Spatiotemporal neural correlations and network dynamics

With fast development of recording techniques, simultaneous recordings of large groups of neurons reveal widely distributed spatiotemporal neural correlations in the cortex. Pairwise neural correlations are related to functional properties of neurons. They affect sensory information processing, learning and plasticity, and cognitive functions such as attention. At the population level, the spatial and temporal modes of correlations intermingle, which possibly reflects underlying anatomical circuit structure, network dynamics and operating regimes of neural activity. However, a systematic approach to disentangle the mixed patterns of spatial and temporal modes in correlations has not been fully developed. Here we develop a theoretical framework that relates the spatial and temporal modes of pairwise neural correlations to the network connectivity structure and the operating regime of dynamics in interacting neurons. We analyze spatiotemporal correlations in network models of binary units with different connectivity structures and dimensions. We derive analytical expressions for spatial and temporal correlations and verify them with numerical simulations. Our theory demonstrates how multiple timescales in auto- and cross-correlations arise from spatial interactions between units. We find that because of spatial dependence of interactions, each timescale is associated with fluctuations of a particular spatial frequency and makes hierarchical contributions to the correlations. We then study how local versus distributed spatial connectivity shapes the timescales and spatial patterns of neural correlations. finally, we evaluate the influence of external inputs on the operating regime of the global network activity and show how it affects the timescales of correlations. Our work reveals the relationship between spatial and temporal patterns of correlations, which is determined by the network structure, dynamics and the operating regime of population activity. Analytical methods developed here can be used to extract and interpret spatiotemporal features of neural dynamics during sensory and cognitive processing, to advance understanding of neural circuit functions