Structural motifs and correlation dynamics in networks of spiking neurons

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Event Abstract Back to Event Structural motifs and correlation dynamics in networks of spiking neurons Volker Pernice1*, Benjamin Staude1 and Stefan Rotter1 1 Albert-Ludwig University, Bernstein Center Freiburg & Faculty of Biology, Germany The dynamics of random recurrent networks has been analyzed in detail, but the influence of non-random connectivity patterns [1] on activity dynamics is not well understood. Here we study the effect of certain structural motifs on pairwise correlations in spiking networks of excitatory and inhibitory neurons in a balanced asynchronous-irregular state. For analytical tractability, spike trains are conceived as linearly interacting stochastic point processes. In this case, firing rates and correlation functions are fully determined by the matrix of linear response kernels. Simple analytic expressions have been derived in [2]. We find that the matrix of integrated cross-covariance functions can be written as a power series of the underlying network’s connectivity matrix. In terms of network structure, higher matrix powers of this series expansion can be interpreted as contributions of motifs of increasing complexity. Generally, such higher order motifs can strongly affect correlations. Their impact can be estimated from the spectral radius of the connectivity matrix. Using numerical simulations, we demonstrate that not only differences in average in-degree and common input but also in higher order motif distributions can lead to dramatic effects regarding pairwise correlations.To illustrate the influence of network structure in more detail, we study connectivity matrices with certain symmetry properties. Specifically we focus on distance dependent connectivity profiles. The distance dependence of correlations can then be determined from the connectivity profile, and the influence of higher order contributions can be understood analytically.