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Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations

Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na(+) activation, h the Na(+) inactivation, and n the K(+) activation. V and m change rapidly, relative to h and n...

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Autor principal: Fitzhugh, Richard
Formato: Texto
Lenguaje:English
Publicado: The Rockefeller University Press 1960
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2195039/
https://www.ncbi.nlm.nih.gov/pubmed/13823315
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author Fitzhugh, Richard
author_facet Fitzhugh, Richard
author_sort Fitzhugh, Richard
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description Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na(+) activation, h the Na(+) inactivation, and n the K(+) activation. V and m change rapidly, relative to h and n. The (V, m) phase plane of a reduced system of equations, with h and n held constant at their resting values, has three singular points: a stable resting point, a threshold saddle point, and a stable excited point. When h and n are allowed to vary, recovery and refractoriness result from the movement with subsequent disappearance of the threshold and excited points. Multiplying the time constant of n by 100 or more, and that of h by one-third, reproduces the experimental plateau action potentials obtained with tetraethylammonium by Tasaki and Hagiwara, including the phenomena of abolition and of refractoriness of the plateau duration. The equations have, transiently, two stable states, as found in the real axon by these authors. Since the theoretical membrane conductance curves differ significantly from the experimental ones, further experimental analysis of ionic currents with tetraethylammonium is needed to decide whether the Hodgkin-Huxley model can be generalized to explain these experiments completely.
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spelling pubmed-21950392008-04-23 Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations Fitzhugh, Richard J Gen Physiol Article Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na(+) activation, h the Na(+) inactivation, and n the K(+) activation. V and m change rapidly, relative to h and n. The (V, m) phase plane of a reduced system of equations, with h and n held constant at their resting values, has three singular points: a stable resting point, a threshold saddle point, and a stable excited point. When h and n are allowed to vary, recovery and refractoriness result from the movement with subsequent disappearance of the threshold and excited points. Multiplying the time constant of n by 100 or more, and that of h by one-third, reproduces the experimental plateau action potentials obtained with tetraethylammonium by Tasaki and Hagiwara, including the phenomena of abolition and of refractoriness of the plateau duration. The equations have, transiently, two stable states, as found in the real axon by these authors. Since the theoretical membrane conductance curves differ significantly from the experimental ones, further experimental analysis of ionic currents with tetraethylammonium is needed to decide whether the Hodgkin-Huxley model can be generalized to explain these experiments completely. The Rockefeller University Press 1960-05-01 /pmc/articles/PMC2195039/ /pubmed/13823315 Text en Copyright © Copyright, 1960, by The Rockefeller Institute This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms). After six months it is available under a Creative Commons License (Attribution–Noncommercial–Share Alike 4.0 Unported license, as described at http://creativecommons.org/licenses/by-nc-sa/4.0/).
spellingShingle Article
Fitzhugh, Richard
Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title_full Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title_fullStr Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title_full_unstemmed Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title_short Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations
title_sort thresholds and plateaus in the hodgkin-huxley nerve equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2195039/
https://www.ncbi.nlm.nih.gov/pubmed/13823315
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