Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures

Criticality in Alzheimer's and healthy brains: insights from phase-ordering

Criticality, observed during second-order phase transitions, is an emergent phenomenon. The brain operates near criticality where complex systems exhibit high correlations. As a system approaches criticality, it develops "domain"-like regions with competing phases and increased spatio-temporal correlations that diverge. The dynamics of these domains depend on the system's proximity to criticality. This study explores the differences in the proximity to criticality of Alzheimer's-afflicted and cognitively normal brains through the use of a spin-lattice model derived from resting-state fMRI data and investigates the type of criticality found in the human brain - whether it is of the Ising class or something more complex. The temporal correlations in both groups display a stretched exponential nature, indicating closer alignment with the criticality of the spin-glass class rather than the Ising class. Longer relaxation times observed in cognitively normal subjects suggest increased proximity to the phase boundary. The weak distinction observed in the spatial characteristics related to proximity to criticality might once more point to a spin-glass scenario, necessitating nuanced order parameters to distinguish between phase-ordering in Alzheimer's and cognitively normal brains.

Keeping Your Brain in Balance: Homeostatic Regulation of Network Function

To perform computations with the efficiency necessary for animal survival, neocortical microcircuits must be capable of reconfiguring in response to experience, while carefully regulating excitatory and inhibitory connectivity to maintain stable function. This dynamic fine-tuning is accomplished through a rich array of cellular homeostatic plasticity mechanisms that stabilize important cellular and network features such as firing rates, information flow, and sensory tuning properties. Further, these functional network properties can be stabilized by different forms of homeostatic plasticity, including mechanisms that target excitatory or inhibitory synapses, or that regulate intrinsic neuronal excitability. Here we discuss which aspects of neocortical circuit function are under homeostatic control, how this homeostasis is realized on the cellular and molecular levels, and the pathological consequences when circuit homeostasis is impaired. A remaining challenge is to elucidate how these diverse homeostatic mechanisms cooperate within complex circuits to enable them to be both flexible and stable.

Criticality and partial synchronization analysis in Wilson-Cowan and Jansen-Rit neural mass models

Synchronization is a phenomenon observed in neuronal networks involved in diverse brain activities. Neural mass models such as Wilson-Cowan (WC) and Jansen-Rit (JR) manifest synchronized states. Despite extensive research on these models over the past several decades, their potential of manifesting second-order phase transitions (SOPT) and criticality has not been sufficiently acknowledged. In this study, two networks of coupled WC and JR nodes with small-world topologies were constructed and Kuramoto order parameter (KOP) was used to quantify the amount of synchronization. In addition, we investigated the presence of SOPT using the synchronization coefficient of variation. Both networks reached high synchrony by changing the coupling weight between their nodes. Moreover, they exhibited abrupt changes in the synchronization at certain values of the control parameter not necessarily related to a phase transition. While SOPT was observed only in JR model, neither WC nor JR model showed power-law behavior. Our study further investigated the global synchronization phenomenon that is known to exist in pathological brain states, such as seizure. JR model showed global synchronization, while WC model seemed to be more suitable in producing partially synchronized patterns.

Stereotyped spatiotemporal dynamics of spontaneous activity in visual cortex prior to eye-opening

Over the course of development, functional sensory representations emerge in the visual cortex. Prior to eye-opening, modular patterns of spontaneous activity form long-range networks that may serve as a precursor for mature network organization. Although the spatial structure of these networks has been well studied, their temporal features, which may contribute to their continued plasticity and development, remain largely uncharacterized. To address this, we imaged hours of spontaneous network activity in the visual cortex of developing ferrets of both sexes utilizing a fast calcium indicator (GCaMP8m) and widefield imaging at high temporal resolution (50Hz), then segmented out spatiotemporal events. The spatial structure of this activity was highly modular, exhibiting spatially segregated active domains consistent with prior work. We found that the vast majority of events showed a clear dynamic component in which modules activated sequentially across the field of view, but only a minority of events were well-fit with a linear traveling wave. We found that spatiotemporal events occur in repeated and stereotyped motifs, reoccurring across hours of imaging. Finally, we found that the most frequently occurring single-frame spatial activity patterns were predictive of future activity patterns over hundreds of milliseconds. Together, our results demonstrate that spontaneous activity in the early developing cortex exhibits a rich spatiotemporal structure, suggesting a potential role in the maturation and refinement of future functional representations.

Neuronal avalanche dynamics regulated by spike-timing-dependent plasticity under different topologies and heterogeneities

Neuronal avalanches, a critical state of network self-organization, have been widely observed in electrophysiological records at different signal levels and spatial scales of the brain, which has significant influence on information transmission and processing in the brain. In this paper, the collective behavior of neuron firing is studied based on Leaky Integrate-and-Fire model and we induce spike-timing-dependent plasticity (STDP) to update the connection weight through competition between adjacent neurons in different network topologies. The result shows that STDP can facilitate the synchronization of the network and increase the probability of large-scale neuron avalanche obviously. Moreover, both the structure of STDP and network connection density can affect the generation of avalanche critical states, specifically, learning rate has positive correlation effect on the slope of power-law distribution and time constant has negative correction on it. However, when we the increase of heterogeneity in network, STDP can only has obvious promotion in synchrony under suitable level of heterogeneity. And we find that the process of long-term potentiation is sensitive to the adjustment of time constant and learning rate, unlike long-term depression, which is only sensitive to learning rate in heterogeneity network. It is suggested that presented results could facilitate our understanding on synchronization in various neural networks under the effect of STDP learning rules.

