Ising-like model replicating time-averaged spiking behaviour of in vitro neuronal networks

We analyze time-averaged experimental data from in vitro activities of neuronal networks. Through a Pairwise Maximum-Entropy method, we identify through an inverse binary Ising-like model the local fields and interaction couplings which best reproduce the average activities of each neuron as well as the statistical correlations between the activities of each pair of neurons in the system. The specific information about the type of neurons is mainly stored in the local fields, while a symmetric distribution of interaction constants seems generic. Our findings demonstrate that, despite not being directly incorporated into the inference approach, the experimentally observed correlations among groups of three neurons are accurately captured by the derived Ising-like model. Within the context of the thermodynamic analogy inherent to the Ising-like models developed in this study, our findings additionally indicate that these models demonstrate characteristics of second-order phase transitions between ferromagnetic and paramagnetic states at temperatures above, but close to, unity. Considering that the operating temperature utilized in the Maximum-Entropy method isT o = 1 , this observation further expands the thermodynamic conceptual parallelism postulated in this work for the manifestation of criticality in neuronal network behavior.

The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

Scaling relationships characterize complex systems at criticality. In the brain, these relationships are evident in scale-invariant activity cascades, so-called neuronal avalanches, quantified by power laws in avalanche size and duration. At the cellular level, neuronal avalanches are identified in spatially distributed groups of neurons that participate in cascades of coincident action potential firing. Such spatiotemporal synchronization is central to theories on brain function, yet scaling relationships in avalanche synchronization have been challenging to study when only a fraction of neurons is observed, underestimating avalanche properties. Here, we study these biases from fractional sampling in an all-to-all, balanced network of excitatory and inhibitory neurons with critical branching process dynamics. We focus on the growth of mean avalanche size with avalanche duration. For parabolic avalanches, this growth is quadratic, quantified by the scaling exponent, χ = 2 , which signifies rapid spatial expansion of coincident firing within a relatively short period of time. In contrast, χ < < 2 for fractionally sampled networks. We show that temporal coarse-graining combined with a threshold for the minimally required coincident firing in the network recovers χ = 2 , even when sampling as few as 0.1% of the neurons. In contrast, a commonly proposed 'crackling noise' approach fails to recover χ under those conditions. Our approach robustly identifies χ = 2 for ongoing neuronal activity in frontal cortex of awake mice using cellular 2-photon imaging. Our findings demonstrate how to correct scaling bias from fractional sampling and identifies rapid, scale-invariant synchronization of cell assemblies in the brain.

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.

Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state

Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations-the "waxing and waning" phenomenon-are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the "waning" phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition).

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.

Oligodendrocyte-mediated myelin plasticity and its role in neural synchronization

Temporal synchrony of signals arriving from different neurons or brain regions is essential for proper neural processing. Nevertheless, it is not well understood how such synchrony is achieved and maintained in a complex network of time-delayed neural interactions. Myelin plasticity, accomplished by oligodendrocytes (OLs), has been suggested as an efficient mechanism for controlling timing in brain communications through adaptive changes of axonal conduction velocity and consequently conduction time delays, or latencies; however, local rules and feedback mechanisms that OLs use to achieve synchronization are not known. We propose a mathematical model of oligodendrocyte-mediated myelin plasticity (OMP) in which OLs play an active role in providing such feedback. This is achieved without using arrival times at the synapse or modulatory signaling from astrocytes; instead, it relies on the presence of global and transient OL responses to local action potentials in the axons they myelinate. While inspired by OL morphology, we provide the theoretical underpinnings that motivated the model and explore its performance for a wide range of its parameters. Our results indicate that when the characteristic time of OL's transient intracellular responses to neural spikes is between 10 and 40 ms and the firing rates in individual axons are relatively low (⪅ 10 Hz), the OMP model efficiently synchronizes correlated and time-locked signals while latencies in axons carrying independent signals are unaffected. This suggests a novel form of selective synchronization in the CNS in which oligodendrocytes play an active role by modulating the conduction delays of correlated spike trains as they traverse to their targets.

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.

Long-term stability of avalanche scaling and integrative network organization in prefrontal and premotor cortex

Ongoing neuronal activity in the brain establishes functional networks that reflect normal and pathological brain function. Most estimates of these functional networks suffer from low spatiotemporal resolution and indirect measures of neuronal population activity, limiting the accuracy and reliability in their reconstruction over time. Here, we studied the stability of neuronal avalanche dynamics and corresponding reconstructed functional networks in the adult brain. Using chronically implanted high-density microelectrode arrays, the local field potential (LFP) of resting-state activity was recorded in prefrontal and premotor cortex of awake nonhuman primates. Avalanche dynamics revealed stable scaling exhibiting an inverted parabolic profile and collapse exponent of 2 in line with a critical branching process over many days and weeks. Functional networks were based on a Bayesian-derived estimator and demonstrated stable integrative properties characterized by nontrivial high neighborhood overlap between strongly connected nodes and robustness to weak-link pruning. Entropy-based mixing analysis revealed significant changes in strong link weights over weeks. The long-term stability in avalanche scaling and integrative network organization in the face of individual link weight changes should support the development of noninvasive biomarkers to characterize normal and abnormal brain states in the adult brain.

