Criticality and universality in neuronal cultures during "up" and "down" states.

The brain can be seen as a self-organized dynamical system that optimizes information processing and storage capabilities. This is supported by studies across scales, from small neuronal assemblies to the whole brain, where neuronal activity exhibits features typically associated with phase transitions in statistical physics. Such a critical state is characterized by the emergence of scale-free statistics as captured, for example, by the sizes and durations of activity avalanches corresponding to a cascading process of information flow. Another phenomenon observed during sleep, under anesthesia, and in in vitro cultures, is that cortical and hippocampal neuronal networks alternate between "up" and "down" states characterized by very distinct firing rates. Previous theoretical work has been able to relate these two concepts and proposed that only up states are critical whereas down states are subcritical, also indicating that the brain spontaneously transitions between the two. Using high-speed high-resolution calcium imaging recordings of neuronal cultures, we test this hypothesis here by analyzing the neuronal avalanche statistics in populations of thousands of neurons during "up" and "down" states separately. We find that both "up" and "down" states can exhibit scale-free behavior when taking into account their intrinsic time scales. In particular, the statistical signature of "down" states is indistinguishable from those observed previously in cultures without "up" states. We show that such behavior can not be explained by network models of non-conservative leaky integrate-and-fire neurons with short-term synaptic depression, even when realistic noise levels, spatial network embeddings, and heterogeneous populations are taken into account, which instead exhibits behavior consistent with previous theoretical models. Similar differences were also observed when taking into consideration finite-size scaling effects, suggesting that the intrinsic dynamics and self-organization mechanisms of these cultures might be more complex than previously thought. In particular, our findings point to the existence of different mechanisms of neuronal communication, with different time scales, acting during either high-activity or low-activity states, potentially requiring different plasticity mechanisms.

Dependence of rhythmic activity and oddball effects in the rat cortex on the depth of sedation during dissociative anesthesia.

The reactions to novelty manifesting in mismatch negativity in the rat brain were studied. During dissociative anesthesia, mismatch negativity-like waves were recorded from the somatosensory cortex using an epidural 32-electrode array. Experimental animals: 7 wild-type Wistar rats and 3 transgenic rats. During high-dose anesthesia, deviant 1,500 Hz tones were presented randomly among many standard 1,000 Hz tones in the oddball paradigm. "Deviant minus standard_before_deviant" difference waves were calculated using both the classical method of Naatanen and method of cross-correlation of sub-averages. Both methods gave consistent results: an early phasic component of the N40 and later N100 to 200 (mismatch negativity itself) tonic component. The gamma and delta rhythms power and the frequency of down-states (suppressed activity periods) were assessed. In all rats, the amplitude of tonic component grew with increasing sedation depth. At the same time, a decrease in gamma power with a simultaneous increase in delta power and the frequency of down-states. The earlier phasic frontocentral component is associated with deviance detection, while the later tonic one over the auditory cortex reflects the orienting reaction. Under anesthesia, this slow mismatch negativity-like wave most likely reflects the tendency of the system to respond to any influences with delta waves, K-complexes and down-states, or produce them spontaneously.

Hippocampal sharp-wave ripples and their spike assembly content are regulated by the medial entorhinal cortex.

Hippocampal sharp-wave ripples (SPW-Rs) are critical for memory consolidation and retrieval. The neuronal content of spiking during SPW-Rs is believed to be under the influence of neocortical inputs via the entorhinal cortex (EC). Optogenetic silencing of the medial EC (mEC) reduced the incidence of SPW-Rs with minor impacts on their magnitude or duration, similar to local CA1 silencing. The effect of mEC silencing on CA1 firing and field potentials was comparable to the effect of transient cortex-wide DOWN states of non-REM (NREM) sleep, implying that decreased SPW-R incidence in both cases is due to tonic disfacilitation of hippocampal circuits. The neuronal composition of CA1 pyramidal neurons during SPW-Rs was altered by mEC silencing but was restored immediately after silencing. We suggest that the mEC provides both tonic and transient influences on hippocampal network states by timing the occurrence of SPW-Rs and altering their neuronal content.

