Non-reducibility of structural effects in gene regulatory dynamics: a minimal symmetry- breaking model

Non-reducibility of structural effects in gene regulatory dynamics: a minimal symmetry- breaking 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 Article Non-reducibility of structural effects in gene regulatory dynamics: a minimal symmetry- breaking model Nobuchika Yamaki, Tenna Churiki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9410970/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Genes are often modeled as regulators that alter quantitative parameters within a fixed dynamical system. However, it remains unclear whether all genomic effects can be reduced to parameter variation alone, or whether some instead require modification of the underlying dynamical structure. Here, we address this question using a minimal two-variable model. The baseline system is a symmetric mutual repression model, in which exchange symmetry imposes a strict constraint on admissible attractors: any non-diagonal fixed point must be accompanied by its mirror counterpart. We then introduce a minimal structural perturbation by adding a self-activation term to one variable, thereby breaking the symmetry while preserving analytical tractability. The central test is whether the structurally induced attractor class can be reproduced anywhere within the symmetric baseline family by parameter tuning alone. We show that the baseline system does not generate unpaired stable fixed points across the explored parameter domain, whereas the structurally modified system consistently does. This demonstrates a concrete case of non-reducibility: a qualitative dynamical effect that is excluded from the baseline topology yet produced by minimal structural change. The result provides a proof of principle that some genomic effects are better interpreted as modifications of state-space structure than as parameter variation within a fixed regulatory class. Biological sciences/Biophysics Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing Physical sciences/Physics Biological sciences/Systems biology gene regulatory networks dynamical systems structural perturbation symmetry breaking attractor dynamics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 24 Apr, 2026 Editor invited by journal 22 Apr, 2026 Editor assigned by journal 16 Apr, 2026 Submission checks completed at journal 16 Apr, 2026 First submitted to journal 14 Apr, 2026 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-9410970","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":630075709,"identity":"dcc4908d-1703-4f8d-91ab-383bb9393366","order_by":0,"name":"Nobuchika Yamaki","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYFACHgYGxgYJAygvgYcfxiJei2QbkDpAWAsDXAuDwTECWszZe49J/NxhYczfwGP46UZNmozx/d6Dtz9U2OUxsDcffIBFi2XPuTTJ3jMSZhIHeIylc47l8Jgd40u2OHAmuZiB51iyARYtBjdyzKQZ2yRsGA7wGEjnsFUAtfCYSRxsO5DYIJFjJoFPizzQlt85/yp4jNtAWv4R1mJmcIDHTDq3LYfHgA2kpQGPljPnki172ySMDQ+zlVnn9qXxSBzLMbY4cyw5sQ2XX473Hrzxs63OcN7x5s23c74l2/M3nzG8UVFjl9iPI8QQgJkDYSTYPWx4lYMBO8JIbF4YBaNgFIyCkQsAmIthmvIjDLMAAAAASUVORK5CYII=","orcid":"","institution":"TNQ Tech","correspondingAuthor":true,"prefix":"","firstName":"Nobuchika","middleName":"","lastName":"Yamaki","suffix":""},{"id":630075710,"identity":"8f584bac-daac-4298-918c-1cf803f85b19","order_by":1,"name":"Tenna Churiki","email":"","orcid":"","institution":"TNQ Tech","correspondingAuthor":false,"prefix":"","firstName":"Tenna","middleName":"","lastName":"Churiki","suffix":""}],"badges":[],"createdAt":"2026-04-14 05:55:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9410970/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9410970/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108494180,"identity":"c5c6d3ea-5529-4012-9cb4-c8f9da8f9dd5","added_by":"auto","created_at":"2026-05-05 10:02:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":445496,"visible":true,"origin":"","legend":"","description":"","filename":"Nonreducibilityofstructuraleffectsingene.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9410970/v1_covered_f125ca25-2de2-4b22-b651-bec50240fe0a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Non-reducibility of structural effects in gene regulatory dynamics: a minimal symmetry- breaking model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"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":"gene regulatory networks, dynamical systems, structural perturbation, symmetry breaking, attractor dynamics","lastPublishedDoi":"10.21203/rs.3.rs-9410970/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9410970/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGenes are often modeled as regulators that alter quantitative parameters within a fixed dynamical system. 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