A diversity of localized timescales in network activity

Abstract

Neurons show diverse timescales, so that different parts of a network respond with disparate temporal dynamics. Such diversity is observed both when comparing timescales across brain areas and among cells within local populations; the underlying circuit mechanism remains unknown. We examine conditions under which spatially local connectivity can produce such diverse temporal behavior.In a linear network, timescales are segregated if the eigenvectors of the connectivity matrix are localized to different parts of the network. We develop a framework to predict the shapes of localized eigenvectors. Notably, local connectivity alone is insufficient for separate timescales. However, localization of timescales can be realized by heterogeneity in the connectivity profile, and we demonstrate two classes of network architecture that allow such localization. Our results suggest a framework to relate structural heterogeneity to functional diversity and, beyond neural dynamics, are generally applicable to the relationship between structure and dynamics in biological networks.Many biological systems can be thought of as networks in which a large number of elements, called ‘nodes’, are connected to each other. The brain, for example, is a network of interconnected neurons, and the changing activity patterns of this network underlie our experience of the world around us. Within the brain, different parts can process information at different speeds: sensory areas of the brain respond rapidly to the current environment, while the cognitive areas of the brain, involved in complex thought processes, are able to gather information over longer periods of time. However, it has been largely unknown what properties of a network allow different regions to process information over different timescales, and how variations in structural properties translate into differences in the timescales over which parts of a network can operate.Now Chaudhuri et al. have addressed these issues using a simple but ubiquitous class of networks called linear networks. The activity of a linear network can be broken down into simpler patterns called eigenvectors that can be combined to predict the responses of the whole network. If these eigenvectors ‘map’ to different parts of the network, this could explain how distinct regions process information on different timescales.Chaudhuri et al. developed a mathematical theory to predict what properties would cause such eigenvectors to be separated from each other and applied it to networks with architectures that resemble the wiring of the brain. This revealed that gradients in the connectivity across the network, such that nodes share more properties with neighboring nodes than distant nodes, combined with random differences in the strength of inter-node connections, are general motifs that give rise to such separated activity patterns. Intriguingly, such gradients and randomness are both common features of biological systems.