Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure

A modular and adaptable analysis pipeline to compare slow cerebral rhythms across heterogeneous datasets

Neuroscience is moving toward a more integrative discipline where understanding brain function requires consolidating the accumulated evidence seen across experiments, species, and measurement techniques. A remaining challenge on that path is integrating such heterogeneous data into analysis workflows such that consistent and comparable conclusions can be distilled as an experimental basis for models and theories. Here, we propose a solution in the context of slow-wave activity (<1 Hz), which occurs during unconscious brain states like sleep and general anesthesia and is observed across diverse experimental approaches. We address the issue of integrating and comparing heterogeneous data by conceptualizing a general pipeline design that is adaptable to a variety of inputs and applications. Furthermore, we present the Collaborative Brain Wave Analysis Pipeline (Cobrawap) as a concrete, reusable software implementation to perform broad, detailed, and rigorous comparisons of slow-wave characteristics across multiple, openly available electrocorticography (ECoG) and calcium imaging datasets.

Recording physiological and pathological cortical activity and exogenous electric fields using graphene microtransistor arrays in vitro

Graphene-based solution-gated field-effect transistors (gSGFETs) allow the quantification of the brain's full-band signal. Extracellular alternating current (AC) signals include local field potentials (LFP, population activity within a reach of hundreds of micrometers), multiunit activity (MUA), and ultimately single units. Direct current (DC) potentials are slow brain signals with a frequency under 0.1 Hz, and commonly filtered out by conventional AC amplifiers. This component conveys information about what has been referred to as "infraslow" activity. We used gSGFET arrays to record full-band patterns from both physiological and pathological activity generated by the cerebral cortex. To this end, we used an in vitro preparation of cerebral cortex that generates spontaneous rhythmic activity, such as that occurring in slow wave sleep. This examination extended to experimentally induced pathological activities, including epileptiform discharges and cortical spreading depression. Validation of recordings obtained via gSGFETs, including both AC and DC components, was accomplished by cross-referencing with well-established technologies, thereby quantifying these components across different activity patterns. We then explored an additional gSGFET potential application, which is the measure of externally induced electric fields such as those used in therapeutic neuromodulation in humans. Finally, we tested the gSGFETs in human cortical slices obtained intrasurgically. In conclusion, this study offers a comprehensive characterization of gSGFETs for brain recordings, with a focus on potential clinical applications of this emerging technology.

Propagating population activity patterns during spontaneous slow waves in the thalamus of rodents

Slow waves (SWs) represent the most prominent electrophysiological events in the thalamocortical system under anesthesia and during deep sleep. Recent studies have revealed that SWs have complex spatiotemporal dynamics and propagate across neocortical regions. However, it is still unclear whether neuronal activity in the thalamus exhibits similar propagation properties during SWs. Here, we report propagating population activity in the thalamus of ketamine/xylazine-anesthetized rats and mice visualized by high-density silicon probe recordings. In both rodent species, propagation of spontaneous thalamic activity during up-states was most frequently observed in dorsal thalamic nuclei such as the higher order posterior (Po), lateral posterior (LP) or laterodorsal (LD) nuclei. The preferred direction of thalamic activity spreading was along the dorsoventral axis, with over half of the up-states exhibiting a gradual propagation in the ventral-to-dorsal direction. Furthermore, simultaneous neocortical and thalamic recordings collected under anesthesia demonstrated that there is a weak but noticeable interrelation between propagation patterns observed during cortical up-states and those displayed by thalamic population activity. In addition, using chronically implanted silicon probes, we detected propagating activity patterns in the thalamus of naturally sleeping rats during slow-wave sleep. However, in comparison to propagating up-states observed under anesthesia, these propagating patterns were characterized by a reduced rate of occurrence and a faster propagation speed. Our findings suggest that the propagation of spontaneous population activity is an intrinsic property of the thalamocortical network during synchronized brain states such as deep sleep or anesthesia. Additionally, our data implies that the neocortex may have partial control over the formation of propagation patterns within the dorsal thalamus under anesthesia.

Diversity of cortical activity changes beyond depression during Spreading Depolarizations

Spreading depolarizations (SDs) are classically thought to be associated with spreading depression of cortical activity. Here, we found that SDs in patients with subarachnoid hemorrhage produce variable, ranging from depression to booming, changes in electrocorticographic activity, especially in the delta frequency band. In rats, depression of activity was characteristic of high-potassium-induced full SDs, whereas partial superficial SDs caused either little change or a boom of activity at the cortical vertex, supported by volume conduction of signals from spared delta generators in the deep cortical layers. Partial SDs also caused moderate neuronal depolarization and sustained excitation, organized in gamma oscillations in a narrow sub-SD zone. Thus, our study challenges the concept of homology between spreading depolarization and spreading depression by showing that SDs produce variable, from depression to booming, changes in activity at the cortical surface and in different cortical layers depending on the depth of SD penetration.

M-current modulation of cortical slow oscillations: Network dynamics and computational modeling

The slow oscillation is a synchronized network activity expressed by the cortical network in slow wave sleep and under anesthesia. Waking up requires a transition from this synchronized brain state to a desynchronized one. Cholinergic innervation is critical for the transition from slow-wave-sleep to wakefulness, and muscarinic action is largely exerted through the muscarinic-sensitive potassium current (M-current) block. We investigated the dynamical impact of blocking the M-current on slow oscillations, both in cortical slices and in a cortical network computational model. Blocking M-current resulted in an elongation of Up states (by four times) and in a significant firing rate increase, reflecting an increased network excitability, albeit no epileptiform discharges occurred. These effects were replicated in a biophysical cortical model, where a parametric reduction of the M-current resulted in a progressive elongation of Up states and firing rate. All neurons, and not only those modeled with M-current, increased their firing rates due to network recurrency. Further increases in excitability induced even longer Up states, approaching the microarousals described in the transition towards wakefulness. Our results bridge an ionic current with network modulation, providing a mechanistic insight into network dynamics of awakening.

