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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/772

Title: From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves
Authors: Coombes, S.
Keywords: dendritic spines
travelling waves
mathematical biology
Issue Date: 2000
Abstract: In the vertebrate brain excitatory synaptic contacts typically occur on the tiny evaginations of neuron dendritic surface known as dendritic spines. There is clear evidence that spine heads are endowed with voltage dependent excitable channels and that action potentials invade spines. Computational models are being increasingly used to gain insight into the functional significance for a spine with excitable membrane. The spike-diffuse-spike (SDS) model is one such model that admits to a relatively straightforward mathematical analysis. In this paper we demonstrate that not only can the SDS model support solitary travelling pulses, already observed numerically in more detailed biophysical models, but that it has periodic travelling wave solutions. The exact mathematical treatment of periodic travelling waves in the SDS model is used, within a kinematic framework, to predict the existence of connections between two periodic spike trains of different interspike interval. The associated wave front in the sequence of interspike intervals travels with a constant velocity without degradation of shape, and might therefore be used for robust encoding of information.
Description: This is a pre-print. The definitive version: COOMBES, S., 2001. From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves. Mathematical Biosciences, 170(2), pp. 155-172.
URI: https://dspace.lboro.ac.uk/2134/772
Appears in Collections:Pre-prints (Maths)

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