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TitleA stochastic-field description of finite-size spiking neural networks.
Publication TypeJournal Article
Year of Publication2017
AuthorsDumont, Grégory, Alexandre Payeur, and Andre Longtin
JournalPLoS Comput Biol
Volume13
Issue8
Paginatione1005691
Date Published2017 Aug
ISSN1553-7358
KeywordsAction Potentials, Animals, Brain, Computational Biology, Models, Neurological, Nerve Net, Neurons, Stochastic Processes
Abstract

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity-the density of active neurons per unit time-is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.

DOI10.1371/journal.pcbi.1005691
Alternate JournalPLoS Comput. Biol.
PubMed ID28787447
PubMed Central IDPMC5560761