Interdependence of sodium and potassium gating variables in the Hodgkin-Huxley model

Interdependence of sodium and potassium gating variables in the Hodgkin-Huxley model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Interdependence of sodium and potassium gating variables in the Hodgkin-Huxley model Lízia Branco, Rui Dilão This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6227956/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We explore the relationship between sodium (Na$^+$) and potassium (K$^+$) gating variables in the 4-dimensional (4D) Hodgkin-Huxley (HH) electrophysiology model and reduce its complexity by deriving new 3D and 2D models that retain the original model's dynamic properties. The new 3D and 2D models are based on the relationship $h \simeq c - n$ between the gating variables $h$ and $n$ of the 4D HH model, where $c$ is a constant, which suggests an interdependence between the dynamics of Na$^+$ and K$^+$ transmembrane voltage-gated channels. The presence of Na$^+$/K$^+$-ATPase pump may explain this interdependence. We derive the corresponding cable equations for the three HH-type models and demonstrate that the action potential propagates along the axon at with the speed $v(R, C_m) = \alpha / (C_m R^{\beta}) = \gamma D^{\beta}$, where $\alpha > 0$, $0 < \beta < 1$, and $\gamma$ are constants independent of the local stimulus intensity, $D$ is the diffusion coefficient of the electric signal along the axon, $C_m$ is the axon transmembrane capacitance, and $R$ is the axon conducting resistivity. Sodium and potassium voltage-gated channels Na+ /K+ -ATPase pump New 2D Hodgkin- Huxley reduced cable model Action potential propagation speed Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6227956","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":432775524,"identity":"1dbb98e0-ae5f-4516-9604-8e5e1d7492ae","order_by":0,"name":"Lízia Branco","email":"","orcid":"","institution":"University of Lisbon","correspondingAuthor":false,"prefix":"","firstName":"Lízia","middleName":"","lastName":"Branco","suffix":""},{"id":432775525,"identity":"049dd11a-62f0-4def-ae91-11118618c720","order_by":1,"name":"Rui Dilão","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCUlEQVRIiWNgGAWjYFACxgaJhAIGBn4wxwBEMDccYGwgpAWoUrINroURpoUZpyYJkEqDY0iGMODTYj4jufHGAwM7OeP7zQc/FxTYyTFIJDYe/LnDRp5Buv8ANi0yNxKbLRIMko3NjrElS88AMoBaGg7znkkzbJA5jN1REoltQL8wJ247xmPGzGNwILEBpIWx7TDQj8n4tNQnbm7j/wbXcvBn22F7AloOJ25g42GDaznA23Y4EacWnocgvxw3ljiWZizNA/QLG89DsF+S22QOG2DVwp7+8OaPimo5/ubDDz/z/LGT42dPPvwRGGK2/dKND7BagwHY4AwJ4jSguIB0LaNgFIyCUTAsAQAOhVv0cSYDowAAAABJRU5ErkJggg==","orcid":"","institution":"University of Lisbon","correspondingAuthor":true,"prefix":"","firstName":"Rui","middleName":"","lastName":"Dilão","suffix":""}],"badges":[],"createdAt":"2025-03-14 16:08:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6227956/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6227956/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82399058,"identity":"4e70223d-408f-4ced-8b5b-80c2de548607","added_by":"auto","created_at":"2025-05-09 21:31:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1855592,"visible":true,"origin":"","legend":"","description":"","filename":"Archive.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6227956/v1_covered_2d150be3-5cb2-4001-840a-9a719eb888e9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Interdependence of sodium and potassium gating variables in the Hodgkin-Huxley model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Sodium and potassium voltage-gated channels, Na+ /K+ -ATPase pump, New 2D Hodgkin- Huxley reduced cable model, Action potential propagation speed","lastPublishedDoi":"10.21203/rs.3.rs-6227956/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6227956/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We explore the relationship between sodium (Na$^+$) and potassium (K$^+$) gating variables in the 4-dimensional (4D) Hodgkin-Huxley (HH) electrophysiology model and reduce its complexity by deriving new 3D and 2D models that retain the original model's dynamic properties. The new 3D and 2D models are based on the relationship $h \\simeq c - n$ between the gating variables $h$ and $n$ of the 4D HH model, where $c$ is a constant, which suggests an interdependence between the dynamics of Na$^+$ and K$^+$ transmembrane voltage-gated channels. The presence of Na$^+$/K$^+$-ATPase pump may explain this interdependence. 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