Skip to main content

Some NLM-NCBI services and products are experiencing heavy traffic, which may affect performance and availability. We apologize for the inconvenience and appreciate your patience. For assistance, please contact our Help Desk at info@ncbi.nlm.nih.gov.

Biophysical Journal logoLink to Biophysical Journal
. 1997 May;72(5):2068–2074. doi: 10.1016/S0006-3495(97)78850-7

Stochastic versions of the Hodgkin-Huxley equations.

R F Fox 1
PMCID: PMC1184401  PMID: 9129809

Abstract

A Hodgkin-Huxley model algorithm for the numerical simulation of noise in neurons is contracted from a master equation description (cellular automoton) into a Langevin description. This reduction reduces the time required for a simulation by about two orders of magnitude. Earlier work is summarized, condensed, and made explicit to make the algorithm transparent and facilitate applications. Two approximate treatments are reported. An extension of this approach is presented that includes spatial dependence and the propagation of a noisy action potential along an axon.

Full text

PDF
2068

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bertram R., Sherman A., Stanley E. F. Single-domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol. 1996 May;75(5):1919–1931. doi: 10.1152/jn.1996.75.5.1919. [DOI] [PubMed] [Google Scholar]
  2. Chow C. C., White J. A. Spontaneous action potentials due to channel fluctuations. Biophys J. 1996 Dec;71(6):3013–3021. doi: 10.1016/S0006-3495(96)79494-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Collins J. J., Chow C. C., Imhoff T. T. Stochastic resonance without tuning. Nature. 1995 Jul 20;376(6537):236–238. doi: 10.1038/376236a0. [DOI] [PubMed] [Google Scholar]
  4. Collins JJ, Chow CC, Imhoff TT. Aperiodic stochastic resonance in excitable systems. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1995 Oct;52(4):R3321–R3324. doi: 10.1103/physreve.52.r3321. [DOI] [PubMed] [Google Scholar]
  5. Fox RF, Lu Yn. Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Apr;49(4):3421–3431. doi: 10.1103/physreve.49.3421. [DOI] [PubMed] [Google Scholar]
  6. Fox RF. Second-order algorithm for the numerical integration of colored-noise problems. Phys Rev A. 1991 Mar 15;43(6):2649–2654. doi: 10.1103/physreva.43.2649. [DOI] [PubMed] [Google Scholar]
  7. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Lecar H., Nossal R. Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing. Biophys J. 1971 Dec;11(12):1048–1067. doi: 10.1016/S0006-3495(71)86277-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Lecar H., Nossal R. Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. Biophys J. 1971 Dec;11(12):1068–1084. doi: 10.1016/S0006-3495(71)86278-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Mannella R, Palleschi V., V Fast and precise algorithm for computer simulation of stochastic differential equations. Phys Rev A Gen Phys. 1989 Sep 15;40(6):3381–3386. doi: 10.1103/physreva.40.3381. [DOI] [PubMed] [Google Scholar]
  11. Neher E., Sakmann B. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature. 1976 Apr 29;260(5554):799–802. doi: 10.1038/260799a0. [DOI] [PubMed] [Google Scholar]
  12. Rubinstein J. T. Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophys J. 1995 Mar;68(3):779–785. doi: 10.1016/S0006-3495(95)80252-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Skaugen E., Walløe L. Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol Scand. 1979 Dec;107(4):343–363. doi: 10.1111/j.1748-1716.1979.tb06486.x. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES