

Preprint 32/2006
Computation of spiking activity for a stochastic spatial neuron model: effects of spatial distribution of input on bimodality and CV of the ISI distribution
Henry Tuckwell
Contact the author: Please use for correspondence this email.
Submission date: 24. Mar. 2006 (revised version: September 2006)
published in: Mathematical biosciences, 207 (2007) 2, p. 246-260
DOI number (of the published article): 10.1016/j.mbs.2006.08.021
Bibtex
Keywords and phrases: Stochastic neuron, Spatial Model, Balanced input
Abstract:
We obtain computational results for a new
extended spatial neuron model in which the
neuronal electrical depolarization from resting level satisfies
a cable partial differential equation and the
synaptic input current is also a function
of space and time, obeying a first order linear partial
differential equation driven by a two-parameter random process.
The model is first described explicitly with the inclusion of all biophysical parameters. Simplified
equations are obtained with dimensionless space and time variables.
A standard parameter set is described, based mainly on values appropriate
for cortical pyramidal cells. When the noise is small and the mean
voltage crosses threshold, a formula is derived
for the expected time to spike. A simulation algorithm, involving one-dimensional
random processes is given and used to obtain moments and distributions
of the interspike interval (ISI). The parameters used are those for a near balanced state and there is great sensitivity of the firing rate around the balance point. This sensitivity may be related to genetically
induced pathological brain properties (Rett's syndrome). The simulation procedure is employed to find the
ISI distribution for some simple patterns of synaptic input with various
relative strengths for excitation and inhibition. With excitation only, the ISI distribution is unimodal of exponential type and with a large coefficient
of variation. As inhibition near the soma grows, two striking effects emerge.
The ISI distribution shifts first to bimodal and then to unimodal with an approximately Gaussian shape with a concentration at large intervals. At the same time the coefficient of variation of the ISI drops dramatically to less than 1/5 of its value without inhibition.