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Correlated fluctuations in the activity of neural populations reflect thenetwork's dynamics and connectivity. The temporal and spatial dimensions ofneural correlations are interdependent. However, prior theoretical work mainlyanalyzed correlations in either spatial or temporal domains, oblivious to theirinterplay. We show that the network dynamics and connectivity jointly definethe spatiotemporal profile of neural correlations. We derive analyticalexpressions for pairwise correlations in networks of binary units withspatially arranged connectivity in one and two dimensions. We find that spatialinteractions among units generate multiple timescales in auto- andcross-correlations. Each timescale is associated with fluctuations at aparticular spatial frequency, making a hierarchical contribution to thecorrelations. External inputs can modulate the correlation timescales whenspatial interactions are nonlinear, and the modulation effect depends on theoperating regime of network dynamics. These theoretical results open new waysto relate connectivity and dynamics in cortical networks via measurements ofspatiotemporal neural correlations.

Spatial and temporal correlations in neural networks with structured connectivity