Physics of the extended neuron
File(s)
Accepted version
Author(s)
Bressloff, PC
Coombes, S
Type
Journal Article
Abstract
We review recent work concerning the effects of dendritic structure on single neuron response and the dynamics of neural populations. We highlight a number of concepts and techniques from physics useful in studying the behaviour of the spatially extended neuron. First we show how the single neuron Green's function, which incorporates details concerning the geometry of the dendritic tree, can be determined using the theory of random walks. We then exploit the formal analogy between a neuron with dendritic structure and the tight-binding model of excitations on a disordered lattice to analyse various Dyson-like equations arising from the modelling of synaptic inputs and random synaptic background activity. Finally, we formulate the dynamics of interacting populations of spatially extended neurons in terms of a set of Volterra integro-differential equations whose kernels are the single neuron Green's functions. Linear stability analysis and bifurcation theory are then used to investigate two particular aspects of population dynamics (i) pattern formation in a strongly coupled network of analog neurons and (ii) phase-synchronization in a weakly coupled network of integrate-and-fire neurons.
Date Issued
1997-08-10
Date Acceptance
1997-08-01
Citation
International Journal of Modern Physics B, 1997, 11 (20), pp.2343-2392
ISSN
0217-9792
Publisher
World Scientific Publishing
Start Page
2343
End Page
2392
Journal / Book Title
International Journal of Modern Physics B
Volume
11
Issue
20
Copyright Statement
© 2024 World Scientific Publishing Co Pte Ltd Bressloff, Paul C., and Stephen Coombes. "Physics of the extended neuron." International Journal of Modern Physics B 11.20 (1997): 2343-2392.
Identifier
http://dx.doi.org/10.1142/s0217979297001209
Publication Status
Published
Date Publish Online
2012-01-25