Macroscopic description for networks of spiking neurons
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- dc.contributor.author Montbrió, Ernest, 1974-ca
- dc.contributor.author Pazó, Diegoca
- dc.contributor.author Roxin, Alexca
- dc.date.accessioned 2016-05-18T14:57:04Z
- dc.date.available 2016-05-18T14:57:04Z
- dc.date.issued 2015
- dc.description.abstract A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here, we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network, including states of synchronous spiking activity. Finally, we show that the firing-rate description is related, via a conformal map, to a low-dimensional description in terms of the Kuramoto order parameter, called Ott-Antonsen theory. We anticipate that our results will be an important tool in investigating how large networks of spiking neurons self-organize in time to process and encode information in the brain.en
- dc.description.sponsorship D. P. and A. R. acknowledge support by MINECO (Spain) under the Ramón y Cajal program. E. M. and A. R. acknowledge support from a grants from the Spanish Ministry of Economics and Competitiveness PSI2013-42091 and BFU2012-33413.en
- dc.format.mimetype application/pdfca
- dc.identifier.citation Montbrio E, Pazo D, Roxin A. Macroscopic description for networks of spiking neurons. Phys Rev X. 2015;5(2):021028. doi: 10.1103/PhysRevX.5.021028en
- dc.identifier.doi http://dx.doi.org/10.1103/PhysRevX.5.021028
- dc.identifier.issn 2160-3308
- dc.identifier.uri http://hdl.handle.net/10230/26296
- dc.language.iso engen
- dc.publisher American Physical Societyen
- dc.relation.ispartof Physical Review X. 2015;5(2):021028en
- dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/PSI2013-42091
- dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/BFU2012-33413
- dc.rights Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.en
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by/3.0/
- dc.subject.keyword Biological physicsen
- dc.subject.keyword Interdisciplinary physicsen
- dc.subject.keyword Nonlinear dynamicsen
- dc.title Macroscopic description for networks of spiking neuronsen
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion