Mechanical membrane model quantifies selectivity of protein assemblies for compact growth due to membrane bending

Membrane remodeling is the process of membrane undergoing an induced curvature change, which is essential in multiple cellular processes including fission and fusion, exo- and endocytosis, and matrix formation in mitochondria. The bending of the membrane introduces surface tension and is thus unfavorable in terms of membrane energy by itself. Therefore, to induce curvature change in cellular membrane, membrane remodeling is facilitated with a wide range of proteins. This process appears to be generally coupled between the proteins and the bending of the membrane, and it is not known how the energetic coupling between the assembly and the membrane bending can shape the assembly pathways of the protein lattice. We show here using our mechanical continuum membrane models that employ the finite element method (FEM) coupled to particle-based assemblies that lattice structures that deviate from compact and idealized spherical structures require significantly more energy per protein to bend the membrane. We thus demonstrate how the coupled process of assembly and membrane bending can select for specific assembly pathways where the protein assembles in a compact and regular way. We established an analytical model for the shape function of the lattice attached membrane with finite relaxation and compared it with the result of simulation. This mechanical membrane model will ultimately provide an open source resource to the community for detailed understanding of membrane remodeling in cell biology.