Macroscopic description for networks of spiking neurons
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 formu...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/26296 |
| Acceso en línea: | http://hdl.handle.net/10230/26296 http://dx.doi.org/10.1103/PhysRevX.5.021028 |
| Access Level: | acceso abierto |
| Palabra clave: | Biological physics Interdisciplinary physics Nonlinear dynamics |
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Macroscopic description for networks of spiking neuronsMontbrió, Ernest, 1974-Pazó, DiegoRoxin, AlexBiological physicsInterdisciplinary physicsNonlinear dynamicsA 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.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.American Physical Society201620162015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/26296http://dx.doi.org/10.1103/PhysRevX.5.021028reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésPhysical Review X. 2015;5(2):021028info:eu-repo/grantAgreement/ES/1PE/PSI2013-42091info:eu-repo/grantAgreement/ES/3PN/BFU2012-33413Published 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.http://creativecommons.org/licenses/by/3.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/262962026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Macroscopic description for networks of spiking neurons |
| title |
Macroscopic description for networks of spiking neurons |
| spellingShingle |
Macroscopic description for networks of spiking neurons Montbrió, Ernest, 1974- Biological physics Interdisciplinary physics Nonlinear dynamics |
| title_short |
Macroscopic description for networks of spiking neurons |
| title_full |
Macroscopic description for networks of spiking neurons |
| title_fullStr |
Macroscopic description for networks of spiking neurons |
| title_full_unstemmed |
Macroscopic description for networks of spiking neurons |
| title_sort |
Macroscopic description for networks of spiking neurons |
| dc.creator.none.fl_str_mv |
Montbrió, Ernest, 1974- Pazó, Diego Roxin, Alex |
| author |
Montbrió, Ernest, 1974- |
| author_facet |
Montbrió, Ernest, 1974- Pazó, Diego Roxin, Alex |
| author_role |
author |
| author2 |
Pazó, Diego Roxin, Alex |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Biological physics Interdisciplinary physics Nonlinear dynamics |
| topic |
Biological physics Interdisciplinary physics Nonlinear dynamics |
| description |
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. |
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2015 |
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2015 2016 2016 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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http://hdl.handle.net/10230/26296 http://dx.doi.org/10.1103/PhysRevX.5.021028 |
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http://hdl.handle.net/10230/26296 http://dx.doi.org/10.1103/PhysRevX.5.021028 |
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Inglés |
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Inglés |
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Physical Review X. 2015;5(2):021028 info:eu-repo/grantAgreement/ES/1PE/PSI2013-42091 info:eu-repo/grantAgreement/ES/3PN/BFU2012-33413 |
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http://creativecommons.org/licenses/by/3.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/3.0/ |
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openAccess |
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application/pdf application/pdf |
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American Physical Society |
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American Physical Society |
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