Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

Journal of Mathematical Biology
Daniele Avitable, Kyle C A Wedgwood

Abstract

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. S...Continue Reading

Citations

Oct 1, 1979·Biological cybernetics·G B Ermentrout, J D Cowan
Jan 1, 1975·Biological cybernetics·S Amari
Feb 1, 1989·Journal of Neurophysiology·S FunahashiP S Goldman-Rakic
Jan 1, 1972·Biophysical Journal·H R Wilson, J D Cowan
Mar 1, 1995·Neuron·P S Goldman-Rakic
Sep 1, 1995·Cerebral Cortex·C L ColbyM E Goldberg
Nov 11, 1999·Proceedings of the National Academy of Sciences of the United States of America·D Golomb, G B Ermentrout
May 8, 2000·Journal of Computational Neuroscience·A OmurtagL Sirovich
Sep 20, 2001·Biological cybernetics·H Werner, T Richter
May 8, 2004·Proceedings of the National Academy of Sciences of the United States of America·David CaiDavid W McLaughlin
Aug 6, 2004·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Marcello MassiminiGiulio Tononi
Dec 31, 2005·Physical Review Letters·S E Folias, P C Bressloff
Mar 3, 2006·Journal of Computational Neuroscience·C R Laing
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C A Brackley, M S Turner
Feb 23, 2008·Proceedings of the National Academy of Sciences of the United States of America·Eugene M Izhikevich, Gerald M Edelman
Mar 4, 2009·Frontiers in Computational Neuroscience·Olivier FaugerasBruno Cessac
Apr 2, 2009·Annual Review of Physical Chemistry·Ioannis G Kevrekidis, Giovanni Samaey
Feb 26, 2010·Journal of Computational Neuroscience·C R LaingIoannis G Kevrekidis
May 18, 2010·European Neuropsychopharmacology : the Journal of the European College of Neuropsychopharmacology·Martijn P van den Heuvel, Hilleke E Hulshoff Pol
Dec 9, 2010·Biological cybernetics·Thomas M WasylenkoIoannis G Kevrekidis
Jun 5, 2012·Journal of Mathematical Neuroscience·Javier BaladronJonathan Touboul
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pulin Gong, Peter A Robinson
Apr 17, 2013·Physiological Reviews·Björn Rasch, Jan Born
Oct 19, 2013·Nature Reviews. Neuroscience·Gaute T EinevollStefano Panzeri
Mar 25, 2014·Current Opinion in Neurobiology·Adrienne Fairhall, Haim Sompolinsky
Apr 20, 2014·Journal of Mathematical Neuroscience·Christian Kuehn, Martin G Riedler
Jul 11, 2015·Nature Reviews. Neuroscience·Rafael Yuste
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yang Qi, Pulin Gong
Oct 10, 2015·Cell·Henry MarkramFelix Schürmann
Nov 19, 2015·Biological cybernetics·C R Laing, Ioannis G Kevrekidis

Related Concepts

In Silico
Biological Neural Networks
Stochastic Processes
Patterns
Anatomic Bifurcation
Operator of Medical Device
Profile (Lab Procedure)
Neural Network Simulation
Synapses
Protein Domain

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.

Sexual Dimorphism in Neurodegeneration

There exist sex differences in neurodevelopmental and neurodegenerative disorders. For instance, multiple sclerosis is more common in women, whereas Parkinson’s disease is more common in men. Here is the latest research on sexual dimorphism in neurodegeneration

HLA Genetic Variation

HLA genetic variation has been found to confer risk for a wide variety of diseases. Identifying these associations and understanding their molecular mechanisms is ongoing and holds promise for the development of therapeutics. Find the latest research on HLA genetic variation here.

Super-resolution Microscopy

Super-resolution microscopy is the term commonly given to fluorescence microscopy techniques with resolutions that are not limited by the diffraction of light. Here are the latest discoveries pertaining to super-resolution microscopy.

Genetic Screens in iPSC-derived Brain Cells

Genetic screening is a critical tool that can be employed to define and understand gene function and interaction. This feed focuses on genetic screens conducted using induced pluripotent stem cell (iPSC)-derived brain cells.

Brain Lower Grade Glioma

Low grade gliomas in the brain form from oligodendrocytes and astrocytes and are the slowest-growing glioma in adults. Discover the latest research on these brain tumors here.

CD4/CD8 Signaling

Cluster of differentiation 4 and 8 (CD8 and CD8) are glycoproteins founds on the surface of immune cells. Here is the latest research on their role in cell signaling pathways.

Alignment-free Sequence Analysis Tools

Alignment-free sequence analyses have been applied to problems ranging from whole-genome phylogeny to the classification of protein families, identification of horizontally transferred genes, and detection of recombined sequences. Here is the latest research.

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.

Related Papers

Mathematical Biosciences
Stefania ScarsoglioLuca Ridolfi
Journal of Mathematical Biology
F SpillH M Byrne
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Stephen Coombes, C R Laing
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Xinzhong ChenHongling Rao
© 2020 Meta ULC. All rights reserved