Theory of Self-Assembled Tubules and Helical Ribbons

Many types of amphiphilic molecules self-assemble in solution to form cylindrical tubules and helical ribbons. Some examples include diacetylenic lipids, amide amphiphiles, bile, and diblock copolymers. Researchers have proposed a variety of models to explain the formation of these high-curvature structures. These models can be divided into two broad categories:  models based on the chiral elastic properties of membranes, and models based on other effects, including electrostatic interactions, elasticity of orientational order, and spontaneous curvature. In this paper, we review the range of theoretical approaches and compare them with relevant experiments. We argue that the category of models based on chiral elastic properties provides the most likely explanation of current experimental results, and we propose further theoretical and experimental research to give a more detailed test of these models.