Liquid crystal theory of biomembranes

Biomembranes, which are primarily composed of lipid bilayers, are not merely passive barriers, but dynamic, complex materials whose shapes are governed by the principles of soft-matter physics. This review examines the shape problem in biomembranes from the perspectives of materials science and liquid-crystal theory. We apply the Helfrich elastic model to the biomembrane shape in an electromagnetic field, and we extend the Helfrich free energy to multilayer systems, drawing parallels between the focal-conic structures of smectic liquid crystals and the geometries of fullerenes, carbon nanotubes, and the icosahedral virus. The review concludes by highlighting the unifying power of continuum elastic theories in describing a wide range of membrane morphologies across biological and synthetic systems.