Delacour, JuliaDoumic, MarieMartens, SaschaSchmeiser, ChristianZaffagnini, Gabriele2022-03-252022-03-252021Delacour J, Doumic M, Martens S, Schmeiser C, Zaffagnini G. A mathematical model of p62-ubiquitin aggregates in autophagy. J Math Biol. 2021 Dec 14;84(1-2):3. DOI: 10.1007/s00285-021-01659-20303-6812http://hdl.handle.net/10230/52773Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.application/pdfeng© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00285-021-01659-292C40 BiochemistryMolecular biologyinfo:eu-repo/semantics/openAccess