Physics of the Extended Neuron
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.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Aug 2001.