Nutrient–response modeling with a single and interpretable artificial neuron

Nutrient–response modeling with a single and interpretable artificial neuron | 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 Article Nutrient–response modeling with a single and interpretable artificial neuron Hamed Ahmadi, Markus Rodehutscord This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7700387/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted 8 You are reading this latest preprint version Abstract Precise estimation of nutrient requirements and utilization efficiency is fundamental to nutritional sciences, yet it is mainly performed using classical nonlinear regression models. These models are interpretable but require careful selection of the functional form and initial parameter values. Flexible machine learning (ML) methods are seemingly disliked due to their perceived “black box” nature, which can obscure biological insight. A minimal and interpretable ML framework addresses this gap in nutrient–response modeling. The proposed approach uses a single artificial neuron with a hyperbolic tangent activation. Mathematically, this resembles a four-parameter sigmoidal function but with greater flexibility and distinct parameter definitions, allowing capture of the monotonic, saturating dynamics typical of essential nutrient responses. The method is enhanced with modern ML best practices, including data augmentation, Bayesian regularization, and bootstrap resampling, providing robust, uncertainty-quantified estimates of key nutritional metrics—such as asymptotic response, inflection point, and nutrient requirements—even from small datasets. Evaluations across 12 diverse datasets from poultry and fish studies, including amino acids and phosphorus, demonstrated that the single artificial neuron matches or exceeds the performance of classical models while providing full analytical transparency. The framework is implemented as a no-code graphical application, ‘NutriCurvist’, offering an easy-to-use alternative tool for nutrient–response modeling to support data-driven, precision nutrition. Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing Interpretable machine learning Nutrient–response modeling Parameter visualization Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformation.docx Cite Share Download PDF Status: Published Journal Publication published 24 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 04 Nov, 2025 Reviews received at journal 17 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers invited by journal 29 Sep, 2025 Editor invited by journal 29 Sep, 2025 Editor assigned by journal 26 Sep, 2025 Submission checks completed at journal 25 Sep, 2025 First submitted to journal 24 Sep, 2025 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. 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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-7700387","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":520063196,"identity":"d9e08b9b-2d65-4fbb-9da3-d4bd55d22816","order_by":0,"name":"Hamed 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neuron","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Interpretable machine learning, Nutrient–response modeling, Parameter visualization","lastPublishedDoi":"10.21203/rs.3.rs-7700387/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7700387/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePrecise estimation of nutrient requirements and utilization efficiency is fundamental to nutritional sciences, yet it is mainly performed using classical nonlinear regression models. These models are interpretable but require careful selection of the functional form and initial parameter values. Flexible machine learning (ML) methods are seemingly disliked due to their perceived \u0026ldquo;black box\u0026rdquo; nature, which can obscure biological insight. A minimal and interpretable ML framework addresses this gap in nutrient\u0026ndash;response modeling. The proposed approach uses a single artificial neuron with a hyperbolic tangent activation. Mathematically, this resembles a four-parameter sigmoidal function but with greater flexibility and distinct parameter definitions, allowing capture of the monotonic, saturating dynamics typical of essential nutrient responses. The method is enhanced with modern ML best practices, including data augmentation, Bayesian regularization, and bootstrap resampling, providing robust, uncertainty-quantified estimates of key nutritional metrics\u0026mdash;such as asymptotic response, inflection point, and nutrient requirements\u0026mdash;even from small datasets. Evaluations across 12 diverse datasets from poultry and fish studies, including amino acids and phosphorus, demonstrated that the single artificial neuron matches or exceeds the performance of classical models while providing full analytical transparency. The framework is implemented as a no-code graphical application, \u0026lsquo;NutriCurvist\u0026rsquo;, offering an easy-to-use alternative tool for nutrient\u0026ndash;response modeling to support data-driven, precision nutrition.\u003c/p\u003e","manuscriptTitle":"Nutrient–response modeling with a single and interpretable artificial neuron","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-25 08:59:23","doi":"10.21203/rs.3.rs-7700387/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-04T17:37:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-17T13:09:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"93410430690529330434016339989146180672","date":"2025-10-09T09:30:24+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-29T11:18:36+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-29T10:31:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-26T12:20:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-25T09:03:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-24T07:01:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"afb4801a-68de-4fe6-ace9-15197e30630d","owner":[],"postedDate":"September 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":55278677,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":55278678,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2025-12-01T16:13:36+00:00","versionOfRecord":{"articleIdentity":"rs-7700387","link":"https://doi.org/10.1038/s41598-025-29267-w","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-11-24 15:57:56","publishedOnDateReadable":"November 24th, 2025"},"versionCreatedAt":"2025-09-25 08:59:23","video":"","vorDoi":"10.1038/s41598-025-29267-w","vorDoiUrl":"https://doi.org/10.1038/s41598-025-29267-w","workflowStages":[]},"version":"v1","identity":"rs-7700387","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7700387","identity":"rs-7700387","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}