The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes

A membrane inclusion can be defined as a complex of protein or peptide and the surrounding significantly distorted lipids. We suggest a theoretical model that allows for the estimation of the influence of membrane inclusions on the curvature elastic properties of lipid membranes. Our treatment includes anisotropic inclusions whose energetics depends on their in-plane orientation within the membrane. On the basis of continuum elasticity theory, we calculate the inclusion-membrane interaction energy that reflects the protein or peptide-induced short-ranged elastic deformation of a bent lipid layer. A numerical estimate of the corresponding interaction constants indicates the ability of inclusions to sense membrane bending and to accumulate at regions of favorable curvature, matching the effective shape of the inclusions. Strongly anisotropic inclusions interact favorably with lipid layers that adopt saddlelike curvature; such structures may be stabilized energetically. We explore this possibility for the case of vesicle budding where we consider a shape sequence of closed, axisymmetric vesicles that form a (saddle-curvature adopting) membrane neck. It appears that not only isotropic but also strongly anisotropic inclusions can significantly contribute to the budding energetics, a finding that we discuss in terms of recent experiments.