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

Abstract

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.AUTHOR SUMMARYIn the brain, groups of neurons often fire together which is considered essential for normal brain function. A particular form of coincident firing has been identified for “neuronal avalanches” which are scale-invariant cascades of neuronal activity that rapidly engage large numbers of neurons. However, studying these avalanches when observing only a few neurons in the network is challenging. We used simulations and recordings from ongoing brain activity to explore how to overcome this challenge. We found that adjusting our temporal resolution and focusing on increasingly larger avalanches allows us to accurately detect rapid, parabolic expansions of these patterns even when examining a minuscule fraction of neurons. This identifies a general rule for how the brain operates best in engaging neurons to fire together, despite the limitations in our observations.