Trial-by-trial variability in cortical responses exhibits scaling of spatial correlations predicted from critical dynamics

In the mammalian cortex, even simple sensory inputs or movements activate many neurons, with each neuron responding variably to repeated stimuli-a phenomenon known as trial-by-trial variability. Understanding the spatial patterns and dynamics of this variability is challenging. Using cellular 2-photon imaging, we study visual and auditory responses in the primary cortices of awake mice. We focus on how individual neurons' responses differed from the overall population. We find consistent spatial correlations in these differences that are unique to each trial and linearly scale with the cortical area observed, a characteristic of critical dynamics as confirmed in our neuronal simulations. Using chronic multi-electrode recordings, we observe similar scaling in the prefrontal and premotor cortex of non-human primates during self-initiated and visually cued motor tasks. These results suggest that trial-by-trial variability, rather than being random noise, reflects a critical, fluctuation-dominated state in the cortex, supporting the brain's efficiency in processing information.

Beehive scale-free emergent dynamics

It has been repeatedly reported that the collective dynamics of social insects exhibit universal emergent properties similar to other complex systems. In this note, we study a previously published data set in which the positions of thousands of honeybees in a hive are individually tracked over multiple days. The results show that the hive dynamics exhibit long-range spatial and temporal correlations in the occupancy density fluctuations, despite the characteristic short-range bees' mutual interactions. The variations in the occupancy unveil a non-monotonic function between density and bees' flow, reminiscent of the car traffic dynamic near a jamming transition at which the system performance is optimized to achieve the highest possible throughput. Overall, these results suggest that the beehive collective dynamics are self-adjusted towards a point near its optimal density.

Scale-free correlations in the dynamics of a small (N∼10000) cortical network

The advent of novel optogenetics technology allows the recording of brain activity with a resolution never seen before. The characterization of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlations of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both the correlation length ξ and the correlation time τ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers evidence consistent with the view that the large-scale brain cortical dynamics corresponds to critical phenomena.

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.

Self-tuned criticality: Controlling a neuron near its bifurcation point via temporal correlations

Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such correlations behave similarly near instabilities across nonlinear dynamical systems, it is expected that the principle should control also low-dimensional dynamical systems exhibiting continuous or discontinuous bifurcations from fixed points to limit cycles. Here we present numerical evidence that the dynamics of a single neuron can be controlled in the vicinity of its bifurcation point. The approach is tested in two models: a two-dimensional generic excitable map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in both cases, the system can be self-tuned to its bifurcation point by modifying the control parameter according to the first coefficient of the autocorrelation function.

Finite-size correlation behavior near a critical point: A simple metric for monitoring the state of a neural network

In this article, a correlation metric κ_{c} is proposed for the inference of the dynamical state of neuronal networks. κ_{C} is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

Tricritical behavior in a neural model with excitatory and inhibitory units

While the support for the relevance of critical dynamics to brain function is increasing, there is much less agreement on the exact nature of the advocated critical point. Thus, a considerable number of theoretical efforts are currently concentrated on which mechanisms and what type(s) of transition can be exhibited by neuronal network models. In that direction, the present work describes the effect of incorporating a fraction of inhibitory neurons on the collective dynamics. As we show, this results in the appearance of a tricritical point for highly connected networks and a nonzero fraction of inhibitory neurons.

Learning by mistakes in memristor networks

Recent results revived the interest in the implementation of analog devices able to perform brainlike operations. Here we introduce a training algorithm for a memristor network which is inspired by previous work on biological learning. Robust results are obtained from computer simulations of a network of voltage-controlled memristive devices. Its implementation in hardware is straightforward, being scalable and requiring very little peripheral computation overhead.

Non-linear Functional Brain Co-activations in Short-Term Memory Distortion Tasks

Recent works shed light on the neural correlates of true and false recognition and the influence of time of day on cognitive performance. The current study aimed to investigate the modulation of the false memory formation by the time of day using a non-linear correlation analysis originally designed for fMRI resting-state data. Fifty-four young and healthy participants (32 females, mean age: 24.17 ± 3.56 y.o.) performed in MR scanner the modified Deese-Roediger-McDermott paradigm in short-term memory during one session in the morning and another in the evening. Subjects’ responses were modeled with a general linear model, which includes as a predictor the non-linear correlations of regional BOLD activity with the stimuli, separately for encoding and retrieval phases. The results show the dependence of the non-linear correlations measures with the time of day and the type of the probe. In addition, the results indicate differences in the correlations measures with hippocampal regions between positive and lure probes. Besides confirming previous results on the influence of time-of-day on cognitive performance, the study demonstrates the effectiveness of the non-linear correlation analysis method for the characterization of fMRI task paradigms.

