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

Maryam Ghorbani1, Mayank Mehta1,2,3,4, Robijn Bruinsma1, and Alex J. Levine1,5

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

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

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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Outline

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Phys. Rev. E 85, 021908– Published 13 February, 2012
  • Received 7 July 2011

©2012 American Physical Society

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