Modeling Natural Root Branching with Geometric and Reaction Diffusion Approaches

Modeling Natural Root Branching with Geometric and Reaction Diffusion Approaches | 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 Modeling Natural Root Branching with Geometric and Reaction Diffusion Approaches Daniela Moreno-Chaparro, Gustavo Vargas-Silva, Diego Alexander Garzón Alvarado This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7814859/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 Branching structures are ubiquitous in nature, appearing in phenomena such as thunder, fungi, and plant growth. In plants, root systems exemplify complex branching formations necessary for structural support, anchorage, and nutrient uptake. This paper presents two computational models for simulating root branching, focusing on both architectural archetypes and tropism responses. The first model employs a geometric stochastic approach to represent primary and adventitious root types in both 2D and 3D, using variable branching angles and orders to replicate distinct structural patterns. The second, more advanced model, the Reaction-Diffusion Root Branching (RDRB) model, utilizes reaction-diffusion equations within a finite element method (FEM) framework in 1D and 2D to capture the influence of biochemical, biophysical, and tropism stimuli on root development. Both models qualitatively emulate real-world root growth, with parameters calibrated through visual analysis of empirical root data. These simulations provide baseline tools for future models that incorporate environmental interactions, such as obstacles or heterogeneous nutrient distributions. Furthermore, the modeling techniques extend beyond root plants, offering a framework for exploring other natural branching systems. Full Text Additional Declarations No competing interests reported. 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. 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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-7814859","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":538656348,"identity":"7e0339b8-c991-4091-9ad5-d2b390a23c82","order_by":0,"name":"Daniela Moreno-Chaparro","email":"","orcid":"","institution":"National University of Colombia","correspondingAuthor":false,"prefix":"","firstName":"Daniela","middleName":"","lastName":"Moreno-Chaparro","suffix":""},{"id":538656349,"identity":"ff64191e-56ec-4adf-b625-51d9478dd0c0","order_by":1,"name":"Gustavo Vargas-Silva","email":"data:image/png;base64,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","orcid":"","institution":"Universidad Pública de Navarra, UPNA","correspondingAuthor":true,"prefix":"","firstName":"Gustavo","middleName":"","lastName":"Vargas-Silva","suffix":""},{"id":538656350,"identity":"7166993f-f1f4-40b7-81f1-52da600cc7cc","order_by":2,"name":"Diego Alexander Garzón Alvarado","email":"","orcid":"","institution":"National University of Colombia","correspondingAuthor":false,"prefix":"","firstName":"Diego","middleName":"Alexander Garzón","lastName":"Alvarado","suffix":""}],"badges":[],"createdAt":"2025-10-09 08:23:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7814859/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7814859/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94975884,"identity":"826fd8d2-752d-4d54-99a7-a457f96738ef","added_by":"auto","created_at":"2025-11-03 03:26:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7394716,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript2025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7814859/v1/1d5fcc5ba16b911bd45a7e20.pdf"},{"id":94975883,"identity":"c3464d7b-6f54-47bc-8b6e-c4d0bc105685","added_by":"auto","created_at":"2025-11-03 03:26:50","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5395,"visible":true,"origin":"","legend":"","description":"","filename":"c9a0a1bc2439493d84c8b1e5e959e5fd.json","url":"https://assets-eu.researchsquare.com/files/rs-7814859/v1/88d07828a651d88c8a53fff2.json"},{"id":102746100,"identity":"c4fbc09a-48b4-488f-9fbf-9316a47881dc","added_by":"auto","created_at":"2026-02-16 08:55:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1306124,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript2025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7814859/v1_covered_f1cf9d92-abf9-44a0-80c3-270fc10aeb38.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling Natural Root Branching with Geometric and Reaction Diffusion Approaches","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"","lastPublishedDoi":"10.21203/rs.3.rs-7814859/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7814859/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Branching structures are ubiquitous in nature, appearing in phenomena such as thunder, fungi, and plant growth. In plants, root systems exemplify complex branching formations necessary for structural support, anchorage, and nutrient uptake. This paper presents two computational models for simulating root branching, focusing on both architectural archetypes and tropism responses. The first model employs a geometric stochastic approach to represent primary and adventitious root types in both 2D and 3D, using variable branching angles and orders to replicate distinct structural patterns. The second, more advanced model, the Reaction-Diffusion Root Branching (RDRB) model, utilizes reaction-diffusion equations within a finite element method (FEM) framework in 1D and 2D to capture the influence of biochemical, biophysical, and tropism stimuli on root development. Both models qualitatively emulate real-world root growth, with parameters calibrated through visual analysis of empirical root data. 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