Energy analysis of bursting Hindmarsh-Rose neurons with time-delayed coupling

TL;DR

This study investigates the energy requirements of coupled Hindmarsh-Rose neurons with time delays, revealing how electrical and chemical synapses differently influence energy consumption and synaptic contribution.

Contribution

It provides the first energy-based analysis of delayed coupled neurons, highlighting the distinct effects of electrical and chemical synapses on energy dynamics.

Findings

Electrical coupling delay reduces synaptic energy contribution.

Chemical coupling delay increases average synaptic energy contribution.

Certain coupling strengths invert the importance of instantaneous versus delayed synaptic effects.

Abstract

Mathematical modeling is an important tool to study the role of delay in neural systems and to evaluate its effects on the signaling activity of coupled neurons. Models for delayed neurons are often used to represent the dynamics of real neurons, but rarely to assess the energy required to maintain these dynamics. In this work, we address these questions from an energy perspective by considering a pair of Hindmarsh-Rose burst neurons coupled by reciprocal time-delayed coupling with electrical and chemical synapses. We examine the average energy consumption required to maintain cooperative behavior and quantify the contribution of synapses to total energy consumption. We show that unlike electrical coupling, where the time delay appears to reduce the instantaneous average relative weight of the synaptic contribution, in chemical coupling this average synaptic contribution appears to be much higher in delayed coupling than in instantaneous coupling, except at certain values of coupling strength where the instantaneous synaptic contribution is more important.