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A continuous reaction-diffusion-advection model for the establishment of actin-mediated polarity in yeast

Presented by: 
Natalie Emken Universität Münster
Tuesday 8th December 2015 - 15:30 to 16:15
INI Seminar Room 1
Co-author: Prof. Dr. Christian Engwer (Institute for Computational and Applied Mathematics, University of Muenster)
Cell polarity plays a crucial role for many different cell types. In the yeast cell, the model system to study the underlying mechanisms of polarization, the GTPase Cdc42 is a key regulator of this process. Its clustering relies on multiple parallel acting mechanisms. A common model explains polarity by a Turing-type mechanism. Based on reaction-diffusion equations it simulates a Bem1-mediated Cdc42 recruitment. Since cell polarity occurs even in the absence of Bem1, recent papers emphasize the exchange between the cytosol and the plasma membrane. However, studies combining biological experiments and mathematical simulations also suggest an actin-mediated feedback of Cdc42. Stochastic vesicle trafficking models demonstrate that transport of Cdc42 via actin cables can either reinforce or perturb polarization . We present a minimal mathematical model, based on reaction-diffusion-advection equations, that is able to reproduce the experimentally observed phenomena, in particular those of knock-down experiments. Contrary to former approaches which only incorporate the diffusive transport, our system explicitly simulates exocytosis and endocytosis of Cdc42. Vesicles move along actin cables, thus we further consider actin polymerization and depolymerization. Since we consider five substances, either cytosolic or membrane-bound, and model the full geometry we have a coupled bulk-surface problem. We present numerical results in 3D and compare those to experimental data. This way, we show that the model is able to reproduce experimentally observed pathological cases and demonstrate how vesicle transport could reinforce polarity. Based on this specific model, we develop a general system of three membrane reaction-diffusion equations coupled to two diffusion equations inside the cell. We perform a linearized stability analysis and derive conditions for a transport-mediated instability. We complete our theoretical analysis by numerical simulations for different geometries.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons