Are dragon-king neuronal avalanches dungeons for self-organized brain activity?

Recent experiments have detected a novel form of spontaneous neuronal activity both in vitro and in vivo: neuronal avalanches. The statistical properties of this activity are typical of critical phenomena, with power laws characterizing the distributions of avalanche size and duration. A critical behaviour for the spontaneous brain activity has important consequences on stimulated activity and learning. Very interestingly, these statistical properties can be altered in significant ways in epilepsy and by pharmacological manipulations. In particular, there can be an increase in the number of large events anticipated by the power law, referred to herein as dragon-king avalanches. This behaviour, as verified by numerical models, can originate from a number of different mechanisms. For instance, it is observed experimentally that the emergence of a critical behaviour depends on the subtle balance between excitatory and inhibitory mechanisms acting in the system. Perturbing this balance, by increasing either synaptic excitation or the incidence of depolarized neuronal up-states causes frequent dragon-king avalanches. Conversely, an unbalanced GABAergic inhibition or long periods of low activity in the network give rise to sub-critical behaviour. Moreover, the existence of power laws, common to other stochastic processes, like earthquakes or solar flares, suggests that correlations are relevant in these phenomena. The dragon-king avalanches may then also be the expression of pathological correlations leading to frequent avalanches encompassing all neurons. We will review the statistics of neuronal avalanches in experimental systems. We then present numerical simulations of a neuronal network model introducing within the self-organized criticality framework ingredients from the physiology of real neurons, as the refractory period, synaptic plasticity and inhibitory synapses. The avalanche critical behaviour and the role of dragon-king avalanches will be discussed in relation to different drives, neuronal states and microscopic mechanisms of charge storage and release in neuronal networks.     

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background  

Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task.     

Criticality in a simple model for brain functioning

We introduce a simple model for a set of interacting idealized neurons. The model presents a self-organized state in which avalanches of all sizes are observed and activity is detected in the whole extension of the simulated system without a typical length scale. The basic elements of the model are endowed with the main features of a neuron function. On this basis it is speculated that the collective system that they form, i.e., the brain, could display self-organized criticality in some situations.     

Neuronal avalanches and coherence potentials

The mammalian cortex consists of a vast network of weakly interacting excitable cells called neurons. Neurons must synchronize their activities in order to trigger activity in neighboring neurons. Moreover, interactions must be carefully regulated to remain weak (but not too weak) such that cascades of active neuronal groups avoid explosive growth yet allow for activity propagation over long-distances. Such a balance is robustly realized for neuronal avalanches, which are defined as cortical activity cascades that follow precise power laws. In experiments, scale-invariant neuronal avalanche dynamics have been observed during spontaneous cortical activity in isolated preparations in vitro as well as in the ongoing cortical activity of awake animals and in humans. Theory, models, and experiments suggest that neuronal avalanches are the signature of brain function near criticality at which the cortex optimally responds to inputs and maximizes its information capacity. Importantly, avalanche dynamics allow for the emergence of a subset of avalanches, the coherence potentials. They emerge when the synchronization of a local neuronal group exceeds a local threshold, at which the system spawns replicas of the local group activity at distant network sites. The functional importance of coherence potentials will be discussed in the context of propagating structures, such as gliders in balanced cellular automata. Gliders constitute local population dynamics that replicate in space after a finite number of generations and are thought to provide cellular automata with universal computation. Avalanches and coherence potentials are proposed to constitute a modern framework of cortical synchronization dynamics that underlies brain function.     

The role of neural architecture and the speed of signal propagation in the process of synchronization of bursting neurons

Synchronized neuronal activity has been observed at all levels of human and any other nervous systems and was suggested as particularly relevant in information processing and coding. In the present paper we investigate the synchronization of bursting neuronal activity. Motivated by the fact that in neural systems the interplay between the network structure and the dynamics taking place on it is closely interrelated, we develop a spatial network representation of neural architecture in which we can tune the network organization between a scale-free network with dominating long-range connections and a homogeneous network with mostly adjacent neurons connected. Our results reveal that the most synchronized response is obtained for the intermediate regime where long- as well as short-range connections constitute the neural architecture. Moreover, the optimal response is additionally enhanced when the speed of signal propagation is optimized.     