Similar local neuronal dynamics may lead to different collective behavior

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

Revisiting Nonlinear Functional Brain Co-activations: Directed, Dynamic, and Delayed

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In the previous study, we first demonstrated that the relatively stronger blood oxygenated level dependent (BOLD) activations contain most of the information relevant to understand functional connectivity, and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this study, we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different and complementary perspective in the analysis of brain co-activation patterns. In this study, we provide further details for the computations of these measures and for a proof of concept based on replicating existing results from an Autistic Syndrome database, and discuss the main features and advantages of the proposed strategy for the study of brain functional correlations.

Observing changes in human functioning during induced sleep deficiency and recovery periods

Prolonged periods of sleep restriction seem to be common in the contemporary world. Sleep loss causes perturbations of circadian rhythmicity and degradation of waking alertness as reflected in attention, cognitive efficiency and memory. Understanding whether and how the human brain recovers from chronic sleep loss is important not only from a scientific but also from a public health perspective. In this work we report on behavioral, motor, and neurophysiological correlates of sleep loss in healthy adults in an unprecedented study conducted in natural conditions and comprising 21 consecutive days divided into periods of 4 days of regular life (a baseline), 10 days of chronic partial sleep restriction (30% reduction relative to individual sleep need) and 7 days of recovery. Throughout the whole experiment we continuously measured the spontaneous locomotor activity by means of actigraphy with 1-minute resolution. On a daily basis the subjects were undergoing EEG measurements (64-electrodes with 500 Hz sampling frequency): resting state with eyes open and closed (8 minutes long each) followed by Stroop task lasting 22 minutes. Altogether we analyzed actigraphy (distributions of rest and activity durations), behavioral measures (reaction times and accuracy from Stroop task) and EEG (amplitudes, latencies and scalp maps of event-related potentials from Stroop task and power spectra from resting states). We observed unanimous deterioration in all the measures during sleep restriction. Further results indicate that a week of recovery subsequent to prolonged periods of sleep restriction is insufficient to recover fully. Only one measure (mean reaction time in Stroop task) reverted to baseline values, while the others did not.

Box scaling as a proxy of finite size correlations

The scaling of correlations as a function of size provides important hints to understand critical phenomena on a variety of systems. Its study in biological structures offers two challenges: usually they are not of infinite size, and, in the majority of cases, dimensions can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small extent, by computing correlations inside of a reduced field of view of various widths (we will refer to this procedure as "box-scaling"). A relation among the size of the field of view, and measured correlation length, is derived at, and away from, the critical regime. Numerical simulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify such approximations. Numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

The study of neuronal interactions is at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, and the Brainome) that attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott (2006), we extend them to heavy-tailed distributions of interactions. More important, we analytically derive the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that on imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong nonorthogonality of associated eigenvectors. This leads us to the conclusion that understanding the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.

Evaluating the reliability of neurocognitive biomarkers of neurodegenerative diseases across countries: A machine learning approach

Accurate early diagnosis of neurodegenerative diseases represents a growing challenge for current clinical practice. Promisingly, current tools can be complemented by computational decision-support methods to objectively analyze multidimensional measures and increase diagnostic confidence. Yet, widespread application of these tools cannot be recommended unless they are proven to perform consistently and reproducibly across samples from different countries. We implemented machine-learning algorithms to evaluate the prediction power of neurocognitive biomarkers (behavioral and imaging measures) for classifying two neurodegenerative conditions –Alzheimer Disease (AD) and behavioral variant frontotemporal dementia (bvFTD)– across three different countries (>200 participants). We use machine-learning tools integrating multimodal measures such as cognitive scores (executive functions and cognitive screening) and brain atrophy volume (voxel based morphometry from fronto-temporo-insular regions in bvFTD, and temporo-parietal regions in AD) to identify the most relevant features in predicting the incidence of the diseases. In the Country-1 cohort, predictions of AD and bvFTD became maximally improved upon inclusion of cognitive screenings outcomes combined with atrophy levels. Multimodal training data from this cohort allowed predicting both AD and bvFTD in the other two novel datasets from other countries with high accuracy (>90%), demonstrating the robustness of the approach as well as the differential specificity and reliability of behavioral and neural markers for each condition. In sum, this is the first study, across centers and countries, to validate the predictive power of cognitive signatures combined with atrophy levels for contrastive neurodegenerative conditions, validating a benchmark for future assessments of reliability and reproducibility.