The brain is spontaneously active even in the absence of specific sensations or movements. This ongoing activity arises from the interactions among hundreds of thousands of neurons, which has been captured by a variety of distinct functional networks predictive of healthy and pathological brain functions. The global dynamical states and overarching network principles that underlie such ongoing brain activity are not well understood. Here we identify avalanche dynamics and “friendship” networks as two major features of ongoing activity in the frontal cortex of nonhuman primates. We demonstrate their stability over weeks in the face of local network changes. Deviation from avalanche dynamics and “friendship” organization might provide robust biomarkers to identify normal and pathological brain states.

Selective Participation of Single Cortical Neurons in Neuronal Avalanches

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

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.

Stability of neuronal avalanches and long-range temporal correlations during the first year of life in human infants

During infancy, the human brain rapidly expands in size and complexity as neural networks mature and new information is incorporated at an accelerating pace. Recently, it was shown that single-electrode EEG in preterms at birth exhibits scale-invariant intermittent bursts. Yet, it is currently not known whether the normal infant brain, in particular, the cortex, maintains a distinct dynamical state during development that is characterized by scale-invariant spatial as well as temporal aspects. Here we employ dense-array EEG recordings acquired from the same infants at 6 and 12 months of age to characterize brain activity during an auditory odd-ball task. We show that suprathreshold events organize as spatiotemporal clusters whose size and duration are power-law distributed, the hallmark of neuronal avalanches. Time series of local suprathreshold EEG events display significant long-range temporal correlations (LRTCs). No differences were found between 6 and 12 months, demonstrating stability of avalanche dynamics and LRTCs during the first year after birth. These findings demonstrate that the infant brain is characterized by distinct spatiotemporal dynamical aspects that are in line with expectations of a critical cortical state. We suggest that critical state dynamics, which theory and experiments have shown to be beneficial for numerous aspects of information processing, are maintained by the infant brain to process an increasingly complex environment during development.

Neuronal Avalanches in Input and Associative Layers of Auditory Cortex

The primary auditory cortex processes acoustic sequences for the perception of behaviorally meaningful sounds such as speech. Sound information arrives at its input layer four from where activity propagates to associative layer 2/3. It is currently not known whether there is a characteristic organization of neuronal population activity across layers and sound levels during sound processing. Here, we identify neuronal avalanches, which in theory and experiments have been shown to maximize dynamic range and optimize information transfer within and across networks, in primary auditory cortex. We used in vivo 2-photon imaging of pyramidal neurons in cortical layers L4 and L2/3 of mouse A1 to characterize the populations of neurons that were active spontaneously, i.e., in the absence of a sound stimulus, and those recruited by single-frequency tonal stimuli at different sound levels. Single-frequency sounds recruited neurons of widely ranging frequency selectivity in both layers. We defined neuronal ensembles as neurons being active within or during successive temporal windows at the temporal resolution of our imaging. For both layers, neuronal ensembles were highly variable in size during spontaneous activity as well as during sound presentation. Ensemble sizes distributed according to power laws, the hallmark of neuronal avalanches, and were similar across sound levels. Avalanches activated by sound were composed of neurons with diverse tuning preference, yet with selectivity independent of avalanche size. Our results suggest that optimization principles identified for avalanches guide population activity in L4 and L2/3 of auditory cortex during and in-between stimulus processing.

Stability of neuronal avalanches and long-range temporal correlations during the first year of life in human infant

During infancy, the human brain rapidly expands in size and complexity as neural networks mature and new information is incorporated at an accelerating pace. Recently, it was shown that single electrode EEG in preterms at birth exhibits scale-invariant intermittent bursts. Yet, it is currently not known whether the normal infant brain, in particular, the cortex maintains a distinct dynamical state during development that is characterized by scale-invariant spatial as well as temporal aspects. Here we employ dense-array EEG recordings acquired from the same infants at 6 and 12 months of age to characterize brain activity during an auditory oddball task. We show that suprathreshold events organize as spatiotemporal clusters whose size and duration are power-law distributed, the hallmark of neuronal avalanches. Time series of local suprathreshold EEG events display significant long-range temporal correlations (LRTCs). No differences were found between 6 and 12 months, demonstrating stability of avalanche dynamics and LRTCs during the first year after birth. These findings demonstrate that the infant brain is characterized by distinct spatiotemporal dynamical aspects that are in line with expectations of a critical cortical state. We suggest that critical state dynamics, which theory and experiments have shown to be beneficial for numerous aspects of information processing, are maintained by the infant brain to process an increasingly complex environment during development.

Brain active transmembrane water cycling measured by MR is associated with neuronal activity

PURPOSE

fMRI is widely used to study brain activity. Unfortunately, conventional fMRI methods assess neuronal activity only indirectly, through hemodynamic coupling. Here, we show that active, steady-state transmembrane water cycling (AWC) could serve as a basis for a potential fMRI mechanism for direct neuronal activity detection.

METHODS

AWC and neuronal actitivity in rat organotypic cortical cultures were simultaneously measured with a hybrid MR-fluorescence system. Perfusion with a paramagnetic MRI contrast agent, Gadoteridol, allows NMR determination of the kinetics of transcytolemmal water exchange. Changes in intracellular calcium concentration, [Ca_i ²⁺ ] were used as a proxy of neuronal activity and were monitored by fluorescence imaging.

RESULTS

When we alter neuronal activity by titrating with extracellular [K⁺ ] near the normal value, we see an AWC response resembling Na⁺ -K⁺ -ATPase (NKA) Michaelis-Menten behavior. When we treat with the voltage-gated sodium channel inhibitor, or with an excitatory postsynaptic inhibitor cocktail, we see AWC decrease by up to 71%. AWC was found also to be positively correlated with the basal level of spontaneous activity, which varies in different cultures.

CONCLUSIONS

These results suggest that AWC is associated with neuronal activity and NKA activity is a major contributor in coupling AWC to neuronal activity. Although AWC comprises steady-state, homeostatic transmembrane water exchange, our analysis also yields a simultaneous measure of the average cell volume, which reports any slower net transmembrane water transport.

Altered avalanche dynamics in a developmental NMDAR hypofunction model of cognitive impairment

Disturbed activity patterns in cortical networks contribute to the pathophysiology of schizophrenia (SZ). Several lines of evidence implicate NMDA receptor hypofunction in SZ, and blocking NMDA receptor signaling during early neurodevelopment produces cognitive deficits in rodent models that resemble those seen in schizophrenic patients. However, the altered network dynamics underlying these cognitive impairments largely remain to be characterized, especially at the cellular level. Here, we use in vivo two-photon calcium imaging to describe pathological dynamics, occurring in parallel with cognitive dysfunction, in a developmental NMDA receptor hypofunction model. We observed increased synchrony and specific alterations in spatiotemporal activity propagation, which could be causally linked to a previously unidentified persistent bursting phenotype. This phenotype was rescued by acute treatment with the NMDA receptor co-agonist D-serine or the GABA_B receptor agonist baclofen, which similarly rescued working memory performance. It was not reproduced by optogenetic inhibition of fast-spiking interneurons. These results provide novel insight into network-level abnormalities mediating the cognitive impairment induced by NMDA receptor hypofunction.

Maintained avalanche dynamics during task-induced changes of neuronal activity in nonhuman primates

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.

Fast, Na+ /K+ pump driven, steady-state transcytolemmal water exchange in neuronal tissue: A study of rat brain cortical cultures

PURPOSE

Water homeostasis and transport play important roles in brain function (e.g., ion homeostasis, neuronal excitability, cell volume regulation, etc.). However, specific mechanisms of water transport across cell membranes in neuronal tissue have not been completely elaborated.

METHODS

The kinetics of transcytolemmal water exchange were measured in neuronal tissue using simultaneous, real-time fluorescence and nuclear magnetic resonance (NMR) measurements of perfused, active brain organotypic cortical cultures. Perfusion with a paramagnetic MRI contrast agent, gadoteridol, allows NMR determination of the unidirectional rate constant for steady-state cellular water efflux (k_io ), and the mole fraction of intracellular water ( pi), related to the average cell volume (V). Changes in intracellular calcium concentration [Cai2+] were used as a proxy for neuronal activity and were monitored by fluorescence imaging.

RESULTS

The k_io value, averaged over all cultures (N = 99) at baseline, was 2.02 (±1.72) s^-1 , indicating that on average, the equivalent of the entire intracellular water volume turns over twice each second. To probe possible molecular pathways, the specific Na⁺ -K⁺ -ATPase (NKA) inhibitor, ouabain (1 mM), was transiently introduced into the perfusate. This caused significant transient changes (N = 8): [Cai2+] rose ∼250%, V rose ∼89%, and k_io fell ∼45%, with a metabolically active k_io contribution probably eliminated by ouabain saturation.

CONCLUSIONS

These results suggest that transcytolemmal water exchange in neuronal tissue involves mechanisms affected by NKA activity as well as passive pathways. The active pathway may account for half of the basal homeostatic water flux. Magn Reson Med 79:3207-3217, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Decline of long-range temporal correlations in the human brain during sustained wakefulness

Sleep is crucial for daytime functioning, cognitive performance and general well-being. These aspects of daily life are known to be impaired after extended wake, yet, the underlying neuronal correlates have been difficult to identify. Accumulating evidence suggests that normal functioning of the brain is characterized by long-range temporal correlations (LRTCs) in cortex, which are supportive for decision-making and working memory tasks. Here we assess LRTCs in resting state human EEG data during a 40-hour sleep deprivation experiment by evaluating the decay in autocorrelation and the scaling exponent of the detrended fluctuation analysis from EEG amplitude fluctuations. We find with both measures that LRTCs decline as sleep deprivation progresses. This decline becomes evident when taking changes in signal power into appropriate consideration. In contrast, the presence of strong signal power increases in some frequency bands over the course of sleep deprivation may falsely indicate LRTC changes that do not reflect the underlying long-range temporal correlation structure. Our results demonstrate the importance of sleep to maintain LRTCs in the human brain. In complex networks, LRTCs naturally emerge in the vicinity of a critical state. The observation of declining LRTCs during wake thus provides additional support for our hypothesis that sleep reorganizes cortical networks towards critical dynamics for optimal functioning.