Ex Vivo Cortical Circuits Learn to Predict and Spontaneously Replay Temporal Patterns

It has been proposed that prediction and timing are computational primitives of neocortical microcircuits, specifically, that neural mechanisms are in place to allow neocortical circuits to autonomously learn the temporal structure of external stimuli and generate internal predictions. To test this hypothesis, we trained cortical organotypic slices on two specific temporal patterns using dual-optical stimulation. After 24-hours of training, whole-cell recordings revealed network dynamics consistent with training-specific timed prediction. Unexpectedly, there was replay of the learned temporal structure during spontaneous activity. Furthermore, some neurons exhibited timed prediction errors. Mechanistically our results indicate that learning relied in part on asymmetric connectivity between distinct neuronal ensembles with temporally-ordered activation. These findings further suggest that local cortical microcircuits are intrinsically capable of learning temporal information and generating predictions, and that the learning rules underlying temporal learning and spontaneous replay can be intrinsic to local cortical microcircuits and not necessarily dependent on top-down interactions.

Stimulus encoding by specific inactivation of cortical neurons

Neuronal ensembles are groups of neurons with correlated activity associated with sensory, motor, and behavioral functions. To explore how ensembles encode information, we investigated responses of visual cortical neurons in awake mice using volumetric two-photon calcium imaging during visual stimulation. We identified neuronal ensembles employing an unsupervised model-free algorithm and, besides neurons activated by the visual stimulus (termed "onsemble"), we also find neurons that are specifically inactivated (termed "offsemble"). Offsemble neurons showed faster calcium decay during stimuli, suggesting selective inhibition. In response to visual stimuli, each ensemble (onsemble+offsemble) exhibited small trial-to-trial variability, high orientation selectivity, and superior predictive accuracy for visual stimulus orientation, surpassing the sum of individual neuron activity. Thus, the combined selective activation and inactivation of cortical neurons enhances visual encoding as an emergent and distributed neural code.

Neuronal ensembles: Building blocks of neural circuits

Neuronal ensembles, defined as groups of neurons displaying recurring patterns of coordinated activity, represent an intermediate functional level between individual neurons and brain areas. Novel methods to measure and optically manipulate the activity of neuronal populations have provided evidence of ensembles in the neocortex and hippocampus. Ensembles can be activated intrinsically or in response to sensory stimuli and play a causal role in perception and behavior. Here we review ensemble phenomenology, developmental origin, biophysical and synaptic mechanisms, and potential functional roles across different brain areas and species, including humans. As modular units of neural circuits, ensembles could provide a mechanistic underpinning of fundamental brain processes, including neural coding, motor planning, decision-making, learning, and adaptability.

Stationary stable cross-correlation pattern and task specific deviations in unresponsive wakefulness syndrome as well as clinically healthy subjects

Brain dynamics is highly non-stationary, permanently subject to ever-changing external conditions and continuously monitoring and adjusting internal control mechanisms. Finding stationary structures in this system, as has been done recently, is therefore of great importance for understanding fundamental dynamic trade relationships. Here we analyse electroencephalographic recordings (EEG) of 13 subjects with unresponsive wakefulness syndrome (UWS) during rest and while being influenced by different acoustic stimuli. We compare the results with a control group under the same experimental conditions and with clinically healthy subjects during overnight sleep. The main objective of this study is to investigate whether a stationary correlation pattern is also present in the UWS group, and if so, to what extent this structure resembles the one found in healthy subjects. Furthermore, we extract transient dynamical features via specific deviations from the stationary interrelation pattern. We find that (i) the UWS group is more heterogeneous than the two groups of healthy subjects, (ii) also the EEGs of the UWS group contain a stationary cross-correlation pattern, although it is less pronounced and shows less similarity to that found for healthy subjects and (iii) deviations from the stationary pattern are notably larger for the UWS than for the two groups of healthy subjects. The results suggest that the nervous system of subjects with UWS receive external stimuli but show an overreaching reaction to them, which may disturb opportune information processing.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Long Timescales, Individual Differences, and Scale Invariance in Animal Behavior

The explosion of data on animal behavior in more natural contexts highlights the fact that these behaviors exhibit correlations across many timescales. However, there are major challenges in analyzing these data: records of behavior in single animals have fewer independent samples than one might expect. In pooling data from multiple animals, individual differences can mimic long-ranged temporal correlations; conversely, long-ranged correlations can lead to an overestimate of individual differences. We suggest an analysis scheme that addresses these problems directly, apply this approach to data on the spontaneous behavior of walking flies, and find evidence for scale-invariant correlations over nearly three decades in time, from seconds to one hour. Three different measures of correlation are consistent with a single underlying scaling field of dimension Δ=0.180±0.005.

