Spatial and temporal correlations in neural networks with structured connectivity

TL;DR

This paper develops a theoretical framework to understand how the interplay of spatial connectivity and temporal dynamics shapes neural correlations in networks, revealing multiple timescales and hierarchical spatial contributions.

Contribution

It provides analytical expressions for spatiotemporal correlations in structured neural networks, highlighting the joint influence of connectivity and dynamics on correlation profiles.

Findings

Spatial interactions generate multiple correlation timescales.

External inputs modulate correlation timescales depending on network regime.

Hierarchical spatial frequencies contribute to neural correlations.

Abstract

Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed correlations in either spatial or temporal domains, oblivious to their interplay. We show that the network dynamics and connectivity jointly define the spatiotemporal profile of neural correlations. We derive analytical expressions for pairwise correlations in networks of binary units with spatially arranged connectivity in one and two dimensions. We find that spatial interactions among units generate multiple timescales in auto- and cross-correlations. Each timescale is associated with fluctuations at a particular spatial frequency, making a hierarchical contribution to the correlations. External inputs can modulate the correlation timescales when spatial interactions are nonlinear, and the modulation effect depends on the operating regime of network dynamics. These theoretical results open new ways to relate connectivity and dynamics in cortical networks via measurements of spatiotemporal neural correlations.