Biophysical Feasibility Constraints Govern Phase Transitions in Tumor Control Dynamics

Biophysical Feasibility Constraints Govern Phase Transitions in Tumor Control Dynamics | 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 Biophysical Feasibility Constraints Govern Phase Transitions in Tumor Control Dynamics Enrique Rosario Aloma, Luis Rodriguez, Carolina Vigo, Maymunah Ray, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8959124/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 17 You are reading this latest preprint version Abstract Tumor behavior is strongly influenced by microenvironmental acidity, molecular transport, and metabolic resource limitations, yet quantitative principles governing their coupled effects remain incompletely understood. Here we present a biophysical modeling framework showing that sustained tumor control is governed by feasibility constraints rather than by individual parameter magnitudes. Three dimensionless control parameters (Ξ, Λ, Ψ) capture independent dynamical, spatial, and energetic limitations arising from nonlinear tumor–immune interactions, reaction–diffusion transport of acidity, and metabolic costs of alkalinization. Analytical feasibility boundaries defined by these parameters predict distinct outcome regimes, including tumor persistence, partial control, and clearance. Numerical parameter sweeps reveal sharp transitions across feasibility thresholds, and sensitivity analysis demonstrates that regime structure depends primarily on the dimensionless constraint geometry rather than on specific kinetic coefficients. These results introduce a constraint-based interpretation of tumor regulation and clarify how transport and energetic limitations can fundamentally restrict therapeutic outcomes. The framework provides a generalizable approach for analyzing environmentally coupled biological systems subject to physical constraints. Biological sciences/Biophysics Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing Physical sciences/Physics Biological sciences/Systems biology Nonlinear dynamical systems Bifurcation structure Phase transitions Reaction–diffusion systems Multistability Environmental coupling Stability analysis Dimensionless control parameters Transport-limited dynamics Energetic constraints Full Text Additional Declarations No competing interests reported. Supplementary Files GraphicalAbstract.jpeg Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 May, 2026 Reviews received at journal 01 May, 2026 Reviews received at journal 27 Apr, 2026 Reviews received at journal 27 Apr, 2026 Reviews received at journal 25 Apr, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers invited by journal 08 Apr, 2026 Editor invited by journal 02 Mar, 2026 Editor assigned by journal 25 Feb, 2026 Submission checks completed at journal 25 Feb, 2026 First submitted to journal 24 Feb, 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. 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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-8959124","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":597327786,"identity":"c2dbbf08-9294-4816-a580-9d4a9dcb8010","order_by":0,"name":"Enrique Rosario 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