Measuring neuronal avalanches to inform brain-computer interfaces

Large-scale interactions among multiple brain regions manifest as bursts of activations called neuronal avalanches, which reconfigure according to the task at hand and, hence, might constitute natural candidates to design brain-computer interfaces (BCIs). To test this hypothesis, we used source-reconstructed magneto/electroencephalography during resting state and a motor imagery task performed within a BCI protocol. To track the probability that an avalanche would spread across any two regions, we built an avalanche transition matrix (ATM) and demonstrated that the edges whose transition probabilities significantly differed between conditions hinged selectively on premotor regions in all subjects. Furthermore, we showed that the topology of the ATMs allows task-decoding above the current gold standard. Hence, our results suggest that neuronal avalanches might capture interpretable differences between tasks that can be used to inform brain-computer interfaces.

Conceptual foundations of physiological regulation incorporating the free energy principle and self-organized criticality

Bettinger, J. S., K. J. Friston. Conceptual Foundations of Physiological Regulation incorporating the Free Energy Principle & Self-Organized Criticality. NEUROSCI BIOBEHAV REV 23(x) 144-XXX, 2022. Since the late nineteen-nineties, the concept of homeostasis has been contextualized within a broader class of "allostatic" dynamics characterized by a wider-berth of causal factors including social, psychological and environmental entailments; the fundamental nature of integrated brain-body dynamics; plus the role of anticipatory, top-down constraints supplied by intrinsic regulatory models. Many of these evidentiary factors are integral in original descriptions of homeostasis; subsequently integrated; and/or cite more-general operating principles of self-organization. As a result, the concept of allostasis may be generalized to a larger category of variational systems in biology, engineering and physics in terms of advances in complex systems, statistical mechanics and dynamics involving heterogenous (hierarchical/heterarchical, modular) systems like brain-networks and the internal milieu. This paper offers a three-part treatment. 1) interpret "allostasis" to emphasize a variational and relational foundation of physiological stability; 2) adapt the role of allostasis as "stability through change" to include a "return to stability" and 3) reframe the model of homeostasis with a conceptual model of criticality that licenses the upgrade to variational dynamics.

How network structure affects the dynamics of a network of stochastic spiking neurons

Up to now, it still remains an open question about the relation between the structure of brain networks and their functions. The effects of structure on the dynamics of neural networks are usually investigated via extensive numerical simulations, while analytical analysis is always very difficult and thus rare. In this work, we explored the effects of a random regular graph on the dynamics of a neural network of stochastic spiking neurons, which has a bistable region when fully connected. We showed by numerical simulations that as the number of each neuron's neighbors decreases, the bistable region shrinks and eventually seems to disappear, and a critical-like transition appears. In the meantime, we made analytical analysis that explains numerical results. We hope this would give some insights into how structure affects the dynamics of neural networks from a theoretical perspective, rather than merely by numerical simulations.

Critical dynamics arise during structured information presentation within embodied in vitro neuronal networks

Understanding how brains process information is an incredibly difficult task. Amongst the metrics characterising information processing in the brain, observations of dynamic near-critical states have generated significant interest. However, theoretical and experimental limitations associated with human and animal models have precluded a definite answer about when and why neural criticality arises with links from attention, to cognition, and even to consciousness. To explore this topic, we used an in vitro neural network of cortical neurons that was trained to play a simplified game of 'Pong' to demonstrate Synthetic Biological Intelligence (SBI). We demonstrate that critical dynamics emerge when neural networks receive task-related structured sensory input, reorganizing the system to a near-critical state. Additionally, better task performance correlated with proximity to critical dynamics. However, criticality alone is insufficient for a neuronal network to demonstrate learning in the absence of additional information regarding the consequences of previous actions. These findings offer compelling support that neural criticality arises as a base feature of incoming structured information processing without the need for higher order cognition.

Neuronal avalanches: Sandpiles of self-organized criticality or critical dynamics of brain waves?

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics [Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Biases in inverse Ising estimates of near-critical behavior

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as pseudo-likelihood maximization (PLM), are biased. Using the Sherrington-Kirkpatrick model as a benchmark, we show that these biases are large in critical regimes close to phase boundaries, and they may alter the qualitative interpretation of the inferred model. In particular, we show that the small-sample bias causes models inferred through PLM to appear closer to criticality than one would expect from the data. Data-driven methods to correct this bias are explored and applied to a functional magnetic resonance imaging data set from neuroscience. Our results indicate that additional care should be taken when attributing criticality to real-world data sets.

Emerging V1 neuronal ensembles with enhanced connectivity after associative learning

Introduction

The visual stimulus-specific responses in the primary visual cortex (V1) undergo plastic changes after associative learning. During the learning process, neuronal ensembles, defined as groups of coactive neurons, are well known to be related to learning and memory. However, it remains unclear what effect learning has on ensembles, and which neuronal subgroups within those ensembles play a key role in associative learning.

Methods

We used two-photon calcium imaging in mice to record the activity of V1 neurons before and after fear conditioning associated with a visual cue (blue light). We first defined neuronal ensembles by thresholding their functional connectivity in response to blue (conditioned) or green (control) light. We defined neurons that existed both before and after conditioning as stable neurons. Neurons which were recruited after conditioning were defined as new neurons. The graph theory-based analysis was performed to quantify the changes in connectivity within ensembles after conditioning.

