Motif Statistics and Spike Correlations in Neuronal Networks

TL;DR

This paper demonstrates that in recurrent neuronal networks, pairwise spike correlations can be effectively predicted using only three key connectivity statistics, highlighting the influence of specific motifs like diverging and chain structures.

Contribution

The study introduces a motif-based analytical framework that predicts spike correlations in neuronal networks using linear response theory and a resumming technique, focusing on second-order motifs.

Findings

Correlation coefficients are well approximated by three network statistics.

Diverging and chain motifs increase spike correlations.

Method isolates network architecture effects perturbatively.

Abstract

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state.