Parabolic avalanche scaling in the synchronization of cortical cell assemblies

Abstract

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

Low-dimensional criticality embedded in high-dimensional awake brain dynamics

“…A distinguishing feature of the 10 cases that reported positive evidence for criticality was that they focused on relatively long timescale fluctuations; they considered coarse-grained spike counts in time bins larger than about 10 ms. In some cases, this temporal coarse-graining was a deliberate choice in the data analysis ( 34 , 36 , 37 ) but, more commonly, was due to the limited time resolution of experimental measurements, which is typical for calcium imaging ( 35 , 38 – 43 ). The most strongly negative reports were based on analyses at the millisecond timescale, with less temporal coarse-graining.…”

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

“…Complex systems, composed of many local components or agents that interact weakly, often exhibit event cascades that cover a wide range of scales in both space and time. Such scale-invariant cascades, typically identified by power-law distributions in their duration and size – defined as the total activity observed during its lifetime, have been observed in many real systems, including solar flares [1], earthquakes [2, 3], superconductors [4], sandpiles [5], forest fires [6], and in the brain in the form of neuronal avalanches [7–9]. The scaling of such system cascades, specifically how their mean size grows with their duration, has been particularly informative as to the potential underlying dynamics of cascade generation.…”

“…Conversely, spatial subsampling, that is, sampling of only a fraction of neurons, is limited in identifying neuronal synchronization largely by failing to identify avalanche continuation in non-sampled neurons. This underestimates avalanche duration and size, biasing outcomes towards expectations for decorrelated, random processes [9, 36, 37]. Accordingly, simulations of avalanche generating critical branching processes and fractional sampling of neurons reduces the expected growth in mean avalanche size with avalanche duration, χ, from χ = 2, to a value of χ closer to 1 – 1.3 [38–40].…”

“…If the exact start and end times of avalanches are known, for example in simulations under the assumption of ‘separation of time scales’, spatially subsampled avalanches can be easily corrected for by temporal integration thereby recovering the correct critical exponents in size and duration [40] (for a review, see also [45]). Avalanche times, however, are largely unattainable in experimental data for which only a small fraction of neurons is observed and temporal integration eventually will degenerate avalanche scaling by indiscriminately concatenating successive avalanches [9]. Recently, Capek & Ribeiro et al [9] demonstrated that, even when the exact times of avalanches are not known, χ = 2 can be recovered for subsampled excitation- inhibition (E-I) balanced networks of integrate-and-fire neurons which are known to belong to the mean-field directed percolation (MF-DP) universality class [46, 47].…”

“…Avalanche times, however, are largely unattainable in experimental data for which only a small fraction of neurons is observed and temporal integration eventually will degenerate avalanche scaling by indiscriminately concatenating successive avalanches [9]. Recently, Capek & Ribeiro et al [9] demonstrated that, even when the exact times of avalanches are not known, χ = 2 can be recovered for subsampled excitation- inhibition (E-I) balanced networks of integrate-and-fire neurons which are known to belong to the mean-field directed percolation (MF-DP) universality class [46, 47]. This rescue requires (1) reducing uncorrelated neuronal action potential firing and (2) using temporal coarse-graining with an increase in minimal synchronization requirements to identify synchronized population activity in the network.…”