Balance between excitation and inhibition controls the temporal organization of neuronal avalanches

Simple model for the prediction of seizure durations

A simple model is used to simulate seizures in a population of spiking excitatory neurons experiencing a uniform effect from inhibitory neurons. A key feature is introduced into the model, i.e., a mechanism that weakens the firing thresholds. This weakening mechanism adds memory to the dynamics. We find a seizure-prone state in a "mode-switching" phase. In this phase, the system can suddenly switch from a "healthy" state with small scale-free avalanches to a "seizure" state with almost periodic large avalanches ("seizures"). Simulations of the model predict statistics for the average time spent in the seizure state (the seizure "duration") that agree with experiments and theoretical examples of similar behavior in neuronal systems. Our study points to. different connections between seizures and fracture and also offers an alternative view on the type of critical point controlling neuronal avalanches.

Mimicking Bidirectional Inhibitory Synapse Using a Porous-Confined Ionic Memristor with Electrolyte/Tris(4-aminophenyl)amine Neurotransmitter

Ionic memristors can emulate brain-like functions of biological synapses for neuromorphic technologies. Apart from the widely studied excitatory-excitatory and excitatory-inhibitory synapses, reports on memristors with the inhibitory-inhibitory synaptic behaviors remain a challenge. Here, the first biaxially inhibited artificial synapse is demonstrated, consisting of a solid electrolyte and conjugated microporous polymers bilayer as neurotransmitter, with the former serving as an ion reservoir and the latter acting as a confined transport. Due to the migration, trapping, and de-trapping of ions within the nanoslits, the device poses inhibitory synaptic plasticity under both positive and negative stimuli. Remarkably, the artificial synapse is able to maintain a low level of stable nonvolatile memory over a long period of time (≈60 min) after multiple stimuli, with feature-inferencing/-training capabilities of neural node in neuromorphic computing. This work paves a reliable strategy for constructing nanochannel ionic memristive materials toward fully inhibitory synaptic devices.

A general description of criticality in neural network models

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state

Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations-the "waxing and waning" phenomenon-are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the "waning" phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition).

Fluctuation-dissipation relations in the imbalanced Wilson-Cowan model

The relation between spontaneous and stimulated brain activity is a fundamental question in neuroscience which has received wide attention in experimental studies. Recently, it has been suggested that the evoked response to external stimuli can be predicted from temporal correlations of spontaneous activity. Previous theoretical results, confirmed by the comparison with magnetoencephalography data for human brains, were obtained for the Wilson-Cowan model in the condition of balance of excitation and inhibition, a signature of a healthy brain. Here we extend previous studies to imbalanced conditions by examining a region of parameter space around the balanced fixed point. Analytical results are compared to numerical simulations of Wilson-Cowan networks. We evidence that in imbalanced conditions the functional form of the time correlation and response functions can show several behaviors, exhibiting also an oscillating regime caused by the emergence of complex eigenvalues. The analytical predictions are fully in agreement with numerical simulations, validating the role of cross-correlations in the response function. Furthermore, we identify the leading role of inhibitory neurons in controlling the overall activity of the system, tuning the level of excitability and imbalance.

Parabolic avalanche scaling in the synchronization of cortical cell assemblies

Neurons in the cerebral cortex fire coincident action potentials during ongoing activity and in response to sensory inputs. These synchronized cell assemblies are fundamental to cortex function, yet basic dynamical aspects of their size and duration are largely unknown. Using 2-photon imaging of neurons in the superficial cortex of awake mice, we show that synchronized cell assemblies organize as scale-invariant avalanches that quadratically grow with duration. The quadratic avalanche scaling was only found for correlated neurons, required temporal coarse-graining to compensate for spatial subsampling of the imaged cortex, and suggested cortical dynamics to be critical as demonstrated in simulations of balanced E/I-networks. The corresponding time course of an inverted parabola with exponent of χ = 2 described cortical avalanches of coincident firing for up to 5 s duration over an area of 1 mm². These parabolic avalanches maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant temporal order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.