Universal and nonuniversal neural dynamics on small world connectomes: A finite-size scaling analysis

Evidence of critical dynamics has been found recently in both experiments and models of large-scale brain dynamics. The understanding of the nature and features of such a critical regime is hampered by the relatively small size of the available connectome, which prevents, among other things, the determination of its associated universality class. To circumvent that, here we study a neural model defined on a class of small-world networks that share some topological features with the human connectome. We find that varying the topological parameters can give rise to a scale-invariant behavior either belonging to the mean-field percolation universality class or having nonuniversal critical exponents. In addition, we find certain regions of the topological parameter space where the system presents a discontinuous, i.e., noncritical, dynamical phase transition into a percolated state. Overall, these results shed light on the interplay of dynamical and topological roots of the complex brain dynamics.

Nrf2 stabilization prevents critical oxidative damage in Down syndrome cells

Mounting evidence implicates chronic oxidative stress as a critical driver of the aging process. Down syndrome (DS) is characterized by a complex phenotype, including early senescence. DS cells display increased levels of reactive oxygen species (ROS) and mitochondrial structural and metabolic dysfunction, which are counterbalanced by sustained Nrf2-mediated transcription of cellular antioxidant response elements (ARE). Here, we show that caspase 3/PKCδdependent activation of the Nrf2 pathway in DS and Dp16 (a mouse model of DS) cells is necessary to protect against chronic oxidative damage and to preserve cellular functionality. Mitochondria-targeted catalase (mCAT) significantly reduced oxidative stress, restored mitochondrial structure and function, normalized replicative and wound healing capacity, and rendered the Nrf2-mediated antioxidant response dispensable. These results highlight the critical role of Nrf2/ARE in the maintenance of DS cell homeostasis and validate mitochondrial-specific interventions as a key aspect of antioxidant and antiaging therapies.

Fibronectin rescues estrogen receptor α from lysosomal degradation in breast cancer cells

Estrogen receptor α (ERα) is expressed in tissues as diverse as brains and mammary glands. In breast cancer, ERα is a key regulator of tumor progression. Therefore, understanding what activates ERα is critical for cancer treatment in particular and cell biology in general. Using biochemical approaches and superresolution microscopy, we show that estrogen drives membrane ERα into endosomes in breast cancer cells and that its fate is determined by the presence of fibronectin (FN) in the extracellular matrix; it is trafficked to lysosomes in the absence of FN and avoids the lysosomal compartment in its presence. In this context, FN prolongs ERα half-life and strengthens its transcriptional activity. We show that ERα is associated with β1-integrin at the membrane, and this integrin follows the same endocytosis and subcellular trafficking pathway triggered by estrogen. Moreover, ERα⁺ vesicles are present within human breast tissues, and colocalization with β1-integrin is detected primarily in tumors. Our work unravels a key, clinically relevant mechanism of microenvironmental regulation of ERα signaling.

How ants move: individual and collective scaling properties

The motion of social insects is often used as a paradigmatic example of complex adaptive dynamics arising from decentralized individual behaviour. In this paper, we revisit the topic of the ruling laws behind the burst of activity in ants. The analysis, done over previously reported data, reconsiders the causation arrows, proposed at individual level, not finding any link between the duration of the ants' activity and their moving speed. Secondly, synthetic trajectories created from steps of different ants demonstrate that a Markov process can explain the previously reported speed shape profile. Finally, we show that as more ants enter the nest, the faster they move, which implies a collective property. Overall, these results provide a mechanistic explanation for the reported behavioural laws, and suggest us a formal way to further study the collective properties in these scenarios.

Critical Fluctuations in the Native State of Proteins

Based on protein structural ensembles determined by nuclear magnetic resonance, we study the position fluctuations of residues by calculating distance-dependent correlations and conducting finite-size scaling analysis. The fluctuations exhibit high susceptibility and long-range correlations up to the protein sizes. The scaling relations between the correlations or susceptibility and protein sizes resemble those in other physical and biological systems near their critical points. These results indicate that, at the native states, motions of each residue are felt by every other one in the protein. We also find that proteins with larger susceptibility are more frequently observed in nature. Overall, our results suggest that the protein's native state is critical.

Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics

Loss of cortical integration and changes in the dynamics of electrophysiological brain signals characterize the transition from wakefulness towards unconsciousness. In this study, we arrive at a basic model explaining these observations based on the theory of phase transitions in complex systems. We studied the link between spatial and temporal correlations of large-scale brain activity recorded with functional magnetic resonance imaging during wakefulness, propofol-induced sedation and loss of consciousness and during the subsequent recovery. We observed that during unconsciousness activity in frontothalamic regions exhibited a reduction of long-range temporal correlations and a departure of functional connectivity from anatomical constraints. A model of a system exhibiting a phase transition reproduced our findings, as well as the diminished sensitivity of the cortex to external perturbations during unconsciousness. This framework unifies different observations about brain activity during unconsciousness and predicts that the principles we identified are universal and independent from its causes.

The Voxel-Wise Functional Connectome Can Be Efficiently Derived from Co-activations in a Sparse Spatio-Temporal Point-Process

Large efforts are currently under way to systematically map functional connectivity between all pairs of millimeter-scale brain regions based on large neuroimaging databases. The exploratory unraveling of this "functional connectome" based on functional Magnetic Resonance Imaging (fMRI) can benefit from a better understanding of the contributors to resting state functional connectivity. In this work, we introduce a sparse representation of fMRI data in the form of a discrete point-process encoding high-amplitude events in the blood oxygenation level-dependent (BOLD) signal and we show it contains sufficient information for the estimation of functional connectivity between all pairs of voxels. We validate this method by replicating results obtained with standard whole-brain voxel-wise linear correlation matrices in two datasets. In the first one (n = 71), we study the changes in node strength (a measure of network centrality) during deep sleep. The second is a large database (n = 1147) of subjects in which we look at the age-related reorganization of the voxel-wise network of functional connections. In both cases it is shown that the proposed method compares well with standard techniques, despite requiring only data on the order of 1% of the original BOLD signal time series. Furthermore, we establish that the point-process approach does not reduce (and in one case increases) classification accuracy compared to standard linear correlations. Our results show how large fMRI datasets can be drastically simplified to include only the timings of large-amplitude events, while still allowing the recovery of all pair-wise interactions between voxels. The practical importance of this dimensionality reduction is manifest in the increasing number of collaborative efforts aiming to study large cohorts of healthy subjects as well as patients suffering from brain disease. Our method also suggests that the electrophysiological signals underlying the dynamics of fMRI time series consist of all-or-none temporally localized events, analogous to the avalanches of neural activity observed in recordings of local field potentials (LFP), an observation of potentially high neurobiological relevance.

Invited review: Fluctuation-induced transport. From the very small to the very large scales

The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average transport depends on three fundamental aspects: the shape of the substrate, the correlations of the fluctuations and the mass, geometry, interaction and density of the particles. These three aspects, reviewed here,  acquire additional relevance because the same notions apply to a bewildering variety of problems at very different scales, from the small nano or micro-scale, where thermal fluctuations effects dominate,  up to very large scales including ubiquitous cooperative phenomena in granular materials. Received: 30 October 2015,  Accepted: 4 February  2016; Edited by: G. Martínez Mekler; Reviewed by: J. Mateos, Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, México.; DOI: http://dx.doi.org/10.4279/PIP.080004Cite as: G P Suárez, M Hoyuelos, D R Chialvo, Papers in Physics 8, 080004 (2016)This paper, by G P Suárez, M Hoyuelos, D R Chialvo, is licensed under the Creative Commons Attribution License 3.0.

Scale-free fluctuations in behavioral performance: delineating changes in spontaneous behavior of humans with induced sleep deficiency

The timing and dynamics of many diverse behaviors of mammals, e.g., patterns of animal foraging or human communication in social networks exhibit complex self-similar properties reproducible over multiple time scales. In this paper, we analyze spontaneous locomotor activity of healthy individuals recorded in two different conditions: during a week of regular sleep and a week of chronic partial sleep deprivation. After separating activity from rest with a pre-defined activity threshold, we have detected distinct statistical features of duration times of these two states. The cumulative distributions of activity periods follow a stretched exponential shape, and remain similar for both control and sleep deprived individuals. In contrast, rest periods, which follow power-law statistics over two orders of magnitude, have significantly distinct distributions for these two groups and the difference emerges already after the first night of shortened sleep. We have found steeper distributions for sleep deprived individuals, which indicates fewer long rest periods and more turbulent behavior. This separation of power-law exponents is the main result of our investigations, and might constitute an objective measure demonstrating the severity of sleep deprivation and the effects of sleep disorders.