A Low-Correlation Resting State of the Striatum during Cortical Avalanches and Its Role in Movement Suppression

During quiet resting behavior, involuntary movements are suppressed. Such movement control is attributed to cortico-basal ganglia loops, yet population dynamics within these loops during resting and their relation to involuntary movements are not well characterized. Here, we show by recording cortical and striatal ongoing population activity in awake rats during quiet resting that intrastriatal inhibition maintains a low-correlation striatal resting state in the presence of cortical neuronal avalanches. Involuntary movements arise from disturbed striatal resting activity through two different population dynamics. Nonselectively reducing intrastriatal γ-aminobutyric acid (GABA) receptor-A inhibition synchronizes striatal dynamics, leading to involuntary movements at low rate. In contrast, reducing striatal interneuron (IN)-mediated inhibition maintains decorrelation and induces intermittent involuntary movements at high rate. This latter scenario was highly effective in modulating cortical dynamics at a subsecond timescale. To distinguish intrastriatal processing from loop dynamics, cortex-striatum-midbrain cultures, which lack feedback to cortex, were used. Cortical avalanches in vitro were accompanied by low-correlated resting activity in the striatum and nonselective reduction in striatal inhibition synchronized striatal neurons similar to in vivo. Importantly, reduction of inhibition from striatal INs maintained low correlations in the striatum while reorganizing functional connectivities among striatal neurons. Our results demonstrate the importance of two major striatal microcircuits in distinctly regulating striatal and cortical resting state dynamics. These findings suggest that specific functional connectivities of the striatum that are maintained by local inhibition are important in movement control.

Why don’t neuronal “avalanches” in resting-state cortex cause involuntary movements? This study shows that a low-correlation striatal resting state suppresses such movements and explores mechanisms that disrupt this inhibition.

Even in the absence of apparent motor output, the brain produces a rich repertoire of neuronal activity patterns known as “resting state” activity. In the outer layer of the cortex, resting state patterns emerge as neuronal avalanches, precisely scale-invariant spatiotemporal bursts that often engage large populations of neurons. Little is known about how the brain suppresses involuntary movements during such activity. Here, we show that the striatum, which is part of the cortex-basal ganglia loop, maintains a low-correlation state during resting activity. By using a combination of in vivo and in vitro approaches with pharmacological manipulations, we demonstrate that the precise configuration of this low-correlation state effectively contributes to involuntary movements. Nonselective blockade of intra-striatal inhibition abolished the low-correlation striatal resting state, barely affected cortical avalanches, and led to involuntary movements at low rate. In contrast, selectively reducing striatal interneuron inhibition strongly affected cortical avalanches and triggered involuntary movements at high rate while maintaining a relatively decorrelated striatal resting state. Our results demonstrate the importance of different inhibitory striatal circuits in the suppression of involuntary movements and suggest that the precise spatiotemporal configuration of striatal activity plays an active role in the regulation of cortical resting state activity and motor control.

Temporal correlations in neuronal avalanche occurrence

Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

Opening bottlenecks on weighted networks by local adaptation to cascade failures

Structure and dynamics of complex systems are often described using weighted networks in which the position, weight and direction of links quantify how activity propagates between system elements, or nodes. Nodes with only few outgoing links of low weight have low out-strength and thus form bottlenecks that hinder propagation. It is currently not well understood how systems can overcome limits imposed by such bottlenecks. Here, we simulate activity cascades on weighted networks and show that, for any cascade length, activity initially propagates towards high out-strength nodes before terminating in low out-strength bottlenecks. Increasing the weights of links that are active early in the cascade further enhances already strong pathways, but worsens the bottlenecks thereby limiting accessibility to other pathways in the network. In contrast, strengthening only links that propagated the activity just prior to cascade termination, i.e. links that point into bottlenecks, eventually removes these bottlenecks and increases the accessibility of all paths on the network. This local adaptation rule simply relies on the relative timing to a global failure signal and allows systems to overcome engrained structure to adapt to new challenges.

Simultaneous calcium fluorescence imaging and MR of ex vivo organotypic cortical cultures: a new test bed for functional MRI

Recently, several new functional (f)MRI contrast mechanisms including diffusion, phase imaging, proton density, etc. have been proposed to measure neuronal activity more directly and accurately than blood-oxygen-level dependent (BOLD) fMRI. However, these approaches have proved difficult to reproduce, mainly because of the dearth of reliable and robust test systems to vet and validate them. Here we describe the development and testing of such a test bed for non-BOLD fMRI. Organotypic cortical cultures were used as a stable and reproducible biological model of neuronal activity that shows spontaneous activity similar to that of in vivo brain cortex without any hemodynamic confounds. An open-access, single-sided magnetic resonance (MR) "profiler" consisting of four permanent magnets with magnetic field of 0.32 T was used in this study to perform MR acquisition. A fluorescence microscope with long working distance objective was mounted on the top of a custom-designed chamber that keeps the organotypic culture vital, and the MR system was mounted on the bottom of the chamber to achieve real-time simultaneous calcium fluorescence optical imaging and MR acquisition on the same specimen. In this study, the reliability and performance of the proposed test bed were demonstrated by a conventional CPMG MR sequence acquired simultaneously with calcium imaging, which is a well-characterized measurement of neuronal activity. This experimental design will make it possible to correlate directly the other candidate functional MR signals to the optical indicia of neuronal activity in the future.

Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state

Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

DOI:http://dx.doi.org/10.7554/eLife.07224.001

Even when we are not engaged in any specific task, the brain shows coordinated patterns of spontaneous activity that can be monitored using electrodes placed on the scalp. This resting activity shapes the way that the brain responds to subsequent stimuli. Changes in resting activity patterns are seen in various neurological and psychiatric disorders, as well as in healthy individuals following sleep deprivation.

The brain's outer layer is known as the cortex. On a large scale, when monitoring many thousands of neurons, resting activity in the cortex demonstrates propagation in the brain in an organized manner. Specifically, resting activity was found to organize as so-called neuronal avalanches, in which large bursts of neuronal activity are grouped with medium-sized and smaller bursts in a very characteristic order. In fact, the sizes of these bursts—that is, the number of neurons that fire—are found to be scale-invariant, that is, the ratio of large bursts to medium-sized bursts is the same as that of medium-sized to small bursts. Such scale-invariance suggests that neuronal bursts are not independent of one another. However, it is largely unclear how neuronal avalanches arise from individual neurons, which fire simply in a noisy, irregular manner.

Bellay, Klaus et al. have now provided insights into this process by examining patterns of firing of a particular type of neuron—known as a pyramidal cell—in the cortex of rats as they recover from anesthesia. As the animals awaken, the firing of individual pyramidal cells in the cortex becomes even more irregular than under anesthesia. However, by considering the activity of a group of these neurons, Bellay, Klaus et al. realized that it is this more irregular firing that gives rise to neuronal avalanches, and that this occurs only when the animals are awake. Further experiments on individual pyramidal cells grown in the laboratory confirmed that neuronal avalanches emerge spontaneously from the irregular firing of individual neurons. These avalanches depend on there being a balance between two types of activity among the cells: ‘excitatory’ activity that causes other neurons to fire, and ‘inhibitory’ activity that prevents neuronal firing.

Given that resting activity influences the brain's responses to the outside world, the origins of neuronal avalanches are likely to provide clues about the way the brain processes information. Future experiments should also examine the possibility that the emergence of neuronal avalanches marks the transition from unconsciousness to wakefulness within the brain.

DOI:http://dx.doi.org/10.7554/eLife.07224.002

Critical slowing down governs the transition to neuron spiking

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws.

Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.

Neurons efficiently convey information by being able to switch rapidly between two different states: quiescence and spiking. Such sudden shifts to a qualitatively different state are observed in many complex systems; the often dramatic consequences of these tipping points for diverse fields such as economics, ecology, and the brain have spurred interest to better understand their transition mechanisms and predict their sudden occurrences. By studying the transition from neuronal quiescence to spiking, we show that the quantitative scaling laws for critical slowing down, i.e., a system’s tendency to recover more slowly from perturbations upon approaching its transition point, inform about the underlying bifurcation mechanism and can be used to improve the prediction of a system’s tipping point.

On the temporal organization of neuronal avalanches

Spontaneous activity of cortex in vitro and in vivo has been shown to organize as neuronal avalanches. Avalanches are cascades of neuronal activity that exhibit a power law in their size and duration distribution, typical features of balanced systems in a critical state. Recently it has been shown that the distribution of quiet times between consecutive avalanches in rat cortex slice cultures displays a non-monotonic behavior with a power law decay at short time scales. This behavior has been attributed to the slow alternation between up and down-states. Here we further characterize the avalanche process and investigate how the functional behavior of the quiet time distribution depends on the fine structure of avalanche sequences. By systematically removing smaller avalanches from the experimental time series we show that size and quiet times are correlated and highlight that avalanche occurrence exhibits the characteristic periodicity of θ and β/γ oscillations, which jointly emerge in most of the analyzed samples. Furthermore, our analysis indicates that smaller avalanches tend to be associated with faster β/γ oscillations, whereas larger ones are associated with slower θ and 1-2 Hz oscillations. In particular, large avalanches corresponding to θ cycles trigger cascades of smaller ones, which occur at β/γ frequency. This temporal structure follows closely the one of nested θ - β/γ oscillations. Finally we demonstrate that, because of the multiple time scales characterizing avalanche dynamics, the distributions of quiet times between avalanches larger than a certain size do not collapse onto a unique function when rescaled by the average occurrence rate. However, when considered separately in the up-state and in the down-state, these distributions are solely controlled by the respective average rate and two different unique function can be identified.

Powerlaw: a Python package for analysis of heavy-tailed distributions

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.