Recurrent activity in neuronal avalanches

A new statistical analysis of large neuronal avalanches observed in mouse and rat brain tissues reveals a substantial degree of recurrent activity and cyclic patterns of activation not seen in smaller avalanches. To explain these observations, we adapted a model of structural weakening in materials. In this model, dynamical weakening of neuron firing thresholds closely replicates experimental avalanche size distributions, firing number distributions, and patterns of cyclic activity. This agreement between model and data suggests that a mechanism like dynamical weakening plays a key role in recurrent activity found in large neuronal avalanches. We expect these results to illuminate the causes and dynamics of large avalanches, like those seen in seizures.

Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain

Neurons in the brain are wired into adaptive networks that exhibit collective dynamics as diverse as scale-specific oscillations and scale-free neuronal avalanches. Although existing models account for oscillations and avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically or intractable to infer from data rigorously. Here we propose a feedback-driven Ising-like class of neural networks that captures avalanches and oscillations simultaneously and quantitatively. In the simplest yet fully microscopic model version, we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations to collective behaviors of extreme events and neuronal avalanches. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.

Spontaneous neuronal avalanches as a correlate of access consciousness

Decades of research have advanced our understanding of the biophysical mechanisms underlying consciousness. However, an overarching framework bridging between models of consciousness and the large-scale organization of spontaneous brain activity is still missing. Based on the observation that spontaneous brain activity dynamically switches between epochs of segregation and large-scale integration of information, we hypothesize a brain-state dependence of conscious access, whereby the presence of either segregated or integrated states marks distinct modes of information processing. We first review influential works on the neuronal correlates of consciousness, spontaneous resting-state brain activity and dynamical system theory. Then, we propose a test experiment to validate our hypothesis that conscious access occurs in aperiodic cycles, alternating windows where new incoming information is collected but not experienced, to punctuated short-lived integration events, where conscious access to previously collected content occurs. In particular, we suggest that the integration events correspond to neuronal avalanches, which are collective bursts of neuronal activity ubiquitously observed in electrophysiological recordings. If confirmed, the proposed framework would link the physics of spontaneous cortical dynamics, to the concept of ignition within the global neuronal workspace theory, whereby conscious access manifest itself as a burst of neuronal activity.

Addressing skepticism of the critical brain hypothesis

The hypothesis that living neural networks operate near a critical phase transition point has received substantial discussion. This “criticality hypothesis” is potentially important because experiments and theory show that optimal information processing and health are associated with operating near the critical point. Despite the promise of this idea, there have been several objections to it. While earlier objections have been addressed already, the more recent critiques of Touboul and Destexhe have not yet been fully met. The purpose of this paper is to describe their objections and offer responses. Their first objection is that the well-known Brunel model for cortical networks does not display a peak in mutual information near its phase transition, in apparent contradiction to the criticality hypothesis. In response I show that it does have such a peak near the phase transition point, provided it is not strongly driven by random inputs. Their second objection is that even simple models like a coin flip can satisfy multiple criteria of criticality. This suggests that the emergent criticality claimed to exist in cortical networks is just the consequence of a random walk put through a threshold. In response I show that while such processes can produce many signatures criticality, these signatures (1) do not emerge from collective interactions, (2) do not support information processing, and (3) do not have long-range temporal correlations. Because experiments show these three features are consistently present in living neural networks, such random walk models are inadequate. Nevertheless, I conclude that these objections have been valuable for refining research questions and should always be welcomed as a part of the scientific process.

