Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed ‘quasi-orbits’, which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network’s firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.Author Summary: The spontaneous neural activity is the dynamic floor on which the cortex builds its response to incoming stimuli and organizes its information processing, thereby the importance of understanding its dynamical underpinnings. In-vitro preparations, as well as the intact cortex in deep sleep or anesthesia, display a variety of spontaneous collective events, including quasi-synchronous ‘network spikes’ and a complex spectrum of ‘avalanches’, which has been considered suggestive of a ‘typically critical’ state. Light has been shed on selected aspects of such events; still, a unified picture stays elusive, also due to varying statistical definitions of network events. Our work aims to take a step in this direction. We first introduce a probabilistic definition of population events that naturally adapts to different scales of analysis; it reveals, in the activity of cultured networks, as well as in a simple rate model, the co-occurrence of network spikes, ‘quasi-orbits’ and avalanches. Model’s analysis suggests that their emergence is governed by a single parameter measuring the proximity to an oscillatory instability, where the network can amplify fluctuations on a wide range of scales in space and time. We also propose a procedure to infer from neural activity the slow underlying time-scales of the dynamics.