Computational models of Idling brain activity for memory processing.

Studying the underlying neural mechanisms of cognitive functions of the brain is one of the central questions in modern biology. Moreover, it has significantly impacted the development of novel technologies in artificial intelligence. Spontaneous activity is a unique feature of the brain and is currently lacking in many artificially constructed intelligent machines. Spontaneous activity may represent the brain's idling states, which are internally driven by neuronal networks and possibly participate in offline processing during awake, sleep, and resting states. Evidence is accumulating that the brain's spontaneous activity is not mere noise but part of the mechanisms to process information about previous experiences. A bunch of literature has shown how previous sensory and behavioral experiences influence the subsequent patterns of brain activity with various methods in various animals. It seems, however, that the patterns of neural activity and their computational roles differ significantly from area to area and from function to function. In this article, I review the various forms of the brain's spontaneous activity, especially those observed during memory processing, and some attempts to model the generation mechanisms and computational roles of such activities.

Deterministic and Stochastic Components of Cortical Down States: Dynamics and Modulation.

Slow oscillations are an emergent activity of the cerebral cortex network consisting of alternating periods of activity (Up states) and silence (Down states). Up states are periods of persistent cortical activity that share properties with that of underlying wakefulness. However, the occurrence of Down states is almost invariably associated with unconsciousness, both in animal models and clinical studies. Down states have been attributed relevant functions, such as being a resetting mechanism or breaking causal interactions between cortical areas. But what do Down states consist of? Here, we explored in detail the network dynamics (e.g., synchronization and phase) during these silent periods in vivo (male mice), in vitro (ferrets, either sex), and in silico, investigating various experimental conditions that modulate them: anesthesia levels, excitability (electric fields), and excitation/inhibition balance. We identified metastability as two complementary phases composing such quiescence states: a highly synchronized "deterministic" period followed by a low-synchronization "stochastic" period. The balance between these two phases determines the dynamical properties of the resulting rhythm, as well as the responsiveness to incoming inputs or refractoriness. We propose detailed Up and Down state cycle dynamics that bridge cortical properties emerging at the mesoscale with their underlying mechanisms at the microscale, providing a key to understanding unconscious states.SIGNIFICANCE STATEMENT The cerebral cortex expresses slow oscillations consisting of Up (active) and Down (silent) states. Such activity emerges not only in slow wave sleep, but also under anesthesia and in brain lesions. Down states functionally disconnect the network, and are associated with unconsciousness. Based on a large collection of data, novel data analysis approaches and computational modeling, we thoroughly investigate the nature of Down states. We identify two phases: a highly synchronized "deterministic" period, followed by a low-synchronization "stochastic" period. The balance between these two phases determines the dynamic properties of the resulting rhythm and responsiveness to incoming inputs. This finding reconciles different theories of slow rhythm generation and provides clues about how the brain switches from conscious to unconscious brain states.

Accelerated Aging Characterizes the Early Stage of Alzheimer's Disease.

For Alzheimer's disease (AD), aging is the main risk factor, but whether cognitive impairments due to aging resemble early AD deficits is not yet defined. When working with mouse models of AD, the situation is just as complicated, because only a few studies track the progression of the disease at different ages, and most ignore how the aging process affects control mice. In this work, we addressed this problem by comparing the aging process of PS2APP (AD) and wild-type (WT) mice at the level of spontaneous brain electrical activity under anesthesia. Using local field potential recordings, obtained with a linear probe that traverses the posterior parietal cortex and the entire hippocampus, we analyzed how multiple electrical parameters are modified by aging in AD and WT mice. With this approach, we highlighted AD specific features that appear in young AD mice prior to plaque deposition or that are delayed at 12 and 16 months of age. Furthermore, we identified aging characteristics present in WT mice but also occurring prematurely in young AD mice. In short, we found that reduction in the relative power of slow oscillations (SO) and Low/High power imbalance are linked to an AD phenotype at its onset. The loss of SO connectivity and cortico-hippocampal coupling between SO and higher frequencies as well as the increase in UP-state and burst durations are found in young AD and old WT mice. We show evidence that the aging process is accelerated by the mutant PS2 itself and discuss such changes in relation to amyloidosis and gliosis.

