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Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays
Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distributio...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6799936/ https://www.ncbi.nlm.nih.gov/pubmed/31593569 http://dx.doi.org/10.1371/journal.pcbi.1007404 |
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author | Mattia, Maurizio Biggio, Matteo Galluzzi, Andrea Storace, Marco |
author_facet | Mattia, Maurizio Biggio, Matteo Galluzzi, Andrea Storace, Marco |
author_sort | Mattia, Maurizio |
collection | PubMed |
description | Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity. |
format | Online Article Text |
id | pubmed-6799936 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-67999362019-10-25 Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays Mattia, Maurizio Biggio, Matteo Galluzzi, Andrea Storace, Marco PLoS Comput Biol Research Article Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity. Public Library of Science 2019-10-08 /pmc/articles/PMC6799936/ /pubmed/31593569 http://dx.doi.org/10.1371/journal.pcbi.1007404 Text en © 2019 Mattia 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 Mattia, Maurizio Biggio, Matteo Galluzzi, Andrea Storace, Marco Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title | Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title_full | Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title_fullStr | Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title_full_unstemmed | Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title_short | Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays |
title_sort | dimensional reduction in networks of non-markovian spiking neurons: equivalence of synaptic filtering and heterogeneous propagation delays |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6799936/ https://www.ncbi.nlm.nih.gov/pubmed/31593569 http://dx.doi.org/10.1371/journal.pcbi.1007404 |
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