A theoretical model of Rab proteins localization on endosomal membranes

In this thesis we propose a model for the spatial organization of Rab proteins on cell membranes. We are interested in particular in understanding the process of formation of localized domains of active Rab proteins observed in the experiments. This is a process of symmetry breaking, which is crucial in seteral vital functions, such as directed migration and cell division. Our starting point is the mean-field kinetic model proposed in Bezeljak et al. (PNAS 117:6540, 2020). After a thorough analysis of their hypotheses based on the literature, we extend their model by explicitly introducing the spatial distribution of molecules and their diffusion on the membrane. Numerical simulations of the resulting model are performed and compared to experimental results by Cezanne et al. (eLife 9:e54434, 2020).