Bifurcations of Emergent Bursting in a Neuronal Network

TL;DR

This paper introduces a mathematical approach to simplify complex neuronal networks, revealing mechanisms of emergent bursting that are consistent across different biological systems.

Contribution

It presents a method to reduce complex neuronal models to simpler forms while preserving key features, enabling better understanding of bursting phenomena.

Findings

Emergent bursting can be explained by reduced two-variable models.

Mechanisms for bursting are similar across different biological systems.

The approach uncovers multi-scale spike dynamics at membrane and firing rate levels.

Abstract

Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex neuronal network so that we can fully understand the underlying mechanism. Using an oxytocin network developed earlier as an example, we show how we can reduce a complex model with many variables to a tractable model with two variables, while retaining all key qualitative features of the model. The approach enables us to uncover how emergent synchronous bursting could arise from a neuronal network which embodies all known biological features. Surprisingly, the discovered mechanisms for bursting are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multi-time scale spikes: at the membrane potential level and the firing rate level.