Lipolysis on Lipid Droplets: Mathematical Modelling and Numerical Discretisations

Lipolysis on Lipid Droplets: Mathematical Modelling and Numerical Discretisations | 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 Lipolysis on Lipid Droplets: Mathematical Modelling and Numerical Discretisations Reymart Salcedo Lagunero, Klemens Fellner, Thomas Apel, Volker Kempf, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6255845/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Mar, 2026 Read the published version in Results in Mathematics → Version 1 posted You are reading this latest preprint version Abstract Lipolysis is a life-essential metabolic process, which supplies fatty acids stored in lipid droplets to the body in order to match the demands of building new cells and providing cellular energy. In this paper, we present a first mathematical modelling approach for lipolysis, which takes into account that the involved enzymes act on the surface of lipid droplets. We postulate an active region near the surface where the substrates are within reach of the surface-bound enzymes and formulate a system of reaction-diffusion PDEs, which connect the active region to the inner core of lipid droplets via interface conditions. We establish two numerical discretisations based on finite element method and isogeometric analysis, and validate them to perform reliably. Since numerical tests are best performed on non-zero explicit stationary state solutions, we introduce and analyse a model, which describes besides lipolysis also a reverse process (yet in a physiologically much oversimplified way). The system is not coercive such that establishing well-posedness is a non-standard task. We prove the unique existence of global and equilibrium solutions. We establish exponential convergence to the equilibrium solutions using the entropy method. We then study the stationary state model and compute explicitly for radially symmetric solutions. Concerning the finite element methods, we show numerically the linear and quadratic convergence of the errors with respect to the H 1 - and L 2 -norms, respectively. Finally, we present numerical simulations of a prototypical PDE model of lipolysis and illustrate that ATGL clustering on lipid droplets can significantly slow down lipolysis. Mathematics Subject Classification (2010). Primary 35E20; 35K57; 65N30; Secondary 92C40; 92C45. lipid hydrolysis lipolysis entropy method finite element method transacylation enzyme reaction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Mar, 2026 Read the published version in Results in Mathematics → 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-6255845","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":434866907,"identity":"c8c772c6-5e5b-49ad-8c75-1bba0d970a11","order_by":0,"name":"Reymart Salcedo 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reaction","lastPublishedDoi":"10.21203/rs.3.rs-6255845/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6255845/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLipolysis is a life-essential metabolic process, which supplies fatty acids stored in lipid droplets to the body in order to match the demands of building new cells and providing cellular energy.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this paper, we present a first mathematical modelling approach for lipolysis, which takes into account that the involved enzymes act on the surface of lipid droplets. We postulate an active region near the surface where the substrates are within reach of the surface-bound enzymes and formulate a system of reaction-diffusion PDEs, which connect the active region to the inner core of lipid droplets via interface conditions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe establish two numerical discretisations based on finite element method and isogeometric analysis, and validate them to perform reliably. Since numerical tests are best performed on non-zero explicit stationary state solutions, we introduce and analyse a model, which describes besides lipolysis also a reverse process (yet in a physiologically much oversimplified way). The system is not coercive such that establishing well-posedness is a non-standard task. We prove the unique existence of global and equilibrium solutions. We establish exponential convergence to the equilibrium solutions using the entropy method. We then study the stationary state model and compute explicitly for radially symmetric solutions. Concerning the finite element methods, we show numerically the linear and quadratic convergence of the errors with respect to the H\u003csup\u003e1\u003c/sup\u003e- and L\u003csup\u003e2\u003c/sup\u003e-norms, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinally, we present numerical simulations of a prototypical PDE model of lipolysis and illustrate that ATGL clustering on lipid droplets can significantly slow down lipolysis.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2010). 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