Scaling of avalanche shape and activity power spectrum in neuronal networks

Many systems in nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behavior of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the same conditions was not performed. The puzzling observation is that in the majority of healthy neuronal systems the power spectrum exhibits a behavior close to 1/f, rather than Brown, noise. Here we perform a numerical study of the scaling behavior of the avalanche shape and the power spectrum for a model of integrate and fire neurons with a short-term plasticity parameter able to tune the system to criticality. We confirm that, at criticality, the average avalanche size and the avalanche profile fulfill the general avalanche scaling theory. However, the power spectrum consistently exhibits Brown noise behavior, for both fully excitatory networks and systems with 30% inhibitory networks. Conversely, a behavior closer to 1/f noise is observed in systems slightly off criticality. Results suggest that the power spectrum is a good indicator to determine how close neuronal activity is to criticality.

Variability and task-responsiveness of electrophysiological dynamics: scale-free stability and oscillatory flexibility

Cortical oscillations and scale-free neural activity are thought to influence a variety of cognitive functions, but their differential relationships to neural stability and flexibility has never been investigated. Based on the existing literature, we hypothesize that scale-free and oscillatory processes in the brain exhibit different trade-offs between stability and flexibility; specifically, cortical oscillations may reflect variable, task-responsive aspects of brain activity, while scale-free activity is proposed to reflect a more stable and task-unresponsive aspect. We test this hypothesis using data from two large-scale MEG studies (HCP: n = 89; CamCAN: n = 195), operationalizing stability and flexibility by task-responsiveness and spontaneous intra-subject variability in resting state. We demonstrate that the power-law exponent of scale-free activity is a highly stable parameter, which responds little to external cognitive demands and shows minimal spontaneous fluctuations over time. In contrast, oscillatory power, particularly in the alpha range (8-13 Hz), responds strongly to tasks and exhibits comparatively large spontaneous fluctuations over time. In sum, our data support differential roles for oscillatory and scale-free activity in the brain with respect to neural stability and flexibility. This result carries implications for criticality-based theories of scale-free activity, state-trait models of variability, and homeostatic views of the brain with regulated variables vs. effectors.

Neuronal Population Transitions Across a Quiescent-to-Active Frontier and Bifurcation

The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity.

Critical behaviour of the stochastic Wilson-Cowan model

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.

Scale-specific dynamics of high-amplitude bursts in EEG capture behaviorally meaningful variability

Cascading high-amplitude bursts in neural activity, termed avalanches, are thought to provide insight into the complex spatially distributed interactions in neural systems. In human neuroimaging, for example, avalanches occurring during resting-state show scale-invariant dynamics, supporting the hypothesis that the brain operates near a critical point that enables long range spatial communication. In fact, it has been suggested that such scale-invariant dynamics, characterized by a power-law distribution in these avalanches, are universal in neural systems and emerge through a common mechanism. While the analysis of avalanches and subsequent criticality is increasingly seen as a framework for using complex systems theory to understand brain function, it is unclear how the framework would account for the omnipresent cognitive variability, whether across individuals or tasks. To address this, we analyzed avalanches in the EEG activity of healthy humans during rest as well as two distinct task conditions that varied in cognitive demands and produced behavioral measures unique to each individual. In both rest and task conditions we observed that avalanche dynamics demonstrate scale-invariant characteristics, but differ in their specific features, demonstrating individual variability. Using a new metric we call normalized engagement, which estimates the likelihood for a brain region to produce high-amplitude bursts, we also investigated regional features of avalanche dynamics. Normalized engagement showed not only the expected individual and task dependent variability, but also scale-specificity that correlated with individual behavior. Our results suggest that the study of avalanches in human brain activity provides a tool to assess cognitive variability. Our findings expand our understanding of avalanche features and are supportive of the emerging theoretical idea that the dynamics of an active human brain operate close to a critical-like region and not a singular critical-state.

