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

Sensory events, cognitive processing and motor actions correlate with transient changes in neuronal activity. In cortex, these transients form widespread spatiotemporal patterns with largely unknown statistical regularities. Here, we show that activity associated with behavioral events carry the signature of scale-invariant spatiotemporal clusters, neuronal avalanches. Using high-density microelectrode arrays in nonhuman primates, we recorded extracellular unit activity and the local field potential (LFP) in premotor and prefrontal cortex during motor and cognitive tasks. Unit activity and negative LFP deflections (nLFP) consistently changed in rate at single electrodes during tasks. Accordingly, nLFP clusters on the array deviated from scale-invariance compared to ongoing activity. Scale-invariance was recovered using 'adaptive binning', that is identifying clusters at temporal resolution given by task-induced changes in nLFP rate. Measures of LFP synchronization confirmed and computer simulations detailed our findings. We suggest optimization principles identified for avalanches during ongoing activity to apply to cortical information processing during behavior.

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent . Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Self-organized criticality (SOC) refers to the ability of complex systems to evolve toward a second-order phase transition at which interactions between system components lead to scale-invariant events that are beneficial for system performance. For the last two decades, considerable experimental evidence has accumulated that the mammalian cortex with its diversity in cell types, interconnectivity, and plasticity might exhibit SOC. Here, we review the experimental findings of isolated, layered cortex preparations to self-organize toward four dynamical motifs presently identified in the intact cortex in vivo: up-states, oscillations, neuronal avalanches, and coherence potentials. During up-states, the synchronization observed for nested theta/gamma oscillations embeds scale-invariant neuronal avalanches, which can be identified by robust power law scaling in avalanche sizes with a slope of −3/2 and a critical branching parameter of 1. This precise dynamical coordination, tracked in the negative transients of the local field potential (nLFP) and spiking activity of pyramidal neurons using two-photon imaging, emerges autonomously in superficial layers of organotypic cortex cultures and acute cortex slices, is homeostatically regulated, exhibits separation of time scales, and reveals unique size vs. quiet time dependencies. A subclass of avalanches, the coherence potentials, exhibits precise maintenance of the time course in propagated local synchrony. Avalanches emerge in superficial layers of the cortex under conditions of strong external drive. The balance of excitation and inhibition (E/I), as well as neuromodulators such as dopamine, establishes powerful control parameters for avalanche dynamics. This rich dynamical repertoire is not observed in dissociated cortex cultures, which lack the differentiation into cortical layers and exhibit a dynamical phenotype expected for a first-order phase transition. The precise interactions between up-states, nested oscillations, and avalanches in superficial layers of the cortex provide compelling evidence for SOC in the brain.

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.

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h , the interplay between creation and annihilation of excitable waves leads to an average activity F . It has recently been suggested that in the low-stimulus regime (h approximately 0) the response function F(h) of hypercubic deterministic systems behaves as a power law, F approximately h{m} . Moreover, the response exponent m has been predicted to depend only on the dimensionality d of the lattice, m=1/(1+d) [T. Ohta and T. Yoshimura, Physica D 205, 189 (2005)]. In order to test this prediction, we study the response function of excitable lattices modeled by either coupled Morris-Lecar equations or Greenberg-Hastings cellular automata. We show that the prediction is verified in our model systems for d=1 , 2, and 3, provided that a minimum set of conditions is satisfied. Under these conditions, the dynamic range-which measures the range of stimulus intensities that can be coded by the network activity-increases with the dimensionality d of the network. The power law scenario breaks down, however, if the system can exhibit self-sustained activity (spiral waves). In this case, we recover a scenario that is common to probabilistic excitable media: as a function of the conductance coupling G among the excitable elements, the dynamic range is maximized precisely at the critical value G_{c} above which self-sustained activity becomes stable. We discuss the implications of these results in the context of neural coding.

Neuronal avalanches measured as consecutive bouts of thresholded field potentials represent a statistical signature that the brain operates near a critical point. In theory, criticality optimizes stimulus sensitivity, information transmission, computational capability and mnemonic repertoires size. Field potential avalanches recorded via multielectrode arrays from cortical slice cultures are repeatable spatiotemporal activity patterns. It remains unclear whether avalanches of action potentials observed in forebrain regions of freely-behaving rats also form recursive repertoires, and whether these have any behavioral relevance. Here, we show that spike avalanches, recorded from hippocampus (HP) and sensory neocortex of freely-behaving rats, constitute distinct families of recursive spatiotemporal patterns. A significant number of those patterns were specific to a behavioral state. Although avalanches produced during sleep were mostly similar to others that occurred during waking, the repertoire of patterns recruited during sleep differed significantly from that of waking. More importantly, exposure to novel objects increased the rate at which new patterns arose, also leading to changes in post-exposure repertoires, which were significantly different from those before the exposure. A significant number of families occurred exclusively during periods of whisker contact with objects, but few were associated with specific objects. Altogether, the results provide original evidence linking behavior and criticality at the spike level: spike avalanches form repertoires that emerge in waking, recur during sleep, are diversified by novelty and contribute to object representation.

Neurons in cortex synchronize their spiking in response to local and distant inputs. These synchronized assemblies are fundamental to cortex function, yet basic dynamical aspects about their size and duration are largely unknown. Using 2-photon imaging of neurons in superficial cortex of awake mice, we show that synchronized assemblies organize as scale-invariant avalanches that quadratically grow with duration. This quadratic expansion was found only for correlated neurons and required temporal coarse graining to compensate for spatial subsampling when network dynamics are critical, as demonstrated in simulations. The corresponding time course of an inverted parabola with an exponent of 2 described avalanches of up to 5 s duration and 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 order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.