Simulations approaching data: cortical slow waves in inferred models of the whole hemisphere of mouse

The development of novel techniques to record wide-field brain activity enables estimation of data-driven models from thousands of recording channels and hence across large regions of cortex. These in turn improve our understanding of the modulation of brain states and the richness of traveling waves dynamics. Here, we infer data-driven models from high-resolution in-vivo recordings of mouse brain obtained from wide-field calcium imaging. We then assimilate experimental and simulated data through the characterization of the spatio-temporal features of cortical waves in experimental recordings. Inference is built in two steps: an inner loop that optimizes a mean-field model by likelihood maximization, and an outer loop that optimizes a periodic neuro-modulation via direct comparison of observables that characterize cortical slow waves. The model reproduces most of the features of the non-stationary and non-linear dynamics present in the high-resolution in-vivo recordings of the mouse brain. The proposed approach offers new methods of characterizing and understanding cortical waves for experimental and computational neuroscientists.

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal replay, which is critical for memory consolidation. The sudden and repeated occurrences of these burst states during ongoing neural activity suggest metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to stochastic spiking and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesoscopic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie to obtain a "chemical Langevin equation", which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down-states dynamics) by means of phase-plane analysis. An extension of the Langevin equation for small network sizes is also presented. The stochastic neural mass model constitutes the basic component of our mesoscopic model for replay. We show that the mesoscopic model faithfully captures the statistical structure of individual replayed trajectories in microscopic simulations and in previously reported experimental data. Moreover, compared to the deterministic Romani-Tsodyks model of place-cell dynamics, it exhibits a higher level of variability regarding order, direction and timing of replayed trajectories, which seems biologically more plausible and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.

Spatiotemporal patterns of spontaneous brain activity: a mini-review

The brain exists in a state of constant activity in the absence of any external sensory input. The spatiotemporal patterns of this spontaneous brain activity have been studied using various recording and imaging techniques. This has enabled considerable progress to be made in elucidating the cellular and network mechanisms that are involved in the observed spatiotemporal dynamics. This mini-review outlines different spatiotemporal dynamic patterns that have been identified in four commonly used modalities: electrophysiological recordings, optical imaging, functional magnetic resonance imaging, and electroencephalography. Signal sources for each modality, possible sources of the observed dynamics, and future directions are also discussed.

Slow waves form expanding, memory-rich mesostates steered by local excitability in fading anesthesia

In the arousal process, the brain restores its integrative activity from the synchronized state of slow wave activity (SWA). The mechanisms underpinning this state transition remain, however, to be elucidated. Here we simultaneously probed neuronal assemblies throughout the whole cortex with micro-electrocorticographic recordings in mice. We investigated the progressive shaping of propagating SWA at different levels of isoflurane. We found a form of memory of the wavefront shapes at deep anesthesia, tightly alternating posterior-anterior-posterior patterns. At low isoflurane, metastable patterns propagated in more directions, reflecting an increased complexity. The wandering across these mesostates progressively increased its randomness, as predicted by simulations of a network of spiking neurons, and confirmed in our experimental data. The complexity increase is explained by the elevated excitability of local assemblies with no modifications of the network connectivity. These results shed new light on the functional reorganization of the cortical network as anesthesia fades out.

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Complexity of isoflurane-induced slow waves reliably determines anesthesia level

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In deep anesthesia, the propagation strictly alternates between front-back-front patterns

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In light anesthesia, there is a continuum of directions and faster propagation

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Local excitability underpins the cortical reorganization in fading anesthesia

Local sleep: A new concept in brain plasticity

Traditionally, sleep and wakefulness have been considered as two global, mutually exclusive states. However, this view has been challenged by the discovery that sleep and wakefulness are actually locally regulated and that islands of these two states may often coexist in the same individual. Importantly, such a local regulation seems to be the key for many essential functions of sleep, including the maintenance of cognitive efficiency and the consolidation of new skills and memories. Indeed, local changes in sleep-related oscillations occur in brain areas that are used and involved in learning during wakefulness. In turn, these changes directly modulate experience-dependent brain adaptations and the consolidation of newly acquired memories. In line with these observations, alterations in the regional balance between wake- and sleep-like activity have been shown to accompany many pathologic conditions, including psychiatric and neurologic disorders. In the last decade, experimental research has started to shed light on the mechanisms involved in the local regulation of sleep and wakefulness. The results of this research have opened new avenues of investigation regarding the function of sleep and have revealed novel potential targets for the treatment of several pathologic conditions.

Spatiotemporal Patterns of Adaptation-Induced Slow Oscillations in a Whole-Brain Model of Slow-Wave Sleep

During slow-wave sleep, the brain is in a self-organized regime in which slow oscillations (SOs) between up- and down-states travel across the cortex. While an isolated piece of cortex can produce SOs, the brain-wide propagation of these oscillations are thought to be mediated by the long-range axonal connections. We address the mechanism of how SOs emerge and recruit large parts of the brain using a whole-brain model constructed from empirical connectivity data in which SOs are induced independently in each brain area by a local adaptation mechanism. Using an evolutionary optimization approach, good fits to human resting-state fMRI data and sleep EEG data are found at values of the adaptation strength close to a bifurcation where the model produces a balance between local and global SOs with realistic spatiotemporal statistics. Local oscillations are more frequent, last shorter, and have a lower amplitude. Global oscillations spread as waves of silence across the undirected brain graph, traveling from anterior to posterior regions. These traveling waves are caused by heterogeneities in the brain network in which the connection strengths between brain areas determine which areas transition to a down-state first, and thus initiate traveling waves across the cortex. Our results demonstrate the utility of whole-brain models for explaining the origin of large-scale cortical oscillations and how they are shaped by the connectome.

