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In the arousal process from sleep and anesthesia, the brain restores its integrative and complex activity from the synchronized state of slow wave activity (SWA) characteristic of NREM sleep. The mechanisms and dynamics of the cortical network underpinning this state transition remain however to be elucidated. Here we investigated the progressive shaping of SWA propagating through the cortex on the way to wakefulness. Using micro-electrocorticographical recordings in the mouse, we pharmacologically increased levels of slow-wave frequency and complexity from deep unconsciousness toward wakefulness, and probed several single neuronal assemblies throughout the whole cortex. We found a form of memory in the SWA at deep anesthesia, with a tight alternation of posterior-anterior-posterior modes of slow-wave propagation. When approaching wakefulness, metastable patterns of spiking cortical activity propagated in many more directions, reflecting an increased complexity in the network dynamics. We unveil a temporal component of the dynamics of the waves’ mesostates, predicted by simulations of a model network of spiking neurons and confirmed in our experimental data. Local excitability suffices to explain the transition from sleep to wakefulness without requiring modifications of the network connectivity. These results shed new light on the functional re-organization of the cortical network in the awakening brain.

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=== **Introduction** ===

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During sleep and anesthesia, the brain spontaneously generates patterns of low-frequency, synchronized activity referred to as slow-wave activity (SWA) (Destexhe et al., 1999; Massimini et al., 2004; Mohajerani et al., 2010; Steriade et al., 1993a). This activity coordinates large portions of the cortex into a coherent rhythmic sequence of recurring cortical and cortico-thalamic activations (Destexhe and Sejnowski, 2003; Grenier et al., 1998; Muller et al., 2016, 2018; Sheroziya and Timofeev, 2014). In this state, cortical neurons undergo a slow alternation between periods of depolarization and firing (Up or On states) and periods of almost-silent hyperpolarization (Down or Off states) (Steriade et al., 1993b; Torao-Angosto et al., 2021; Vyazovskiy et al., 2009). This is accompanied by reduced amounts of neuronal excitability and enhanced segregation of cortical areas (Bettinardi et al., 2015; Compte et al., 2003; Fernandez et al., 2017; Fischer et al., 2018; Levenstein et al., 2019; Liu et al., 2013; Massimini et al., 2004, 2005; Mattia and Sanchez-Vives, 2012; Muller and Destexhe, 2012; Sanchez-Vives and Mattia, 2014; Sanchez-Vives and McCormick, 2000). Slow oscillations are believed to interact with the other characteristic signatures of sleep, like spindles reaching the cortex from the thalamus. These nested oscillations might be responsible for cognitive processes such as memory consolidation (Muller et al., 2016, 2018). However, a characterization of the modes of propagation of the slow oscillations at the level of single neuronal assemblies during the process of emergence to consciousness is still missing.

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In the last two decades, several studies have approached the transition between the unconscious and the awake state, by means of recordings at various depths of either natural sleep or anesthesia, as well as during the process of awakening (Barttfeld et al., 2015; Bettinardi et al., 2015; Dasilva et al., 2021; Fischer et al., 2018; Hahn et al., 2012; Hudetz et al., 2015; Hudson et al., 2014; Lee et al., 2020; Li and Mashour, 2019; Liu et al., 2013; Schartner et al., 2017; Tort-Colet et al., 2019). Results from single – or a small number of simultaneously recorded – areas (including primary visual (Hudetz et al., 2015; Lee et al., 2020; Vizuete et al., 2012), cingulate (Hudson et al., 2014), retrospenial (Hudson et al., 2014), temporo-parieto-occipital (Fischer et al., 2018) cortices and the thalamus (Hudson et al., 2014)), as well as from the whole cortex (Barttfeld et al., 2015; Bettinardi et al., 2015; Dasilva et al., 2021; Grandjean et al., 2014; Li and Mashour, 2019; Liu et al., 2013; Schartner et al., 2017), showed that during the emergence from deep anesthesia (NREM sleep) the frequency of the slow oscillations increases and the network activity strengthens its integration and complexity dynamical properties, possibly starting to wander among so-called micro-states that involve a varying number of frequency bands (Brodbeck et al., 2012; Dasilva et al., 2021; Hudson et al., 2014; Lee et al., 2020; Liu et al., 2013). These studies support the hypothesis that the anesthetized (sleeping) brain is not confined in a static dynamical state, but actually explores a more complex landscape, eventually operating a rather progressive state transition to wakefulness (Barttfeld et al., 2015; Dasilva et al., 2021; Li and Mashour, 2019; Stevner et al., 2019). However, these studies investigated the features of the brain activity during the recovery of consciousness either at a coarse spatial scale, or focused on general signatures of the neuronal activity. How the activity of single neuronal assemblies propagates through the cortex, and which mechanisms lead to its emergence and transmission, is still to be described.