Thalamus mediates neocortical Down state transition via GABAB-receptor-targeting interneurons.

Slow-wave sleep is characterized by near-synchronous alternation of active Up states and quiescent Down states in the neocortex. Although the cortex itself can maintain these oscillations, the full expression of Up-Down states requires intact thalamocortical circuits. Sensory thalamic input can drive the cortex into an Up state. Here we show that midline thalamic neurons terminate Up states synchronously across cortical areas. Combining local field potential, single-unit, and patch-clamp recordings in conjunction with optogenetic stimulation and silencing in mice in vivo, we report that thalamic input mediates Down transition via activation of layer 1 neurogliaform inhibitory neurons acting on GABAB receptors. These results strengthen the evidence that thalamocortical interactions are essential for the full expression of slow-wave sleep, show that Down transition is an active process mediated by cortical GABAB receptors, and demonstrate that thalamus synchronizes Down transitions across cortical areas during natural slow-wave sleep.

Brain state-dependent high-frequency activity as a biomarker for abnormal neocortical networks in an epileptic spasms animal model.

OBJECTIVE: Epileptic spasms are a hallmark of a severe epileptic state. A previous study showed neocortical up and down states defined by unit activity play a role in the generation of spasms. However, recording unit activity is challenging in clinical settings, and more accessible neurophysiological signals are needed for the analysis of these brain states. METHODS: In the tetrodotoxin model, we used 16-channel microarrays to record electrophysiological activity in the neocortex during interictal periods and spasms. High-frequency activity (HFA) in the frequency range of fast ripples (200-500 Hz) was analyzed, as were slow wave oscillations (1-8 Hz), and correlated with the neocortical up and down states defined by multiunit activity (MUA). RESULTS: HFA and MUA had high temporal correlation during interictal and ictal periods. Both increased strikingly during interictal up states and ictal events but were silenced during interictal down states and preictal pauses, and their distributions were clustered at the peak of slow oscillations in local field potential recordings. In addition, both HFA power and MUA firing rates were increased to a greater extent during spasms than interictal up states. During non-rapid eye movement sleep, the HFA rhythmicity faithfully followed the MUA up and down states, but during rapid eye movement sleep when MUA up and down states disappeared the HFA rhythmicity was largely absent. We also observed an increase in the number of HFA down state minutes prior to ictal onset, consistent with the results from analyses of MUA down states. SIGNIFICANCE: This study provides evidence that HFA may serve as a biomarker for the pathological up states of epileptic spasms. The availability of HFA recordings makes this a clinically practical technique. These findings will likely provide a novel approach for localizing and studying epileptogenic neocortical networks not only in spasms patients but also in other types of epilepsy.

Energy features in spontaneous up and down oscillations.

Spontaneous brain activities consume most of the brain's energy. So if we want to understand how the brain operates, we must take into account these spontaneous activities. Up and down transitions of membrane potentials are considered to be one of significant spontaneous activities. This kind of oscillation always shows bistable and bimodal distribution of membrane potentials. Our previous theoretical studies on up and down oscillations mainly looked at the ion channel dynamics. In this paper, we focus on energy feature of spontaneous up and down transitions based on a network model and its simulation. The simulated results indicate that the energy is a robust index and distinguishable of excitatory and inhibitory neurons. Meanwhile, one the whole, energy consumption of neurons shows bistable feature and bimodal distribution as well as the membrane potential, which turns out that the indicator of energy consumption encodes up and down states in this spontaneous activity. In detail, energy consumption mainly occurs during up states temporally, and mostly concentrates inside neurons rather than synapses spatially. The stimulation related energy is small, indicating that energy consumption is not driven by external stimulus, but internal spontaneous activity. This point of view is also consistent with brain imaging results. Through the observation and analysis of the findings, we prove the validity of the model again, and we can further explore the energy mechanism of more spontaneous activities.

