Dynamical phase separation on rhythmogenic neuronal networks

Physical Review. E
Mihai BibireataAlex J. Levine

Abstract

We explore the firing-rate model of excitatory neurons with dendritic adaptation (the Feldman-Del Negro model [J. L. Feldman and C. A. Del Negro, Nat. Rev. Neurosci. 7, 232 (2006)10.1038/nrn1871; D. J. Schwab et al., Phys. Rev. E 82, 051911 (2010)10.1103/PhysRevE.82.051911] interacting on a fixed, directed Erdős-Rényi network. This model is applied to the dynamics of the pre-Bötzinger complex, the mammalian central pattern generator with N∼10^{3} neurons, which produces a collective metronomic signal that times inspiration. In the all-to-all coupled variant of the model, there is spontaneous symmetry breaking in which some fraction of the neurons becomes stuck in a high-firing-rate state, while others become quiescent. This separation into firing and nonfiring clusters persists into more sparsely connected networks. In these sparser networks, the clustering is influenced by k cores of the underlying network. The model has a number of features of the dynamical phase diagram that violate the predictions of mean-field analysis. In particular, we observe in the simulated networks that stable oscillations do not persist in the high-sensitivity limit, in contradiction to the predictions of mean-field theory. Moreover, we observe that...Continue Reading

References

Jul 31, 1995·Physical Review Letters·T Mizuguchi, M Sano
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H Sakaguchi
Jun 14, 2002·Neuron·Christopher A Del NegroJack L Feldman
Jan 15, 2003·BMC Bioinformatics·Gary D Bader, Christopher W V Hogue
Feb 21, 2006·Physical Review Letters·S N DorogovtsevJ F F Mendes
Feb 24, 2006·Nature Reviews. Neuroscience·Jack L Feldman, Christopher A Del Negro
Jul 19, 2008·The Journal of Physiology·Consuelo Morgado-ValleJack L Feldman
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David J SchwabAlex J Levine
Sep 24, 2016·Physical Review Letters·Takashi Nishikawa, Adilson E Motter
May 6, 2019·Neuroscience·Francesca Arese LuciniHernán A Makse

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