Models for the study of dynamic phenomena related to bilayer membranes are presented. The first approach uses a
hybrid continuum mechanics description of the bilayer with a discrete description of the individual embedded proteins.
This approach is used to study the bidirectional coupling between curvature inducing proteins and the bilayer. Results
are presented for single protein diffusion for different induced curvatures. Results are also presented for collective effects
for how curvature inducing protein inclusions at sufficient concentrations augment the bilayer elastic mechanics. Also
presented is a coarse-grained model capturing features at the level of of individual lipid molecules. The model takes into
account molecular interactions between lipids, inclusions, hydrodynamic coupling, and thermal fluctuations. Results are
presented which characterize how molecular level interactions contribute to bilayer mechanics (stiffness, tension,
compressibility), bilayer rheology (shear viscosity, normal stress differences), and the mobility of bilayer embedded
particles (single and pair diffusivity tensors). Discussion of applications of the bilayer models to problems
in cell biology will also be discussed throughout.
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