Results

A significant enhancement in the connectivity strength (the average correlation with other neurons) was observed in the blue ensembles after conditioning. We found that stable neurons within the blue ensembles showed a significantly smaller clustering coefficient (the value represented the degree of interconnectedness among a node's neighbors) after conditioning than they were before conditioning. Additionally, new neurons within the blue ensembles had a larger clustering coefficient, similar relative degree (the value represented the number of functional connections between neurons) and connectivity strength compared to stable neurons in the same ensembles.

Discussion

Overall, our results demonstrated that the plastic changes caused by conditioning occurred in subgroups of neurons in the ensembles. Moreover, new neurons from conditioned ensembles may play a crucial role in memory formation, as they exhibited not only similar connection competence in relative degree and connectivity strength as stable neurons, but also showed a significantly larger clustering coefficient compared to the stable neurons within the same ensembles after conditioning.

Neuromodulatory control of complex adaptive dynamics in the brain

How is the massive dimensionality and complexity of the microscopic constituents of the nervous system brought under sufficiently tight control so as to coordinate adaptive behaviour? A powerful means for striking this balance is to poise neurons close to the critical point of a phase transition, at which a small change in neuronal excitability can manifest a nonlinear augmentation in neuronal activity. How the brain could mediate this critical transition is a key open question in neuroscience. Here, I propose that the different arms of the ascending arousal system provide the brain with a diverse set of heterogeneous control parameters that can be used to modulate the excitability and receptivity of target neurons-in other words, to act as control parameters for mediating critical neuronal order. Through a series of worked examples, I demonstrate how the neuromodulatory arousal system can interact with the inherent topological complexity of neuronal subsystems in the brain to mediate complex adaptive behaviour.

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.

Time-resolved correlation of distributed brain activity tracks E-I balance and accounts for diverse scale-free phenomena

Much of systems neuroscience posits the functional importance of brain activity patterns that lack natural scales of sizes, durations, or frequencies. The field has developed prominent, and sometimes competing, explanations for the nature of this scale-free activity. Here, we reconcile these explanations across species and modalities. First, we link estimates of excitation-inhibition (E-I) balance with time-resolved correlation of distributed brain activity. Second, we develop an unbiased method for sampling time series constrained by this time-resolved correlation. Third, we use this method to show that estimates of E-I balance account for diverse scale-free phenomena without need to attribute additional function or importance to these phenomena. Collectively, our results simplify existing explanations of scale-free brain activity and provide stringent tests on future theories that seek to transcend these explanations.

Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks

Numerous studies suggest that biological neuronal networks self-organize toward a critical state with stable recruitment dynamics. Individual neurons would then statistically activate exactly one further neuron during activity cascades termed neuronal avalanches. Yet, it is unclear if and how this can be reconciled with the explosive recruitment dynamics within neocortical minicolumns in vivo and within neuronal clusters in vitro, which indicates that neurons form supercritical local circuits. Theoretical studies propose that modular networks with a mix of regionally subcritical and supercritical dynamics would create apparently critical dynamics, resolving this inconsistency. Here, we provide experimental support by manipulating the structural self-organization process of networks of cultured rat cortical neurons (either sex). Consistent with the prediction, we show that increasing clustering in neuronal networks developing in vitro strongly correlates with avalanche size distributions transitioning from supercritical to subcritical activity dynamics. Avalanche size distributions approximated a power law in moderately clustered networks, indicating overall critical recruitment. We propose that activity-dependent self-organization can tune inherently supercritical networks toward mesoscale criticality by creating a modular structure in neuronal networks.SIGNIFICANCE STATEMENT Critical recruitment dynamics in neuronal networks are considered optimal for information processing in the brain. However, it remains heavily debated how neuronal networks would self-organize criticality by detailed fine-tuning of connectivity, inhibition, and excitability. We provide experimental support for theoretical considerations that modularity tunes critical recruitment dynamics at the mesoscale level of interacting neuron clusters. This reconciles reports of supercritical recruitment dynamics in local neuron clusters with findings on criticality sampled at mesoscopic network scales. Intriguingly, altered mesoscale organization is a prominent aspect of various neuropathological diseases currently investigated in the framework of criticality. We therefore believe that our findings would also be of interest for clinical scientists searching to link the functional and anatomic signatures of such brain disorders.

Putative roles for homeostatic plasticity in epileptogenesis

Homeostatic plasticity allows neural circuits to maintain an average activity level while preserving the ability to learn new associations and efficiently transmit information. This dynamic process usually protects the brain from excessive activity, like seizures. However, in certain contexts, homeostatic plasticity might produce seizures, either in response to an acute provocation or more chronically as a driver of epileptogenesis. Here, we review three seizure conditions in which homeostatic plasticity likely plays an important role: acute drug withdrawal seizures, posttraumatic or disconnection epilepsy, and cyclic seizures. Identifying the homeostatic mechanisms active at different stages of development and in different circuits could allow better targeting of therapies, including determining when neuromodulation might be most effective, proposing ways to prevent epileptogenesis, and determining how to disrupt the cycle of recurring seizure clusters.

