Challenges in theoretical investigations on configurations of lipid membranes

TL;DR

This paper reviews key theoretical results on lipid membrane configurations and discusses challenges such as solving shape equations, understanding membrane elasticity, and the relationship between symmetry and free energy.

Contribution

It highlights current achievements and identifies open problems in the theoretical modeling of lipid membrane shapes and behaviors.

Findings

Exact solutions to shape equations remain elusive.

Nonlocal elasticity theory offers new insights.

Symmetry influences free energy magnitude.

Abstract

This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition of two-phase vesicles in the budding state; (iv) nonlocal theory of membrane elasticity; (v) relationship between symmetry and the magnitude of free energy.