Bridging Genetics and Information Theory: Fisher Information Limits on Genetic Stability, Diversity, and Regulation

Bridging Genetics and Information Theory: Fisher Information Limits on Genetic Stability, Diversity, and Regulation | 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 Bridging Genetics and Information Theory: Fisher Information Limits on Genetic Stability, Diversity, and Regulation Jacqueline Siqueira Glasenapp This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8462833/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 I introduce a Fisher Information (FI) based framework for quantifying the fidelity of genetic information transmission across generations. Genetic inheritance is modeled as a noisy information channel defined by a symmetric circulant transition matrix, allowing closed-form expressions for Fisher Information at both the source population and the transmitted signal. This formulation complements entropy-based approaches by directly characterizing estimation precision and the loss of predictability in genetic systems. I show that information decay is governed entirely by the square of the nontrivial channel eigenvalue, providing a natural and biologically interpretable measure of information retention under mutation and recombination. Within this framework, I identify a sharp loss of predictability in gene regulatory networks (GRNs), detectable both as a collapse of classical Fisher Information, and as an entanglement-collapse threshold in the formally equivalent quantum channel representation. Remarkably, the functional instability limit observed in GRNs coincides with the quantum coherence limit within a narrow parameter range, revealing a shared information-theoretic boundary. This convergence provides a principled explanation for the sharp, non-monotonic boundaries reported in GRN inference from single-cell RNA-seq data. More broadly, the results suggest that biological regulatory stability is constrained by fundamental limits on information transmission, linking population genetics, information geometry, and quantum-inspired models of gene regulation. Computational Biology Fisher Information Geometry Gene Regulatory Stability Quantum-Inspired Genetics 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-8462833","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":566256916,"identity":"6336dcbb-9b33-42b0-8453-833e92a12a88","order_by":0,"name":"Jacqueline Siqueira Glasenapp","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYDACZhBhACIYGxg+ACk2dlK0MM4AaWEmyUYeuCF4gHw78zaJDwX35OXdDzd+tvm1TZ6PmYHxw8cc3FoMDrOVSc4wKDbceCaxWTq377ZhGzMDs+TMbXi0MPOYSfMYJDBubEhskM7tuc0I1MLGzItHi3wzUMsfgwT7jf0Pm39b9ty2J6iF4TBQC4NBQuJ8icQ2aYYftxMJagH6pdiyxyAheYPEwzbL3obbyW3MjM14/SLff3jjjR9/Emzn96c/BjJu285vbz744SM+h0HjkcHgAJBgbAMxgcmAAIBokQer+0NI8SgYBaNgFIxEAAAjiE37m0A7WQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8035-7058","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Jacqueline","middleName":"Siqueira","lastName":"Glasenapp","suffix":""}],"badges":[],"createdAt":"2025-12-27 19:10:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8462833/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8462833/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99793222,"identity":"18dec63e-d365-419c-98b1-160f47066c7a","added_by":"auto","created_at":"2026-01-08 13:31:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":360954,"visible":true,"origin":"","legend":"","description":"","filename":"BridgingGeneticsandInformationTheoryAFisherInformationPerspectiveonGeneticStabilityandDiversity1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8462833/v1_covered_795d9a58-20c2-431c-bfa4-dddb41497309.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eBridging Genetics and Information Theory: Fisher Information Limits on Genetic Stability, Diversity, and Regulation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Arizona","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":"Fisher Information Geometry, Gene Regulatory Stability, Quantum-Inspired Genetics","lastPublishedDoi":"10.21203/rs.3.rs-8462833/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8462833/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eI introduce a Fisher Information (FI) based framework for quantifying the fidelity of genetic information transmission across generations. Genetic inheritance is modeled as a noisy information channel defined by a symmetric circulant transition matrix, allowing closed-form expressions for Fisher Information at both the source population and the transmitted signal. This formulation complements entropy-based approaches by directly characterizing estimation precision and the loss of predictability in genetic systems. I show that information decay is governed entirely by the square of the nontrivial channel eigenvalue, providing a natural and biologically interpretable measure of information retention under mutation and recombination. Within this framework, I identify a sharp loss of predictability in gene regulatory networks (GRNs), detectable both as a collapse of classical Fisher Information, and as an entanglement-collapse threshold in the formally equivalent quantum channel representation. 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