Critical brain wave dynamics of neuronal avalanches

Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Single spikes drive sequential propagation and routing of activity in a cortical network

Single spikes can trigger repeatable firing sequences in cortical networks. The mechanisms that support reliable propagation of activity from such small events and their functional consequences remain unclear. By constraining a recurrent network model with experimental statistics from turtle cortex, we generate reliable and temporally precise sequences from single spike triggers. We find that rare strong connections support sequence propagation, while dense weak connections modulate propagation reliability. We identify sections of sequences corresponding to divergent branches of strongly connected neurons which can be selectively gated. Applying external inputs to specific neurons in the sparse backbone of strong connections can effectively control propagation and route activity within the network. Finally, we demonstrate that concurrent sequences interact reliably, generating a highly combinatorial space of sequence activations. Our results reveal the impact of individual spikes in cortical circuits, detailing how repeatable sequences of activity can be triggered, sustained, and controlled during cortical computations.

Self-organized criticality as a framework for consciousness: A review study

Objective

No current model of consciousness is univocally accepted on either theoretical or empirical grounds, and the need for a solid unifying framework is evident. Special attention has been given to the premise that self-organized criticality (SOC) is a fundamental property of neural system. SOC provides a competitive model to describe the physical mechanisms underlying spontaneous brain activity, and thus, critical dynamics were proposed as general gauges of information processing representing a strong candidate for a surrogate measure of consciousness. As SOC could be a neurodynamical framework, which may be able to bring together existing theories and experimental evidence, the purpose of this work was to provide a comprehensive overview of progress of research on SOC in association with consciousness.

Methods

A comprehensive search of publications on consciousness and SOC published between 1998 and 2021 was conducted. The Web of Science database was searched, and annual number of publications and citations, type of articles, and applied methods were determined.

Results

A total of 71 publications were identified. The annual number of citations steadily increased over the years. Original articles comprised 50.7% and reviews/theoretical articles 43.6%. Sixteen studies reported on human data and in seven studies data were recorded in animals. Computational models were utilized in n = 12 studies. EcoG data were assessed in n = 4 articles, fMRI in n = 4 studies, and EEG/MEG in n = 10 studies. Notably, different analytical tools were applied in the EEG/MEG studies to assess a surrogate measure of criticality such as the detrended fluctuation analysis, the pair correlation function, parameters from the neuronal avalanche analysis and the spectral exponent.

Conclusion

Recent studies pointed out agreements of critical dynamics with the current most influencing theories in the field of consciousness research, the global workspace theory and the integrated information theory. Thus, the framework of SOC as a neurodynamical parameter for consciousness seems promising. However, identified experimental work was small in numbers, and a heterogeneity of applied analytical tools as a surrogate measure of criticality was observable, which limits the generalizability of findings.

Subcritical escape waves in schooling fish

Theoretical physics predicts optimal information processing in living systems near transitions (or pseudo-critical points) in their collective dynamics. However, focusing on potential benefits of proximity to a critical point, such as maximal sensitivity to perturbations and fast dissemination of information, commonly disregards possible costs of criticality in the noisy, dynamic environmental contexts of biological systems. Here, we find that startle cascades in fish schools are subcritical (not maximally responsive to environmental cues) and that distance to criticality decreases when perceived risk increases. Considering individuals' costs related to two detection error types, associated to both true and false alarms, we argue that being subcritical, and modulating distance to criticality, can be understood as managing a trade-off between sensitivity and robustness according to the riskiness and noisiness of the environment. Our work emphasizes the need for an individual-based and context-dependent perspective on criticality and collective information processing and motivates future questions about the evolutionary forces that brought about a particular trade-off.

Simulating epileptic seizures using the bidomain model

Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain's activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.

Optimal reinforcement learning near the edge of a synchronization transition

Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may correspond to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask the following: what is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of a cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.

When to Be Critical? Performance and Evolvability in Different Regimes of Neural Ising Agents

It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial evolutionary systems. We put this hypothesis to test in a system of evolving foraging agents controlled by neural networks that can adapt the agents' dynamical regime throughout evolution. Surprisingly, we find that all populations that discover solutions evolve to be subcritical. By a resilience analysis, we find that there are still benefits of starting the evolution in the critical regime. Namely, initially critical agents maintain their fitness level under environmental changes (for example, in the lifespan) and degrade gracefully when their genome is perturbed. At the same time, initially subcritical agents, even when evolved to the same fitness, are often inadequate to withstand the changes in the lifespan and degrade catastrophically with genetic perturbations. Furthermore, we find the optimal distance to criticality depends on the task complexity. To test it we introduce a hard task and a simple task: For the hard task, agents evolve closer to criticality, whereas more subcritical solutions are found for the simple task. We verify that our results are independent of the selected evolutionary mechanisms by testing them on two principally different approaches: a genetic algorithm and an evolutionary strategy. In summary, our study suggests that although optimal behaviour in the simple task is obtained in a subcritical regime, initializing near criticality is important to be efficient at finding optimal solutions for new tasks of unknown complexity.

Microscale dynamics of electrophysiological markers of epilepsy

OBJECTIVE

Interictal discharges (IIDs) and high frequency oscillations (HFOs) are established neurophysiologic biomarkers of epilepsy, while microseizures are less well studied. We used custom poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) microelectrodes to better understand these markers' microscale spatial dynamics.

METHODS

Electrodes with spatial resolution down to 50 µm were used to record intraoperatively in 30 subjects. IIDs' degree of spread and spatiotemporal paths were generated by peak-tracking followed by clustering. Repeating HFO patterns were delineated by clustering similar time windows. Multi-unit activity (MUA) was analyzed in relation to IID and HFO timing.