Energy-Based Hierarchical Clustering of Cortical Slow Waves in Multi-Electrode Recordings

The recent development of novel multi-electrode recording technologies has revealed the existence of traveling patterns of cortical activity in many species and under different states of awareness. Among these, slow activation waves occurring under sleep and anesthesia have been widely investigated as they provide unique insights into network features such as excitability, connectivity, structure, and dynamics of the cerebral cortex. Such characterization is usually based on clustering methods which are constrained by a priori assumptions as to the number of clusters to be used or rely on wave-by-wave pattern reconstruction. Here, we introduce a new computational tool based on modal analysis of fluid flows which is robustly applied to multivariate electrophysiological data from cortical networks, namely the Energy-based Hierarchical Waves Clustering method (EHWC). EHWC is composed of three main steps: (1) detecting the occurrence of global waves; (2) reducing the data dimensionality via singular value decomposition; (3) clustering hierarchically the singled-out waves. The analysis does not require the single-channel contribution to the waves, which is a typical bottleneck in this kind of analysis due to the unavoidable intrinsic variability of locally recorded activity. For testing and validation, here we used in vivo extracellular recordings from mice cortex under three different levels of anesthesia. As a result, we found slow waves with an increasing number of propagation modes as the anesthesia level decreases, giving an estimate of the increasing complexity of network dynamics. This and other wave's features replicate and extend the findings from previous literature, paving the way to extend the same approach to non-invasive electrophysiological recordings like EEG and fMRI used clinically for the characterization of brain dynamics and clinical stratification in brain lesions.

Nonlinear collision between propagating waves in mouse somatosensory cortex

How does cellular organization shape the spatio-temporal patterns of activity in the cortex while processing sensory information? After measuring the propagation of activity in the mouse primary somatosensory cortex (S1) in response to single whisker deflections with Voltage Sensitive Dye (VSD) imaging, we developed a two dimensional model of S1. We designed an inference method to reconstruct model parameters from VSD data, revealing that a spatially heterogeneous organization of synaptic strengths between pyramidal neurons in S1 is likely to be responsible for the heterogeneous spatio-temporal patterns of activity measured experimentally. The model shows that, for strong enough excitatory cortical interactions, whisker deflections generate a propagating wave in S1. Finally, we report that two consecutive stimuli activating different spatial locations in S1 generate two waves which collide sub-linearly, giving rise to a suppressive wave. In the inferred model, the suppressive wave is explained by a lower sensitivity to external perturbations of neural networks during activated states.

Thalamo-cortical spiking model of incremental learning combining perception, context and NREM-sleep

The brain exhibits capabilities of fast incremental learning from few noisy examples, as well as the ability to associate similar memories in autonomously-created categories and to combine contextual hints with sensory perceptions. Together with sleep, these mechanisms are thought to be key components of many high-level cognitive functions. Yet, little is known about the underlying processes and the specific roles of different brain states. In this work, we exploited the combination of context and perception in a thalamo-cortical model based on a soft winner-take-all circuit of excitatory and inhibitory spiking neurons. After calibrating this model to express awake and deep-sleep states with features comparable with biological measures, we demonstrate the model capability of fast incremental learning from few examples, its resilience when proposed with noisy perceptions and contextual signals, and an improvement in visual classification after sleep due to induced synaptic homeostasis and association of similar memories.

We created a thalamo-cortical spiking model (ThaCo) with the purpose of demonstrating a link among two phenomena that we believe to be essential for the brain capability of efficient incremental learning from few examples in noisy environments. Grounded in two experimental observations—the first about the effects of deep-sleep on pre- and post-sleep firing rate distributions, the second about the combination of perceptual and contextual information in pyramidal neurons—our model joins these two ingredients. ThaCo alternates phases of incremental learning, classification and deep-sleep. Memories of handwritten digit examples are learned through thalamo-cortical and cortico-cortical plastic synapses. In absence of noise, the combination of contextual information with perception enables fast incremental learning. Deep-sleep becomes crucial when noisy inputs are considered. We observed in ThaCo both homeostatic and associative processes: deep-sleep fights noise in perceptual and internal knowledge and it supports the categorical association of examples belonging to the same digit class, through reinforcement of class-specific cortico-cortical synapses. The distributions of pre-sleep and post-sleep firing rates during classification change in a manner similar to those of experimental observation. These changes promote energetic efficiency during recall of memories, better representation of individual memories and categories and higher classification performances.

Impact of GABAA and GABAB Inhibition on Cortical Dynamics and Perturbational Complexity during Synchronous and Desynchronized States

Quantitative estimations of spatiotemporal complexity of cortical activity patterns are used in the clinic as a measure of consciousness levels, but the cortical mechanisms involved are not fully understood. We used a version of the perturbational complexity index (PCI) adapted to multisite recordings from the ferret (either sex) cerebral cortex in vitro (sPCI) to investigate the role of GABAergic inhibition in cortical complexity. We studied two dynamical states: slow-wave activity (synchronous state) and desynchronized activity, that express low and high causal complexity respectively. Progressive blockade of GABAergic inhibition during both regimes revealed its impact on the emergent cortical activity and on sPCI. Gradual GABAA receptor blockade resulted in higher synchronization, being able to drive the network from a desynchronized to a synchronous state, with a progressive decrease of complexity (sPCI). Blocking GABAB receptors also resulted in a reduced sPCI, in particular when in a synchronous, slow wave state. Our findings demonstrate that physiological levels of inhibition contribute to the generation of dynamical richness and spatiotemporal complexity. However, if inhibition is diminished or enhanced, cortical complexity decreases. Using a computational model, we explored a larger parameter space in this relationship and demonstrate a link between excitatory/inhibitory balance and the complexity expressed by the cortical network.SIGNIFICANCE STATEMENT The spatiotemporal complexity of the activity expressed by the cerebral cortex is a highly revealing feature of the underlying network's state. Complexity varies with physiological brain states: it is higher during awake than during sleep states. But it also informs about pathologic states: in disorders of consciousness, complexity is lower in an unresponsive wakefulness syndrome than in a minimally conscious state. What are the network parameters that modulate complexity? Here we investigate how inhibition, mediated by either GABAA or GABAA receptors, influences cortical complexity. And we do this departing from two extreme functional states: a highly synchronous, slow-wave state, and a desynchronized one that mimics wakefulness. We find that there is an optimal level of inhibition in which complexity is highest.

