A Reaction–Diffusion–Advection Model for the Establishment and Maintenance of Transport-Mediated Polarity and Symmetry Breaking - Emken, Natalie; Engwer, Christian (Frontiers in Applied Mathematics and Statistics, 2020)
Cell polarity is a fundamental process in many different cell types. The yeast cell saccharomyces cerevisiae provides an exemplary model system to study the underlying mechanisms. By combination of biological experiments and mathematical simulations previous studies suggested that the clustering of the most important polarity regulator Cdc42 relies on multiple parallel acting mechanisms, including a transport-driven feedback Freisinger et al. [2013]; Layton et al. [2011]; Wedlich-Söldner et al. [2004]. Up to now, many models explain symmetry breaking by a Turing-type mechanism which results from different diffusion rates between the plasma mebrane and the cytosol Madzvamuse et al. [2015]; Rätz and Röger [2014]. But active transport processes, like vesicle transport, can have significant influence on the polarization. To simulate vesicular mediated transport, stochastic equations were commonly used, see e.g. Layton et al. [2011]; Klünder et al. [2013]. The novelty in this paper is a continuous formulation for modelling active transport, like actin mediated vesicle transport. Another important novelty is the actin part which is simulated by an inhomogeneous diffusion controlled by a capacity function which in turn depends on the active membrane bound form. The paper is based on the PhD thesis Emken [2016], where it is used to model budding yeast using a reaction-diffusion-advection system. Model reduction and non-dimensionalization makes it possible to study this model in terms of distinct cell types. Similar to the approach of Rätz and Röger [2014], we present a linear stability analysis and derive conditions for a transport-mediated instability. We complement our theoretical analysis by numerical simulations that confirm our findings. Using a locally mass conservative control volume finite element method we present simulations in 2D and 3D and compare the results to previous ones from the literature.