Liquid Crystal Theory of Biomembranes

Abstract

Biomembranes, primarily composed of lipid bilayers, are not merely passive barriers but dynamic and complex materials whose shapes are governed by the principles of soft matter physics. This review explores the shape problem in biomembranes through the lens of material science and liquid crystal theory. Beginning with classical analogies to crystals and soap bubbles, it details the application of the Helfrich elastic model to explain the biconcave shape of red blood cells. The discussion extends to multi-layer systems, drawing parallels between the focal conic structures of smectic liquid crystals, the geometries of fullerenes and carbon nanotubes, and the reversible transitions in peptide assemblies. Furthermore, it examines icosahedral self-assemblies and shape formation in two-dimensional lipid monolayers at air/water interfaces. At the end of the paper, we find that the shapes such as cylinders, spheres, tori, biconcave discoids and Delaunay surfaces form a group. This result is merely an intrinsic geometric feature of these shapes and is independent of the biomembrane equation. When the pressure on the membrane, surface tension, and bending modules meet certain conditions, the biomembrane will take on these shapes. The review concludes by highlighting the unifying power of continuum elastic theories in describing a vast array of membrane morphologies across biological and synthetic systems.