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

TL;DR

This paper demonstrates that Gibbs distributions naturally describe spike train statistics in neuronal networks and arise from slow synaptic plasticity, using a thermodynamic formalism approach.

Contribution

It introduces a framework linking spike train statistics to Gibbs distributions and explains their emergence from slow synaptic adaptation mechanisms.

Findings

Gibbs distributions effectively characterize spike train statistics.

Slow synaptic plasticity leads to Gibbs distribution emergence.

The framework applies to generalized integrate-and-fire models.

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.