Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map

Document Type

Article

Publication Date

1-1-2007

Abstract

Out-of-phase bursting is a functionally important behavior displayed by central pattern generators and other neural circuits. Understanding this complex activity requires the knowledge of the interplay between the intrinsic cell properties and the properties of synaptic coupling between the cells. Here we describe a simple method that allows us to investigate the existence and stability of anti-phase bursting solutions in a network of two spiking neurons, each possessing a T-type calcium current and coupled by reciprocal inhibition. We derive a one-dimensional map which fully characterizes the genesis and regulation of anti-phase bursting arising from the interaction of the T-current properties with the properties of synaptic inhibition. This map is the burst length return map formed as the composition of two distinct one-dimensional maps that are each regulated by a different set of model parameters. Although each map is constructed using the properties of a single isolated model neuron, the composition of the two maps accurately captures the behavior of the full network. We analyze the parameter sensitivity of these maps to determine the influence of both the intrinsic cell properties and the synaptic properties on the burst length, and to find the conditions under which multistability of several bursting solutions is achieved. Although the derivation of the map relies on a number of simplifying assumptions, we discuss how the principle features of this dimensional reduction method could be extended to more realistic model networks. © Springer Science+Business Media, LLC 2007.

Identifier

34548231662 (Scopus)

Publication Title

Journal of Computational Neuroscience

External Full Text Location

https://doi.org/10.1007/s10827-007-0026-x

ISSN

09295313

PubMed ID

17440801

First Page

169

Last Page

187

Issue

2

Volume

23

Grant

0615168

Fund Ref

National Science Foundation

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