Attractor competition enriches cortical dynamics during awakening from anesthesia

Slow oscillations (≲ 1 Hz), a hallmark of slow-wave sleep and deep anesthesia across species, arise from spatiotemporal patterns of activity whose complexity increases as wakefulness is approached and cognitive functions emerge. The arousal process constitutes an open window to the unknown mechanisms underlying the emergence of such dynamical richness in awake cortical networks. Here, we investigate the changes in network dynamics as anesthesia fades out in the rat visual cortex. Starting from deep anesthesia, slow oscillations gradually increase their frequency, eventually expressing maximum regularity. This stage is followed by the abrupt onset of an infra-slow (~0.2 Hz) alternation between sleep-like oscillations and activated states. A population rate model reproduces this transition driven by an increased excitability that brings it to periodically cross a critical point. Based on our model, dynamical richness emerges as a competition between two metastable attractor states, a conclusion strongly supported by the data.

Cortex-Wide Dynamics of Intrinsic Electrical Activities: Propagating Waves and Their Interactions

Cortical circuits generate patterned activities that reflect intrinsic brain dynamics that lay the foundation for any, including stimuli-evoked, cognition and behavior. However, the spatiotemporal organization properties and principles of this intrinsic activity have only been partially elucidated because of previous poor resolution of experimental data and limited analysis methods. Here we investigated continuous wave patterns in the 0.5-4 Hz (delta band) frequency range on data from high-spatiotemporal resolution optical voltage imaging of the upper cortical layers in anesthetized mice. Waves of population activities propagate in heterogeneous directions to coordinate neuronal activities between different brain regions. The complex wave patterns show characteristics of both stereotypy and variety. The location and type of wave patterns determine the dynamical evolution when different waves interact with each other. Local wave patterns of source, sink, or saddle emerge at preferred spatial locations. Specifically, "source" patterns are predominantly found in cortical regions with low multimodal hierarchy such as the primary somatosensory cortex. Our findings reveal principles that govern the spatiotemporal dynamics of spontaneous cortical activities and associate them with the structural architecture across the cortex.SIGNIFICANCE STATEMENT Intrinsic brain activities, as opposed to external stimulus-evoked responses, have increasingly gained attention, but it remains unclear how these intrinsic activities are spatiotemporally organized at the cortex-wide scale. By taking advantage of the high spatiotemporal resolution of optical voltage imaging, we identified five wave pattern types, and revealed the organization properties of different wave patterns and the dynamical mechanisms when they interact with each other. Moreover, we found a relationship between the emergence probability of local wave patterns and the multimodal structure hierarchy across cortical areas. Our findings reveal the principles of spatiotemporal wave dynamics of spontaneous activities and associate them with the underlying hierarchical architecture across the cortex.

Modulation of intercolumnar synchronization by endogenous electric fields in cerebral cortex

Neurons synaptically interacting in a conductive medium generate extracellular endogenous electric fields (EFs) that reciprocally affect membrane potential. Exogenous EFs modulate neuronal activity, and their clinical applications are being profusely explored. However, whether endogenous EFs contribute to network synchronization remains unclear. We analyzed spontaneously generated slow-wave activity in the cerebral cortex network in vitro, which allowed us to distinguish synaptic from nonsynaptic mechanisms of activity propagation and synchronization. Slow oscillations generated EFs that propagated independently of synaptic transmission. We demonstrate that cortical oscillations modulate spontaneous rhythmic activity of neighboring synaptically disconnected cortical columns if layers are aligned. We provide experimental evidence that these EF-mediated effects are compatible with electric dipoles. With a model of interacting dipoles, we reproduce the experimental measurements and predict that endogenous EF-mediated synchronizing effects should be relevant in the brain. Thus, experiments and models suggest that electric-dipole interactions contribute to synchronization of neighboring cortical columns.

Modulation of cortical slow oscillations and complexity across anesthesia levels

The ability of different groups of cortical neurons to engage in causal interactions that are at once differentiated and integrated results in complex dynamic patterns. Complexity is low during periods of unconsciousness (deep sleep, anesthesia, unresponsive wakefulness syndrome) in which the brain tends to generate a stereotypical pattern consisting of alternating active and silent periods of neural activity-slow oscillations- and is high during wakefulness. But how is cortical complexity built up? Is it a continuum? An open question is whether cortical complexity can vary within the same brain state. Here we recorded with 32-channel multielectrode arrays from the cortical surface of the mouse and used both spontaneous dynamics (wave propagation entropy and functional complexity) and a perturbational approach (a variation of the perturbation complexity index) to measure complexity at different anesthesia levels. Variations in anesthesia level within the bistable regime of slow oscillations (0.1-1.5 Hz) resulted in a modulation of the slow oscillation frequency. Both perturbational and spontaneous complexity increased with decreasing anesthesia levels, in correlation with the decrease in coherence of the underlying network. Changes in complexity level are related to, but not dependent on, changes in excitability. We conclude that cortical complexity can vary within a single brain state dominated by slow oscillations, building up to the higher complexity associated with consciousness.

