Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map |
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Authors: | Victor Matveev Amitabha Bose Farzan Nadim |
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Institution: | (1) Department of Mathematical Sciences, New Jersey Institute of Technology, Cullimore Hall, University Heights, Newark, NJ 07102-1982, USA;(2) Department of Biological Sciences, Rutgers University, Newark, NJ 07102, USA |
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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.
Action Editor: John Rinzel |
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Keywords: | Half-center bursting T-type calcium current Poincaré return map Multistability Dimensional reduction |
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