How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

B. Cessac, H. Rostro, J. C. Vasquez, T. Viéville

Research output: Indexed journal article Articlepeer-review

10 Citations (Scopus)

Abstract

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks? and; (ii) what are the effects of synaptic plasticity on these statistics? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.

Original languageEnglish
Pages (from-to)565-602
Number of pages38
JournalJournal of Statistical Physics
Volume136
Issue number3
DOIs
Publication statusPublished - Aug 2009
Externally publishedYes

Keywords

  • Gibbs distributions
  • Neurons dynamics
  • Spike coding
  • Statistical physics
  • Thermodynamic formalism

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