The effects of quasi-active membrane on multiply periodic traveling waves in integrate-and-fire systems

Matthew James, Steve Coombes, and Paul Bressloff

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Submission date: 10. Sep. 2002
Pages: 17
published in: The European physical journal / C, 67 (2003) 5, art-no. 051905-1 - 051905-6 
DOI number (of the published article): 10.1103/PhysRevE.67.051905
Bibtex
with the following different title: Effects of quasiactive membrane on multiply periodic traveling waves in integrate-and-fire systems
PACS-Numbers: 87.19.La, 05.45.-a, 87.10.+e
Keywords and phrases: quasi-active dendrites, traveling waves, integrate-and-fire, kinematic
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Abstract:
We consider the dynamics of a one-dimensional continuum of synaptically-interacting integrate-and-fire neurons with realistic forms of axo-dendritic interaction. The speed and stability of traveling waves are investigated as a function of discrete communication delays, distributed synaptic delays and axo-dendritic delays arising from the spatially extended nature of the model neuron. In particular, dispersion curves for periodic traveling waves are constructed. Nonlinear ionic channels in the dendrite responsible for a so-called quasi-active bandpass response are shown to significantly influence the shape of dispersion curves. Moreover, a kinematic theory of spike train propagation suggests that period doubling bifurcations of a singly periodic wave can occur in dendritic systems with quasi-active membrane. The explicit construction of period doubled solutions is used to confirm this prediction.