Stability of lipid membranes with orthotropic symmetry

Lipid membranes routinely undergo protein-mediated morphological remodeling during vital processes such as cellular transport and division. These membrane remodeling proteins can be broadly classified into two categories: one that generates a spherical shape and another that generates a cylindrical shape. To gain physical insights into membrane shape transitions, it is important to investigate the stability of membranes in the presence of these two types of proteins. However, the existing membrane theory is mostly restricted to the class of membranes that interact with the sphere shape-generating proteins and possess isotropic symmetry. In this work, we use curvature elasticity of the lipid membranes to derive the stability criterion for membranes that interact with the cylindrical-shape-generating proteins that possess orthotropic symmetry. We derive the convexity condition followed by the stability criterion for a generalized form of strain energy that can entertain material heterogeneity. The proposed framework would allow for a rigorous analysis of a broader set of membrane–protein interactions during key cellular processes.