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Theoretical analysis of mechanisms of nerve impulse conduction along myelinated fiber after a functional change in the properties of individual nodes

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Abstract

It is shown in a mathematical model of a myelinated nerve fiber that the development of a local response in an inexcitable node plays an important role in the mechanism of the "jumping" of an action potential (AP) across the inexcitable node. In the absence of such a response (for example, in the case of a 1000-fold decrease in the maximum sodium permeability,\(\bar P\) Na) in fibers with normal relations between the length of the internodal segment (L) and its diameter (D) (L/D>100), the conduction is blocked. It is possible only in fibers with relatively short internodal segments (L/D<90). With a decrease in the\(\bar P\) Na in several nodes, the transmission of excitation from the first to the second altered node is of critical importance for propagation of the impulse. The conduction of an AP becomes decremental if in each of the altered nodes the AP acquires a gradual character, for example, in the case of acceleration of sodium inactivation through the rate constant βh.

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Literature cited

  1. M. B. Berkinblit, "Periodic blocking of impulses in excitable tissues," in: Models of Structural and Functional Organization of Some Biological Systems [in Russian], Nauka, Moscow (1966). pp. 131–158.

    Google Scholar 

  2. N. E. Vvedenskii, "Excitation, Inhibition, and Narcosis," Collection of Papers edited by A. A. Ukhtomskii [in Russian], Vol. 3, Izd-vo LGU (1935).

  3. D. N. Nasonov, Local Reaction of Protoplasm and Propagating Excitation [in Russian], Izd. Akad. Nauk SSSR, Moscow-Leningrad (1959), p. 246.

    Google Scholar 

  4. I. Tasaki, Nerve Impulse Conduction [Russian translation], IL, Moscow (1957), pp. 63, 145.

  5. B. I. Khodorov, E. N. Timin, S. Ya. Vilenkin, and F. B. Gul'ko, "Theoretical analysis of mechanisms of conduction of nerve impulse through nonuniform axon. I. Conduction through segment with increased diameter," Biofizika,14, 304–315 (1969).

    PubMed  Google Scholar 

  6. B. I. Khodorov, E. N. Timin, S. Ya. Vilenkin, and F. B. Gul'ko, "Theoretical analysis of mechanisms of nerve impulse conduction through nonuniform axon. II. Conduction of single impulse through area of fiber with functionally altered properties," Biofizika,15, 140–146 (1970).

    PubMed  Google Scholar 

  7. B. I. Khodorov and E. N. Timin, "Theoretical analysis of mechanisms of nerve impulse conduction through nonuniform axon. III. Transformation of rhythms in cooled segment of fiber," Biofizika,15, 503–511 (1970).

    PubMed  Google Scholar 

  8. J. Cooley and F. Dodge, "Digital computer solutions for excitation and propagation of the nerve impulse," Biophys. J.,6, 583–599 (1966).

    PubMed  Google Scholar 

  9. R. FitzHugh, "Computation of impulse initiation and saltatory conduction in myelinated nerve fiber," Biophys. J.,2, 11–21 (1962).

    PubMed  Google Scholar 

  10. B. Frankenhaeuser and A. F. Huxley, "The action potential in the myelinated nerve fiber ofXenopus laevis as computed on the basis of voltage clamp data," J. Physiol. (London),171, 302–315 (1964).

    PubMed  Google Scholar 

  11. L. Goldman and J. Albus, "Computation of impulse conduction in myelinated fibers: theoretical basis of velocity-diameter relation," Biophys. J.,8, 596–607 (1968).

    PubMed  Google Scholar 

  12. L. Herman, "Zur theorie der erregunsleitung und der elektrischen. Erregung," Pfl. Arch.,75, 574–590 (1899).

    Google Scholar 

  13. G. Kato, "The theory of decrementless conduction in narcotized region of nerve," Hongo, Tokyo, Japan (1924).

  14. P. Müller, "Effects of external currents on duration and amplitude of normal and prolonged action potentials from single node of Ranvier," J. Gen. Physiol.,42, 163–190 (1958).

    PubMed  Google Scholar 

  15. R. Stämpfli, "Bau und funktion isolierter markhaltiger nervenfasern.," Ergebn. der Physiol.,47, 70–165 (1954).

    Google Scholar 

  16. J. Uehara, "Graduated nodal response in NaCl-deficient media and the critical NaCl concentration for excitation," Jap. J. Physiol.,9, 304–310 (1959).

    PubMed  Google Scholar 

  17. B. Werigo, "Zur frage über die Beriehungen zwischen erregbarkeit und leitungsfahigkeit des Nerven," Pfl. Arch. Physiol.,76, 552–607 (1899).

    Google Scholar 

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A. V. Vishnevskii Institute of Surgery, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 3, No. 3, pp. 316–324, May–June, 1971.

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Khodorov, B.I., Timin, E.N. Theoretical analysis of mechanisms of nerve impulse conduction along myelinated fiber after a functional change in the properties of individual nodes. Neurophysiology 3, 237–244 (1971). https://doi.org/10.1007/BF01065499

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