Modeling local pattern formation on membrane surfaces using nonlocal interactions
Date
2015
Authors
Adkins, Melissa, author
Zhou, Yongcheng, advisor
Krapf, Diego, committee member
Liu, James, committee member
Mueller, Jennifer, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
The cell membrane is of utmost importance in the transportation of nutrients and signals to the cell which are needed for survival. The magnitude of this is the inspiration for our study of the lipid bilayer which forms the cell membrane. It has been recently accepted that the lipid bilayer consists of lipid microdomains (lipid rafts), as opposed to freely moving lipids. We present two lipid raft models using the Ginzburg-Landau energy with addition of the electrostatic energy and the geodesic curvature energy to describe the local pattern formation of these lipid rafts. The development and implementation of a C⁰ interior penalty surface finite element method along with an implicit time iteration scheme will also be discussed as the optimal solution technique.