From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves

In the vertebrate brain excitatory synaptic contacts typically occur on the tiny evaginations of neuron dendritic surface known as dendritic spines. T here 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 sign ificance of a spine with an excitable membrane. The spike-diffuse-spike (SD S) model is one such model that admits to a relatively straightforward math ematical analysis. In this paper we demonstrate that not only can the SDS m odel support solitary travelling pulses, already observed numerically in mo re detailed biophysical models, but that it has periodic travelling wave so lutions. The exact mathematical treatment of periodic travelling waves in t he SDS model is used, within a kinematic framework, to predict the existenc e 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 t herefore be used for the robust encoding of information. (C) 2001 Elsevier Science Inc. All rights reserved.