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

Aaditya Rangan, Gregor Kovačič, David Cai

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number041915
JournalPhysical Review E
Volume77
Issue number4
DOIs
StatePublished - Apr 18 2008

Fingerprint

Neuronal Network
Kinetic Theory
Conductance
kinetic theory
Spike
Ludwig Boltzmann
spikes
Neuron
neurons
Moment Equations
fire point
Kinetic Equation
Probability density function
moments
Activation
Kinetics
Integrate
Entropy
kinetics
Moment

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train. / Rangan, Aaditya; Kovačič, Gregor; Cai, David.

In: Physical Review E, Vol. 77, No. 4, 041915, 18.04.2008.

Research output: Contribution to journalArticle

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