

Preprint 87/2004
Time to first spike in stochastic Hodgkin-Huxley systems
Henry Tuckwell and Frederic Y. M. Wan
Contact the author: Please use for correspondence this email.
Submission date: 02. Dec. 2004
published in: Physica / A, 351 (2005) 2/4, p. 427-438
DOI number (of the published article): 10.1016/j.physa.2004.11.059
Bibtex
with the following different title: Time to first spike in Hodgkin-Huxley stochastic systems
Keywords and phrases: spiking neuron, stochastic model
Abstract:
The time to first spike is an experimentally
observed quantity in laboratory experiments. In the auditory, somatic and
visual sensory modalities,
the times of first spikes in the corresponding
cortical neurons have been implicated as coding much of the information
about
stimulus properties. We describe an analytical approach for determining
the
time to first spike from a given initial state which may be applied to a
general nonlinear stochastic model neuron.
We illustrate with a standard Hodgkin-Huxley model with a Gaussian white
noise input current
whose drift parameter is and whose variance parameter is
.
Partial differential equations (PDE's) of second order
are obtained for the first two moments of the
time taken for the depolarization to reach a threshold value from rest
state,
as functions of the initial values.
Simulation confirms that for small noise amplitudes a 2-component
model is reasonably accurate.
For small values of the noise parameter
, including the
deterministic case
, perturbation methods are used to find
the moments of the firing time and the results compare
favorably with those from simulation. The approach is accurate
for almost all
when
is above threshold for action
potentials in the absence of noise
and over a considerable range of values of
when
is as small
as 2.
The same methods may be applied to models similar to Hodgkin-Huxley
which involve channels for additional or different ionic currents.