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Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability

Excitability—a threshold-governed transient in transmembrane voltage—is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitab...

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Autores principales: Ori, Hillel, Hazan, Hananel, Marder, Eve, Marom, Shimon
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7035484/
https://www.ncbi.nlm.nih.gov/pubmed/32024761
http://dx.doi.org/10.1073/pnas.1916514117
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author Ori, Hillel
Hazan, Hananel
Marder, Eve
Marom, Shimon
author_facet Ori, Hillel
Hazan, Hananel
Marder, Eve
Marom, Shimon
author_sort Ori, Hillel
collection PubMed
description Excitability—a threshold-governed transient in transmembrane voltage—is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin–Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model’s sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin–Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function.
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spelling pubmed-70354842020-02-28 Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability Ori, Hillel Hazan, Hananel Marder, Eve Marom, Shimon Proc Natl Acad Sci U S A Biological Sciences Excitability—a threshold-governed transient in transmembrane voltage—is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin–Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model’s sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin–Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function. National Academy of Sciences 2020-02-18 2020-02-05 /pmc/articles/PMC7035484/ /pubmed/32024761 http://dx.doi.org/10.1073/pnas.1916514117 Text en Copyright © 2020 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/ https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Biological Sciences
Ori, Hillel
Hazan, Hananel
Marder, Eve
Marom, Shimon
Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title_full Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title_fullStr Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title_full_unstemmed Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title_short Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability
title_sort dynamic clamp constructed phase diagram for the hodgkin and huxley model of excitability
topic Biological Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7035484/
https://www.ncbi.nlm.nih.gov/pubmed/32024761
http://dx.doi.org/10.1073/pnas.1916514117
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