Brain states govern the spatio-temporal dynamics of resting-state functional connectivity

Previously, using simultaneous resting-state functional magnetic resonance imaging (fMRI) and photometry-based neuronal calcium recordings in the anesthetized rat, we identified blood oxygenation level-dependent (BOLD) responses directly related to slow calcium waves, revealing a cortex-wide and spatially organized correlate of locally recorded neuronal activity (Schwalm et al., 2017). Here, using the same techniques, we investigate two distinct cortical activity states: persistent activity, in which compartmentalized network dynamics were observed; and slow wave activity, dominated by a cortex-wide BOLD component, suggesting a strong functional coupling of inter-cortical activity. During slow wave activity, we find a correlation between the occurring slow wave events and the strength of functional connectivity between different cortical areas. These findings suggest that down-up transitions of neuronal excitability can drive cortex-wide functional connectivity. This study provides further evidence that changes in functional connectivity are dependent on the brain's current state, directly linked to the generation of slow waves.

Integrity of Corpus Callosum Is Essential for theCross-Hemispheric Propagation of Sleep Slow Waves:A High-Density EEG Study in Split-Brain Patients

The slow waves of non-rapid eye movement (NREM) sleep reflect experience-dependent plasticity and play a direct role in the restorative functions of sleep. Importantly, slow waves behave as traveling waves, and their propagation is assumed to occur through cortico-cortical white matter connections. In this light, the corpus callosum (CC) may represent the main responsible for cross-hemispheric slow-wave propagation. To verify this hypothesis, we performed overnight high-density (hd)-EEG recordings in five patients who underwent total callosotomy due to drug-resistant epilepsy (CPs; two females), in three noncallosotomized neurologic patients (NPs; two females), and in a sample of 24 healthy adult subjects (HSs; 13 females). In all CPs slow waves displayed a significantly reduced probability of cross-hemispheric propagation and a stronger inter-hemispheric asymmetry. In both CPs and HSs, the incidence of large slow waves within individual NREM epochs tended to differ across hemispheres, with a relative overall predominance of the right over the left hemisphere. The absolute magnitude of this asymmetry was greater in CPs relative to HSs. However, the CC resection had no significant effects on the distribution of slow-wave origin probability across hemispheres. The present results indicate that CC integrity is essential for the cross-hemispheric traveling of slow waves in human sleep, which is in line with the assumption of a direct relationship between white matter integrity and slow-wave propagation. Our findings also revealed a residual cross-hemispheric slow-wave propagation that may rely on alternative pathways, including cortico-subcortico-cortical loops. Finally, these data indicate that the lack of the CC does not lead to differences in slow-wave generation across brain hemispheres.

SIGNIFICANCE STATEMENT The slow waves of NREM sleep behave as traveling waves, and their propagation has been suggested to reflect the integrity of white matter cortico-cortical connections. To directly assess this hypothesis, here we investigated the role of the corpus callosum in the cortical spreading of NREM slow waves through the study of a rare population of totally callosotomized patients. Our results demonstrate a causal role of the corpus callosum in the cross-hemispheric traveling of sleep slow waves. Additionally, we found that callosotomy does not affect the relative tendency of each hemisphere at generating slow waves. Incidentally, we also found that slow waves tend to originate more often in the right than in the left hemisphere in both callosotomized and healthy adult individuals.

State-dependent mean-field formalism to model different activity states in conductance-based networks of spiking neurons

More interest has been shown in recent years to large-scale spiking simulations of cerebral neuronal networks, coming both from the presence of high-performance computers and increasing details in experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, which is the question addressed by mean-field theories. Despite analytic solutions for the mean-field dynamics already being proposed for current-based neurons (CUBA), a complete analytic description has not been achieved yet for more realistic neural properties, such as conductance-based (COBA) network of adaptive exponential neurons (AdEx). Here, we propose a principled approach to map a COBA on a CUBA. Such an approach provides a state-dependent approximation capable of reliably predicting the firing-rate properties of an AdEx neuron with noninstantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular and synchronous irregular (slow oscillations). This result shows that a state-dependent approximation can be successfully introduced to take into account the subtle effects of COBA integration and to deal with a theory capable of correctly predicting the activity in regimes of alternating states like slow oscillations.

A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

Altered Neocortical Dynamics in a Mouse Model of Williams-Beuren Syndrome

Williams-Beuren syndrome (WBS) is a rare neurodevelopmental disorder characterized by moderate intellectual disability and learning difficulties alongside behavioral abnormalities such as hypersociability. Several structural and functional brain alterations are characteristic of this syndrome, as well as disturbed sleep and sleeping patterns. However, the detailed physiological mechanisms underlying WBS are mostly unknown. Here, we characterized the cortical dynamics in a mouse model of WBS previously reported to replicate most of the behavioral alterations described in humans. We recorded the laminar local field potential generated in the frontal cortex during deep anesthesia and characterized the properties of the emergent slow oscillation activity. Moreover, we performed micro-electrocorticogram recordings using multielectrode arrays covering the cortical surface of one hemisphere. We found significant differences between the cortical emergent activity and functional connectivity between wild-type mice and WBS model mice. Slow oscillations displayed Up states with diminished firing rate and lower high-frequency content in the gamma range. Lower firing rates were also recorded in the awake WBS animals while performing a marble burying task and could be associated with the decreased spine density and thus synaptic connectivity in this cortical area. We also found an overall increase in functional connectivity between brain areas, reflected in lower clustering and abnormally high integration, especially in the gamma range. These results expand previous findings in humans, suggesting that the cognitive deficits characterizing WBS might be associated with reduced excitability, plus an imbalance in the capacity to functionally integrate and segregate information.