Universal organization of resting brain activity at the thermodynamic critical point

Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian cortex, one type of complex dynamics that spontaneously emerges from neuronal interactions has been characterized as neuronal avalanches. Several aspects of neuronal avalanches such as their size and life time distributions are described by power laws with unique exponents, indicating an underlying critical branching process that governs avalanche formation. Here, we show that neuronal avalanches also reflect an organization of brain dynamics close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing a control parameter equivalent to thermodynamic temperature, we observed typical critical behavior in cortical activities near the actual physiological condition, including the phase transition of an order parameter, as well as the divergence of susceptibility and specific heat. Finite-size scaling of these quantities allowed us to derive robust critical exponents highly consistent across monkey and humans that uncover a distinct, yet universal organization of brain dynamics. Our results demonstrate that normal brain dynamics at rest resides near or at criticality, which maximizes several aspects of information processing such as input sensitivity and dynamic range.

Neuronal avalanches in the resting MEG of the human brain

What constitutes normal cortical dynamics in healthy human subjects is a major question in systems neuroscience. Numerous in vitro and in vivo animal studies have shown that ongoing or resting cortical dynamics are characterized by cascades of activity across many spatial scales, termed neuronal avalanches. In experiment and theory, avalanche dynamics are identified by two measures: (1) a power law in the size distribution of activity cascades with an exponent of -3/2 and (2) a branching parameter of the critical value of 1, reflecting balanced propagation of activity at the border of premature termination and potential blowup. Here we analyzed resting-state brain activity recorded using noninvasive magnetoencephalography (MEG) from 124 healthy human subjects and two different MEG facilities using different sensor technologies. We identified large deflections at single MEG sensors and combined them into spatiotemporal cascades on the sensor array using multiple timescales. Cascade size distributions obeyed power laws. For the timescale at which the branching parameter was close to 1, the power law exponent was -3/2. This relationship was robust to scaling and coarse graining of the sensor array. It was absent in phase-shuffled controls with the same power spectrum or empty scanner data. Our results demonstrate that normal cortical activity in healthy human subjects at rest organizes as neuronal avalanches and is well described by a critical branching process. Theory and experiment have shown that such critical, scale-free dynamics optimize information processing. Therefore, our findings imply that the human brain attains an optimal dynamical regime for information processing.

Balance between excitation and inhibition controls the temporal organization of neuronal avalanches

Neuronal avalanches, measured in vitro and in vivo, exhibit a robust critical behavior. Their temporal organization hides the presence of correlations. Here we present experimental measurements of the waiting time distribution between successive avalanches in the rat cortex in vitro. This exhibits a nonmonotonic behavior not usually found in other natural processes. Numerical simulations provide evidence that this behavior is a consequence of the alternation between states of high and low activity, named up and down states, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods, both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homeostatic mechanisms.

The Functional Benefits of Criticality in the Cortex

Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.

The organization of strong links in complex networks

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

Multi-electrode array recordings of neuronal avalanches in organotypic cultures

The cortex is spontaneously active, even in the absence of any particular input or motor output. During development, this activity is important for the migration and differentiation of cortex cell types and the formation of neuronal connections¹. In the mature animal, ongoing activity reflects the past and the present state of an animal into which sensory stimuli are seamlessly integrated to compute future actions. Thus, a clear understanding of the organization of ongoing i.e. spontaneous activity is a prerequisite to understand cortex function.

Numerous recording techniques revealed that ongoing activity in cortex is comprised of many neurons whose individual activities transiently sum to larger events that can be detected in the local field potential (LFP) with extracellular microelectrodes, or in the electroencephalogram (EEG), the magnetoencephalogram (MEG), and the BOLD signal from functional magnetic resonance imaging (fMRI). The LFP is currently the method of choice when studying neuronal population activity with high temporal and spatial resolution at the mesoscopic scale (several thousands of neurons). At the extracellular microelectrode, locally synchronized activities of spatially neighbored neurons result in rapid deflections in the LFP up to several hundreds of microvolts. When using an array of microelectrodes, the organizations of such deflections can be conveniently monitored in space and time.

Neuronal avalanches describe the scale-invariant spatiotemporal organization of ongoing neuronal activity in the brain^2,3. They are specific to the superficial layers of cortex as established in vitro^4,5, in vivo in the anesthetized rat ⁶, and in the awake monkey⁷. Importantly, both theoretical and empirical studies^2,8-10 suggest that neuronal avalanches indicate an exquisitely balanced critical state dynamics of cortex that optimizes information transfer and information processing.

In order to study the mechanisms of neuronal avalanche development, maintenance, and regulation, in vitro preparations are highly beneficial, as they allow for stable recordings of avalanche activity under precisely controlled conditions. The current protocol describes how to study neuronal avalanches in vitro by taking advantage of superficial layer development in organotypic cortex cultures, i.e. slice cultures, grown on planar, integrated microelectrode arrays (MEA; see also ^11-14).

Statistical analyses support power law distributions found in neuronal avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Simultaneous multi-electrode array recording and two-photon calcium imaging of neural activity

A complete understanding of how brain circuits function will require measurement techniques which monitor large-scale network activity simultaneously with the activity of local neural populations at a small scale. Here we present a useful step towards achieving this aim: simultaneous two-photon calcium imaging and multi-electrode array (MEA) recordings. The primary challenge of this method is removing an electrical artifact from the MEA signals that is caused by the imaging laser. Here we show that artifact removal can be achieved with a simple filtering scheme. As a demonstration of this technique we compare large-scale local field potential signals to single-neuron activity in a small-scale group of cells recorded from rat acute slices under two conditions: suppressed vs. intact inhibitory interactions between neurons.

