Electrodiffusion on the surface of bilayer membranes

Abstract

The cell memebrane is of utmost importance in the transportation of nutrients 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. In this paper we present a continuum model of electrodiffusion of lipids on the surface of bilayer membranes. Offering three derivations of the surface electrodiffusion equation, and proofs for the existence and uniqueness of the solution. A method for calculating integration constants using slotboom variables is emloyed. The development of a linear surface finite element method to solve the surface electrodiffusion equation is presented. Numerical simulations implementing the model are also given. The stability of the model is analyzed and a stability scheme using Streamline Upwind Petrov-Galerkin equations is applied. We test our code for robustness using other examples and a complex mesh. The implementation is validated by comparing with the known solution for the equations.