RESULTS

We detected IIDs encompassing the entire array in 93% of subjects, while localized IIDs, observed across < 50% of channels, were seen in 53%. IIDs traveled along specific paths. HFOs appeared in small, repeated spatiotemporal patterns. Finally, we identified microseizure events that spanned 50-100 µm. HFOs covaried with MUA, but not with IIDs.

CONCLUSIONS

Overall, these data suggest that irritable cortex micro-domains may form part of an underlying pathologic architecture which could contribute to the seizure network.

SIGNIFICANCE

These results, supporting the possibility that epileptogenic cortex comprises a mosaic of irritable domains, suggests that microscale approaches might be an important perspective in devising novel seizure control therapies.

Neuronal avalanches in Watts-Strogatz networks of stochastic spiking neurons

Networks of stochastic leaky integrate-and-fire neurons, both at the mean-field level and in square lattices, present a continuous absorbing phase transition with power-law neuronal avalanches at the critical point. Here we complement these results showing that small-world Watts-Strogatz networks have mean-field critical exponents for any rewiring probability p>0. For the ring (p=0), the exponents are the same from the dimension d=1 of the directed-percolation class. In the model, firings are stochastic and occur in discrete time steps, based on a sigmoidal firing probability function. Each neuron has a membrane potential that integrates the signals received from its neighbors. The membrane potentials are subject to a leakage parameter. We study topologies with a varied number of neuron connections and different values of the leakage parameter. Results indicate that the dynamic range is larger for p=0. We also study a homeostatic synaptic depression mechanism to self-organize the network towards the critical region. These stochastic oscillations are characteristic of the so-called self-organized quasicriticality.

Long-term stability of cortical ensembles

Neuronal ensembles, coactive groups of neurons found in spontaneous and evoked cortical activity, are causally related to memories and perception, but it is still unknown how stable or flexible they are over time. We used two-photon multiplane calcium imaging to track over weeks the activity of the same pyramidal neurons in layer 2/3 of the visual cortex from awake mice and recorded their spontaneous and visually evoked responses. Less than half of the neurons remained active across any two imaging sessions. These stable neurons formed ensembles that lasted weeks, but some ensembles were also transient and appeared only in one single session. Stable ensembles preserved most of their neurons for up to 46 days, our longest imaged period, and these 'core' cells had stronger functional connectivity. Our results demonstrate that neuronal ensembles can last for weeks and could, in principle, serve as a substrate for long-lasting representation of perceptual states or memories.

Ensemble synchronization in the reassembly of Hydra's nervous system

Although much is known about how the structure of the nervous system develops, it is still unclear how its functional modularity arises. A dream experiment would be to observe the entire development of a nervous system, correlating the emergence of functional units with their associated behaviors. This is possible in the cnidarian Hydra vulgaris, which, after its complete dissociation into individual cells, can reassemble itself back together into a normal animal. We used calcium imaging to monitor the complete neuronal activity of dissociated Hydra as they reaggregated over several days. Initially uncoordinated neuronal activity became synchronized into coactive neuronal ensembles. These local modules then synchronized with others, building larger functional ensembles that eventually extended throughout the entire reaggregate, generating neuronal rhythms similar to those of intact animals. Global synchronization was not due to neurite outgrowth but to strengthening of functional connections between ensembles. We conclude that Hydra's nervous system achieves its functional reassembly through the hierarchical modularity of neuronal ensembles.

Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration–a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration–determined from partial information decomposition–varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow.

Networks compute information. That is, they modify inputs to generate distinct outputs. These computations are an important component of network information processing. Knowing how the routing of information in a network influences computation is therefore crucial. Here we asked how a key form of computation—synergistic integration—is related to the direction of local information flow in networks of spiking cortical neurons. Specifically, we asked how information flow between input neurons (i.e., recurrent information flow) and information flow from output neurons to input neurons (i.e., feedback information flow) was related to the amount of synergistic integration performed by output neurons. We found that greater synergistic integration occurred where there was more recurrent information flow. And, lesser synergistic integration occurred where there was more feedback information flow relative to feedforward information flow. These results show that computation, in the form of synergistic integration, is distinctly influenced by the directionality of local information flow. Such work is valuable for predicting where and how network computation occurs and for designing networks with desired computational abilities.

The structural connectome constrains fast brain dynamics

Brain activity during rest displays complex, rapidly evolving patterns in space and time. Structural connections comprising the human connectome are hypothesized to impose constraints on the dynamics of this activity. Here, we use magnetoencephalography (MEG) to quantify the extent to which fast neural dynamics in the human brain are constrained by structural connections inferred from diffusion MRI tractography. We characterize the spatio-temporal unfolding of whole-brain activity at the millisecond scale from source-reconstructed MEG data, estimating the probability that any two brain regions will significantly deviate from baseline activity in consecutive time epochs. We find that the structural connectome relates to, and likely affects, the rapid spreading of neuronal avalanches, evidenced by a significant association between these transition probabilities and structural connectivity strengths (r = 0.37, p<0.0001). This finding opens new avenues to study the relationship between brain structure and neural dynamics.

