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Biophys J. Dec 1996; 71(6): 3013–3021.
PMCID: PMC1233790

Spontaneous action potentials due to channel fluctuations.


A theoretical and numerical analysis of the Hodgkin-Huxley equations with the inclusion of stochastic channel dynamics is presented. It is shown that the system can be approximated by a one-dimensional bistable Langevin equation. Spontaneous action potentials can arise from the channel fluctuations and are analogous to escape by a particle over a potential barrier. The mean firing rate can be calculated using Kramers' classic result for barrier escape. The probability density function of the interspike intervals can also be estimated. The analytical results compare favorably with numerical simulations of the complete stochastic system.

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Selected References

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  • Conti F, Wanke E. Channel noise in nerve membranes and lipid bilayers. Q Rev Biophys. 1975 Nov;8(4):451–506. [PubMed]
  • 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. [PubMed]
  • Hines M. A program for simulation of nerve equations with branching geometries. Int J Biomed Comput. 1989 Mar;24(1):55–68. [PubMed]
  • HODGKIN AL, HUXLEY AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. [PMC free article] [PubMed]
  • Ito H, Ono K, Noma A. Background conductance attributable to spontaneous opening of muscarinic K+ channels in rabbit sino-atrial node cells. J Physiol. 1994 Apr 1;476(1):55–68. [PMC free article] [PubMed]
  • 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. [PMC free article] [PubMed]
  • Rubinstein JT. Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophys J. 1995 Mar;68(3):779–785. [PMC free article] [PubMed]
  • Sigworth FJ. The variance of sodium current fluctuations at the node of Ranvier. J Physiol. 1980 Oct;307:97–129. [PMC free article] [PubMed]
  • 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. [PubMed]

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