Enhanced repertoire of brain dynamical states during the psychedelic experience

The study of rapid changes in brain dynamics and functional connectivity (FC) is of increasing interest in neuroimaging. Brain states departing from normal waking consciousness are expected to be accompanied by alterations in the aforementioned dynamics. In particular, the psychedelic experience produced by psilocybin (a substance found in "magic mushrooms") is characterized by unconstrained cognition and profound alterations in the perception of time, space and selfhood. Considering the spontaneous and subjective manifestation of these effects, we hypothesize that neural correlates of the psychedelic experience can be found in the dynamics and variability of spontaneous brain activity fluctuations and connectivity, measurable with functional Magnetic Resonance Imaging (fMRI). Fifteen healthy subjects were scanned before, during and after intravenous infusion of psilocybin and an inert placebo. Blood-Oxygen Level Dependent (BOLD) temporal variability was assessed computing the variance and total spectral power, resulting in increased signal variability bilaterally in the hippocampi and anterior cingulate cortex. Changes in BOLD signal spectral behavior (including spectral scaling exponents) affected exclusively higher brain systems such as the default mode, executive control, and dorsal attention networks. A novel framework enabled us to track different connectivity states explored by the brain during rest. This approach revealed a wider repertoire of connectivity states post-psilocybin than during control conditions. Together, the present results provide a comprehensive account of the effects of psilocybin on dynamical behavior in the human brain at a macroscopic level and may have implications for our understanding of the unconstrained, hyper-associative quality of consciousness in the psychedelic state.

The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs

Entropy is a dimensionless quantity that is used for measuring uncertainty about the state of a system but it can also imply physical qualities, where high entropy is synonymous with high disorder. Entropy is applied here in the context of states of consciousness and their associated neurodynamics, with a particular focus on the psychedelic state. The psychedelic state is considered an exemplar of a primitive or primary state of consciousness that preceded the development of modern, adult, human, normal waking consciousness. Based on neuroimaging data with psilocybin, a classic psychedelic drug, it is argued that the defining feature of "primary states" is elevated entropy in certain aspects of brain function, such as the repertoire of functional connectivity motifs that form and fragment across time. Indeed, since there is a greater repertoire of connectivity motifs in the psychedelic state than in normal waking consciousness, this implies that primary states may exhibit "criticality," i.e., the property of being poised at a "critical" point in a transition zone between order and disorder where certain phenomena such as power-law scaling appear. Moreover, if primary states are critical, then this suggests that entropy is suppressed in normal waking consciousness, meaning that the brain operates just below criticality. It is argued that this entropy suppression furnishes normal waking consciousness with a constrained quality and associated metacognitive functions, including reality-testing and self-awareness. It is also proposed that entry into primary states depends on a collapse of the normally highly organized activity within the default-mode network (DMN) and a decoupling between the DMN and the medial temporal lobes (which are normally significantly coupled). These hypotheses can be tested by examining brain activity and associated cognition in other candidate primary states such as rapid eye movement (REM) sleep and early psychosis and comparing these with non-primary states such as normal waking consciousness and the anaesthetized state.

Disruption of transfer entropy and inter-hemispheric brain functional connectivity in patients with disorder of consciousness

Severe traumatic brain injury can lead to disorders of consciousness (DOC) characterized by deficit in conscious awareness and cognitive impairment including coma, vegetative state, minimally consciousness, and lock-in syndrome. Of crucial importance is to find objective markers that can account for the large-scale disturbances of brain function to help the diagnosis and prognosis of DOC patients and eventually the prediction of the coma outcome. Following recent studies suggesting that the functional organization of brain networks can be altered in comatose patients, this work analyzes brain functional connectivity (FC) networks obtained from resting-state functional magnetic resonance imaging (rs-fMRI). Two approaches are used to estimate the FC: the Partial Correlation (PC) and the Transfer Entropy (TE). Both the PC and the TE show significant statistical differences between the group of patients and control subjects; in brief, the inter-hemispheric PC and the intra-hemispheric TE account for such differences. Overall, these results suggest two possible rs-fMRI markers useful to design new strategies for the management and neuropsychological rehabilitation of DOC patients.

Brain organization into resting state networks emerges at criticality on a model of the human connectome

The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatiotemporal patterns of brain activity emerge from the empirically derived network of human brain neuroanatomical connections. The results show that critical dynamics unfolding on the structural connectivity of the human brain allow the recovery of many key experimental findings obtained from functional magnetic resonance imaging, such as divergence of the correlation length, the anomalous scaling of correlation fluctuations, and the emergence of large-scale resting state networks.

What kind of noise is brain noise: anomalous scaling behavior of the resting brain activity fluctuations

The study of spontaneous fluctuations of brain activity, often referred as brain noise, is getting increasing attention in functional magnetic resonance imaging (fMRI) studies. Despite important efforts, much of the statistical properties of such fluctuations remain largely unknown. This work scrutinizes these fluctuations looking at specific statistical properties which are relevant to clarify its dynamical origins. Here, three statistical features which clearly differentiate brain data from naive expectations for random processes are uncovered: First, the variance of the fMRI mean signal as a function of the number of averaged voxels remains constant across a wide range of observed clusters sizes. Second, the anomalous behavior of the variance is originated by bursts of synchronized activity across regions, regardless of their widely different sizes. Finally, the correlation length (i.e., the length at which the correlation strength between two regions vanishes) as well as mutual information diverges with the cluster's size considered, such that arbitrarily large clusters exhibit the same collective dynamics than smaller ones. These three properties are known to be exclusive of complex systems exhibiting critical dynamics, where the spatio-temporal dynamics show these peculiar type of fluctuations. Thus, these findings are fully consistent with previous reports of brain critical dynamics, and are relevant for the interpretation of the role of fluctuations and variability in brain function in health and disease.

Criticality in large-scale brain FMRI dynamics unveiled by a novel point process analysis

Functional magnetic resonance imaging (fMRI) techniques have contributed significantly to our understanding of brain function. Current methods are based on the analysis of gradual and continuous changes in the brain blood oxygenated level dependent (BOLD) signal. Departing from that approach, recent work has shown that equivalent results can be obtained by inspecting only the relatively large amplitude BOLD signal peaks, suggesting that relevant information can be condensed in discrete events. This idea is further explored here to demonstrate how brain dynamics at resting state can be captured just by the timing and location of such events, i.e., in terms of a spatiotemporal point process. The method allows, for the first time, to define a theoretical framework in terms of an order and control parameter derived from fMRI data, where the dynamical regime can be interpreted as one corresponding to a system close to the critical point of a second order phase transition. The analysis demonstrates that the resting brain spends most of the time near the critical point of such transition and exhibits avalanches of activity ruled by the same dynamical and statistical properties described previously for neuronal events at smaller scales. Given the demonstrated functional relevance of the resting state brain dynamics, its representation as a discrete process might facilitate large-scale analysis of brain function both in health and disease.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle

BACKGROUND

Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function.

METHODOLOGY/PRINCIPAL FINDINGS

To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus.

CONCLUSIONS/SIGNIFICANCE

Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

Modular organization of brain resting state networks in chronic back pain patients

Recent work on functional magnetic resonance imaging large-scale brain networks under resting conditions demonstrated its potential to evaluate the integrity of brain function under normal and pathological conditions. A similar approach is used in this work to study a group of chronic back pain patients and healthy controls to determine the impact of long enduring pain over brain dynamics. Correlation networks were constructed from the mutual partial correlations of brain activity's time series selected from ninety regions using a well validated brain parcellation atlas. The study of the resulting networks revealed an organization of up to six communities with similar modularity in both groups, but with important differences in the membership of key communities of frontal and temporal regions. The bulk of these findings were confirmed by a surprisingly naive analysis based on the pairwise correlations of the strongest and weakest correlated healthy regions. Beside confirming the brain effects of long enduring pain, these results provide a framework to study the effect of other chronic conditions over cortical function.

Self-similar correlation function in brain resting-state functional magnetic resonance imaging

Adaptive behaviour, cognition and emotion are the result of a bewildering variety of brain spatio-temporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e. they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatio-temporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state functional magnetic resonance imaging data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behaviour of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being in both health and disease.

