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 is T 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.

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.

Retraction Note to: Stability of neuronal avalanches and long-range temporal correlations during the first year of life in human infant.

The authors have retracted this article Jannesari et al. (2019) because an incorrect version of the article was published in error. The manuscript has been republished as Jannesari et al. (2020). All authors agree to this retraction.

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.

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.

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ-oscillations.

Activity cascades are found in many complex systems. In the cortex, they arise in the form of neuronal avalanches that capture ongoing and evoked neuronal activities at many spatial and temporal scales. The scale-invariant nature of avalanches suggests that the brain is in a critical state, yet predictions from critical theory on the temporal unfolding of avalanches have yet to be confirmed in vivo. Here we show in awake nonhuman primates that the temporal profile of avalanches follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds. This parabola constrains how avalanches initiate locally, extend spatially and shrink as they evolve in time. Importantly, parabolas of different durations can be collapsed with a scaling exponent close to 2 supporting critical generational models of neuronal avalanches. Spontaneously emerging, transient γ-oscillations coexist with and modulate these avalanche parabolas thereby providing a temporal segmentation to inherently scale-invariant, critical dynamics. Our results identify avalanches and oscillations as dual principles in the temporal organization of brain activity.

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, [Cai2+ ] 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 GABAB 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.

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 (kio ), 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 kio 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 kio fell ∼45%, with a metabolically active kio 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.

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.