Self-organized criticality in neural networks from activity-based rewiring

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis, which suggests that neural systems reach such a state by self-organizing toward the critical point of a dynamical phase transition. Here, we study a minimal neural network model that exhibits self-organized criticality in the presence of stochastic noise using a rewiring rule which only utilizes local information. For network evolution, incoming links are added to a node or deleted, depending on the node's average activity. Based on this rewiring-rule only, the network evolves toward a critical state, showing typical power-law-distributed avalanche statistics. The observed exponents are in accord with criticality as predicted by dynamical scaling theory, as well as with the observed exponents of neural avalanches. The critical state of the model is reached autonomously without the need for parameter tuning, is independent of initial conditions, is robust under stochastic noise, and independent of details of the implementation as different variants of the model indicate. We argue that this supports the hypothesis that real neural systems may utilize such a mechanism to self-organize toward criticality, especially during early developmental stages.

Network Physiology of Exercise: Vision and Perspectives

The basic theoretical assumptions of Exercise Physiology and its research directions, strongly influenced by reductionism, may hamper the full potential of basic science investigations, and various practical applications to sports performance and exercise as medicine. The aim of this perspective and programmatic article is to: (i) revise the current paradigm of Exercise Physiology and related research on the basis of principles and empirical findings in the new emerging field of Network Physiology and Complex Systems Science; (ii) initiate a new area in Exercise and Sport Science, Network Physiology of Exercise (NPE), with focus on basic laws of interactions and principles of coordination and integration among diverse physiological systems across spatio-temporal scales (from the sub-cellular level to the entire organism), to understand how physiological states and functions emerge, and to improve the efficacy of exercise in health and sport performance; and (iii) to create a forum for developing new research methodologies applicable to the new NPE field, to infer and quantify nonlinear dynamic forms of coupling among diverse systems and establish basic principles of coordination and network organization of physiological systems. Here, we present a programmatic approach for future research directions and potential practical applications. By focusing on research efforts to improve the knowledge about nested dynamics of vertical network interactions, and particularly, the horizontal integration of key organ systems during exercise, NPE may enrich Basic Physiology and diverse fields like Exercise and Sports Physiology, Sports Medicine, Sports Rehabilitation, Sport Science or Training Science and improve the understanding of diverse exercise-related phenomena such as sports performance, fatigue, overtraining, or sport injuries.

Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

Network structure of cascading neural systems predicts stimulus propagation and recovery

OBJECTIVE

Many neural systems display spontaneous, spatiotemporal patterns of neural activity that are crucial for information processing. While these cascading patterns presumably arise from the underlying network of synaptic connections between neurons, the precise contribution of the network's local and global connectivity to these patterns and information processing remains largely unknown.

APPROACH

Here, we demonstrate how network structure supports information processing through network dynamics in empirical and simulated spiking neurons using mathematical tools from linear systems theory, network control theory, and information theory.

MAIN RESULTS

In particular, we show that activity, and the information that it contains, travels through cycles in real and simulated networks.

SIGNIFICANCE

Broadly, our results demonstrate how cascading neural networks could contribute to cognitive faculties that require lasting activation of neuronal patterns, such as working memory or attention.

Time-dependent branching processes: a model of oscillating neuronal avalanches

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results.

Power-law correlations and coupling of active and quiet states underlie a class of complex systems with self-organization at criticality

Physical and biological systems often exhibit intermittent dynamics with bursts or avalanches (active states) characterized by power-law size and duration distributions. These emergent features are typical of systems at the critical point of continuous phase transitions, and have led to the hypothesis that such systems may self-organize at criticality, i.e. without any fine tuning of parameters. Since the introduction of the Bak-Tang-Wiesenfeld (BTW) model, the paradigm of self-organized criticality (SOC) has been very fruitful for the analysis of emergent collective behaviors in a number of systems, including the brain. Although considerable effort has been devoted in identifying and modeling scaling features of burst and avalanche statistics, dynamical aspects related to the temporal organization of bursts remain often poorly understood or controversial. Of crucial importance to understand the mechanisms responsible for emergent behaviors is the relationship between active and quiet periods, and the nature of the correlations. Here we investigate the dynamics of active (θ-bursts) and quiet states (δ-bursts) in brain activity during the sleep-wake cycle. We show the duality of power-law (θ, active phase) and exponential-like (δ, quiescent phase) duration distributions, typical of SOC, jointly emerge with power-law temporal correlations and anti-correlated coupling between active and quiet states. Importantly, we demonstrate that such temporal organization shares important similarities with earthquake dynamics, and propose that specific power-law correlations and coupling between active and quiet states are distinctive characteristics of a class of systems with self-organization at criticality.

Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake

Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

Towards dewetting monoclonal antibodies for therapeutical purposes

Dewetting transition - a concept borrowed from fluid mechanics - is a physiological process that takes place inside the hydrophobic pores of ion channels. This transient phenomenon causes a metastable state that forbids water molecules to cross microscopic receptor cavities. This leads to a decreased conductance, a closure of the pore and, subsequently, severe impairment of cellular performance. We suggest that artificially-provoked dewetting transition in ion channel hydrophobic pores might stand for a molecular candidate to erase detrimental organisms, such as viruses, bacteria, and cancer cells. We describe a novel type of high-affinity monoclonal antibody, that: a) targets specific trans-membrane receptor structures of harmful or redundant cells; b) is equipped with lipophilic and/or hydrophobic fragments that prevent physiological water flow inside ion channels. Therefore, we achieve an artificial dewetting transition inside receptor cavities, that causes discontinuity within transmembrane ionic flows, channel blockage, and subsequent damage of morbid cells. As an example, we describe dewetting monoclonal antibodies that target the M2 channel of the Influenza A virus: they might prevent water from entering pores thus leading to virion impairment.

Time-series thresholding and the definition of avalanche size

Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here we show that there is a hidden peril in thresholding continuous times series-from either empirical or synthetic data-for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used, e.g., in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) if-as sometimes done in the literature-avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem-that we have detected in some recent works-leads to misinterpretations of the resulting scaling regimes.

Spectral peculiarity and criticality of a human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

Effects of inhibitory and excitatory neurons on the dynamics and control of avalanching neural networks

The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche size and duration, and transitions the power spectral density of the network into an "epileptic" regime. We propose that the brain operates away from this power-law regime of low inhibitory fraction to protect itself from the dominating avalanches present in these extended distributions. We present control strategies that curtail these power-law distributions through either random or, more effectively, targeted disabling of excitatory neurons.

Multi-Scale Expressions of One Optimal State Regulated by Dopamine in the Prefrontal Cortex

The prefrontal cortex (PFC), which plays key roles in many higher cognitive processes, is a hierarchical system consisting of multi-scale organizations. Optimizing the working state at each scale is essential for PFC's information processing. Typical optimal working states at different scales have been separately reported, including the dopamine-mediated inverted-U profile of the working memory (WM) at the system level, critical dynamics at the network level, and detailed balance of excitatory and inhibitory currents (E/I balance) at the cellular level. However, it remains unclear whether these states are scale-specific expressions of the same optimal state and, if so, what is the underlying mechanism for its regulation traversing across scales. Here, by studying a neural network model, we show that the optimal performance of WM co-occurs with the critical dynamics at the network level and the E/I balance at the level of individual neurons, suggesting the existence of a unified, multi-scale optimal state for the PFC. Importantly, such a state could be modulated by dopamine at the synaptic level through a series of U or inverted-U profiles. These results suggest that seemingly different optimal states for specific scales are multi-scale expressions of one condition regulated by dopamine. Our work suggests a cross-scale perspective to understand the PFC function and its modulation.