Analysis and Model of Cortical Slow Waves Acquired with Optical Techniques

Slow waves (SWs) are spatio-temporal patterns of cortical activity that occur both during natural sleep and anesthesia and are preserved across species. Even though electrophysiological recordings have been largely used to characterize brain states, they are limited in the spatial resolution and cannot target specific neuronal population. Recently, large-scale optical imaging techniques coupled with functional indicators overcame these restrictions, and new pipelines of analysis and novel approaches of SWs modelling are needed to extract relevant features of the spatio-temporal dynamics of SWs from these highly spatially resolved data-sets. Here we combined wide-field fluorescence microscopy and a transgenic mouse model expressing a calcium indicator (GCaMP6f) in excitatory neurons to study SW propagation over the meso-scale under ketamine anesthesia. We developed a versatile analysis pipeline to identify and quantify the spatio-temporal propagation of the SWs. Moreover, we designed a computational simulator based on a simple theoretical model, which takes into account the statistics of neuronal activity, the response of fluorescence proteins and the slow waves dynamics. The simulator was capable of synthesizing artificial signals that could reliably reproduce several features of the SWs observed in vivo, thus enabling a calibration tool for the analysis pipeline. Comparison of experimental and simulated data shows the robustness of the analysis tools and its potential to uncover mechanistic insights of the Slow Wave Activity (SWA).

Cholinergic Switch between Two Types of Slow Waves in Cerebral Cortex

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory versus excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

A roadmap to integrate astrocytes into Systems Neuroscience

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease.

Bridging Single Neuron Dynamics to Global Brain States

Biological neural networks produce information backgrounds of multi-scale spontaneous activity that become more complex in brain states displaying higher capacities for cognition, for instance, attentive awake versus asleep or anesthetized states. Here, we review brain state-dependent mechanisms spanning ion channel currents (microscale) to the dynamics of brain-wide, distributed, transient functional assemblies (macroscale). Not unlike how microscopic interactions between molecules underlie structures formed in macroscopic states of matter, using statistical physics, the dynamics of microscopic neural phenomena can be linked to macroscopic brain dynamics through mesoscopic scales. Beyond spontaneous dynamics, it is observed that stimuli evoke collapses of complexity, most remarkable over high dimensional, asynchronous, irregular background dynamics during consciousness. In contrast, complexity may not be further collapsed beyond synchrony and regularity characteristic of unconscious spontaneous activity. We propose that increased dimensionality of spontaneous dynamics during conscious states supports responsiveness, enhancing neural networks' emergent capacity to robustly encode information over multiple scales.

Analysis Pipeline for Extracting Features of Cortical Slow Oscillations

Cortical slow oscillations (≲1 Hz) are an emergent property of the cortical network that integrate connectivity and physiological features. This rhythm, highly revealing of the characteristics of the underlying dynamics, is a hallmark of low complexity brain states like sleep, and represents a default activity pattern. Here, we present a methodological approach for quantifying the spatial and temporal properties of this emergent activity. We improved and enriched a robust analysis procedure that has already been successfully applied to both in vitro and in vivo data acquisitions. We tested the new tools of the methodology by analyzing the electrocorticography (ECoG) traces recorded from a custom 32-channel multi-electrode array in wild-type isoflurane-anesthetized mice. The enhanced analysis pipeline, named SWAP (Slow Wave Analysis Pipeline), detects Up and Down states, enables the characterization of the spatial dependency of their statistical properties, and supports the comparison of different subjects. The SWAP is implemented in a data-independent way, allowing its application to other data sets (acquired from different subjects, or with different recording tools), as well as to the outcome of numerical simulations. By using the SWAP, we report statistically significant differences in the observed slow oscillations (SO) across cortical areas and cortical sites. Computing cortical maps by interpolating the features of SO acquired at the electrode positions, we give evidence of gradients at the global scale along an oblique axis directed from fronto-lateral toward occipito-medial regions, further highlighting some heterogeneity within cortical areas. The results obtained using the SWAP will be essential for producing data-driven brain simulations. A spatial characterization of slow oscillations will also trigger a discussion on the role of, and the interplay between, the different regions in the cortex, improving our understanding of the mechanisms of generation and propagation of delta rhythms and, more generally, of cortical properties.

Scaling of a Large-Scale Simulation of Synchronous Slow-Wave and Asynchronous Awake-Like Activity of a Cortical Model With Long-Range Interconnections

Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during wakefulness (AW). Such dynamic diversity poses a challenge for producing efficient large-scale simulations that embody realistic metaphors of short- and long-range synaptic connectivity. In fact, during SWA and AW different spatial extents of the cortical tissue are active in a given timespan and at different firing rates, which implies a wide variety of loads of local computation and communication. A balanced evaluation of simulation performance and robustness should therefore include tests of a variety of cortical dynamic states. Here, we demonstrate performance scaling of our proprietary Distributed and Plastic Spiking Neural Networks (DPSNN) simulation engine in both SWA and AW for bidimensional grids of neural populations, which reflects the modular organization of the cortex. We explored networks up to 192 × 192 modules, each composed of 1,250 integrate-and-fire neurons with spike-frequency adaptation, and exponentially decaying inter-modular synaptic connectivity with varying spatial decay constant. For the largest networks the total number of synapses was over 70 billion. The execution platform included up to 64 dual-socket nodes, each socket mounting 8 Intel Xeon Haswell processor cores @ 2.40 GHz clock rate. Network initialization time, memory usage, and execution time showed good scaling performances from 1 to 1,024 processes, implemented using the standard Message Passing Interface (MPI) protocol. We achieved simulation speeds of between 2.3 × 109 and 4.1 × 109 synaptic events per second for both cortical states in the explored range of inter-modular interconnections.

Sleep-like slow oscillations improve visual classification through synaptic homeostasis and memory association in a thalamo-cortical model

The occurrence of sleep passed through the evolutionary sieve and is widespread in animal species. Sleep is known to be beneficial to cognitive and mnemonic tasks, while chronic sleep deprivation is detrimental. Despite the importance of the phenomenon, a complete understanding of its functions and underlying mechanisms is still lacking. In this paper, we show interesting effects of deep-sleep-like slow oscillation activity on a simplified thalamo-cortical model which is trained to encode, retrieve and classify images of handwritten digits. During slow oscillations, spike-timing-dependent-plasticity (STDP) produces a differential homeostatic process. It is characterized by both a specific unsupervised enhancement of connections among groups of neurons associated to instances of the same class (digit) and a simultaneous down-regulation of stronger synapses created by the training. This hierarchical organization of post-sleep internal representations favours higher performances in retrieval and classification tasks. The mechanism is based on the interaction between top-down cortico-thalamic predictions and bottom-up thalamo-cortical projections during deep-sleep-like slow oscillations. Indeed, when learned patterns are replayed during sleep, cortico-thalamo-cortical connections favour the activation of other neurons coding for similar thalamic inputs, promoting their association. Such mechanism hints at possible applications to artificial learning systems.

Analysis of Propagation of Slow Rhythmic Activity Induced in Ex Vivo Rat Brain Slices

Slow wave oscillation is a synchronous oscillatory mechanism that is a characteristic wave type of the cerebral cortex during physiological deep sleep or anesthesia. It may play an important role in cortical analysis of sensory input. Our goal was (1) to develop optimal conditions for the induction of this slow rhythmic activity in adult rat cortical slices, (2) to identify connections through which the activity propagates between coupled cortical regions, and (3) to study the pattern of horizontal and vertical flow of activity developed spontaneously in cortical slices. Experiments were performed on intact or differently incised rat cortical slices. According to our results, spontaneous cortical activity develops reliably in slightly modified artificial cerebrospinal fluid, first in the entorhinal cortical region of horizontally cut slices and then it spreads directly to the perirhinal (PRh) cortex. The activity readily generated in layer 2/3 of the entorhinal cortex then quickly spreads vertically to upper layer 2-3 in the same area and to the neighboring regions, that is, to the PRh cortex. Synchronization of activity in neighboring cortical areas occurs through both callosal connections and layer 2-3 intrinsic network, which are important in the propagation of spontaneous, inherent cortical slow wave activity.

Local Aspects of Avian Non-REM and REM Sleep

Birds exhibit two types of sleep that are in many respects similar to mammalian rapid eye movement (REM) and non-REM (NREM) sleep. As in mammals, several aspects of avian sleep can occur in a local manner within the brain. Electrophysiological evidence of NREM sleep occurring more deeply in one hemisphere, or only in one hemisphere – the latter being a phenomenon most pronounced in dolphins – was actually first described in birds. Such asymmetric or unihemispheric NREM sleep occurs with one eye open, enabling birds to visually monitor their environment for predators. Frigatebirds primarily engage in this form of sleep in flight, perhaps to avoid collisions with other birds. In addition to interhemispheric differences in NREM sleep intensity, the intensity of NREM sleep is homeostatically regulated in a local, use-depended manner within each hemisphere. Furthermore, the intensity and temporo-spatial distribution of NREM sleep-related slow waves varies across layers of the avian hyperpallium – a primary visual area – with the slow waves occurring first in, and propagating through and outward from, thalamic input layers. Slow waves also have the greatest amplitude in these layers. Although most research has focused on NREM sleep, there are also local aspects to avian REM sleep. REM sleep-related reductions in skeletal muscle tone appear largely restricted to muscles involved in maintaining head posture. Other local aspects of sleep manifest as a mixture of features of NREM and REM sleep occurring simultaneously in different parts of the neuroaxis. Like monotreme mammals, ostriches often exhibit brainstem-mediated features of REM sleep (muscle atonia and REMs) while the hyperpallium shows EEG slow waves typical of NREM sleep. Finally, although mice show slow waves in thalamic input layers of primary sensory cortices during REM sleep, this is not the case in the hyperpallium of pigeons, suggesting that this phenomenon is not a universal feature of REM sleep. Collectively, the local aspects of sleep described in birds and mammals reveal that wakefulness, NREM sleep, and REM sleep are not always discrete states.

Distribution of GABAergic Neurons and VGluT1 and VGAT Immunoreactive Boutons in the Ferret (Mustela putorius) Piriform Cortex and Endopiriform Nucleus. Comparison With Visual Areas 17, 18 and 19

We studied the cellular organization of the piriform network [comprising the piriform cortex (PC) and endopiriform nucleus (EP)] of the ferret (Mustela putorius)-a highly excitable region prone to seizures-and, more specifically, the distribution and morphology of different types of gamma-aminobutyric acid (GABA)ergic neurons, and the distribution and ratio of glutamatergic and GABAergic boutons, and we compared our findings to those in primary visual area 17, and secondary areas 18 and 19. We accomplished this by using cytochrome oxidase and immunohistochemistry for mature neuronal nuclei (NeuN), GABAergic neurons [glutamic acid decarboxylase-67 (GAD67), calretinin (CR) and parvalbumin (PV)], and for excitatory (vesicular glutamate transporter 1; VGluT1) and inhibitory (vesicular GABA transporter; VGAT) boutons. In the ferret, the cellular organization of the piriform network is similar to that described in other species such as cats, rats and opossums although some differences also exist. GABAergic immunolabeling showed similarities between cortical layers I-III of the PC and visual areas, such as the relative distribution of GABAergic neurons and the density and area of VGluT1- and VGAT-immunoreactive boutons. However, multiple differences between the piriform network and visual areas (layers I-VI) were found, such as the percentage of GABAergic neurons with respect to the total number of neurons and the ratio of VGluT1- and VGAT-immunoreactive boutons. These findings are relevant to better understand the high excitability of the piriform network.

Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

Neurophysiology of Avian Sleep: Comparing Natural Sleep and Isoflurane Anesthesia

Propagating slow-waves in electroencephalogram (EEG) or local field potential (LFP) recordings occur during non-rapid eye-movement (NREM) sleep in both mammals and birds. Moreover, in both, input from the thalamus is thought to contribute to the genesis of NREM sleep slow-waves. Interestingly, the general features of slow-waves are also found under isoflurane anesthesia. However, it is unclear to what extent these slow-waves reflect the same processes as those giving rise to NREM sleep slow-waves. Similar slow-wave spatio-temporal properties during NREM sleep and isoflurane anesthesia would suggest that both types of slow-waves are based on related processes. We used a 32-channel silicon probe connected to a transmitter to make intra-cortical recordings of the visual hyperpallium in naturally sleeping and isoflurane anesthetized pigeons (Columba livia) using a within-bird design. Under anesthesia, the amplitude of LFP slow-waves was higher when compared to NREM sleep. Spectral power density across all frequencies (1.5–100 Hz) was also elevated. In addition, slow-wave coherence between electrode sites was higher under anesthesia, indicating higher synchrony when compared to NREM sleep. Nonetheless, the spatial distribution of slow-waves under anesthesia was more comparable to NREM sleep than to wake or REM sleep. Similar to NREM sleep, slow-wave propagation under anesthesia mainly occurred in the thalamic input layers of the hyperpallium, regions which also showed the greatest slow-wave power during both recording conditions. This suggests that the thalamus could be involved in the genesis of slow-waves under both conditions. Taken together, although slow-waves under isoflurane anesthesia are stronger, they share spatio-temporal activity characteristics with slow-waves during NREM sleep.

High-resolution mapping of infraslow cortical brain activity enabled by graphene microtransistors

Recording infraslow brain signals (<0.1 Hz) with microelectrodes is severely hampered by current microelectrode materials, primarily due to limitations resulting from voltage drift and high electrode impedance. Hence, most recording systems include high-pass filters that solve saturation issues but come hand in hand with loss of physiological and pathological information. In this work, we use flexible epicortical and intracortical arrays of graphene solution-gated field-effect transistors (gSGFETs) to map cortical spreading depression in rats and demonstrate that gSGFETs are able to record, with high fidelity, infraslow signals together with signals in the typical local field potential bandwidth. The wide recording bandwidth results from the direct field-effect coupling of the active transistor, in contrast to standard passive electrodes, as well as from the electrochemical inertness of graphene. Taking advantage of such functionality, we envision broad applications of gSGFET technology for monitoring infraslow brain activity both in research and in the clinic.

An ultra-compact integrated system for brain activity recording and stimulation validated over cortical slow oscillations in vivo and in vitro

The understanding of brain processing requires monitoring and exogenous modulation of neuronal ensembles. To this end, it is critical to implement equipment that ideally provides highly accurate, low latency recording and stimulation capabilities, that is functional for different experimental preparations and that is highly compact and mobile. To address these requirements, we designed a small ultra-flexible multielectrode array and combined it with an ultra-compact electronic system. The device consists of a polyimide microelectrode array (8 µm thick and with electrodes measuring as low as 10 µm in diameter) connected to a miniaturized electronic board capable of amplifying, filtering and digitalizing neural signals and, in addition, of stimulating brain tissue. To evaluate the system, we recorded slow oscillations generated in the cerebral cortex network both from in vitro slices and from in vivo anesthetized animals, and we modulated the oscillatory pattern by means of electrical and visual stimulation. Finally, we established a preliminary closed-loop algorithm in vitro that exploits the low latency of the electronics (<0.5 ms), thus allowing monitoring and modulating emergent cortical activity in real time to a desired target oscillatory frequency.

Excitable neuronal assemblies with adaptation as a building block of brain circuits for velocity-controlled signal propagation

The time scale of neuronal network dynamics is determined by synaptic interactions and neuronal signal integration, both of which occur on the time scale of milliseconds. Yet many behaviors like the generation of movements or vocalizations of sounds occur on the much slower time scale of seconds. Here we ask the question of how neuronal networks of the brain can support reliable behavior on this time scale. We argue that excitable neuronal assemblies with spike-frequency adaptation may serve as building blocks that can flexibly adjust the speed of execution of neural circuit function. We show in simulations that a chain of neuronal assemblies can propagate signals reliably, similar to the well-known synfire chain, but with the crucial difference that the propagation speed is slower and tunable to the behaviorally relevant range. Moreover we study a grid of excitable neuronal assemblies as a simplified model of the somatosensory barrel cortex of the mouse and demonstrate that various patterns of experimentally observed spatial activity propagation can be explained.

Models of activity propagation in cortical networks have often been based on feedforward structures. Here we propose a model of activity propagation, called excitation chain, which does not need such a feedforward structure. The model is composed of excitable neural assemblies with spike-frequency adaptation, connected bidirectionally in a row or a grid. This prototypical neural circuit can propagate activity forwards, backwards or in both directions. Furthermore, the propagation speed is slow enough to trigger the generation of behaviors on the time scale of hundreds of milliseconds. A two-dimensional variant of the model is able to generate different activity propagation patterns, similar to spontaneous activity and stimulus-evoked responses in anesthetized mouse barrel cortex. We propose the excitation chain model as a basic component that can be employed in various ways to create spiking neural circuit models that generate signals on behavioral time scales. In contrast to abstract models of excitable media, our model makes an explicit link to the time scale of neuronal spikes.

Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity

Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.