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.

Universal dynamics of mitochondrial networks: a finite-size scaling analysis.

Evidence from models and experiments suggests that the networked structure observed in mitochondria emerges at the critical point of a phase transition controlled by fission and fusion rates. If mitochondria are poised at criticality, the relevant network quantities should scale with the system's size. However, whether or not the expected finite-size effects take place has not been demonstrated yet. Here, we first provide a theoretical framework to interpret the scaling behavior of mitochondrial network quantities by analyzing two conceptually different models of mitochondrial dynamics. Then, we perform a finite-size scaling analysis of real mitochondrial networks extracted from microscopy images and obtain scaling exponents comparable with critical exponents from models and theory. Overall, we provide a universal description of the structural phase transition in mammalian mitochondria.

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.

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.

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.

Controlling a complex system near its critical point via temporal correlations.

Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.

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.

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.

On the pros and cons of using temporal derivatives to assess brain functional connectivity.

The study of correlations between brain regions is an important chapter of the analysis of large-scale brain spatiotemporal dynamics. In particular, novel methods suited to extract dynamic changes in mutual correlations are needed. Here we scrutinize a recently reported metric dubbed "Multiplication of Temporal Derivatives" (MTD) which is based on the temporal derivative of each time series. The formal comparison of the MTD formula with the Pearson correlation of the derivatives reveals only minor differences, which we find negligible in practice. A comparison with the sliding window Pearson correlation of the raw time series in several stationary and non-stationary set-ups, including a realistic stationary network detection, reveals lower sensitivity of derivatives to low frequency drifts and to autocorrelations but also lower signal-to-noise ratio. It does not indicate any evident mathematical advantages of the proposed metric over commonly used correlation methods.

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.