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. 1974 Oct;14(10):731–757. doi: 10.1016/S0006-3495(74)85947-3

Changes of Action Potential Shape and Velocity for Changing Core Conductor Geometry

Steven S Goldstein, Wilfrid Rall
PMCID: PMC1334570  PMID: 4420585

Abstract

The theoretical changes in shape and velocity of an action potential were computed in regions of changing core conductor geometry. Step decrease and step increase of diameter, branch points, and gradual taper or flare of diameter were studied. Results showed increase of both velocity and peak height as the action potential approaches a point of step decrease. A step increase causes decrease of both velocity and peak height with approach; propagation may either fail, succeed with brief delay, or, with longer delay, succeed in both forward and reverse directions. With branching, both the shape and the dimensionless velocity, τθ/λ, remain unchanged when the d3/2 values are matched. Without such matching, the changes of shape and dimensionless velocity of an action potential correspond to those found for step decrease or step increase of diameter. For regions of flare or taper, it was found (for a specific previously defined class) that velocity changed in proportion with the changing length constant. A simple formula was found to predict how this proportionality constant depends upon the amount of flare or taper.

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Selected References

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

  1. BROCK L. G., COOMBS J. S., ECCLES J. C. Intracellular recording from antidromically activated motoneurones. J Physiol. 1953 Dec 29;122(3):429–461. doi: 10.1113/jphysiol.1953.sp005013. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Chung S. H., Raymond S. A., Lettvin J. Y. Multiple meaning in single visual units. Brain Behav Evol. 1970;3(1):72–101. doi: 10.1159/000125464. [DOI] [PubMed] [Google Scholar]
  3. Evans J., Shenk N. Solutions to axon equations. Biophys J. 1970 Nov;10(11):1090–1101. doi: 10.1016/S0006-3495(70)86355-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. FUORTES M. G., FRANK K., BECKER M. C. Steps in the production of motoneuron spikes. J Gen Physiol. 1957 May 20;40(5):735–752. doi: 10.1085/jgp.40.5.735. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. FitzHugh R. Dimensional analysis of nerve models. J Theor Biol. 1973 Aug 22;40(3):517–541. doi: 10.1016/0022-5193(73)90008-8. [DOI] [PubMed] [Google Scholar]
  6. Fitzhugh R. Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J. 1961 Jul;1(6):445–466. doi: 10.1016/s0006-3495(61)86902-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Grossman Y., Spira M. E., Parnas I. Differential flow of information into branches of a single axon. Brain Res. 1973 Dec 21;64:379–386. doi: 10.1016/0006-8993(73)90191-1. [DOI] [PubMed] [Google Scholar]
  8. 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]
  9. KATZ B., MILEDI R. PROPAGATION OF ELECTRIC ACTIVITY IN MOTOR NERVE TERMINALS. Proc R Soc Lond B Biol Sci. 1965 Feb 16;161:453–482. doi: 10.1098/rspb.1965.0015. [DOI] [PubMed] [Google Scholar]
  10. Khodorov B. I., Timin E. N., Vilenkin S. Ia, Gul'ko F. B. Teoreticheskii analiz mekhanizmov provedeniia nervnogo impul&sa po neodnorodnomu aksonu. I. Provedenie cherez uchastok s uveilichennym diametrom. Biofizika. 1969 Mar-Apr;14(2):304–315. [PubMed] [Google Scholar]
  11. Pastushenko V. F., Markin V. S., Chizmadzhev Iu A. Rasprostranenie vozbuzhdeniia v odnoi modeli neodnorodnogo nervnogo volokna. 3. Vzaimodeistvie impul'sov v oblasti uzla vetvleniia nervnogo volokna. Biofizika. 1969 Sep-Oct;14(5):883–890. [PubMed] [Google Scholar]
  12. RALL W. Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol. 1959 Nov;1:491–527. doi: 10.1016/0014-4886(59)90046-9. [DOI] [PubMed] [Google Scholar]
  13. RALL W. Theory of physiological properties of dendrites. Ann N Y Acad Sci. 1962 Mar 2;96:1071–1092. doi: 10.1111/j.1749-6632.1962.tb54120.x. [DOI] [PubMed] [Google Scholar]
  14. Rall W., Shepherd G. M. Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. J Neurophysiol. 1968 Nov;31(6):884–915. doi: 10.1152/jn.1968.31.6.884. [DOI] [PubMed] [Google Scholar]

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