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Mathematical Modelling of p62-Ubiquitin aggregates involved in cellular autophagy

Abstract : This thesis aims to model the aggregation of ubiquitinated cargo by oligomers of the protein p62, which is an important preparatory step in cellular autophagy. A new mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. The main contribution of this new model lies on the fact that we are considering two different particles, namely p62 and Ubiquitin, attaching to each other in a very specific way, which increases drastically the complexity level of the model compared to classical ones. In a first part, 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. The qualitative results are illustrated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model. In a second part, a partial analysis of this model using dynamical systems tools is also made. The local stability of the regime where the aggregates are unstable is proved using blow-up. The locally quadratic growth in the third regime is also proved using geometric singular perturbation analysis. The end of the thesis is dedicated to the improvement of the former model. Based on biological observations, a coagulation term is added, which leads to a prohibitively complex growth-coagulation model. This is why a simplified version based on a multiscale analysis is formulated where aggregates are only described by one parameter. To conclude, a first basic study of unidimensional growth-coagulation equations is made.
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Contributor : Julia Delacour <>
Submitted on : Sunday, February 14, 2021 - 7:54:09 PM
Last modification on : Thursday, April 15, 2021 - 3:08:19 PM


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  • HAL Id : tel-03141004, version 1


Julia Delacour. Mathematical Modelling of p62-Ubiquitin aggregates involved in cellular autophagy. Mathematics [math]. Sorbonne Université UPMC; University of Vienna [Vienna]; INRIA Paris Research Centre, MAMBA Team, F-75012, Paris, France, 2020. English. ⟨tel-03141004⟩



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