Up and Down States During Slow Oscillations in Slow-Wave Sleep and Different Levels of Anesthesia.

Slow oscillations are a pattern of synchronized network activity generated by the cerebral cortex. They consist of Up and Down states, which are periods of activity interspersed with periods of silence, respectively. However, even when this is a unique dynamic regime of transitions between Up and Down states, this pattern is not constant: there is a range of oscillatory frequencies (0.1-4 Hz), and the duration of Up vs. Down states during the cycles is variable. This opens many questions. Is there a constant relationship between the duration of Up and Down states? How much do they vary across conditions and oscillatory frequencies? Are there different sub regimes within the slow oscillations? To answer these questions, we aimed to explore a concrete aspect of slow oscillations, Up and Down state durations, across three conditions: deep anesthesia, light anesthesia, and slow-wave sleep (SWS), in the same chronically implanted rats. We found that light anesthesia and SWS have rather similar properties, occupying a small area of the Up and Down state duration space. Deeper levels of anesthesia occupy a larger region of this space, revealing that a large variety of Up and Down state durations can emerge within the slow oscillatory regime. In a network model, we investigated the network parameters that can explain the different points within our bifurcation diagram in which slow oscillations are expressed.

Dynamic Configuration of Coactive Micropatterns in the Default Mode Network During Wakefulness and Sleep.

Background: The default mode network (DMN) is a prominent intrinsic network that is observable in many mammalian brains. However, a few studies have investigated the temporal dynamics of this network based on direct physiological recordings. Methods: Herein, we addressed this issue by characterizing the dynamics of local field potentials from the rat DMN during wakefulness and sleep with an exploratory analysis. We constructed a novel coactive micropattern (CAMP) algorithm to evaluate the configurations of rat DMN dynamics, and further revealed the relationship between DMN dynamics with different wakefulness and alertness levels. Results: From the gamma activity (40-80 Hz) in the DMN across wakefulness and sleep, three spatially stable CAMPs were detected: a common low-activity level micropattern (cDMN), an anterior high-activity level micropattern (aDMN), and a posterior high-activity level micropattern (pDMN). A dynamic balance across CAMPs emerged during wakefulness and was disrupted in sleep stages. In the slow-wave sleep (SWS) stage, cDMN became the primary activity pattern, whereas aDMN and pDMN were the major activity patterns in the rapid eye movement sleep stage. In addition, further investigation revealed phasic relationships between CAMPs and the up-down states of the slow DMN activity in the SWS stage. Conclusion: Our study revealed that the dynamic configurations of CAMPs were highly associated with different stages of wakefulness, and provided a potential three-state model to describe the DMN dynamics for wakefulness and alertness. Impact statement In the current study, a novel coactive micropattern (CAMP) method was developed to elucidate fast default mode network (DMN) dynamics during wakefulness and sleep. Our findings demonstrated that the dynamic configurations of DMN activity are specific to different wakefulness stages and provided a three-state DMN CAMP model to depict wakefulness levels, thus revealing a potentially new neurophysiological representation of alertness levels. This work could elucidate the DMN dynamics underlying different stages of wakefulness and have important implications for the theoretical understanding of the neural mechanism of wakefulness and alertness.

Layer 3 Pyramidal Cells in the Medial Entorhinal Cortex Orchestrate Up-Down States and Entrain the Deep Layers Differentially.

Up-down states (UDS) are synchronous cortical events of neuronal activity during non-REM sleep. The medial entorhinal cortex (MEC) exhibits robust UDS during natural sleep and under anesthesia. However, little is known about the generation and propagation of UDS-related activity in the MEC. Here, we dissect the circuitry underlying UDS generation and propagation across layers in the MEC using both in vivo and in vitro approaches. We provide evidence that layer 3 (L3) MEC is crucial in the generation and maintenance of UDS in the MEC. Furthermore, we find that the two sublayers of the L5 MEC participate differentially during UDS. Our findings show that L5b, which receives hippocampal output, is strongly innervated by UDS activity originating in L3 MEC. Our data suggest that L5b acts as a coincidence detector during information transfer between the hippocampus and the cortex and thereby plays an important role in memory encoding and consolidation.