Emergent self-organized complex network topology out of stability constraints

Although most networks in nature exhibit complex topologies, the origins of such complexity remain unclear. We propose a general evolutionary mechanism based on global stability. This mechanism is incorporated into a model of a growing network of interacting agents in which each new agent's membership in the network is determined by the agent's effect on the network's global stability. It is shown that out of this stability constraint complex topological properties emerge in a self-organized manner, offering an explanation for their observed ubiquity in biological networks.

Unraveling the fluctuations of animal motor activity

Human and animal behavior exhibits power law correlations whose origin is controversial. In this work, the spontaneous motion of laboratory rodents was recorded during several days. It is found that animal motion is scale-free and that the scaling is introduced by the inactivity pauses both by its length as well as by its specific ordering. Furthermore, the scaling is also demonstrable in the rates of event's occurrence. A comparison with related results in humans is made and candidate models are discussed to provide clues for the origin of such dynamics.

Ising-like dynamics in large-scale functional brain networks

Brain "rest" is defined--more or less unsuccessfully--as the state in which there is no explicit brain input or output. This work focuses on the question of whether such state can be comparable to any known dynamical state. For that purpose, correlation networks from human brain functional magnetic resonance imaging are contrasted with correlation networks extracted from numerical simulations of the Ising model in two dimensions at different temperatures. For the critical temperature Tc, striking similarities appear in the most relevant statistical properties, making the two networks indistinguishable from each other. These results are interpreted here as lending support to the conjecture that the dynamics of the functioning brain is near a critical point.

Flattened cortical maps of cerebral function in the rat: a region-of-interest approach to data sampling, analysis and display

We describe a method for the measurement, analysis and display of cerebral cortical data obtained from coronal brain sections of the adult rat. In this method, regions-of-interest (ROI) are selected in the cortical mantle in a semiautomated fashion using a radial grid overlay, spaced in 15 degrees intervals from the midline. ROI measurements of intensity are mapped on a flattened two-dimensional surface. Topographic maps of statistical significance at each ROI allow for the rapid viewing of group differences. Cortical z-scores are displayed with the boundaries of brain regions defined according to a standard atlas of the rat brain. This method and accompanying software implementation (Matlab, Labview) allow for compact data display in a variety of autoradiographic and histologic studies of the structure and function of the rat brain.

Identifying directed links in large scale functional networks: application to brain fMRI

Background

Biological experiments increasingly yield data representing large ensembles of interacting variables, making the application of advanced analytical tools a forbidding task. We present a method to extract networks of correlated activity, specifically from functional MRI data, such that: (a) network nodes represent voxels, and (b) the network links can be directed or undirected, representing temporal relationships between the nodes. The method provides a snapshot of the ongoing dynamics of the brain without sacrificing resolution, as the analysis is tractable even for very large numbers of voxels.

Results

We find that, based on topological properties of the networks, the method provides enough information about the dynamics to discriminate between subtly different brain states. Moreover, the statistical regularities previously reported are qualitatively preserved, i.e. the resulting networks display scale-free and small-world topologies.

Conclusion

Our method expands previous approaches to render large scale functional networks, and creates the basis for an extensive and -due to the presence of mixtures of directed and undirected links- richer motif analysis of functional relationships.

Chronic pain and the emotional brain: specific brain activity associated with spontaneous fluctuations of intensity of chronic back pain

Living with unrelenting pain (chronic pain) is maladaptive and is thought to be associated with physiological and psychological modifications, yet there is a lack of knowledge regarding brain elements involved in such conditions. Here, we identify brain regions involved in spontaneous pain of chronic back pain (CBP) in two separate groups of patients (n = 13 and n = 11), and contrast brain activity between spontaneous pain and thermal pain (CBP and healthy subjects, n = 11 each). Continuous ratings of fluctuations of spontaneous pain during functional magnetic resonance imaging were separated into two components: high sustained pain and increasing pain. Sustained high pain of CBP resulted in increased activity in the medial prefrontal cortex (mPFC; including rostral anterior cingulate). This mPFC activity was strongly related to intensity of CBP, and the region is known to be involved in negative emotions, response conflict, and detection of unfavorable outcomes, especially in relation to the self. In contrast, the increasing phase of CBP transiently activated brain regions commonly observed for acute pain, best exemplified by the insula, which tightly reflected duration of CBP. When spontaneous pain of CBP was contrasted to thermal stimulation, we observe a double-dissociation between mPFC and insula with the former correlating only to intensity of spontaneous pain and the latter correlating only to pain intensity for thermal stimulation. These findings suggest that subjective spontaneous pain of CBP involves specific spatiotemporal neuronal mechanisms, distinct from those observed for acute experimental pain, implicating a salient role for emotional brain concerning the self.

