Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements

TL;DR

This paper investigates how structural variability in random tree networks of strongly coupled excitable elements affects collective dynamics, using Hodgkin-Huxley models to relate tree structure to spike train statistics.

Contribution

It provides a statistical framework linking tree structure variability to network dynamics and derives an effective single-element model for strong coupling conditions.

Findings

Structural variability influences spike train statistics.

In strong coupling, network behavior can be approximated by an effective single element.

The joint distribution of leaves and nodes determines response variability.

Abstract

We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.