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. 1986 Jul;50(1):27–40. doi: 10.1016/S0006-3495(86)83436-1

Poisson process stimulation of an excitable membrane cable model.

M D Goldfinger
PMCID: PMC1329656  PMID: 3730505

Abstract

The convergence of multiple inputs within a single-neuronal substrate is a common design feature of both peripheral and central nervous systems. Typically, the result of such convergence impinges upon an intracellularly contiguous axon, where it is encoded into a train of action potentials. The simplest representation of the result of convergence of multiple inputs is a Poisson process; a general representation of axonal excitability is the Hodgkin-Huxley/cable theory formalism. The present work addressed multiple input convergence upon an axon by applying Poisson process stimulation to the Hodgkin-Huxley axonal cable. The results showed that both absolute and relative refractory periods yielded in the axonal output a random but non-Poisson process. While smaller amplitude stimuli elicited a type of short-interval conditioning, larger amplitude stimuli elicited impulse trains approaching Poisson criteria except for the effects of refractoriness. These results were obtained for stimulus trains consisting of pulses of constant amplitude and constant or variable durations. By contrast, with or without stimulus pulse shape variability, the post-impulse conditional probability for impulse initiation in the steady-state was a Poisson-like process. For stimulus variability consisting of randomly smaller amplitudes or randomly longer durations, mean impulse frequency was attenuated or potentiated, respectively. Limitations and implications of these computations are discussed.

