Broadband Criticality of Human Brain Network Synchronization

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.     

Neuronal Avalanches Differ from Wakefulness to Deep Sleep – Evidence from Intracranial Depth Recordings in Humans

Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches – spatiotemporal waves of enhanced activity - from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law – the hallmark feature of SOC - for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.     

Collective predator evasion: Putting the criticality hypothesis to the test

According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.     

Changes in resting neural connectivity during propofol sedation

Background

The default mode network consists of a set of functionally connected brain regions (posterior cingulate, medial prefrontal cortex and bilateral parietal cortex) maximally active in functional imaging studies under “no task” conditions. It has been argued that the posterior cingulate is important in consciousness/awareness, but previous investigations of resting interactions between the posterior cingulate cortex and other brain regions during sedation and anesthesia have produced inconsistent results.

Methodology/Principal Findings

We examined the connectivity of the posterior cingulate at different levels of consciousness. “No task” fMRI (BOLD) data were collected from healthy volunteers while awake and at low and moderate levels of sedation, induced by the anesthetic agent propofol. Our data show that connectivity of the posterior cingulate changes during sedation to include areas that are not traditionally considered to be part of the default mode network, such as the motor/somatosensory cortices, the anterior thalamic nuclei, and the reticular activating system.

Conclusions/Significance

This neuroanatomical signature resembles that of non-REM sleep, and may be evidence for a system that reduces its discriminable states and switches into more stereotypic patterns of firing under sedation.     

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson’s disease

Parkinson’s disease motor symptoms are associated with an increase in subthalamic nucleus beta band oscillatory power. However, these oscillations are phasic, and there is a growing body of evidence suggesting that beta burst duration may be of critical importance to motor symptoms. This makes insights into the dynamics of beta bursting generation valuable, in particular to refine closed-loop deep brain stimulation in Parkinson’s disease. In this study, we ask the question “Can average burst duration reveal how dynamics change between the ON and OFF medication states?”. Our analysis of local field potentials from the subthalamic nucleus demonstrates using linear surrogates that the system generating beta oscillations is more likely to act in a non-linear regime OFF medication and that the change in a non-linearity measure is correlated with motor impairment. In addition, we pinpoint the simplest dynamical changes that could be responsible for changes in the temporal patterning of beta oscillations between medication states by fitting to data biologically inspired models, and simpler beta envelope models. Finally, we show that the non-linearity can be directly extracted from average burst duration profiles under the assumption of constant noise in envelope models. This reveals that average burst duration profiles provide a window into burst dynamics, which may underlie the success of burst duration as a biomarker. In summary, we demonstrate a relationship between average burst duration profiles, dynamics of the system generating beta oscillations, and motor impairment, which puts us in a better position to understand the pathology and improve therapies such as deep brain stimulation.     

Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.     

Learning to Estimate Dynamical State with Probabilistic Population Codes

Tracking moving objects, including one’s own body, is a fundamental ability of higher organisms, playing a central role in many perceptual and motor tasks. While it is unknown how the brain learns to follow and predict the dynamics of objects, it is known that this process of state estimation can be learned purely from the statistics of noisy observations. When the dynamics are simply linear with additive Gaussian noise, the optimal solution is the well known Kalman filter (KF), the parameters of which can be learned via latent-variable density estimation (the EM algorithm). The brain does not, however, directly manipulate matrices and vectors, but instead appears to represent probability distributions with the firing rates of population of neurons, “probabilistic population codes.” We show that a recurrent neural network—a modified form of an exponential family harmonium (EFH)—that takes a linear probabilistic population code as input can learn, without supervision, to estimate the state of a linear dynamical system. After observing a series of population responses (spike counts) to the position of a moving object, the network learns to represent the velocity of the object and forms nearly optimal predictions about the position at the next time-step. This result builds on our previous work showing that a similar network can learn to perform multisensory integration and coordinate transformations for static stimuli. The receptive fields of the trained network also make qualitative predictions about the developing and learning brain: tuning gradually emerges for higher-order dynamical states not explicitly present in the inputs, appearing as delayed tuning for the lower-order states.     

Tyrosine Phosphorylation of Dbl Regulates GTPase Signaling

Rho GTPases are molecular “switches” that cycle between “on” (GTP-bound) and “off” (GDP-bound) states and regulate numerous cellular activities such as gene expression, protein synthesis, cytoskeletal rearrangements, and metabolic responses. Dysregulation of GTPases is a key feature of many diseases, especially cancers. Guanine nucleotide exchange factors (GEFs) of the Dbl family are activated by mitogenic cell surface receptors and activate the Rho family GTPases Cdc42, Rac1, and RhoA. The molecular mechanisms that regulate GEFs from the Dbl family are poorly understood. Our studies reveal that Dbl is phosphorylated on tyrosine residues upon stimulation by growth factors and that this event is critical for the regulated activation of the GEF. These findings uncover a novel layer of complexity in the physiological regulation of this protein.     

