Tiankui Zhang
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Abstract: Vesicles are important model systems for cells. They are basically closed lipid bilayers. Their equilibrium shapes and dynamical shapes help us understand cellular processes involving membrane deformation, such as signal transduction between neurons, endocytosis, influenza viral escaping etc.
Their shape dynamics depend on lipid species, osmotic pressure, conservation of lipid mass, lateral phase separation, protein diffusion and interaction etc. In this dissertation, we will first introduce the necessary background in molecular biology of membranes. Then, differential geometry of surfaces and curves will be introduced as the mathematical language for biomembranes. Hamiltonian and elastic forces for the vesicle will be shown. Next, we introduce the level set framework within which we develop our numerical schemes. We will present numerical simulation (movies) for the shape dynamics of single phase vesicles, biphasic vesicles and vesicles with protein interactions and explore effects of different parameters in the model.
Zoom Link:https://arizona.zoom.us/my/tiankuizhang