Semi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics

Semi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics | 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 Semi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics Vaitheeswaran Gnanaraj, Balakrishanan Vellaikannan, P Balamanikandan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9262374/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 A dual-substrate reaction-diffusion framework is developed, validated, and extended to electrochemical analysis for glucose oxidase biosensors, incorporating oxygen co-substrate dependence through the dimensionless oxygen-to-glucose ratio γ. Two independent semi-analytical methods — the Rajendran-Joy Method (RJM) and the Akbari-Ganji Method (AGM) — are applied to the coupled nonlinear Michaelis–Menten governing system. Inter-method validation across 500 parameter combinations yields a mean relative difference of 3.88% (maximum 6.93%), with 94% of cases below 7%. Validation against 17 glucose oxidase K m values from the BRENDA database (EC 1.1.3.4) yields mean R² = 0.9981 across Low, Mid, and High kinetic categories. Three kinetic regimes are identified: oxygen-limited (γ 1.0); implanted CGM sensors operate firmly in the oxygen-limited regime (γ ≈ 0.003–0.01). A revised Butler–Volmer electrode boundary condition replaces the passive zero-flux assumption, introducing the electrode kinetic parameter Λ. An analytical electrochemical impedance spectroscopy model predicts Nyquist spectra with a Warburg slope deviation |Δθ| = 5°-12° under physiological conditions, providing a direct experimental diagnostic for oxygen co-limitation. Charge transfer resistance R ct = 36–90 Ω across BRENDA categories is consistent with published GOx electrode data. Quantitative membrane engineering guidelines for oxygen-independent CGM operation are derived. Applied Mathematics Applied Biochemistry Glucose oxidase Biosensor modelling Michaelis–Menten kinetics Oxygen dependence Continuous glucose monitoring Semi-analytical methods Butler–Volmer electrode kinetics Electrochemical impedance spectroscopy Full Text Additional Declarations The authors declare no competing interests. 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-9262374","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614267111,"identity":"17afa6c6-1e68-4f5b-8274-3dc2d4307f8c","order_by":0,"name":"Vaitheeswaran Gnanaraj","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYFCCA1CavQFIGFiQooUHxDCQIMU2iQQwSViheePZoxu/7rDL45/5/OqGHwUSDPzt3Ql4tcgcOJd2W/ZMcrHE7Zyymz1Ah0mcObsBv3MYzpjdlmxjTmy4nZN2gweoxUAilygt9Ynzb55Ju/mHWC03P7YdTtxwg/3YbSJtAfqFse144sYzOWy3ZQwkeAj7ReLssZs/26oT5x0//uzmmz82cvztvfi1AAOIgZkHzOIxAJP4lYMAfw8D4w8wi/0BYdWjYBSMglEwIgEAEtJO9SqVxSMAAAAASUVORK5CYII=","orcid":"","institution":"Thiagarajar College of Engineering","correspondingAuthor":true,"prefix":"","firstName":"Vaitheeswaran","middleName":"","lastName":"Gnanaraj","suffix":""},{"id":614267112,"identity":"b154bae5-3573-4f95-a2be-bd3ed619ab4b","order_by":1,"name":"Balakrishanan Vellaikannan","email":"","orcid":"","institution":"Thiagarajar College of Engineering","correspondingAuthor":false,"prefix":"","firstName":"Balakrishanan","middleName":"","lastName":"Vellaikannan","suffix":""},{"id":614267113,"identity":"e22d4ac6-293f-4275-b98b-35f8ded59983","order_by":2,"name":"P Balamanikandan","email":"","orcid":"","institution":"Thiagarajar College of Engineering","correspondingAuthor":false,"prefix":"","firstName":"P","middleName":"","lastName":"Balamanikandan","suffix":""}],"badges":[],"createdAt":"2026-03-30 04:38:30","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9262374/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9262374/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106093207,"identity":"10493255-4a76-4d68-9165-dc7657cdaada","added_by":"auto","created_at":"2026-04-03 11:36:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1511059,"visible":true,"origin":"","legend":"","description":"","filename":"CompleteRevisedManuscriptV6.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9262374/v1_covered_d7b2ff77-fe1d-43c9-9a02-f00ba74ea6ce.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSemi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Thiagarajar College of Engineering","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":"Glucose oxidase, Biosensor modelling, Michaelis–Menten kinetics, Oxygen dependence, Continuous glucose monitoring, Semi-analytical methods, Butler–Volmer electrode kinetics, Electrochemical impedance spectroscopy","lastPublishedDoi":"10.21203/rs.3.rs-9262374/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9262374/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA dual-substrate reaction-diffusion framework is developed, validated, and extended to electrochemical analysis for glucose oxidase biosensors, incorporating oxygen co-substrate dependence through the dimensionless oxygen-to-glucose ratio γ. Two independent semi-analytical methods\u0026nbsp;— the Rajendran-Joy Method (RJM) and the Akbari-Ganji Method (AGM)\u0026nbsp;— are applied to the coupled nonlinear Michaelis–Menten governing system. Inter-method validation across 500 parameter combinations yields a mean relative difference of 3.88% (maximum 6.93%), with 94% of cases below 7%. Validation against 17 glucose oxidase K\u003csub\u003em\u003c/sub\u003e values from the BRENDA database (EC 1.1.3.4) yields mean R²\u0026nbsp;=\u0026nbsp;0.9981 across Low, Mid, and High kinetic categories. Three kinetic regimes are identified: oxygen-limited (γ\u0026nbsp;\u0026lt;\u0026nbsp;0.2), transition (0.2\u0026nbsp;≤\u0026nbsp;γ\u0026nbsp;≤\u0026nbsp;1.0), and glucose-limited (γ\u0026nbsp;\u0026gt;\u0026nbsp;1.0); implanted CGM sensors operate firmly in the oxygen-limited regime (γ\u0026nbsp;≈\u0026nbsp;0.003–0.01). A revised Butler–Volmer electrode boundary condition replaces the passive zero-flux assumption, introducing the electrode kinetic parameter Λ. An analytical electrochemical impedance spectroscopy model predicts Nyquist spectra with a Warburg slope deviation |Δθ|\u0026nbsp;=\u0026nbsp;5°-12° under physiological conditions, providing a direct experimental diagnostic for oxygen co-limitation. Charge transfer resistance R\u003csub\u003ect\u003c/sub\u003e\u0026nbsp;=\u0026nbsp;36–90\u0026nbsp;Ω across BRENDA categories is consistent with published GOx electrode data. Quantitative membrane engineering guidelines for oxygen-independent CGM operation are derived.\u003c/p\u003e","manuscriptTitle":"Semi-Analytical Dual-Substrate Modeling of Glucose Oxidase Biosensors: Butler-Volmer Boundary Conditions, Impedance Spectroscopy, and Oxygen Co-Limitation Diagnostics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-31 07:50:56","doi":"10.21203/rs.3.rs-9262374/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"73e72b12-a688-48b6-bf47-fc1fb12ec193","owner":[],"postedDate":"March 31st, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65360993,"name":"Applied Mathematics"},{"id":65360994,"name":"Applied Biochemistry"}],"tags":[],"updatedAt":"2026-03-31T07:50:56+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-31 07:50:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9262374","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9262374","identity":"rs-9262374","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}