Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

TL;DR

This paper provides a comprehensive resource for modeling rhythmic neural circuits, detailing cellular and synaptic dynamics, analyzing bifurcations, introducing a new synapse model, and examining two fundamental rhythm-generating networks.

Contribution

It introduces a detailed analysis of cellular and synaptic models, including a new logistic synapse model, and elucidates principles underlying basic rhythm-generating neural networks.

Findings

Characterization of cell and synapse models for neural circuits

Introduction of a logistic model for slow synapses

Analysis of hysteresis in rhythm-generating networks

Abstract

The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in iii) two canonical pair-wise rhythm-generating networks. We document the properties of basic network components: cell models and synaptic models, which are prerequisites for proper network assembly. Using the slow-fast decomposition we present a detailed analysis of the cellular dynamics including a discussion of the most relevant bifurcations. Several approaches to model synaptic coupling are also discussed, and a new logistic model of slow synapses is introduced. Finally, we describe and examine two types of bicellular rhythm-generating networks: i) half-center oscillators ii) excitatory-inhibitory pairs and elucidate a key principle -- the network hysteresis underlying the stable onset of emergent slow bursting in these neural building blocks. These two cell networks are a basis for more complicated neural circuits of rhythmogensis and feature in our models of swim central pattern generators.