Up and Down States and Memory Consolidation Across Somatosensory, Entorhinal, and Hippocampal Cortices.

In the course of a day, brain states fluctuate, from conscious awake information-acquiring states to sleep states, during which previously acquired information is further processed and stored as memories. One hypothesis is that memories are consolidated and stored during "offline" states such as sleep, a process thought to involve transfer of information from the hippocampus to other cortical areas. Up and Down states (UDS), patterns of activity that occur under anesthesia and sleep states, are likely to play a role in this process, although the nature of this role remains unclear. Here we review what is currently known about these mechanisms in three anatomically distinct but interconnected cortical areas: somatosensory cortex, entorhinal cortex, and the hippocampus. In doing so, we consider the role of this activity in the coordination of "replay" during sleep states, particularly during hippocampal sharp-wave ripples. We conclude that understanding the generation and propagation of UDS may provide key insights into the cortico-hippocampal dialogue linking archi- and neocortical areas during memory formation.

Cholinergic modulation inhibits cortical spreading depression in mouse neocortex through activation of muscarinic receptors and decreased excitatory/inhibitory drive.

Cortical spreading depression (CSD) is a wave of transient network hyperexcitability leading to long lasting depolarization and block of firing, which initiates focally and slowly propagates in the cerebral cortex. It causes migraine aura and it has been implicated in the generation of migraine headache. Cortical excitability can be modulated by cholinergic actions, leading in neocortical slices to the generation of rhythmic synchronous activities (UP/DOWN states). We investigated the effect of cholinergic activation with the cholinomimetic agonist carbachol on CSD triggered with 130 mM KCl pulse injections in acute mouse neocortical brain slices, hypothesizing that the cholinergic-induced increase of cortical network excitability during UP states could facilitate CSD. We observed instead an inhibitory effect of cholinergic activation on both initiation and propagation of CSD, through the action of muscarinic receptors. In fact, carbachol-induced CSD inhibition was blocked by atropine or by the preferential M1 muscarinic antagonist telenzepine; the preferential M1 muscarinic agonist McN-A-343 inhibited CSD similarly to carbachol, and its effect was blocked by telenzepine. Recordings of spontaneous excitatory and inhibitory post-synaptic currents in pyramidal neurons showed that McN-A-343 induced overall a decrease of the excitatory/inhibitory ratio. This inhibitory action may be targeted for novel pharmacological approaches in the treatment of migraine with muscarinic agonists.

Thalamic Drive of Cortical Parvalbumin-Positive Interneurons during Down States in Anesthetized Mice.

Up and down states are among the most prominent features of the thalamo-cortical system during non-rapid eye movement (NREM) sleep and many forms of anesthesia. Cortical interneurons, including parvalbumin (PV) cells, display firing activity during cortical down states, and this GABAergic signaling is associated with prolonged down-state durations. However, what drives PV interneurons to fire during down states remains unclear. We here tested the hypothesis that background thalamic activity may lead to suprathreshold activation of PV cells during down states. To this aim, we performed two-photon guided juxtasomal recordings from PV interneurons in the barrel field of the somatosensory cortex (S1bf) of anesthetized mice, while simultaneously collecting the local field potential (LFP) in S1bf and the multi-unit activity (MUA) in the ventral posteromedial (VPM) thalamic nucleus. We found that activity in the VPM was associated with longer down-state duration in S1bf and that down states displaying PV cell firing were associated with increased VPM activity. Moreover, thalamic inhibition through application of muscimol reduced the fraction of spikes discharged by PV cells during cortical down states. Finally, we inhibited PV interneurons using optogenetics during down states while monitoring cortical LFP under control conditions and after thalamic muscimol injection. We found increased latency of the optogenetically triggered down-to-up transitions upon thalamic pharmacological blockade compared to controls. These findings demonstrate that spontaneous thalamic activity inhibits cortex during down states through the activation of PV interneurons.