Inferring Excitatory and Inhibitory Connections in Neuronal Networks

The comprehension of neuronal network functioning, from most basic mechanisms of signal transmission to complex patterns of memory and decision making, is at the basis of the modern research in experimental and computational neurophysiology. While mechanistic knowledge of neurons and synapses structure increased, the study of functional and effective networks is more complex, involving emergent phenomena, nonlinear responses, collective waves, correlation and causal interactions. Refined data analysis may help in inferring functional/effective interactions and connectivity from neuronal activity. The Transfer Entropy (TE) technique is, among other things, well suited to predict structural interactions between neurons, and to infer both effective and structural connectivity in small- and large-scale networks. To efficiently disentangle the excitatory and inhibitory neural activities, in the article we present a revised version of TE, split in two contributions and characterized by a suited delay time. The method is tested on in silico small neuronal networks, built to simulate the calcium activity as measured via calcium imaging in two-dimensional neuronal cultures. The inhibitory connections are well characterized, still preserving a high accuracy for excitatory connections prediction. The method could be applied to study effective and structural interactions in systems of excitable cells, both in physiological and in pathological conditions.     

Statistics of avalanches in the self-organized criticality state of a Josephson junction

Magnetic flux avalanches in Josephson junctions that include superconductor-insulator-superconductor (SIS) tunnel junctions and are magnetized at temperatures lower than approximately 5 K have been studied in detail. Avalanches are of stochastic character and appear when the magnetic field penetration depth λ into a junction becomes equal to the length a of the Josephson junction with a decrease in the temperature. The statistical properties of such avalanches are presented. The size distribution of the avalanches is a power law with a negative noninteger exponent about unity, indicating the self-organized criticality state. The self-organized criticality state is not observed in Josephson junctions with a superconductor-normal metal-superconductor (SNS) junction.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

Coherent periodic activity in excitatory Erdös-Renyi neural networks: the role of network connectivity

In this article, we investigate the role of connectivity in promoting coherent activity in excitatory neural networks. In particular, we would like to understand if the onset of collective oscillations can be related to a minimal average connectivity and how this critical connectivity depends on the number of neurons in the networks. For these purposes, we consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erdo?s-Renyi graph with average connectivity scaling as a power law with the number of neurons in the network. The scaling is controlled by a parameter γ, which allows to pass from massively connected to sparse networks and therefore to modify the topology of the system. At a macroscopic level, we observe two distinct dynamical phases: an asynchronous state corresponding to a desynchronized dynamics of the neurons and a regime of partial synchronization (PS) associated with a coherent periodic activity of the network. At low connectivity, the system is in an asynchronous state, while PS emerges above a certain critical average connectivity (c). For sufficiently large networks, (c) saturates to a constant value suggesting that a minimal average connectivity is sufficient to observe coherent activity in systems of any size irrespectively of the kind of considered network: sparse or massively connected. However, this value depends on the nature of the synapses: reliable or unreliable. For unreliable synapses, the critical value required to observe the onset of macroscopic behaviors is noticeably smaller than for reliable synaptic transmission. Due to the disorder present in the system, for finite number of neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form of chaos, which vanishes in the thermodynamic limit. In such a limit, the disordered systems exhibit regular (non chaotic) dynamics and their properties correspond to that of a homogeneous fully connected network for any γ-value. Apart for the peculiar exception of sparse networks, which remain intrinsically inhomogeneous at any system size.     

动态突触、神经耦合与时间延迟对神经元发放的影响

神经元膜电位的受激发放在神经系统的信息传递中起着重要作用.基于一个受动态突触刺激的突触后神经元发放模型,采用数值模拟和傅里叶变换分析的方法研究了动态突触、神经耦合与时间延迟对突触后神经元发放的影响.结果发现:突触前神经元发放频率与Hodgkin-Huxley神经元的固有频率发生共振决定了突触后神经元发放的难易,特定频率范围内的电流刺激有利于神经元激发,动态突触输出的随机突触电流中这些电流刺激所占的比率在很大程度上影响了突触后神经元的发放次数;将突触后神经元换成神经网络后,网络中神经元之间的耦合可以促进神经元的发放,耦合中的时间延迟可以增强这种促进作用,但是不会改变神经耦合对神经元发放的促进模式.     

Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks

Neuronal networks are characterized by highly heterogeneous connectivity, and this disorder was recently related experimentally to qualitative properties of the network. The motivation of this paper is to mathematically analyze the role of these disordered connectivities on the large-scale properties of neuronal networks. To this end, we analyze here large-scale limit behaviors of neural networks including, for biological relevance, multiple populations, random connectivities and interaction delays. Due to the randomness of the connectivity, usual mean-field methods (e.g. coupling) cannot be applied, but, similarly to studies developed for spin glasses, we will show that the sequences of empirical measures satisfy a large deviation principle, and converge towards a self-consistent non-Markovian process. From a mathematical viewpoint, the proof differs from previous works in that we are working in infinite-dimensional spaces (interaction delays) and consider multiple cell types. The limit obtained formally characterizes the macroscopic behavior of the network. We propose a dynamical systems approach in order to address the qualitative nature of the solutions of these very complex equations, and apply this methodology to three instances in order to show how non-centered coefficients, interaction delays and multiple populations networks are affected by disorder levels. We identify a number of phase transitions in such systems upon changes in delays, connectivity patterns and dispersion, and particularly focus on the emergence of non-equilibrium states involving synchronized oscillations.     

Universal phenomenon of self-organized criticality in magnetic flux dynamics

Magnetization curves of square arrays of Josephson junctions of two basic types were investigated: superconductor–insulator–superconductor (SIS) and superconductor–normal metal–superconductor (SNS).

Magnetic flux avalanches were observed in SIS arrays. A statistical analysis of flux avalanches showed that their size distribution can be described by a power law with a crossover where the exponent n varies from −1.2 for small avalanches to −3.5 for the large ones. Such a behavior of avalanches is interpreted as the self-organized criticality (SOC) manifestation. In SNS arrays, the flux avalanches were not observed, but a considerable asymmetry of a hysteresis curve was revealed.     

Toward a physical basis of attention and self-regulation

The concept of self-regulation is central to the understanding of human development. Self-regulation allows effective socialization and predicts both psychological pathologies and levels of achievement in schools. What has been missing are neural mechanisms to provide understanding of the cellular and molecular basis for self-regulation. We show that self-regulation can be measured during childhood by parental reports and by self-reports of adolescents and adults. These reports are summarized by a higher order factor called effortful control, which reflects perceptions about the ability of a given person to regulate their behavior in accord with cultural norms. Throughout childhood effortful control is related to children's performance in computerized conflict related tasks. Conflict tasks have been shown in neuroimaging studies to activate specific brain networks of executive attention. Several brain areas work together at rest and during cognitive tasks to regulate competing brain activity and thus control resulting behavior. The cellular structure of the anterior cingulate and insula contain cells, unique to humans and higher primates that provide strong links to remote brain areas. During conflict tasks, anterior cingulate activity is correlated with activity in remote sensory and emotional systems, depending upon the information selected for the task. During adolescence the structure and activity of the anterior cingulate has been found to be correlated with self-reports of effortful control.Studies have provided a perspective on how genes and environment act to shape the executive attention network, providing a physical basis for self-regulation. The anterior cingulate is regulated by dopamine. Genes that influence dopamine levels in the CNS have been shown to influence the efficiency of self-regulation. For example, alleles of the COMT gene that influence the efficiency of dopamine transmission are related to the ability to resolve conflict. Humans with disorders involving deletion of this gene exhibit large deficits in self-regulation. Alleles of other genes influencing dopamine and serotonin transmission have also been found to influence ability to resolve conflict in cognitive tasks. However, as is the case for many genes, the effectiveness of COMT alleles in shaping self-regulation depends upon cultural influences such as parenting. Studies find that aspects of parenting quality and parent training can influence child behavior and the efficiency of self-regulation.During development, the network that relates to self-regulation undergoes important changes in connectivity. Infants can use parts of the self-regulatory network to detect errors in sensory information, but the network does not yet have sufficient connectivity to organize brain activity in a coherent way. During middle childhood, along with increased projection cells involved in remote connections of dorsal anterior cingulate and prefrontal and parietal cortex, executive network connectivity increases and shifts from predominantly short to longer range connections. During this period specific exercises can influence network development and improve self-regulation. Understanding the physical basis of self-regulation has already cast light on individual differences in normal and pathological states and gives promise of allowing the design of methods to improve aspects of human development.     