Neuronal avalanches in spontaneous activity in vivo

Many complex systems give rise to events that are clustered in space and time, thereby establishing a correlation structure that is governed by power law statistics. In the cortex, such clusters of activity, called "neuronal avalanches," were recently found in local field potentials (LFPs) of spontaneous activity in acute cortex slices, slice cultures, the developing cortex of the anesthetized rat, and premotor and motor cortex of awake monkeys. At present, it is unclear whether neuronal avalanches also exist in the spontaneous LFPs and spike activity in vivo in sensory areas of the mature brain. To address this question, we recorded spontaneous LFPs and extracellular spiking activity with multiple 4 × 4 microelectrode arrays (Michigan Probes) in area 17 of adult cats under anesthesia. A cluster of events was defined as a consecutive sequence of time bins Δt (1-32 ms), each containing at least one LFP event or spike anywhere on the array. LFP cluster sizes consistently distributed according to a power law with a slope largely above -1.5. In two thirds of the corresponding experiments, spike clusters also displayed a power law that displayed a slightly steeper slope of -1.8 and was destroyed by subsampling operations. The power law in spike clusters was accompanied with stronger temporal correlations between spiking activities of neurons that spanned longer time periods compared with spike clusters lacking power law statistics. The results suggest that spontaneous activity of the visual cortex under anesthesia has the properties of neuronal avalanches.

Hierarchical interaction structure of neural activities in cortical slice cultures

Recent advances in the analysis of neuronal activities suggest that the instantaneous activity patterns can be mostly explained by considering only first-order and pairwise interactions between recorded elements, i.e., action potentials or local field potentials (LFP), and do not require higher-than-pairwise-order interactions. If generally applicable, this pairwise approach greatly simplifies the description of network interactions. However, an important question remains: are the recorded elements the units of interaction that best describe neuronal activity patterns? To explore this, we recorded spontaneous LFP peak activities in cortical organotypic cultures using planar, integrated 60-microelectrode arrays. We compared predictions obtained using a pairwise approach with those using a hierarchical approach that uses two different spatial units for describing the activity interactions: single electrodes and electrode clusters. In this hierarchical model, short-range interactions within each cluster were modeled by pairwise interactions of electrode activities and long-range interactions were modeled by pairwise interactions of cluster activities. Despite the relatively low number of parameters used, the hierarchical model provided a more accurate description of the activity patterns than the pairwise model when applied to ensembles of 10 electrodes. Furthermore, the hierarchical model was successfully applied to a larger-scale data of approximately 60 electrodes. Electrode activities within clusters were highly correlated and spatially contiguous. In contrast, long-range interactions were diffuse, suggesting the presence of higher-than-pairwise-order interactions involved in the LFP peak activities. Thus, the identification of appropriate units of interaction may allow for the successful characterization of neuronal activities in large-scale networks.

Angiogenic factors stimulate growth of adult neural stem cells

BACKGROUND

The ability to grow a uniform cell type from the adult central nervous system (CNS) is valuable for developing cell therapies and new strategies for drug discovery. The adult mammalian brain is a source of neural stem cells (NSC) found in both neurogenic and non-neurogenic zones but difficulties in culturing these hinders their use as research tools.

METHODOLOGY/PRINCIPAL FINDINGS

Here we show that NSCs can be efficiently grown in adherent cell cultures when angiogenic signals are included in the medium. These signals include both anti-angiogenic factors (the soluble form of the Notch receptor ligand, Dll4) and pro-angiogenic factors (the Tie-2 receptor ligand, Angiopoietin 2). These treatments support the self renewal state of cultured NSCs and expression of the transcription factor Hes3, which also identifies the cancer stem cell population in human tumors. In an organotypic slice model, angiogenic factors maintain vascular structure and increase the density of dopamine neuron processes.

CONCLUSIONS/SIGNIFICANCE

We demonstrate new properties of adult NSCs and a method to generate efficient adult NSC cultures from various central nervous system areas. These findings will help establish cellular models relevant to cancer and regeneration.

Coherence potentials: loss-less, all-or-none network events in the cortex

Transient associations among neurons are thought to underlie memory and behavior. However, little is known about how such associations occur or how they can be identified. Here we recorded ongoing local field potential (LFP) activity at multiple sites within the cortex of awake monkeys and organotypic cultures of cortex. We show that when the composite activity of a local neuronal group exceeds a threshold, its activity pattern, as reflected in the LFP, occurs without distortion at other cortex sites via fast synaptic transmission. These large-amplitude LFPs, which we call coherence potentials, extend up to hundreds of milliseconds and mark periods of loss-less spread of temporal and amplitude information much like action potentials at the single-cell level. However, coherence potentials have an additional degree of freedom in the diversity of their waveforms, which provides a high-dimensional parameter for encoding information and allows identification of particular associations. Such nonlinear behavior is analogous to the spread of ideas and behaviors in social networks.

