Nonlinear-dynamics theory of up-down transitions in neocortical neural networks

Maryam Ghorbani, Mayank Mehta, Robijn Bruinsma, and Alex J. Levine

Phys. Rev. E 85, 021908 – Published 13 February 2012

Abstract

The neurons of the neocortex show ∼1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.

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Received 7 July 2011

DOI:https://doi.org/10.1103/PhysRevE.85.021908

Authors & Affiliations

Maryam Ghorbani¹, Mayank Mehta^1,2,3,4, Robijn Bruinsma¹, and Alex J. Levine^1,5

¹Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California 90095-1547, USA
²Department of Neurology, Department of Neurobiology, University of California, Los Angeles, Los Angeles, California 90095-1547, USA
³Integrative Center for Learning and Memory, University of California, Los Angeles, Los Angeles, California 90095-1547, USA
⁴Keck Center for Neurophysics, University of California, Los Angeles, Los Angeles, California 90095-1547, USA
⁵Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90095-1547, USA

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Vol. 85, Iss. 2 — February 2012

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics