USask Mathematics & Statistics Colloquium: Anotida Madzvamuse

Live Stream: 

https://usask-ca.zoom.us/j/95534967223?pwd=0souQ0erQt4B3mWbYTcw19oQgnrJld.1

Details/Abstract: 

In this talk, I will present a new mathematical formalism of a coupled system of bulk-surface partial differential equations (semilinear parabolic type) for describing molecular interactions (active and inactive Rho GTPases) taking place in the cytosol and the cortex (where the cortex is assumed to be a sharp surface). The model couples Laplace (in the cytosol) and Laplace-Beltrami (on the surface) operators. The first result is the generalisation of Turing diffusion-driven instability for bulk-surface reaction-diffusion equations. Theoretical implications of these generalised conditions will be explored and pattern generation exhibited on various 3-dimensional domains and surfaces will be presented. As an application, I will present the bulk-surface wave pinning model, and show how this framework captures more faithfully the physical representing of the molecular interactions between active and inactive Rho GTPAses through a minimalistic model. To support theoretical findings, the bulk-surface finite element method is employed to numerically solve the coupled system of bulk-surface PDEs. If time permits, I will demonstrate how this numerical method captures the inherent theoretical properties of the bulk-surface wave pinning model.