Directional Connectivity between Frontal and Posterior Brain Regions Is Altered with Increasing Concentrations of Propofol

Recent studies using electroencephalography (EEG) suggest that alteration of coherent activity between the anterior and posterior brain regions might be used as a neurophysiologic correlate of anesthetic-induced unconsciousness. One way to assess causal relationships between brain regions is given by renormalized partial directed coherence (rPDC). Importantly, directional connectivity is evaluated in the frequency domain by taking into account the whole multichannel EEG, as opposed to time domain or two channel approaches. rPDC was applied here in order to investigate propofol induced changes in causal connectivity between four states of consciousness: awake (AWA), deep sedation (SED), loss (LOC) and return of consciousness (ROC) by gathering full 10/20 system human EEG data in ten healthy male subjects. The target-controlled drug infusion was started at low rate with subsequent gradual stepwise increases at 10 min intervals in order to carefully approach LOC (defined as loss of motor responsiveness to a verbal stimulus). The direction of the causal EEG-network connections clearly changed from AWA to SED and LOC. Propofol induced a decrease (p = 0.002–0.004) in occipital-to-frontal rPDC of 8-16 Hz EEG activity and an increase (p = 0.001–0.040) in frontal-to-occipital rPDC of 10–20 Hz activity on both sides of the brain during SED and LOC. In addition, frontal-to-parietal rPDC within 1–12 Hz increased in the left hemisphere at LOC compared to AWA (p = 0.003). However, no significant changes were detected between the SED and the LOC states. The observed decrease in back-to-front EEG connectivity appears compatible with impaired information flow from the posterior sensory and association cortices to the executive prefrontal areas, possibly related to decreased ability to perceive the surrounding world during sedation. The observed increase in the opposite (front-to-back) connectivity suggests a propofol concentration dependent association and is not directly related to the level of consciousness per se.     

Is Buffer a Good Proxy for a Crowded Cell-Like Environment? A Comparative NMR Study of Calmodulin Side-Chain Dynamics in Buffer and E. coli Lysate

Biophysical studies of protein structure and dynamics are typically performed in a highly controlled manner involving only the protein(s) of interest. Comparatively fewer such studies have been carried out in the context of a cellular environment that typically involves many biomolecules, ions and metabolites. Recently, solution NMR spectroscopy, focusing primarily on backbone amide groups as reporters, has emerged as a powerful technique for investigating protein structure and dynamics in vivo and in crowded “cell-like” environments. Here we extend these studies through a comparative analysis of Ile, Leu, Val and Met methyl side-chain motions in apo, Ca²⁺-bound and Ca²⁺, peptide-bound calmodulin dissolved in aqueous buffer or in E. coli lysate. Deuterium spin relaxation experiments, sensitive to pico- to nano-second time-scale processes and Carr-Purcell-Meiboom-Gill relaxation dispersion experiments, reporting on millisecond dynamics, have been recorded. Both similarities and differences in motional properties are noted for calmodulin dissolved in buffer or in lysate. These results emphasize that while significant insights can be obtained through detailed “test-tube” studies, experiments performed under conditions that are “cell-like” are critical for obtaining a comprehensive understanding of protein motion in vivo and therefore for elucidating the relation between motion and function.     

Modeling Signal Propagation Mechanisms and Ligand-Based Conformational Dynamics of the Hsp90 Molecular Chaperone Full-Length Dimer

Hsp90 is a molecular chaperone essential for protein folding and activation in normal homeostasis and stress response. ATP binding and hydrolysis facilitate Hsp90 conformational changes required for client activation. Hsp90 plays an important role in disease states, particularly in cancer, where chaperoning of the mutated and overexpressed oncoproteins is important for function. Recent studies have illuminated mechanisms related to the chaperone function. However, an atomic resolution view of Hsp90 conformational dynamics, determined by the presence of different binding partners, is critical to define communication pathways between remote residues in different domains intimately affecting the chaperone cycle. Here, we present a computational analysis of signal propagation and long-range communication pathways in Hsp90. We carried out molecular dynamics simulations of the full-length Hsp90 dimer, combined with essential dynamics, correlation analysis, and a signal propagation model. All-atom MD simulations with timescales of 70 ns have been performed for complexes with the natural substrates ATP and ADP and for the unliganded dimer. We elucidate the mechanisms of signal propagation and determine “hot spots” involved in interdomain communication pathways from the nucleotide-binding site to the C-terminal domain interface. A comprehensive computational analysis of the Hsp90 communication pathways and dynamics at atomic resolution has revealed the role of the nucleotide in effecting conformational changes, elucidating the mechanisms of signal propagation. Functionally important residues and secondary structure elements emerge as effective mediators of communication between the nucleotide-binding site and the C-terminal interface. Furthermore, we show that specific interdomain signal propagation pathways may be activated as a function of the ligand. Our results support a “conformational selection model” of the Hsp90 mechanism, whereby the protein may exist in a dynamic equilibrium between different conformational states available on the energy landscape and binding of a specific partner can bias the equilibrium toward functionally relevant complexes.     

