Microphysical derivation of the Canham--Helfrich free-energy density

TL;DR

This paper derives the Canham--Helfrich free-energy density for lipid bilayers from microphysical principles, clarifying the origin of spontaneous curvature and providing explicit expressions for elastic moduli.

Contribution

It offers a microphysical derivation of the Canham--Helfrich model, linking spontaneous curvature to bilayer asymmetry and expressing elastic moduli through potential derivatives.

Findings

Spontaneous curvature mainly arises from leaflet asymmetry.

Expressions for splay and saddle-splay moduli are derived.

The derivation justifies common assumptions in membrane physics.

Abstract

The Canham--Helfrich free-energy density for a lipid bilayer has drawn considerable attention. Aside from the mean and Gaussian curvatures, this free-energy density involves a spontaneous mean-curvature that encompasses information regarding the preferred, natural shape of the lipid bilayer. We use a straightforward microphysical argument to derive the Canham--Helfrich free-energy density. Our derivation (i) provides a justification for the common assertion that spontaneous curvature originates primarily from asymmetry between the leaflets comprising a bilayer and (ii) furnishes expressions for the splay and saddle-splay moduli in terms of derivatives of the underlying potential.