corresponding to the three main clusters. State labels were color-coded and overlaid (more...)

Cluster boundaries could be determined in one of two ways: (1) when enough data points were available (preferentially at least 24 h continuous recording), cluster boundaries could be determined objectively by identifying nonoverlapping contours in the 2-D histogram around the main clusters (Figure 8.4, upper panel); (2) In smaller datasets, however, cluster boundaries have to be manually determined. However, with the incorporation of state trajectory information, the choice of the actual cluster boundaries mattered less to the final state identifications.

Our state identification algorithm purposefully left state trajectories between clusters not assigned to particular states, because those epochs represented state transitions during which the dynamics of the forebrain network does not resemble any of the global brain states. This ensured that the global brain states we identified are physiologically homogeneous. State transitions were studied with trajectory analyses and will be discussed later.

Validation against EMG Activity in Mice

We have also applied the state-space framework to describe the forebrain dynamics of wild-type mice. Using LFPs recorded from mice hippocampus, similar clusters and topography were observed (Figure 8.5A and Figure 8.5B). As one distinctive feature of REM state is the lack of muscle tone, the REM epochs should have much lower EMG activity. As predicted, when neck muscle EMG activity was plotted as the third dimension of the state space, REM epochs showed little or absent EMG activity, while the adjacent WK cluster had maximal EMG activity (Figure 8.5C).

FIGURE 8.5

(See color insert following page 140.) Global brain states in mice. Scatter plot (A) and density plot (B) of the 2-D state space generated using hippocampal LFPs recorded in one mouse. Similar cluster structures as those described in rats (Figure 8.3A) (more...)

Taken together, these experiments demonstrated the existence of at least three global brain states in both rats and mice. We further showed a strong correspondence between global brain states and behaviorally coded wake-sleep states. These results indicate that global brain states represent the neural correlates of wake-sleep states.

GRADIENTS AND FUNCTIONAL SUBDIVISIONS WITHIN GLOBAL BRAIN STATES

In addition to the categorically different global brain states represented by the main clusters, several observations indicated that gradient subdivisions exist within the global brain states, especially within the SWS and WK clusters.

The SWS cluster was typically elongated with an elliptical shape. The two poles of the cluster were asymmetric because the SWS cluster connected with other clusters only through one pole. Further supporting this asymmetry, we observed that within the SWS clusters, there were graded changes in the average spectral power and coherence in multiple frequency bands over the long axis of the cluster (Figure 8.6). The pole of entrance and exit of the SWS cluster showed higher spindle power (8–14 Hz), whereas the other pole of SW showed more prominent delta activity (1–4 Hz). Parallel changes in spectral coherence were also observed. These graded differences within the SWS cluster resemble the distinction between light and deep SWS. As animals fall asleep, the light SWS is characterized by more spindle activity, whereas deep SWS is characterized by more delta oscillations. These observations also suggest that the distinction between light and deep SW is a graded one, but not a categorical one.

FIGURE 8.6

(See color insert following page 140.) Gradients within global brain states. Overlay of spectral power and coherence in different frequency bands on the 2-D state space of one rat. Spectral power was calculated on the log scale, averaged across all forebrain (more...)

Similarly, asymmetry and gradients were observed in the WK cluster (Figure 8.6). The WK cluster was comprised of a main cluster with an extension on the left side toward the REM cluster. The WK cluster connected with other clusters primarily through the main cluster, but not through the leftward-extending part. Graded changes in theta oscillation (5–8 Hz) power and coherence were observed along the horizontal axis of the WK cluster, with theta oscillations being more prominent on the left side of the WK cluster.^* A similar gradient was also observed for gamma oscillation (25–55 Hz) power. This division of the WK cluster corresponds to the behavioral distinction between QW and AE epochs, with the main WK cluster corresponds to QW epochs and the AE epochs correspond to the leftward extension of the WK cluster (see Figure 8.3A). This distinction also appears to be a graded subdivision and could reflect variations in the attentional and arousal levels within the WK state.

