Deconstructing scale-free neuronal avalanches: behavioral transitions and neuronal response

Observations of neurons in a resting brain and neurons in cultures often display spontaneous scale-free collective dynamics in the form of information cascades, also called “neuronal avalanches”. This has motivated the so called critical brain hypothesis which posits that the brain is self-tuned to a critical point or regime, separating exponentially-growing dynamics from quiescent states, to achieve optimality. Yet, how such optimality of information transmission is related to behaviour and whether it persists under behavioural transitions has remained a fundamental knowledge gap. Here, we aim to tackle this challenge by studying behavioural transitions in mice using two-photon calcium imaging of the retrosplenial cortex -- an area of the brain well positioned to integrate sensory, mnemonic, and cognitive information by virtue of its strong connectivity with the hippocampus, medial prefrontal cortex, and primary sensory cortices. Our work shows that the response of the underlying neural population to behavioural transitions can vary significantly between different sub-populations such that one needs to take the structural and functional network properties of these sub-populations into account to understand the properties at the total population level. Specifically, we show that the retrosplenial cortex contains at least one sub-population capable of switching between two different scale-free regimes, indicating an intricate relationship between behaviour and the optimality of neuronal response at the subgroup level. This asks for a potential reinterpretation of the emergence of self-organized criticality in neuronal systems.

Neuronal Avalanches Across the Rat Somatosensory Barrel Cortex and the Effect of Single Whisker Stimulation

Since its first experimental signatures, the so called “critical brain hypothesis” has been extensively studied. Yet, its actual foundations remain elusive. According to a widely accepted teleological reasoning, the brain would be poised to a critical state to optimize the mapping of the noisy and ever changing real-world inputs, thus suggesting that primary sensory cortical areas should be critical. We investigated whether a single barrel column of the somatosensory cortex of the anesthetized rat displays a critical behavior. Neuronal avalanches were recorded across all cortical layers in terms of both multi-unit activities and population local field potentials, and their behavior during spontaneous activity compared to the one evoked by a controlled single whisker deflection. By applying a maximum likelihood statistical method based on timeseries undersampling to fit the avalanches distributions, we show that neuronal avalanches are power law distributed for both multi-unit activities and local field potentials during spontaneous activity, with exponents that are spread along a scaling line. Instead, after the tactile stimulus, activity switches to a transient across-layers synchronization mode that appears to dominate the cortical representation of the single sensory input.

Self-Organized Criticality in the Brain

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

Beyond resting state neuronal avalanches in the somatosensory barrel cortex

Since its first experimental signatures, the so called "critical brain hypothesis" has been extensively studied. Yet, its actual foundations remain elusive. According to a widely accepted teleological reasoning, the brain would be poised to a critical state to optimize the mapping of the noisy and ever changing real-world inputs, thus suggesting that primary sensory cortical areas should be critical. We investigated whether a single barrel column of the somatosensory cortex of the anesthetized rat displays a critical behavior. Neuronal avalanches were recorded across all cortical layers in terms of both spikes and population local field potentials, and their behavior during spontaneous activity compared to the one evoked by a controlled single whisker deflection. By applying a maximum likelihood statistical method based on timeseries undersampling to fit the avalanches distributions, we show that neuronal avalanches are power law distributed for both spikes and local field potentials during spontaneous activity, with exponents that are spread along a scaling line. Instead, after the tactile stimulus, activity switches to an across-layers synchronization mode that appears to dominate during cortical representation of the single sensory input.

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.

A unified theory of E/I synaptic balance, quasicritical neuronal avalanches and asynchronous irregular spiking

Neuronal avalanches and asynchronous irregular (AI) firing patterns have been thought to represent distinct frameworks to understand the brain spontaneous activity. The former is typically present in systems where there is a balance between the slow accumulation of tension and its fast dissipation, whereas the latter is accompanied by the balance between synaptic excitation and inhibition (E/I). Here, we develop a new theory of E/I balance that relies on two homeostatic adaptation mechanisms: the short-term depression of inhibition and the spike-dependent threshold increase. First, we turn off the adaptation and show that the so-called static system has a typical critical point commonly attributed to self-organized critical models. Then, we turn on the adaptation and show that the network evolves to a dynamic regime in which: (I) E/I synapses balance regardless of any parameter choice; (II) an AI firing pattern emerges; and (III) neuronal avalanches display visually accurate power laws. This is the first time that these three phenomena appear simultaneously in the same network activity. Thus, we show that the once thought opposing frameworks may be unified into a single dynamics, provided that adaptation mechanisms are in place. In our model, the AI firing pattern is a direct consequence of the hovering close to the critical line where external inputs are compensated by threshold growth, creating synaptic balance for any E/I weight ratio.Author summaryTwo competing frameworks are employed to understand the brain spontaneous activity, both of which are backed by computational and experimental evidence: globally asynchronous and locally irregular (AI) activity arises in excitatory/inhibitory balanced networks subjected to external stimuli, whereas avalanche activity emerge in excitable systems on the critical point between active and inactive states. Here, we develop a new theory for E/I networks and show that there is a state where synaptic balance coexists with AI firing and power-law distributed neuronal avalanches. This regime is achieved through the introducing of short-time depression of inhibitory synapses and spike-dependent threshold adaptation. Thus, the system self-organizes towards the balance point, such that its AI activity arises from quasicritical fluctuations. The need for two independent adaptive mechanisms explains why different dynamical states are observed in the brain.

The structural connectome constrains fast brain dynamics

Brain activity during rest displays complex, rapidly evolving patterns in space and time. Structural connections comprising the human connectome are hypothesized to impose constraints on the dynamics of this activity. Here, we use magnetoencephalography (MEG) to quantify the extent to which fast neural dynamics in the human brain are constrained by structural connections inferred from diffusion MRI tractography. We characterize the spatio-temporal unfolding of whole-brain activity at the millisecond scale from source-reconstructed MEG data, estimating the probability that any two brain regions will activate at consecutive time epochs. We find that the structural connectome profoundly shapes rapid spreading of neuronal avalanches, evidenced by a significant association between these transition probabilities and structural connectivity strengths (r=0.30-0.38, p<0.0001). This finding opens new avenues to study the relationship between brain structure and neural dynamics.