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Reliability of signal transmission in stochastic nerve axon equations

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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.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17, Juni 136, 10623, Berlin, Germany

    Martin Sauer & Wilhelm Stannat

  2. Bernstein Center for Computational Neuroscience, Philippstr. 13, 10115, Berlin, Germany

    Martin Sauer & Wilhelm Stannat

Authors
  1. Martin Sauer
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  2. Wilhelm Stannat
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Correspondence to Wilhelm Stannat.

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The authors declare that they have no conflict of interest.

Additional information

Action Editor: Brent Doiron

This work is supported by the BMBF, FKZ 01GQ1001B

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Sauer, M., Stannat, W. Reliability of signal transmission in stochastic nerve axon equations. J Comput Neurosci 40, 103–111 (2016). https://doi.org/10.1007/s10827-015-0586-0

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  • DOI: https://doi.org/10.1007/s10827-015-0586-0

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