Statistical Physics approach to dendritic computation: The excitable-wave mean-field approximation

TL;DR

This paper introduces an excitable-wave mean-field approximation to better understand how active dendritic trees in neurons process stimuli, improving predictions of their input-output behavior and aligning well with simulations.

Contribution

The paper presents a novel excitable-wave mean-field approach that accurately models dendritic computation, surpassing previous approximations and incorporating finite-size effects.

Findings

The new approximation aligns with simulation results.

Active dendrites enhance neural dynamic range.

Finite-size effects are significant in dendritic processing.

Abstract

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a non-equilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5(6) e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.