Neural field theory of neural avalanche exponents

The power-law exponents of observed size and lifetime distributions of near-critical neural avalanches are calculated from neural field theory using diagrammatic methods. This brings neural avalanches within the ambit of neural field theory, which has also previously explained near-critical 1/f spectra and many other observed features of neural activity. This strengthens the case for near-criticality of the brain and opens the way for these other phenomena to be interrelated with avalanches and their dynamics.

Early functional changes associated with alpha-synuclein proteinopathy in engineered human neural networks

A patterned spread of proteinopathy represents a common characteristic of many neurodegenerative diseases. In Parkinson's disease (PD), misfolded forms of α-synuclein proteins accumulate in hallmark pathological inclusions termed Lewy bodies and Lewy neurites. Such protein aggregates seem to affect selectively vulnerable neuronal populations in the substantia nigra and to propagate within interconnected neuronal networks. Research findings suggest that these proteinopathic inclusions are present at very early time points in disease development, even before clear behavioral symptoms of dysfunction arise. In this study, we investigate the early pathophysiology developing after induced formation of such PD-related α-synuclein inclusions in a physiologically relevant in vitro setup using engineered human neural networks. We monitor the neural network activity using multielectrode arrays (MEAs) for a period of 3 wk following proteinopathy induction to identify associated changes in network function, with a special emphasis on the measure of network criticality. Self-organized criticality represents the critical point between resilience against perturbation and adaptational flexibility, which appears to be a functional trait in self-organizing neural networks, both in vitro and in vivo. We show that although developing pathology at early onset is not clearly manifest in standard measurements of network function, it may be discerned by investigating differences in network criticality states.

Entropy estimation within in vitro neural-astrocyte networks as a measure of development instability

The brain demands a significant fraction of the energy budget in an organism; in humans, it accounts for 2% of the body mass, but utilizes 20% of the total energy metabolized. This is due to the large load required for information processing; spiking demands from neurons are high but are a key component to understanding brain functioning. Astrocytic brain cells contribute to the healthy functioning of brain circuits by mediating neuronal network energy and facilitating the formation and stabilization of synaptic connectivity. During development, spontaneous activity influences synaptic formation, shaping brain circuit construction, and adverse astrocyte mutations can lead to pathological processes impacting cognitive impairment due to inefficiencies in network spiking activity. We have developed a measure that quantifies information stability within in vitro networks consisting of mixed neural-astrocyte cells. Brain cells were harvested from mice with mutations to a gene associated with the strongest known genetic risk factor for Alzheimer's disease, APOE. We calculate energy states of the networks and using these states, we present an entropy-based measure to assess changes in information stability over time. We show that during development, stability profiles of spontaneous network activity are modified by exogenous astrocytes and that network stability, in terms of the rate of change of entropy, is allele dependent.

Not One, but Many Critical States: A Dynamical Systems Perspective

The past decade has seen growing support for the critical brain hypothesis, i.e., the possibility that the brain could operate at or very near a critical state between two different dynamical regimes. Such critical states are well-studied in different disciplines, therefore there is potential for a continued transfer of knowledge. Here, I revisit foundations of bifurcation theory, the mathematical theory of transitions. While the mathematics is well-known it's transfer to neural dynamics leads to new insights and hypothesis.

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.

Critical Neural Networks Minimize Metabolic Cost

Brain dynamics show a rich spatiotemporal behavior whose stability is neither ordered nor chaotic, indicating that neural networks operate at intermediate stability regimes including critical dynamics represented by a negative power-law distribution of avalanche sizes with exponent α=−1.5. However, it is unknown which stability regimen allows global and local information transmission with reduced metabolic costs, which are measured in terms of synaptic potentials and action potentials. In this work, using a hierarchical neuron model with rich-club organization, we measure the average number of action potentials required to activate n different neurons (avalanche size). Besides, we develop a mathematical formula to represent the metabolic synaptic potential cost. We develop simulations variating the synaptic amplitude, synaptic time course (ms), and hub excitatory/inhibitory ratio. We compare different dynamic regimes in terms of avalanche sizes vs. metabolic cost. We also implement the dynamic model in a Drosophila and Erdos–Renyi networks to computer dynamics and metabolic costs. The results show that the synaptic amplitude and time course play a key role in information propagation. They can drive the system from subcritical to supercritical regimes. The later result promotes the coexistence of critical regimes with a wide range of excitation/inhibition hub ratios. Moreover, subcritical or silent regimes minimize metabolic cost for local avalanche sizes, whereas critical and intermediate stability regimes show the best compromise between information propagation and reduced metabolic consumption, also minimizing metabolic cost for a wide range of avalanche sizes.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Collective firing patterns of neuronal networks with short-term synaptic plasticity

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Configuration and dynamics of dominant inspiratory multineuronal activity patterns during eupnea and gasping generation in vitro

