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Regimes and mechanisms of transient amplification in abstract and biological neural networks
Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conc...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9377633/ https://www.ncbi.nlm.nih.gov/pubmed/35969604 http://dx.doi.org/10.1371/journal.pcbi.1010365 |
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author | Christodoulou, Georgia Vogels, Tim P. Agnes, Everton J. |
author_facet | Christodoulou, Georgia Vogels, Tim P. Agnes, Everton J. |
author_sort | Christodoulou, Georgia |
collection | PubMed |
description | Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes. |
format | Online Article Text |
id | pubmed-9377633 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-93776332022-08-16 Regimes and mechanisms of transient amplification in abstract and biological neural networks Christodoulou, Georgia Vogels, Tim P. Agnes, Everton J. PLoS Comput Biol Research Article Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes. Public Library of Science 2022-08-15 /pmc/articles/PMC9377633/ /pubmed/35969604 http://dx.doi.org/10.1371/journal.pcbi.1010365 Text en © 2022 Christodoulou et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://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 Christodoulou, Georgia Vogels, Tim P. Agnes, Everton J. Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title | Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title_full | Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title_fullStr | Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title_full_unstemmed | Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title_short | Regimes and mechanisms of transient amplification in abstract and biological neural networks |
title_sort | regimes and mechanisms of transient amplification in abstract and biological neural networks |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9377633/ https://www.ncbi.nlm.nih.gov/pubmed/35969604 http://dx.doi.org/10.1371/journal.pcbi.1010365 |
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