Reliability of signal transmission in stochastic nerve axon equations.

Abstract:

:We introduce a method for computing probabilities for spontaneous activity and propagation failure of the action potential in spatially extended, conductance-based neuronal models subject to noise, based on statistical properties of the membrane potential. We compare different estimators with respect to the quality of detection, computational costs and robustness and propose the integral of the membrane potential along the axon as an appropriate estimator to detect both spontaneous activity and propagation failure. Performing a model reduction we achieve a simplified analytical expression based on the linearization at the resting potential (resp. the traveling action potential). This allows to approximate the probabilities for spontaneous activity and propagation failure in terms of (classical) hitting probabilities of one-dimensional linear stochastic differential equations. The quality of the approximation with respect to the noise amplitude is discussed and illustrated with numerical results for the spatially extended Hodgkin-Huxley equations. Python simulation code is supplied on GitHub under the link https://github.com/deristnochda/Hodgkin-Huxley-SPDE.

journal_name

J Comput Neurosci

authors

Sauer M,Stannat W

doi

10.1007/s10827-015-0586-0

subject

Has Abstract

pub_date

2016-02-01 00:00:00

pages

103-11

issue

1

eissn

0929-5313

issn

1573-6873

pii

10.1007/s10827-015-0586-0

journal_volume

40

pub_type

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