paper

Linking structure and activity in nonlinear spiking networks

arXiv:1610.03828 · doi:10.1371/journal.pcbi.1005583

Abstract

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of {\it structure-driven activity} has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities---including those of different cell types---combine with connectivity to shape population activity and function.

We were recently made aware of an error in this article: in Figure 13, we neglected several one-loop contributions to the two-point correlation. For the networks we studied here, these contributions are small (third order in the coupling strength). For further discussion, please see the correction note appended to the end of the article

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