Efficient network reconstruction from dynamical cascades identifies small-world topology of neuronal avalanches

Cascading activity is commonly found in complex systems with directed interactions such as metabolic networks, neuronal networks, or disease spreading in social networks. Substantial insight into a system's organization can be obtained by reconstructing the underlying functional network architecture from the observed activity cascades. Here we focus on Bayesian approaches and reduce their computational demands by introducing the Iterative Bayesian (IB) and Posterior Weighted Averaging (PWA) methods. We introduce a special case of PWA, cast in nonparametric form, which we call the normalized count (NC) algorithm. NC efficiently reconstructs random and small-world functional network topologies and architectures from subcritical, critical, and supercritical cascading dynamics and yields significant improvements over commonly used correlation methods. With experimental data, NC identified a functional and structural small-world topology and its corresponding traffic in cortical networks with neuronal avalanche dynamics.

In many complex systems found across disciplines, such as biological cells and organisms, social networks, economic systems, and the Internet, individual elements interact with each other, thereby forming large networks whose structure is often not known. In these complex networks, local events can easily propagate, resulting in diverse spatio-temporal activity cascades, or avalanches. Examples of such cascading activity are the propagation of diseases in social networks, cascades of chemical reactions inside a cell, the propagation of neuronal activity in the brain, and e-mail forwarding on the Internet. Although the observation of a single cascade provides limited insight into the organization of a complex network, the observation of many cascades allows for the reconstruction of very robust features of network organization, providing valuable insight into network function as well as network failure. The current work develops new algorithms for an efficient reconstruction of relatively large networks in the context of cascading activity. When applied to the brain, these algorithms uncover the structural and functional features of gray matter networks that display activity cascades in the form of neuronal avalanches.

The organizing principles of neuronal avalanches: cell assemblies in the cortex?

Neuronal avalanches are spatiotemporal patterns of neuronal activity that occur spontaneously in superficial layers of the mammalian cortex under various experimental conditions. These patterns reflect fast propagation of local synchrony, display a rich spatiotemporal diversity and recur over several hours. The statistical organization of pattern sizes is invariant to the choice of spatial scale, demonstrating that the functional linking of cortical sites into avalanches occurs on all spatial scales with a fractal organization. These features suggest an underlying network of neuronal interactions that balances diverse representations with predictable recurrence, similar to what has been theorized for cell assembly formation. We propose that avalanches reflect the transient formation of cell assemblies in the cortex and discuss various models that provide mechanistic insights into the underlying dynamics, suggesting that they arise in a critical regime.

Direct magnetic resonance detection of neuronal electrical activity

Present noninvasive neuroimaging methods measure neuronal activity indirectly, via either cerebrovascular changes or extracranial measurements of electrical/magnetic signals. Recent studies have shown evidence that MRI may be used to directly and noninvasively map electrical activity associated with human brain activation, but results are inconclusive. Here, we show that MRI can detect cortical electrical activity directly. We use organotypic rat-brain cultures in vitro that are spontaneously active in the absence of a cerebrovascular system. Single-voxel magnetic resonance (MR) measurements obtained at 7 T were highly correlated with multisite extracellular local field potential recordings of the same cultures before and after blockade of neuronal activity with tetrodotoxin. Similarly, for MR images obtained at 3 T, the MR signal changed solely in voxels containing the culture, thus allowing the spatial localization of the active neuronal tissue.

Inverted-U profile of dopamine-NMDA-mediated spontaneous avalanche recurrence in superficial layers of rat prefrontal cortex

Prefrontal cortex (PFC) functions, such as working memory, attention selection, and memory retrieval, depend critically on dopamine and NMDA receptor activation by way of an inverted-U-shaped pharmacological profile. Although single neuron responses in the PFC have shown some aspects of this profile, a network dynamic that follows the dopamine-NMDA dependence has not been identified. We studied neuronal network activity in acute medial PFC slices of adult rats by recording local field potentials (LFPs) with microelectrode arrays. Bath application of dopamine or the dopamine D1 agonist SKF38393 [(+/-)-1-phenyl-2,3,4,5-tetrahydro-(1H)-3-benzazepine-7,8-diol hydrochloride] in combination with NMDA induced spontaneous LFPs predominantly in superficial cortex layers. The LFPs at single electrodes were characterized by sharp negative peaks that were clustered in time across electrodes revealing diverse spatiotemporal patterns on the array. The pattern formation required fast GABAergic transmission, coactivation of the dopamine D1 and NMDA receptor, and depended in an inverted-U profile on dopamine. At moderate concentrations of dopamine or the dopamine D1 agonist, the pattern size distribution formed a power law with exponent alpha = -1.5, indicating that patterns are organized in the form of neuronal avalanches, thereby maximizing spatial correlations in the network. At lower or higher concentrations, alpha was more negative than -1.5, indicating reduced spatial correlations. Likewise, at moderate dopamine concentrations, the avalanche rate and recurrence of specific avalanches was maximal with recurrence frequencies after a "power law"-like heavy-tail distribution with a slope of -2.4. We suggest that the dopamine-NMDA-dependent spontaneous recurrence of specific avalanches in superficial cortical layers might facilitate integrative and associative aspects of PFC functions.