Heterogeneity of synaptic input connectivity regulates spike-based neuronal avalanches

Our mysterious brain is believed to operate near a non-equilibrium point and generate critical self-organized avalanches in neuronal activity. A central topic in neuroscience is to elucidate the underlying circuitry mechanisms of neuronal avalanches in the brain. Recent experimental evidence has revealed significant heterogeneity in both synaptic input and output connectivity, but whether the structural heterogeneity participates in the regulation of neuronal avalanches remains poorly understood. By computational modeling, we predict that different types of structural heterogeneity contribute distinct effects on avalanche neurodynamics. In particular, neuronal avalanches can be triggered at an intermediate level of input heterogeneity, but heterogeneous output connectivity cannot evoke avalanche dynamics. In the criticality region, the co-emergence of multi-scale cortical activities is observed, and both the avalanche dynamics and neuronal oscillations are modulated by the input heterogeneity. Remarkably, we show similar results can be reproduced in networks with various types of in- and out-degree distributions. Overall, these findings not only provide details on the underlying circuitry mechanisms of nonrandom synaptic connectivity in the regulation of neuronal avalanches, but also inspire testable hypotheses for future experimental studies.

Critical neural networks with short- and long-term plasticity

In recent years self organized critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behavior of neuronal systems. It has been shown that dynamical synapses, as a form of short-term plasticity, can cause critical neuronal dynamics. Whereas long-term plasticity, such as Hebbian or activity dependent plasticity, have a crucial role in shaping the network structure and endowing neural systems with learning abilities. In this work we provide a model which combines both plasticity mechanisms, acting on two different time scales. The measured avalanche statistics are compatible with experimental results for both the avalanche size and duration distribution with biologically observed percentages of inhibitory neurons. The time series of neuronal activity exhibits temporal bursts leading to 1/f decay in the power spectrum. The presence of long-term plasticity gives the system the ability to learn binary rules such as xor, providing the foundation of future research on more complicated tasks such as pattern recognition.

The characteristic patterns of neuronal avalanches in mice under anesthesia and at rest: An investigation using constrained artificial neural networks

Local perturbations within complex dynamical systems can trigger cascade-like events that spread across significant portions of the system. Cascades of this type have been observed across a broad range of scales in the brain. Studies of these cascades, known as neuronal avalanches, usually report the statistics of large numbers of avalanches, without probing the characteristic patterns produced by the avalanches themselves. This is partly due to limitations in the extent or spatiotemporal resolution of commonly used neuroimaging techniques. In this study, we overcome these limitations by using optical voltage (genetically encoded voltage indicators) imaging. This allows us to record cortical activity in vivo across an entire cortical hemisphere, at both high spatial (~30um) and temporal (~20ms) resolution in mice that are either in an anesthetized or awake state. We then use artificial neural networks to identify the characteristic patterns created by neuronal avalanches in our data. The avalanches in the anesthetized cortex are most accurately classified by an artificial neural network architecture that simultaneously connects spatial and temporal information. This is in contrast with the awake cortex, in which avalanches are most accurately classified by an architecture that treats spatial and temporal information separately, due to the increased levels of spatiotemporal complexity. This is in keeping with reports of higher levels of spatiotemporal complexity in the awake brain coinciding with features of a dynamical system operating close to criticality.

Can a time varying external drive give rise to apparent criticality in neural systems?

The finding of power law scaling in neural recordings lends support to the hypothesis of critical brain dynamics. However, power laws are not unique to critical systems and can arise from alternative mechanisms. Here, we investigate whether a common time-varying external drive to a set of Poisson units can give rise to neuronal avalanches and exhibit apparent criticality. To this end, we analytically derive the avalanche size and duration distributions, as well as additional measures, first for homogeneous Poisson activity, and then for slowly varying inhomogeneous Poisson activity. We show that homogeneous Poisson activity cannot give rise to power law distributions. Inhomogeneous activity can also not generate perfect power laws, but it can exhibit approximate power laws with cutoffs that are comparable to those typically observed in experiments. The mechanism of generating apparent criticality by time-varying external fields, forces or input may generalize to many other systems like dynamics of swarms, diseases or extinction cascades. Here, we illustrate the analytically derived effects for spike recordings in vivo and discuss approaches to distinguish true from apparent criticality. Ultimately, this requires causal interventions, which allow separating internal system properties from externally imposed ones.

Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD

Recent studies have started to elucidate the effects of lysergic acid diethylamide (LSD) on the human brain but the underlying dynamics are not yet fully understood. Here we used 'connectome-harmonic decomposition', a novel method to investigate the dynamical changes in brain states. We found that LSD alters the energy and the power of individual harmonic brain states in a frequency-selective manner. Remarkably, this leads to an expansion of the repertoire of active brain states, suggestive of a general re-organization of brain dynamics given the non-random increase in co-activation across frequencies. Interestingly, the frequency distribution of the active repertoire of brain states under LSD closely follows power-laws indicating a re-organization of the dynamics at the edge of criticality. Beyond the present findings, these methods open up for a better understanding of the complex brain dynamics in health and disease.

Neuronal avalanches: Where temporal complexity and criticality meet

The model of the current paper is an extension of a previous publication, wherein we have used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was a manifestation of supercriticality rather than criticality. Here, however, we show that the continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity, and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may be a numerical artifact originated by the discrete description of the model which may imply a slow numerical convergence of the avalanche distribution compared to temporal complexity.

Stochastic resonance at criticality in a network model of the human cortex

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good candidate to take advantage of stochastic resonance. In this work, we aim to identify the optimal levels of noise that promote signal transmission through a simple network model of the human brain. Specifically, using a dynamic model implemented on an anatomical brain network (connectome), we investigate the similarity between an input signal and a signal that has traveled across the network while the system is subject to different noise levels. We find that non-zero levels of noise enhance the similarity between the input signal and the signal that has traveled through the system. The optimal noise level is not unique; rather, there is a set of parameter values at which the information is transmitted with greater precision, this set corresponds to the parameter values that place the system in a critical regime. The multiplicity of critical points in our model allows it to adapt to different noise situations and remain at criticality.

Criticality meets learning: Criticality signatures in a self-organizing recurrent neural network

Many experiments have suggested that the brain operates close to a critical state, based on signatures of criticality such as power-law distributed neuronal avalanches. In neural network models, criticality is a dynamical state that maximizes information processing capacities, e.g. sensitivity to input, dynamical range and storage capacity, which makes it a favorable candidate state for brain function. Although models that self-organize towards a critical state have been proposed, the relation between criticality signatures and learning is still unclear. Here, we investigate signatures of criticality in a self-organizing recurrent neural network (SORN). Investigating criticality in the SORN is of particular interest because it has not been developed to show criticality. Instead, the SORN has been shown to exhibit spatio-temporal pattern learning through a combination of neural plasticity mechanisms and it reproduces a number of biological findings on neural variability and the statistics and fluctuations of synaptic efficacies. We show that, after a transient, the SORN spontaneously self-organizes into a dynamical state that shows criticality signatures comparable to those found in experiments. The plasticity mechanisms are necessary to attain that dynamical state, but not to maintain it. Furthermore, onset of external input transiently changes the slope of the avalanche distributions – matching recent experimental findings. Interestingly, the membrane noise level necessary for the occurrence of the criticality signatures reduces the model’s performance in simple learning tasks. Overall, our work shows that the biologically inspired plasticity and homeostasis mechanisms responsible for the SORN’s spatio-temporal learning abilities can give rise to criticality signatures in its activity when driven by random input, but these break down under the structured input of short repeating sequences.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

A spatially resolved network spike in model neuronal cultures reveals nucleation centers, circular traveling waves and drifting spiral waves

We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal connection formation is independent of the distance between neurons, then the nucleation centers do not arise and the synchronization of spiking activity during a network spike occurs spatially uniform throughout the network. Therefore one can conclude that spatial proximity of connections between neurons is important for the formation of nucleation centers. It is also shown that fluctuations of the spatial density of neurons at their random homogeneous distribution typical for the experiments in vitro do not determine the locations of the nucleation centers. The simulation results are qualitatively consistent with the experimental observations.

