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Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized u...

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Autores principales: Augustin, Moritz, Ladenbauer, Josef, Baumann, Fabian, Obermayer, Klaus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5507472/
https://www.ncbi.nlm.nih.gov/pubmed/28644841
http://dx.doi.org/10.1371/journal.pcbi.1005545
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author Augustin, Moritz
Ladenbauer, Josef
Baumann, Fabian
Obermayer, Klaus
author_facet Augustin, Moritz
Ladenbauer, Josef
Baumann, Fabian
Obermayer, Klaus
author_sort Augustin, Moritz
collection PubMed
description The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.
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spelling pubmed-55074722017-07-25 Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation Augustin, Moritz Ladenbauer, Josef Baumann, Fabian Obermayer, Klaus PLoS Comput Biol Research Article The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models. Public Library of Science 2017-06-23 /pmc/articles/PMC5507472/ /pubmed/28644841 http://dx.doi.org/10.1371/journal.pcbi.1005545 Text en © 2017 Augustin et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Augustin, Moritz
Ladenbauer, Josef
Baumann, Fabian
Obermayer, Klaus
Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title_full Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title_fullStr Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title_full_unstemmed Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title_short Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
title_sort low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: comparison and implementation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5507472/
https://www.ncbi.nlm.nih.gov/pubmed/28644841
http://dx.doi.org/10.1371/journal.pcbi.1005545
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