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Several mechanisms are thought to play a role during the emergence of slow-wave states, and during the inverse process that leads to awakening (Deco et al., 2014; Destexhe and Sejnowski, 2003; Längkvist et al., 2012; Mattia and Sanchez-Vives, 2012; Pearlmutter and Houghton, 2009; Sanchez-Vives et al., 2017; Stevner et al., 2019; Tort-Colet et al., 2019). These include cortico-thalamic loops (Crunelli and Hughes, 2010; Crunelli et al., 2015; Destexhe and Sejnowski, 2003; Grenier et al., 1998; Merica and Fortune, 2004; Sheroziya and Timofeev, 2014; Steriade et al., 1993a) and the balance between local dynamical features and global connectivity of the brain network shaping its integration and segregation capabilities (Barttfeld et al., 2015; Deco et al., 2014, 2015; Mohajerani et al., 2013). At the cellular and local cortical assembly level, various experimental and modelling studies pointed at two main players playing a critical role in the process of awakening: firing adaptation of excitatory cortical neurons, and neuronal excitability (Compte et al., 2003; Lee et al., 2020; Levenstein et al., 2019; Mattia and Sanchez-Vives, 2012; Muller and Destexhe, 2012; Sanchez-Vives and McCormick, 2000). However, the network mechanisms underlying this state transitions remain to be conclusively elucidated. In particular, an open question is the role played by the restored levels of local excitability and long-range connectivity in shaping the activity observed at different levels of anesthesia as the awake state is approached. Importantly, the presence and the properties of the travelling wavefronts underlying the well-established slow oscillations and of how their propagation mode throughout the cortex changes during the awakening process has not yet fully understood and characterized.

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Here, by probing the electrophysiological activity of neuronal populations across a wide area of the mouse cortical surface in the arousal from deep anesthesia, we addressed the following question: what are the mechanisms and network features that steers the transition between the fully anesthetized and the awake state? We analyzed recordings from different mice and at varying levels of slow-wave anesthesia sorting them on a common fine-grained scale. For that purpose, we used a cocktail of anesthetics that allowed us to progressively approach the wake state in a controlled way. We developed an objective and quantitative measure of the level of complexity of the slow waves based on their frequency and the entropy of the wavefronts of propagation through the cortex, referred to as the wave entropy index (WEI). We described the progression from the simple, irregular spatio-temporal patterns of spiking activity characteristic of sleep and deep anesthesia to the spatially complex, albeit temporally regular patterns that are encountered when approaching wakefulness. We found a significant correlation between the WEI and the number of spontaneously expressed modes of propagation, and the progressive loss and recovery of sequential memory between consecutive waves. Resorting to a spatially-extended spiking neuron network modelling the cortical surface probed in experiments, we show how the rise of complexity is obtained without modifying the underlying “structure”, i.e. the cortico-cortical connectivity. Changes in the local excitability alone suffice to explain the dynamical transition of the global cortical network in the arousal process from deep anesthesia, supporting the hypothesis of a tight binding between scales in the brain.

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=== **Results:** ===

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=== **Lightening up of anesthesia increases frequency and complexity of slow waves** ===