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

Stress and temperature dependence of the avalanche dynamics during creep deformation of metallic glasses

The understanding of the mesoscopic origin of plasticity in metallic glasses remains still an open issue. At the microscopic level, Shear Transformation Zones (STZ), composed by dozens of atoms, have been identified as the basic unit of the deformation process. Macroscopically, metallic glasses perform either homogeneous or inhomogeneous flow depending on the experimental conditions. However, the emergence of macroscopic behavior resulting from STZ interactions is still an open issue and is of great interest. In the current work we present an approach to analyze the different interaction mechanisms of STZ's by studying the statistics of the avalanches produced by a metallic glass during tensile creep deformation. We identified a crossover between different regimes of avalanches, and we analyzed the dependence of such crossover on the experimental conditions, namely stress and temperature. We interpret such crossover as a transition from 3D random STZ activity to localized 2D nano-shear bands. The experimental time at which the crossover takes place seems to depend on the overall strain and strain rate in the sample.

Synaptic plasticity and neuronal refractory time cause scaling behaviour of neuronal avalanches

Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the origin of the mean field behavior observed experimentally. In this study we provide an answer to this open question by investigating the effect of activity dependent plasticity in combination with the neuronal refractory time in a neuronal network. Results show that the refractory time hinders backward avalanches forcing a directed propagation. Hebbian plastic adaptation plays the role of sculpting these directed avalanche patterns into the topology of the network slowly changing it into a branched structure where loops are marginal.

Fractal analysis reveals subclasses of neurons and suggests an explanation of their spontaneous activity

The present work used fractal time series analysis (detrended fluctuation analysis; DFA) to examine the spontaneous activity of single neurons in an anesthetized animal model, specifically, the mitral cells in the rat main olfactory bulb. DFA bolstered previous research in suggesting two subclasses of mitral cells. Although there was no difference in the fractal scaling of the interspike interval series at the shorter timescales, there was a significant difference at longer timescales. Neurons in Group B exhibited fractal, power-law scaled interspike intervals, whereas neurons in Group A exhibited random variation. These results raise questions about the role of these different cells within the olfactory bulb and potential explanations of their dynamics. Specifically, self-organized criticality has been proposed as an explanation of fractal scaling in many natural systems, including neural systems. However, this theory is based on certain assumptions that do not clearly hold in the case of spontaneous neural activity, which likely reflects intrinsic cell dynamics rather than activity driven by external stimulation. Moreover, it is unclear how self-organized criticality might account for the random dynamics observed in Group A, and how these random dynamics might serve some functional role when embedded in the typical activity of the olfactory bulb. These theoretical considerations provide direction for additional experimental work.

Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.

Building a minimum frustration framework for brain functions over long time scales

The minimum frustration principle (MFP) is a computational approach stating that, over the long time scales of evolution, proteins' free energy decreases more than expected by thermodynamical constraints as their amino acids assume conformations progressively closer to the lowest energetic state. This Review shows that this general principle, borrowed from protein folding dynamics, can also be fruitfully applied to nervous function. Highlighting the foremost role of energetic requirements, macromolecular dynamics, and above all intertwined time scales in brain activity, the MFP elucidates a wide range of mental processes from sensations to memory retrieval. Brain functions are compared with trajectories that, over long nervous time scales, are attracted toward the low-energy bottom of funnel-like structures characterized by both robustness and plasticity. We discuss how the principle, derived explicitly from evolution and selection of a funneling structure from microdynamics of contacts, is unlike other brain models equipped with energy landscapes, such as the Bayesian and free energy principles and the Hopfield networks. In summary, we make available a novel approach to brain function cast in a biologically informed fashion, with the potential to be operationalized and assessed empirically. © 2016 Wiley Periodicals, Inc.

Temporal correlations in neuronal avalanche occurrence

Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.