Theory of Cylindrical Tubules and Helical Ribbons of Chiral Lipid Membranes

TL;DR

This paper develops a continuum elastic theory explaining how chirality in lipid membranes leads to the formation of cylindrical tubules and helical ribbons, with phase transitions and stability conditions analyzed.

Contribution

It introduces a general elastic free energy model accounting for molecular tilt and curvature variations, explaining the formation and stability of chiral lipid membrane structures.

Findings

Tubules undergo a first-order transition to a helically modulated state.

Helical ribbons can be stable or serve as intermediate states.

Chirality drives the formation of these membrane structures.

Abstract

We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular tilt and in the curvature of the membrane. The theory shows that the formation of tubules and helical ribbons is driven by the chirality of the membrane. Tubules have a first-order transition from a uniform state to a helically modulated state, with periodic stripes in the tilt direction and ripples in the curvature. Helical ribbons can be stable structures, or they can be unstable intermediate states in the formation of tubules.