Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train

Aaditya V. Rangan, Gregor Kovačič, and David Cai
Phys. Rev. E 77, 041915 – Published 18 April 2008

Abstract

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1)-dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.

  • Figure
  • Received 23 August 2007

DOI:https://doi.org/10.1103/PhysRevE.77.041915

©2008 American Physical Society

Authors & Affiliations

Aaditya V. Rangan1, Gregor Kovačič2, and David Cai1

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1185, USA
  • 2Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA

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Issue

Vol. 77, Iss. 4 — April 2008

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