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Abstract:
Understanding the fundamental principles underlying the "default" modes of activity of the brain is one of the challenges of theoretical neuroscience. The asynchronous irregular state (AIS) --characterized by a low firing rate, highly irregular spiking, and small correlations across the network [1]-- is one of the most studied dynamical regimes of the cortex. The AIS is found mainly at the cortical resting state, and it has been linked with optimal information processing and excitation-inhibition balance in spiking networks [1,2]. However, how the large-scale dynamics emerge from microscopic details, and how these relate to other cortical "default" modes (such as, e.g., avalanching behavior) is a topic of active research [3].
In this work we study an extension of the archetypical "branching process" --often used to model spreading phenomena and criticality in the brain-- that incorporates both excitation and inhibition, leading to a "stochastic Wilson-Cowan" equations at the large scale. We show that when the model is simulated with sparse, finite connectivity, a low-activity phase featuring all the key properties of the AIS emerges. We demonstrate that typical mean-field approaches used to study the macroscopic equations cannot predict the existence of the AIS [4]. Furthermore, we introduce an approach that accounts for input fluctuations and balance beyond mean-field. This approach allows us to compute the real phase diagram and bifurcations analytically. Apart from the AIS, the model shows bistability and tilted avalanches.
Moreover, it is shown that the dynamics of the branching process' usual active phase are substantially different from those of the AIS. While the usual active phase can also display arbitrarily low firing rates, other typical AIS features such as excitation/inhibition lag, low pairwise correlation, or irregular interspike intervals, are not recovered. Hence, a low-activity stable fixed point of the Wilson-Cowan cannot faithfully represent such a state. Furthermore, we show that the AIS time-series can display "quasi-oscillations", a phenomenon observed in data that has been poorly understood until now and which even led Ostojic in 2014 [5] to propose the existence of diverse types of AIS. We explicitly demonstrate for the first time that these low-frequency waves arise from system intrinsic excitability and thus are an integral part of the AIS.
