Mean-field equations for neuronal networks with arbitrary degree distributions

Duane Q. Nykamp, Daniel Friedman, Sammy Shaker, Maxwell Shinn, Michael Vella, Albert Compte, Alex Roxin

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Abstract

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER network. Finally, we relate the degree distributions to so-called cortical motifs.

Original languageEnglish (US)
Article number042323
JournalPhysical Review E
Volume95
Issue number4
DOIs
StatePublished - Apr 27 2017

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    Nykamp, D. Q., Friedman, D., Shaker, S., Shinn, M., Vella, M., Compte, A., & Roxin, A. (2017). Mean-field equations for neuronal networks with arbitrary degree distributions. Physical Review E, 95(4), [042323]. https://doi.org/10.1103/PhysRevE.95.042323