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Abstract

Cortical activity is permeated with endogenously generated fluctuations that affect responses to sensory stimuli and correlate with behavioral variability. These ongoing dynamics have been studied on two different spatial scales. On a local scale of single cortical columns, ongoing activity spontaneously transitions between episodes of vigorous (On) and faint (Off) spiking, synchronously across cortical layers. Dynamics of these local On-Off transitions are modulated during goal-directed behavior and predict behavioral performance [1]. On a wider spatial scale of interacting cortical columns, spontaneous activity propagates as cascades of bursts known as neural avalanches. The size of these avalanches is well approximated by a power-law distribution, suggesting that brain operates close to a critical point [2], which was shown to be optimal for information processing [3,4]. Whether and how local On-Off dynamics can coexist with critical avalanches in the same network is still an open question.

To investigate this question, we developed a branching model capable of capturing both the local On-Off dynamics and the propagation of neural avalanches on a wider spatial scale. Each unit in the model represents a cortical column, with a spatially structured connectivity to other units mimicking the cortex spatial organization. The columns spontaneously transition between On and Off episodes driven by a self-excitation, excitatory inputs from the neighboring columns, and by stochastic external inputs. On and Off episode durations in our model follow exponential distributions, similar to the On-Off dynamics observed in single cortical columns (Fig 1C) [1]. We examined under what conditions these local On-Off dynamics are consistent with the propagation of critical avalanches.

We found that models with local connectivity do not exhibit critical dynamics in the limit of a large system size. In a critical model, the cut-off of the avalanche-size distribution is expected to scale with the system size. In contrast, in models with only nearest-neighbor connectivity, the cut-off stays constant for systems larger than some characteristic size-scale. We demonstrate that the scaling property can be recovered with a larger radius of connections or by rewiring a small fraction of local connections to long-range random connections (Fig 1D-E). Our results highlight the possible role of long-range connections in the cortex in defining the operating regime of the brain dynamics.