Electroencephalographic Variation during End Maintenance and Emergence from Surgical Anesthesia

The re-establishment of conscious awareness after discontinuing general anesthesia has often been assumed to be the inverse of loss of consciousness. This is despite the obvious asymmetry in the initiation and termination of natural sleep. In order to characterize the restoration of consciousness after surgery, we recorded frontal electroencephalograph (EEG) from 100 patients in the operating room during maintenance and emergence from general anesthesia. We have defined, for the first time, 4 steady-state patterns of anesthetic maintenance based on the relative EEG power in the slow-wave (<14 Hz) frequency bands that dominate sleep and anesthesia. Unlike single-drug experiments performed in healthy volunteers, we found that surgical patients exhibited greater electroencephalographic heterogeneity while re-establishing conscious awareness after drug discontinuation. Moreover, these emergence patterns could be broadly grouped according to the duration and rapidity of transitions amongst these slow-wave dominated brain states that precede awakening. Most patients progressed gradually from a pattern characterized by strong peaks of delta (0.5–4 Hz) and alpha/spindle (8–14 Hz) power (‘Slow-Wave Anesthesia’) to a state marked by low delta-spindle power (‘Non Slow-Wave Anesthesia’) before awakening. However, 31% of patients transitioned abruptly from Slow-Wave Anesthesia to waking; they were also more likely to express pain in the post-operative period. Our results, based on sleep-staging classification, provide the first systematized nomenclature for tracking brain states under general anesthesia from maintenance to emergence, and suggest that these transitions may correlate with post-operative outcomes such as pain.     

Large-Scale Information Flow in Conscious and Unconscious States: an ECoG Study in Monkeys

Consciousness is an emergent property of the complex brain network. In order to understand how consciousness is constructed, neural interactions within this network must be elucidated. Previous studies have shown that specific neural interactions between the thalamus and frontoparietal cortices; frontal and parietal cortices; and parietal and temporal cortices are correlated with levels of consciousness. However, due to technical limitations, the network underlying consciousness has not been investigated in terms of large-scale interactions with high temporal and spectral resolution. In this study, we recorded neural activity with dense electrocorticogram (ECoG) arrays and used the spectral Granger causality to generate a more comprehensive network that relates to consciousness in monkeys. We found that neural interactions were significantly different between conscious and unconscious states in all combinations of cortical region pairs. Furthermore, the difference in neural interactions between conscious and unconscious states could be represented in 4 frequency-specific large-scale networks with unique interaction patterns: 2 networks were related to consciousness and showed peaks in alpha and beta bands, while the other 2 networks were related to unconsciousness and showed peaks in theta and gamma bands. Moreover, networks in the unconscious state were shared amongst 3 different unconscious conditions, which were induced either by ketamine and medetomidine, propofol, or sleep. Our results provide a novel picture that the difference between conscious and unconscious states is characterized by a switch in frequency-specific modes of large-scale communications across the entire cortex, rather than the cessation of interactions between specific cortical regions.     

A Generalized Framework for Quantifying the Dynamics of EEG Event-Related Desynchronization

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent—to a large extent—from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a “conditional ERD,” through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli.     

A Sparse Representation-Based Algorithm for Pattern Localization in Brain Imaging Data Analysis

Considering the two-class classification problem in brain imaging data analysis, we propose a sparse representation-based multi-variate pattern analysis (MVPA) algorithm to localize brain activation patterns corresponding to different stimulus classes/brain states respectively. Feature selection can be modeled as a sparse representation (or sparse regression) problem. Such technique has been successfully applied to voxel selection in fMRI data analysis. However, single selection based on sparse representation or other methods is prone to obtain a subset of the most informative features rather than all. Herein, our proposed algorithm recursively eliminates informative features selected by a sparse regression method until the decoding accuracy based on the remaining features drops to a threshold close to chance level. In this way, the resultant feature set including all the identified features is expected to involve all the informative features for discrimination. According to the signs of the sparse regression weights, these selected features are separated into two sets corresponding to two stimulus classes/brain states. Next, in order to remove irrelevant/noisy features in the two selected feature sets, we perform a nonparametric permutation test at the individual subject level or the group level. In data analysis, we verified our algorithm with a toy data set and an intrinsic signal optical imaging data set. The results show that our algorithm has accurately localized two class-related patterns. As an application example, we used our algorithm on a functional magnetic resonance imaging (fMRI) data set. Two sets of informative voxels, corresponding to two semantic categories (i.e., “old people” and “young people”), respectively, are obtained in the human brain.     

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.