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In order to understand the local and global changes underpinning the progressive transition of the cortical network in the arousal process from deep anesthesia, we recorded the ongoing neuronal activity across three levels of anesthesia (isoflurane) in the intact mouse brain. We placed a multi-electrode array (MEA) of 32 channels on the cortical surface of //n=8// wild-type mice (Fig. 1A, left; see Materials and Methods). The probed surface spanned several cortical areas including both sensory and motor cortices of a single hemisphere (Fig. 1A, right). Anesthesia levels were finely tuned to induce slow-wave activity (SWA), i.e. the quasi-periodic alternation between slowly propagating onsets of high-firing Up states and almost quiescent Down periods across the probed surface ((Liu et al., 2013; Ruiz-Mejias et al., 2011; Torao-Angosto et al., 2021; Vijayan et al., 2010); Fig. 1B). Spontaneously occurring spatiotemporal patterns were well visible in the multi-unit activity (MUA) signals although electrophysiological recordings were epicortical and not intraparenchymal (Fig. 1B). This allowed us to characterize the changes in the onsets and offsets of the Up states with the lightening up of the anesthesia levels at multiple spatial and temporal scales. The timing of Down-Up transitions for every channel led to a time-lag matrix (TLM) (Capone et al., 2019; Ruiz-Mejias et al., 2011), where each row corresponds to a wavefront containing the relative delays in the channels activation (Fig. 1C-bottom, Materials and Methods). Computing the principal components (Jolliffe and Cadima, 2016) of the TLM and transforming the eigenvalue distribution of the covariance matrix into probabilities, we estimated the number of the effective dimensions (i.e., the principal components) of the space embedding the activation wavefronts. The number of effective dimensions strongly correlates with the slow-wave frequency across experiments and anesthesia levels (Fig. 1D, //n=24// ). Interestingly, the projection of each of these points onto the first principal component of the distribution (blue line in Fig. 1D) is not only coherent with the corresponding isoflurane level (Fig. 1E), but it also allows to finely classify the experiments according to their effective level of slow-wave anesthesia. We called the projected value on this axis the “wave entropy index” (WEI), and used it to visualize the progression of other relevant quantities across the different anesthesia levels.

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[[image:Fig1_v8.png]]

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,,//Figure 1: Extraction of the wave entropy index (WEI) from slow-wave dimensionality and frequency.//,,

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,,//A. Superficial 32-channel multi-electrode array placed on the cortical surface of anesthetized mice (left) and schematic representation of the recorded cortical areas (right, as in (Dasilva et al., 2021)). B. Representative raw recordings and log(MUA) for one experiment in three anesthesia levels. Grey: average of all channels; black: representative channel. C. Top: representative average log(MUA) (black), threshold used to extract the Up states (red) and identified Up and Down states (grey and white periods, respectively). Middle: single-channel log(MUA) of activation fronts (Down-Up transitions) from an example slow-wave (circles). Bottom right: time-lags δ of each state transition from the center of a wave compose the rows of the blue-red time-lag matrix (TLM, bottom). Bottom left: flow chart of the method used to work out the wave entropy index (WEI) based on measure of the effective dimension of the TLM and the frequency of Down-Up waves occurrence. EV: eigenvalues D. Effective dimension (see Materials and Methods) and mean frequency of the Down-Up transitions normalized by their variance and centered around their mean for each recording (n=24, 8 mice and 3 anesthesia levels each). Blue line: first principal component, onto which the single recordings are projected thus defining the wave entropy index (WEI). E. WEI values versus anesthesia concentration.//,,

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**Figure 1**: Extraction of the wave entropy index (WEI) from slow-wave dimensionality and frequency.

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**A. **Superficial 32-channel multi-electrode array placed on the cortical surface of anesthetized mice (left) and schematic representation of the recorded cortical areas (right, as in (Dasilva et al., 2021)). **B.** Representative raw recordings and log(MUA) for one experiment in three anesthesia levels. Grey: average of all channels; black: representative channel. **C. **Top: representative average log(MUA) (black), threshold used to extract the Up states (red) and identified Up and Down states (grey and white periods, respectively). Middle: single-channel log(MUA) of activation fronts (Down-Up transitions) from an example slow-wave (circles). Bottom right: time-lags δ of each state transition from the center of a wave compose the rows of the blue-red time-lag matrix (TLM, bottom). Bottom left: flow chart of the method used to work out the wave entropy index (WEI) based on measure of the effective dimension of the TLM and the frequency of Down-Up waves occurrence. EV: eigenvalues **D. **Effective dimension (see Materials and Methods) and mean frequency of the Down-Up transitions normalized by their variance and centered around their mean for each recording (//n=24//, 8 mice and 3 anesthesia levels each). Blue line: first principal component, onto which the single recordings are projected thus defining the wave entropy index (WEI). **E.** WEI values //versus// anesthesia concentration.

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As expected, both the number of effective dimensions and the frequency of Down-Up transitions fit well with the WEI (Fig. 2A, B). Furthermore, both the coefficient of variation of the Up-Down cycles (CV) and the duration of the Up states have a significant linear correlation with the WEI (Fig. 2C, D). The increase of SWA frequency is mainly due to the modulation of the Down state duration, which shows the largest exponential-like reduction with the WEI (Fig. 2E). The maximal firing rate of the cortical assemblies, measured as the peak amplitude of the Up states, shows a significant decrease as a function of the WEI (Fig. 2F).

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