Simulating Gene Regulatory Feedback Loops with Ordinary Differential Equations: A Reproducible Python-Based Framework

Simulating Gene Regulatory Feedback Loops with Ordinary Differential Equations: A Reproducible Python-Based Framework | 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 Method Article Simulating Gene Regulatory Feedback Loops with Ordinary Differential Equations: A Reproducible Python-Based Framework Yathu Krishna Y K This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7284270/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 In order to preserve cellular homeostasis, regulate the levels of gene expression, and permit intricate dynamic behaviors like bistability, oscillations, and ultrasensitivity, gene regulatory networks (GRNs) mostly depend on feedback mechanisms. In this study, we introduce a computational framework that is simple and reproducible for simulating the fundamental dynamics of both positive and negative feedback loops in gene regulation through the use of ordinary differential equations (ODEs). With no need for specific software installations and a reliance only on Python and publicly available libraries like NumPy, SciPy, and Matplotlib within Google Colab, our method is intended to be both approachable and instructive. We put into practice canonical models of autoregulatory circuits, in which a gene product either suppresses or increases its own production, and examine how important system characteristics, such as the Hill coefficient, degradation constant, and production rate, influence the system's temporal behavior. By means of numerical integration of the governing ODEs, we demonstrate how positive feedback produces switch-like dynamics and possible bistability under specific parameter regimes, while negative feedback stabilizes gene expression and buffers noise. Additionally, we use comparison simulations to depict the evolution of gene expression over time, analyze phase space trajectories, and compare the response profiles of the two feedback types. We simulate the system under various initial conditions and parameter perturbations to increase the pedagogical value and demonstrate the robustness and sensitivity of feedback-regulated gene expression. Crucially, we show that straightforward, quantitative modeling of regulatory motifs can yield biologically significant insights without claiming any new biological discoveries. We present a simple model that can be used as a teaching template for systems biology courses and for computational studies of feedback in artificial or natural gene circuits. Because the entire code and visualizations are publicly accessible and cloud-executable, this system is ideal for incorporation into instructional modules, reproducible research, and the development of initial hypotheses in computational biology. Computational Biology Bioinformatics Mathematical and Theoretical Biology Gene regulatory networks Ordinary differential equations Feedback loops Systems biology Autoregulation Computational modeling Bistability Python simulation Synthetic biology Gene expression dynamics Minimal models Quantitative biology Reproducible science Positive feedback Negative feedback Full Text Additional Declarations The authors declare no competing interests. Supplementary Files ODEBasedModelforGeneAutoregulatoryFeedbackLoops.ipynb Python Notebook 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-7284270","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":494937038,"identity":"98498830-0ffa-4491-b52a-c89c69c21c10","order_by":0,"name":"Yathu Krishna Y K","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYHACNiBOYGBgbwDSBhbE6GCGauE5ANIiQYoWiQQQjwgtBsfPH3vM25Ymb3Dz+dUNPwokGPjbuxPwazmTzG7M25ZjuOF2TtnNHqDDJM6c3YBfy4FkNmnetgpGoJa0GzxALQYSuQS0nH8M1mK/4eaZtJt/iNJyA2xLTuKGG+zHbhNli+SNx2aSc86lJc88k8N2W8ZAgoegX/jOJz6TeFOWbNt3/Pizm2/+2Mjxt/fi16JwAEgwsoEYPAYgAR68ykFAvgFE/gEx2B8QVD0KRsEoGAUjEwAAWWxMEYqB7uIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0009-8743-2570","institution":"Department of Biosciences, MES College Marampally","correspondingAuthor":true,"prefix":"","firstName":"Yathu","middleName":"Krishna Y","lastName":"K","suffix":""}],"badges":[],"createdAt":"2025-08-03 15:35:41","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-7284270/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7284270/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88295778,"identity":"d0650f9b-70ba-4f42-8b37-45b31402e9b7","added_by":"auto","created_at":"2025-08-05 03:24:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":527169,"visible":true,"origin":"","legend":"","description":"","filename":"SimulatingGeneRegulatoryFeedbackLoopswithOrdinaryDifferentialEquationsAReproduciblePythonBasedFramework.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7284270/v1_covered_8cc2c4ab-b136-4f27-9513-ae2e04b8a1f6.pdf"},{"id":88295184,"identity":"24557682-828b-4ade-9abf-60e749f109d0","added_by":"auto","created_at":"2025-08-05 03:16:47","extension":"ipynb","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":234095,"visible":true,"origin":"","legend":"\u003cp\u003ePython Notebook\u0026nbsp;\u003c/p\u003e","description":"","filename":"ODEBasedModelforGeneAutoregulatoryFeedbackLoops.ipynb","url":"https://assets-eu.researchsquare.com/files/rs-7284270/v1/dfc15ca1f8e3e098c3da4a63.ipynb"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSimulating Gene Regulatory Feedback Loops with Ordinary Differential Equations: A Reproducible Python-Based Framework\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Department of Biosciences , MES College Marampally","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":"Gene regulatory networks, Ordinary differential equations, Feedback loops, Systems biology, Autoregulation, Computational modeling, Bistability, Python simulation, Synthetic biology, Gene expression dynamics, Minimal models, Quantitative biology, Reproducible science, Positive feedback, Negative feedback","lastPublishedDoi":"10.21203/rs.3.rs-7284270/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7284270/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn order to preserve cellular homeostasis, regulate the levels of gene expression, and permit intricate dynamic behaviors like bistability, oscillations, and ultrasensitivity, gene regulatory networks (GRNs) mostly depend on feedback mechanisms. 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