Mean-field equations for neuronal networks with arbitrary degree distributions

Physical Review. E
D Q NykampAlex Roxin

Abstract

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER ne...Continue Reading

References

Jan 1, 1972·Biophysical Journal·H R Wilson, J D Cowan
Apr 25, 1995·Proceedings of the National Academy of Sciences of the United States of America·R Ben-YishaiH Sompolinsky
Sep 1, 1997·Cerebral Cortex·H Markram
Jan 28, 2005·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Pengcheng Song, Xiao-Jing Wang
Mar 2, 2005·PLoS Biology·Sen SongDmitri B Chklovskii
Aug 11, 2005·Physical Review Letters·Alex RoxinDavid Hansel
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan G RestrepoBrian R Hunt
Dec 17, 2009·Frontiers in Neuroscience·Dan F M Goodman, Romain Brette
Mar 9, 2011·Proceedings of the National Academy of Sciences of the United States of America·Rodrigo PerinHenry Markram
Jul 23, 2011·Frontiers in Computational Neuroscience·Liqiong ZhaoDuane Q Nykamp
Nov 11, 2011·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Alex RoxinCarl van Vreeswijk
Apr 6, 2012·PLoS Computational Biology·Gustavo Deco, Etienne Hugues
Sep 25, 2012·Nature Neuroscience·Ashok Litwin-Kumar, Brent Doiron
Mar 18, 2016·Physical Review. E·Johnatan AljadeffTatyana O Sharpee

❮ Previous
Next ❯

Citations

Mar 4, 2020·Biological cybernetics·Carlo R Laing, Christian Bläsche
Oct 3, 2019·Physical Review. E·Marina Vegué, Alex Roxin
Feb 25, 2021·Scientific Reports·Giuseppe GiacopelliMichele Migliore
Mar 2, 2021·Frontiers in Systems Neuroscience·Carlo R LaingShawn Means
Jul 19, 2019·Current Opinion in Neurobiology·Carina Curto, Katherine Morrison
Jun 18, 2021·Physical Review. E·Carlo R Laing

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Frontiers in Computational Neuroscience
Volker PerniceStefan Rotter
Sheng li xue bao : [Acta physiologica Sinica]
David Cai, Louis Tao
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Volker PerniceStefan Rotter
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M Bayati, A Valizadeh
© 2022 Meta ULC. All rights reserved