The pre-Bötzinger complex (preBötC), located within the ventral respiratory column, produces inspiratory bursts in varying degrees of synchronization/amplitude. This wide range of population burst patterns reflects the flexibility of the preBötC neurons, which is expressed in variations in the onset/offset times of their activations and their activity during the population bursts, with respiratory neurons exhibiting a large cycle-to-cycle timing jitter both at the population activity onset and at the population activity peak, suggesting that respiratory neurons are stochastically activated before and during the inspiratory bursts. However, it is still unknown whether this stochasticity is maintained while evaluating the coactivity of respiratory neuronal ensembles. Moreover, the preBötC topology also remains unknown. In this study, by simultaneously recording tens of preBötC neurons and using coactivation analysis during the inspiratory periods, we found that the preBötC has a scale-free configuration (mixture of not many highly connected nodes, hubs, with abundant poorly connected elements) exhibiting the rich-club phenomenon (hubs more likely interconnected with each other). PreBötC neurons also produce multineuronal activity patterns (MAPs) that are highly stable and change during the hypoxia-induced reconfiguration. Moreover, preBötC contains a coactivating core network shared by all its MAPs. Finally, we found a distinctive pattern of sequential coactivation of core network neurons at the beginning of the inspiratory periods, indicating that, when evaluated at the multicellular level, the coactivation of respiratory neurons seems not to be stochastic.NEW & NOTEWORTHY By means of multielectrode recordings of preBötC neurons, we evaluated their configuration in normoxia and hypoxia, finding that the preBötC exhibits a scale-free configuration with a rich-club phenomenon. preBötC neurons produce multineuronal activity patterns that are highly stable but change during hypoxia. The preBötC contains a coactivating core network that exhibit a distinctive pattern of coactivation at the beginning of inspirations. These results reveal some network basis of inspiratory rhythm generation and its reconfiguration during hypoxia.

Selective Participation of Single Cortical Neurons in Neuronal Avalanches

Neuronal avalanches are scale-invariant neuronal population activity patterns in the cortex that emerge in vivo in the awake state and in vitro during balanced excitation and inhibition. Theory and experiments suggest that avalanches indicate a state of cortex that improves numerous aspects of information processing by allowing for the transient and selective formation of local as well as system-wide spanning neuronal groups. If avalanches are indeed involved with information processing, one might expect that single neurons would participate in avalanche patterns selectively. Alternatively, all neurons could participate proportionally to their own activity in each avalanche as would be expected for a population rate code. Distinguishing these hypotheses, however, has been difficult as robust avalanche analysis requires technically challenging measures of their intricate organization in space and time at the population level, while also recording sub- or suprathreshold activity from individual neurons with high temporal resolution. Here, we identify repeated avalanches in the ongoing local field potential (LFP) measured with high-density microelectrode arrays in the cortex of awake nonhuman primates and in acute cortex slices from young and adult rats. We studied extracellular unit firing in vivo and intracellular responses of pyramidal neurons in vitro. We found that single neurons participate selectively in specific LFP-based avalanche patterns. Furthermore, we show in vitro that manipulating the balance of excitation and inhibition abolishes this selectivity. Our results support the view that avalanches represent the selective, scale-invariant formation of neuronal groups in line with the idea of Hebbian cell assemblies underlying cortical information processing.

3-D multi-electrode arrays detect early spontaneous electrophysiological activity in 3-D neuronal-astrocytic co-cultures

Three-dimensional (3-D) neural cultures represent a promising platform for studying disease and drug screening. Tools and methodologies for measuring the electrophysiological function in these cultures are needed. Therefore, the purpose of this work was primarily to develop a methodology to interface engineered 3-D dissociated neural cultures with commercially available 3-D multi-electrode arrays (MEAs) reliably over 3 weeks to enable the recording of their electrophysiological activity. We further compared the functional output of these cultures to their structural and synaptic network development over time. We reliably interfaced a primary rodent neuron-astrocyte (2:1) 3-D co-culture (2500 cells/mm³ plating cell density) in Matrigel™ (7.5 mg/mL) that was up to 750 µm thick (30-40 cell-layers) with spiked 3-D MEAs while maintaining high viability. Using these MEAs we successfully recorded the spontaneous development of neural network-level electrophysiological activity and measured the development of putative synapses and neuronal maturation in these co-cultures using immunocytochemistry over 3 weeks in vitro. Planar (2-D) MEAs interfaced with these cultures served as recording controls. Neurons within this interfaced 3-D culture-MEA system exhibited considerable neurite outgrowth, networking, neuronal maturation, synaptogenesis, and culture-wide spontaneous firing of synchronized spikes and bursts of action potentials. Network-wide spikes and synchronized bursts increased rapidly (first detected at 2 days) during the first week in culture, plateaued during the second week, and reduced slightly in the third week, while maintaining high viability throughout the 3-week culturing period. Early electrophysiology activity occurred prior to neuronal process maturation and significant synaptic density increases in the second week. We successfully interfaced 3-D neural co-cultures with 3-D MEAs and recorded the electrophysiological activity of these cultures over 3 weeks. The initial period of rapid increase in electrophysiological activity, followed by a period of neuronal maturation and high-level of synapse formation in these cultures suggests a developmental homeostatic process. This methodology can enable future applications both in fundamental investigations of neural network behavior and in translational studies involving drug testing and neural interfacing.

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.

Spike-phase coupling as an order parameter in a leaky integrate-and-fire model

It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of N excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons K plays the role of the control parameter that generates criticality when the critical cooperation strength K_{c} is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as m resorts to identify a Kuramoto order parameter. By increasing K, we find a continuous transition from irregular spiking to a phase-locked state at the critical point K_{c}. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.