Learning alters theta amplitude, theta-gamma coupling and neuronal synchronization in inferotemporal cortex

Background

How oscillatory brain rhythms alone, or in combination, influence cortical information processing to support learning has yet to be fully established. Local field potential and multi-unit neuronal activity recordings were made from 64-electrode arrays in the inferotemporal cortex of conscious sheep during and after visual discrimination learning of face or object pairs. A neural network model has been developed to simulate and aid functional interpretation of learning-evoked changes.

Results

Following learning the amplitude of theta (4-8 Hz), but not gamma (30-70 Hz) oscillations was increased, as was the ratio of theta to gamma. Over 75% of electrodes showed significant coupling between theta phase and gamma amplitude (theta-nested gamma). The strength of this coupling was also increased following learning and this was not simply a consequence of increased theta amplitude. Actual discrimination performance was significantly correlated with theta and theta-gamma coupling changes. Neuronal activity was phase-locked with theta but learning had no effect on firing rates or the magnitude or latencies of visual evoked potentials during stimuli. The neural network model developed showed that a combination of fast and slow inhibitory interneurons could generate theta-nested gamma. By increasing N-methyl-D-aspartate receptor sensitivity in the model similar changes were produced as in inferotemporal cortex after learning. The model showed that these changes could potentiate the firing of downstream neurons by a temporal desynchronization of excitatory neuron output without increasing the firing frequencies of the latter. This desynchronization effect was confirmed in IT neuronal activity following learning and its magnitude was correlated with discrimination performance.

Conclusions

Face discrimination learning produces significant increases in both theta amplitude and the strength of theta-gamma coupling in the inferotemporal cortex which are correlated with behavioral performance. A network model which can reproduce these changes suggests that a key function of such learning-evoked alterations in theta and theta-nested gamma activity may be increased temporal desynchronization in neuronal firing leading to optimal timing of inputs to downstream neural networks potentiating their responses. In this way learning can produce potentiation in neural networks simply through altering the temporal pattern of their inputs.     

Conditions for the emergence of spatially asymmetric retrieval states in an attractor neural network

In this paper we show that during the retrieval process in a binary symmetric Hebb neural network, spatially localized states can be observed when the connectivity of the network is distance-dependent and a constraint on the activity of the network is imposed, which forces different levels of activity in the retrieval and learning states. This asymmetry in the activity during retrieval and learning is found to be a sufficient condition to observe spatially localized retrieval states. The result is confirmed analytically and by simulation.     

Nonlinear transfer function encodes synchronization in a neural network from the mammalian brain

Synchronization is one of the mechanisms by which the brain encodes information. The observed synchronization of neuronal activity has, however, several levels of fluctuations, which presumably regulate local features of specific areas. This means that biological neural networks should have an intrinsic mechanism able to synchronize the neuronal activity but also to preserve the firing capability of individual cells. Here, we investigate the input-output relationship of a biological neural network from developing mammalian brain, i.e., the hippocampus. We show that the probability of occurrence of synchronous output activity (which consists in stereotyped population bursts recorded throughout the hippocampus) is encoded by a sigmoidal transfer function of the input frequency. Under this scope, low-frequency inputs will not produce any coherent output while high-frequency inputs will determine a synchronous pattern of output activity (population bursts). We analyze the effect of the network size (N) on the parameters of the transfer function (threshold and slope). We found that sigmoidal functions realistically simulate the synchronous output activity of hippocampal neural networks. This outcome is particularly important in the application of results from neural network models to neurobiology.     

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Self-organized criticality and stock market dynamics: an empirical study

The stock market is a complex self-interacting system, characterized by intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches found in sandpile models, from quiescent. A statistical analysis of the filtered data shows a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution of the laminar times, is not consistent with classical conservative models for self-organized criticality. We argue that a “near-SOC” state or a time dependence in the driver, which may be chaotic, can explain this behaviour.     

Self-organized Criticality in a Model Based on Neural Network

Based on the LISSOM neural network model, we introduce a model to investigate self-organized criticality in the activity of neural populations. The influence of connection (synapse) between neurons has been adequately considered in this model. It is found to exhibit self-organized criticality (SOC) behavior under appropriate conditions. We also find that the learning process has promotive influence on emergence of SOC behavior. In addition, we analyze the influence of various factors of the model on the SOC behavior, which is characterized by the power-law behavior of the avalanche size distribution.