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Novel experimental techniques reveal the simultaneous activity of larger andlarger numbers of neurons. As a result there is increasing interest in thestructure of cooperative -- or correlated -- activity in neural populations,and in the possible impact of such correlations on the neural code. Afundamental theoretical challenge is to understand how the architecture ofnetwork connectivity along with the dynamical properties of single cells shapethe magnitude and timescale of correlations. We provide a general approach tothis problem by extending prior techniques based on linear response theory. Weconsider networks of general integrate-and-fire cells with arbitraryarchitecture, and provide explicit expressions for the approximatecross-correlation between constituent cells. These correlations depend stronglyon the operating point (input mean and variance) of the neurons, even whenconnectivity is fixed. Moreover, the approximations admit an expansion inpowers of the matrices that describe the network architecture. This expansioncan be readily interpreted in terms of paths between different cells. We applyour results to large excitatory-inhibitory networks, and demonstrate first howprecise balance --- or lack thereof --- between the strengths and timescales ofexcitatory and inhibitory synapses is reflected in the overall correlationstructure of the network. We then derive explicit expressions for the averagecorrelation structure in randomly connected networks. These expressions help toidentify the important factors that shape coordinated neural activity in suchnetworks.

Impact of network structure and cellular response on spike time correlations