Brain activity for spontaneous pain of postherpetic neuralgia and its modulation by lidocaine patch therapy

Postherpetic neuralgia (PHN) is a debilitating chronic pain condition, yet there is a lack of knowledge regarding underlying brain activity. Here we identify brain regions involved in spontaneous pain of PHN (n=11) and determine its modulation with Lidoderm therapy (patches of 5% lidocaine applied to the PHN affected body part). Continuous ratings of fluctuations of spontaneous pain during fMRI were contrasted to ratings of fluctuations of a bar observed during scanning, at three sessions: (1) pre-treatment baseline, (2) after 6h of Lidoderm treatment, and (3) after 2 weeks of Lidoderm use. Overall brain activity for spontaneous pain of PHN involved affective and sensory-discriminative areas: thalamus, primary and secondary somatosensory, insula and anterior cingulate cortices, as well as areas involved in emotion, hedonics, reward, and punishment: ventral striatum, amygdala, orbital frontal cortex, and ventral tegmental area. Generally, these activations decreased at sessions 2 and 3, except right anterior insular activity which increased with treatment. The sensory and affective activations only responded to the short-term treatment (6h of Lidoderm); while the ventral striatum and amygdala (reward-related regions) decreased mainly with longer-term treatment (2 weeks of Lidoderm). Pain properties: average magnitude of spontaneous pain, and responses on Neuropathic Pain Scale (NPS), decreased with treatment. The ventral striatal and amygdala activity best reflected changes in NPS, which was modulated only with longer-term treatment. The results show a specific brain activity pattern for PHN spontaneous pain, and implicate areas involved in emotions and reward as best reflecting changes in pain with treatment.

Expression of IL-1beta in supraspinal brain regions in rats with neuropathic pain

We examined mRNA expression of the pro-inflammatory cytokine IL-1beta in the brainstem, thalamus, and prefrontal cortex in two rat models of neuropathic pain. Rats received a neuropathic injury: spared nerve injury (SNI) or chronic constriction injury (CCI), sham injury, or were minimally handled (control). Neuropathic pain-like behavior was monitored by tracking tactile thresholds. SNI-injured animals showed a robust decrease in tactile thresholds of the injured foot, while CCI-injured animals did not show tactile threshold changes. Ten or 24 days after nerve injury, IL-1beta gene expression in the brain was determined by RT-PCR. IL-1beta expression changes were observed mainly at 10 days after injury in the SNI animals, contralateral to the injury side, with increased expression in the brainstem and prefrontal cortex. The results indicate that neuro-immune activation in neuropathic pain conditions includes supraspinal brain regions, suggesting cytokine modulation of supraspinal circuitry of pain in neuropathic conditions.

Circadian rhythms of heart rate and locomotion after treatment with low-dose acetylcholinesterase inhibitors

This study tested the hypothesis that repeated exposure to low levels of sarin, pyridostigmine bromide (PB) or their combination, at doses equivalent to those possibly experienced by veterans of the 1991 Persian Gulf War, could lead to persistent or delayed autonomic effects and thus help to explain the cause of clinical findings in this population. Male Sprague-Dawley rats were treated for 3 weeks with: saline injection (0.5 ml kg(-1), s.c., 3 times weekly) with tap drinking water (control); saline injection with PB (80 mg l(-1) in drinking water); sarin injection (62.5 microg kg(-1), s.c., 0.5 x LD(50), 3 times weekly) with tap drinking water (sarin); or sarin injection with PB in drinking water (sarin + PB). At 2, 4 or 16 weeks post-treatment, heart rate (HR) and locomotor activity (LA) were studied by radiotelemetry. Two weeks posttreatment, HR in drug-treated animals was significantly lower than in controls. A decrease in low-frequency HR power spectrum (PS) was found at 00:00 h and 08:00 h with sarin + PB and at 00:00 h with sarin, while total power was enhanced with sarin + PB at 22:00 h. Minimal effects of drug treatments on HR and HR PS were detected at 4 and 16 weeks post-treatment. No significant differences in LA between control and other groups were found. Since no consistent long-term effects were found in any of the variables studied, these experiments do not support the hypothesis that repeated administration of low doses of PB and the nerve agent sarin can induce persistent or delayed alterations in autonomic function.