Abstract
Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.