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On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation

Ion channels are large transmembrane proteins that are able to conduct small inorganic ions. They are characterized by high selectivity and the ability to gate, i.e. to modify their conductance in response to different stimuli. One of the types of gating follows the ball and chain model, according t...

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Detalles Bibliográficos
Autores principales: Małysiak, Krzysztof, Grzywna, Zbigniew J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: SP Versita 2008
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6275932/
https://www.ncbi.nlm.nih.gov/pubmed/18470658
http://dx.doi.org/10.2478/s11658-008-0015-8
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author Małysiak, Krzysztof
Grzywna, Zbigniew J.
author_facet Małysiak, Krzysztof
Grzywna, Zbigniew J.
author_sort Małysiak, Krzysztof
collection PubMed
description Ion channels are large transmembrane proteins that are able to conduct small inorganic ions. They are characterized by high selectivity and the ability to gate, i.e. to modify their conductance in response to different stimuli. One of the types of gating follows the ball and chain model, according to which a part of the channel’s protein forms a ball connected with the intracellular side of the channel by a polypeptide chain. The ball is able to modify the conductance of the channel by properly binding to and plugging the channel pore. In this study, the polypeptide ball is treated as a Brownian particle, the movements of which are limited by the length of the chain. The probability density of the ball’s position is resolved by different diffusional operators — parabolic (including the case with drift), hyperbolic, and fractional. We show how those different approaches shed light on different aspects of the movement. We also comment on some features of the survival probabilities (which are ready to be compared with electrophysiological measurements) for issues based on the above operators.
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spelling pubmed-62759322018-12-10 On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation Małysiak, Krzysztof Grzywna, Zbigniew J. Cell Mol Biol Lett Research Article Ion channels are large transmembrane proteins that are able to conduct small inorganic ions. They are characterized by high selectivity and the ability to gate, i.e. to modify their conductance in response to different stimuli. One of the types of gating follows the ball and chain model, according to which a part of the channel’s protein forms a ball connected with the intracellular side of the channel by a polypeptide chain. The ball is able to modify the conductance of the channel by properly binding to and plugging the channel pore. In this study, the polypeptide ball is treated as a Brownian particle, the movements of which are limited by the length of the chain. The probability density of the ball’s position is resolved by different diffusional operators — parabolic (including the case with drift), hyperbolic, and fractional. We show how those different approaches shed light on different aspects of the movement. We also comment on some features of the survival probabilities (which are ready to be compared with electrophysiological measurements) for issues based on the above operators. SP Versita 2008-05-10 /pmc/articles/PMC6275932/ /pubmed/18470658 http://dx.doi.org/10.2478/s11658-008-0015-8 Text en © Versita 2008
spellingShingle Research Article
Małysiak, Krzysztof
Grzywna, Zbigniew J.
On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title_full On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title_fullStr On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title_full_unstemmed On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title_short On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
title_sort on the possible methods for the mathematical description of the ball and chain model of ion channel inactivation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6275932/
https://www.ncbi.nlm.nih.gov/pubmed/18470658
http://dx.doi.org/10.2478/s11658-008-0015-8
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