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Selected References

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

  1. Adelman W. J., Jr, Fitzhugh R. Solutions of the Hodgkin-Huxley equations modified for potassium accumulation in a periaxonal space. Fed Proc. 1975 Apr;34(5):1322–1329. [PubMed] [Google Scholar]
  2. Blight A. R. Computer simulation of action potentials and afterpotentials in mammalian myelinated axons: the case for a lower resistance myelin sheath. Neuroscience. 1985 May;15(1):13–31. doi: 10.1016/0306-4522(85)90119-8. [DOI] [PubMed] [Google Scholar]
  3. Bryant H. L., Segundo J. P. Spike initiation by transmembrane current: a white-noise analysis. J Physiol. 1976 Sep;260(2):279–314. doi: 10.1113/jphysiol.1976.sp011516. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Calvin W. H. Generation of spike trains in CNS neurons. Brain Res. 1975 Jan 24;84(1):1–22. doi: 10.1016/0006-8993(75)90796-9. [DOI] [PubMed] [Google Scholar]
  5. Calvin W. H., Stevens C. F. Synaptic noise and other sources of randomness in motoneuron interspike intervals. J Neurophysiol. 1968 Jul;31(4):574–587. doi: 10.1152/jn.1968.31.4.574. [DOI] [PubMed] [Google Scholar]
  6. Connor J. A., Stevens C. F. Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J Physiol. 1971 Feb;213(1):31–53. doi: 10.1113/jphysiol.1971.sp009366. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Craig A. D., Tapper D. N. A dorsal spinal neural network in cat. III. Dynamic nonlinear analysis of responses to random stimulation of single type 1 cutaneous input fibers. J Neurophysiol. 1985 Apr;53(4):995–1015. doi: 10.1152/jn.1985.53.4.995. [DOI] [PubMed] [Google Scholar]
  8. Faber D. S., Korn H. Field effects trigger post-anodal rebound excitation in vertebrate CNS. 1983 Oct 27-Nov 2Nature. 305(5937):802–804. doi: 10.1038/305802a0. [DOI] [PubMed] [Google Scholar]
  9. Fitzhugh R. Anodal excitation in the Hodgkin-Huxley nerve model. Biophys J. 1976 Mar;16(3):209–226. doi: 10.1016/S0006-3495(76)85682-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. French A. S. Dynamic properties of the action potential encoder in an insect mechanosensory neuron. Biophys J. 1984 Aug;46(2):285–289. doi: 10.1016/S0006-3495(84)84023-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. French A. S. The frequency response function and sinusoidal threshold properties of the Hodgkin-Huxley model of action potential encoding. Biol Cybern. 1984;49(3):169–174. doi: 10.1007/BF00334462. [DOI] [PubMed] [Google Scholar]
  12. Funch P. G., Faber D. S. Measurement of myelin sheath resistances: implications for axonal conduction and pathophysiology. Science. 1984 Aug 3;225(4661):538–540. doi: 10.1126/science.6204382. [DOI] [PubMed] [Google Scholar]
  13. George S. A. Changes in interspike interval during propagation: quantitative description. Biol Cybern. 1977 Jun 13;26(4):209–213. doi: 10.1007/BF00366592. [DOI] [PubMed] [Google Scholar]
  14. Goldfinger M. D., Amassian V. E. Response of forelimb guard hair afferent units to air-jet stimulation of entire receptive field. J Neurophysiol. 1980 Nov;44(5):961–978. doi: 10.1152/jn.1980.44.5.961. [DOI] [PubMed] [Google Scholar]
  15. Goldfinger M. D., Fukami Y. Interaction of activity in frog skin touch afferent units. J Neurophysiol. 1981 Jun;45(6):1096–1108. doi: 10.1152/jn.1981.45.6.1096. [DOI] [PubMed] [Google Scholar]
  16. Goldfinger M. D. Superposition of impulse activity in a rapidly-adapting afferent unit model. Biol Cybern. 1984;50(6):385–394. doi: 10.1007/BF00335195. [DOI] [PubMed] [Google Scholar]
  17. Goldman L., Albus J. S. Computation of impulse conduction in myelinated fibers; theoretical basis of the velocity-diameter relation. Biophys J. 1968 May;8(5):596–607. doi: 10.1016/S0006-3495(68)86510-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Goldstein S. S., Rall W. Changes of action potential shape and velocity for changing core conductor geometry. Biophys J. 1974 Oct;14(10):731–757. doi: 10.1016/S0006-3495(74)85947-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. 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]
  20. Hines M. Efficient computation of branched nerve equations. Int J Biomed Comput. 1984 Jan-Feb;15(1):69–76. doi: 10.1016/0020-7101(84)90008-4. [DOI] [PubMed] [Google Scholar]
  21. Horn R., Vandenberg C. A. Statistical properties of single sodium channels. J Gen Physiol. 1984 Oct;84(4):505–534. doi: 10.1085/jgp.84.4.505. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Horwitz B. Unequal diameters and their effects on time-varying voltages in branched neurons. Biophys J. 1983 Jan;41(1):51–66. doi: 10.1016/S0006-3495(83)84405-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Jahnsen H., Llinás R. Ionic basis for the electro-responsiveness and oscillatory properties of guinea-pig thalamic neurones in vitro. J Physiol. 1984 Apr;349:227–247. doi: 10.1113/jphysiol.1984.sp015154. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Krylov B. V., Makovsky V. S. Spike frequency adaptation in amphibian sensory fibres is probably due to slow K channels. Nature. 1978 Oct 12;275(5680):549–551. doi: 10.1038/275549a0. [DOI] [PubMed] [Google Scholar]
  25. 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]
  26. Moore J. W., Stockbridge N., Westerfield M. On the site of impulse initiation in a neurone. J Physiol. 1983 Mar;336:301–311. doi: 10.1113/jphysiol.1983.sp014582. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. POGGIO G. F., VIERNSTEIN L. J. TIME SERIES ANALYSIS OF IMPULSE SEQUENCES OF THALAMIC SOMATIC SENSORY NEURONS. J Neurophysiol. 1964 Jul;27:517–545. doi: 10.1152/jn.1964.27.4.517. [DOI] [PubMed] [Google Scholar]
  28. Redman S. J., Lampard D. G. Monosynaptic stochastic stimulation of cat spinal motoneurons. I. Response of motoneurons to sustained stimulation. J Neurophysiol. 1968 Jul;31(4):485–498. doi: 10.1152/jn.1968.31.4.485. [DOI] [PubMed] [Google Scholar]
  29. Sclabassi R. J., Vries J. K., Bursick D. M. Somatosensory evoked potentials to random stimulus trains. Ann N Y Acad Sci. 1982;388:695–701. doi: 10.1111/j.1749-6632.1982.tb50837.x. [DOI] [PubMed] [Google Scholar]
  30. Tuckwell H. C., Wan F. Y., Wong Y. S. The interspike interval of a cable model neuron with white noise input. Biol Cybern. 1984;49(3):155–167. doi: 10.1007/BF00334461. [DOI] [PubMed] [Google Scholar]
  31. Waxman S. G., Ritchie J. M. Organization of ion channels in the myelinated nerve fiber. Science. 1985 Jun 28;228(4707):1502–1507. doi: 10.1126/science.2409596. [DOI] [PubMed] [Google Scholar]

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