The state-space representation using continuous scales thus provides quantitative descriptions of gradient substates within global brain states. Such functional subdivision within the main behavioral states could contribute to, and potentially account for, variabilities observed at behavioral and neurophysiological levels. These observations also demonstrate that overlaying state-dependent information on the 2-D state space provides a comprehensive assessment of all behavioral states at the same time.

FOREBRAIN DYNAMICS DURING STATE TRANSITIONS

The 2-D state space also provides information about the temporal dynamics of state evolution in the form of “state trajectories.” The trajectory information is most valuable when one intends to study how forebrain dynamics evolves from one state to another, defining a series of state transition processes. In the state space, state transitions can be defined as trajectories directly connecting two clusters. These state-transition trajectories turned out to have well-defined stereotypical trajectory patterns, along with characteristic transition durations (Figure 8.7A).

FIGURE 8.7

(see facing page) (See color insert following page 140.) Trajectory analysis. (A) Five state transition trajectories were illustrated, along with example LFP epochs. The first two trajectories, WK→SWS and REM→WK, represent typical fast (more...)

Several examples of state transitions are illustrated in Figure 8.7A. The first two state transition trajectories, WK→SWS and REM→WK, represent typical fast state transitions with straight paths linking the two clusters. The durations of these trajectories are typically less than 20 s. Inspection of the corresponding LFP epochs showed that these state transitions were typically fast and steplike (Figure 8.7A, right panel in the top two rows), without involving an intermediate stage during the transition.^* The other state transition in this category is SWS→WK (data not shown).

The most notable finding resulting from state trajectory analyses was the clear demonstration of the intermediate stage of sleep (IS) (Gottesmann 1996). Even though IS epochs were not behaviorally scored, IS state was clearly identified in three state transition trajectories: SWS→IS→REM, SWS→IS→WK and REM→IS→WK (Figure 8.7A, three lower rows). These state trajectories invariantly traversed through the left upper corner of the state space with stereotypical pathway patterns. Unlike the fast transitions with straight trajectories discussed in the last paragraph, these trajectories were curved and lasted longer than 30 s, indicating the presence of an intermediate stage during the transitions. The presence of an intermediate stage was further evidenced by the reduced trajectory speed in the left upper corner of the state space compared to areas around it (Figure 8.3C), indicating the presence of a relatively stable regime. The corresponding LFPs showed prominent oscillations present simultaneously in all forebrain regions (Figure 8.7A, right panel in the three lower rows).

The upper left corner of the state space where IS state is located corresponds to LFP epochs with high-amplitude low-frequency (<20 Hz) oscillations (y-axis) and high-amplitude theta oscillations (x-axis) (Figure 8.6). These properties are consistent with the description of IS, characterized by high-amplitude spindle oscillations in the cortex and prominent theta oscillations in the hippocampus (Gottesmann 1996). Our observation that high-amplitude spindle oscillations were present in all forebrain regions led to the demonstration that these oscillations were coherent across forebrain regions over a wide frequency range (8–20 Hz) (Figure 8.7B). Indeed, the IS state possessed the highest coherence in this frequency range in the entire state space (Figure 8.6).

These results also reveal that when animals wake up from SWS, two possible and parallel transition sequences exist, through SWS→WK or through SWS→IS→WK. Although the two transitions could be behaviorally indistinguishable, they could have opposite effects on the learning ability in rats (Vescia et al. 1996). Our results therefore strongly argue that the IS state should be independently identified in any state-coding algorithms designed to describe the structure of sleep.

GENERAL DISCUSSION

The Driving Forces: Neuromodulatory Systems

The identification of global brain states relies only on LFP spectral patterns, which reflect the summation of synaptic potentials and intrinsic currents, the amplitude of which is correlated to the degree of coherent activity in a population of neurons. These coherent activities are generated either locally or through long-range interactions between different forebrain regions.

The existence of multiple dynamic regimes in the same anatomical forebrain network is intriguing. Previous work in invertebrate systems has demonstrated that anatomical connectivity alone does not determine the dynamics of the system (Marder 1998; Selverston et al. 1998). Even in simple networks of 30 neurons where the circuit connectivity has been completely mapped out, these networks are capable of generating different dynamic patterns that cannot be derived directly from the connectivity. Instead, the dynamics of the network is mainly determined by short-term synaptic plasticity and, most importantly, by neuromodulatory inputs.

The same design principle is probably preserved evolutionarily as an efficient mechanism to dynamically modulate the activity of the mammalian forebrain. Global brain states are associated with, and directly modulated by, systematic changes in neuromodulatory activity arising from ascending neuromodulatory systems, including the pontine and basal forebrain cholinergic nuclei (Gu 2002; Jones 2003). Based on microdialysis and recording of neuronal activity (Jones 2003), most neuromodulatory systems, including acetylcholine (ACh), norepinephrine (NE), serotonin (5-HT), and histamine (Hist) systems have been shown to be active during WK and decrease their activity during SWS. During REM sleep, however, monoaminergic systems (NE, 5-HT, and HIst) virtually shut down, and only the cholinergic system remains active (Figure 8.8). These neuromodulatory systems project extensively to the entire forebrain and exert great influences on the excitability of neurons and the amplitude of synaptic potentials through metabotropic receptors (Kaczmarek and Levitan 1987; Marder and Calabrese 1996), thus sculpturing the dynamics of the forebrain network in different ways across distinct behavioral states.

FIGURE 8.8

Global brain states reflect neuromodulatory drives and mediate behavioral states. The state space is represented in three dimensions (z-axis corresponds to the value in the density plot). The concerted influence of multiple neuromodulatory systems located (more...)

In conclusion, neuromodulatory systems serve as the main driving force that determines the dynamics of the forebrain network, which, in turn, gates neuronal responses and behavioral outputs (Figure 8.8). In that regard, global brain states can also be considered as neural correlates of the activity of the underlying neuromodulatory systems.

CONCLUSIONS

Global brain states revealed by the state-space framework proposed here represent the neural correlates of behavioral wake-sleep states. These states can also be regarded as reflecting the underlying neuromodulatory drive provided by a vast and distributed neural circuitry (Figure 8.8). In addition to revealing the global brain states, the 2-D state space provides a quantitative description of gradient substates and state transition dynamics. As such, the 2-D state-space approach defines a novel and powerful method of studying state-dependent processes in behaving animals.

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Footnotes

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LFP amplitude spectrograms were calculated by running a sliding window Fourier transform with window size 2 s and step size 1 s. The resulting spectrogram was further smoothed, per frequency bin, with a 10-bin Hanning window to reduce spectral variations and increase the reliability of PCA transformation. When smoothing was not used, the first two PCs explained about 40% variability.

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The only exception was the location of the WT cluster. The general spectra of WT were very similar across animals, with the dominant oscillation at 7–12 Hz and resonant frequencies at 14–18 and 20–28 Hz. However, the relative amplitude at the resonant frequencies was substantially different among animals. There is a positive correlation between the amount of WT in each animal and the relative power at the resonant frequencies. This spectral difference at the resonant frequencies among animals accounted for the varying location of the WT cluster in the 2-D state map.

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Notice that while the SWS cluster possessed more spectral power in the theta range compared to the REM and WK clusters, theta coherence was more prominent in the REM cluster and the left half of the WK cluster than that of the SWS cluster.

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As a result of temporal smoothing in constructing the state space, the duration of trajectories (<20 s) is visibly longer than the duration of state transition revealed by inspecting LFP traces. In these direct and fast state transitions, the duration of state transition trajectories therefore primarily reflected the length of smoothing kernel.