Slow spindles are associated with cortical high frequency activity.

Thalamocortical network shows self-sustained oscillations in a broad frequency range especially during slow wave sleep when cortical neurons show synchronized transitions between a quiescent down state and an active up state with beta and gamma oscillations. Inconsistent with previous models, thalamocortical spindles are separated into slow spindles (8_12 Hz) and fast spindles (13_17 Hz) with differential properties. We proposed that cortical high frequency (∼ 25 Hz) activity during up states is the key ingredient for the generation of slow spindles. In fact, the nonlinear interaction between cortical high frequency and thalamic oscillations at fast spindle frequency reproduces oscillations in the range of the difference between the two frequencies that lies into the range of slow spindle. The developed simple deterministic thalamocortical model is able to reproduce up and down states with stochastic high-frequency up-state activity as well as both fast and slow spindles. In agreement with the previous experimental observations, the fast and slow spindles are generated at opposing phases of the up state. To further confirm the causal relationship between slow spindles and cortical high frequency oscillations, we next showed that externally applied high frequency stimulation enhanced the slow spindle activity. Moreover, the prediction of the model was validated experimentally by recording EEG from subjects during nap. Both model and experimental results show increase in high frequency activity before slow spindles. Our findings suggest the important role of cortical high frequency activity in the generation of slow spindles.

Criteria on Balance, Stability, and Excitability in Cortical Networks for Constraining Computational Models.

During ongoing and Up state activity, cortical circuits manifest a set of dynamical features that are conserved across these states. The present work systematizes these phenomena by three notions: excitability, the ability to sustain activity without external input; balance, precise coordination of excitatory and inhibitory neuronal inputs; and stability, maintenance of activity at a steady level. Slice preparations exhibiting Up states demonstrate that balanced activity can be maintained by small local circuits. While computational models of cortical circuits have included different combinations of excitability, balance, and stability, they have done so without a systematic quantitative comparison with experimental data. Our study provides quantitative criteria for this purpose, by analyzing in-vitro and in-vivo neuronal activity and characterizing the dynamics on the neuronal and population levels. The criteria are defined with a tolerance that allows for differences between experiments, yet are sufficient to capture commonalities between persistently depolarized cortical network states and to help validate computational models of cortex. As test cases for the derived set of criteria, we analyze three widely used models of cortical circuits and find that each model possesses some of the experimentally observed features, but none satisfies all criteria simultaneously, showing that the criteria are able to identify weak spots in computational models. The criteria described here form a starting point for the systematic validation of cortical neuronal network models, which will help improve the reliability of future models, and render them better building blocks for larger models of the brain.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise : Spontaneous activity in networks with synaptic noise.

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Intrinsic sodium currents and excitatory synaptic transmission influence spontaneous firing in up and down activities.

Periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity. These kinds of oscillations always accompany with some spontaneous firing in up state. Our previous theoretical studies mainly looked at the subthreshold up and down transitions and characteristics of up and down dynamics. In this paper, we focus on suprathreshold spontaneous firing of up and down transitions based on improved network model and its stimulations. The simulated results indicate that fast sodium current is critical to the generation of spontaneous neural firing. While persistent sodium current plays a part in spontaneous fluctuation. Both intrinsic fast and persistent sodium dynamics influence spontaneous firing rate and synchronous activity in up and down behavior. Meanwhile, blocking excitatory synaptic transmission decreases neural firing and reveals spontaneous firing. These simulated results are basically in accordance with experimental results. Through the observation and analysis of the findings, we prove the validity of the model so we can further adopt this model to study other properties and characteristics of the network, laying the foundation for further work on cortex activity.

New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics.

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca2+ dependent K+ current and the persistent Na+ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.