Membrane Phase Transitions in Lipid-Wrapped Nanoparticles

A Landau theory is constructed for the gel/fluid transition of a lipid bilayer wrapped around a spherical nanoparticle (lipid-wrapped nanoparticle, LNP). The bilayer is regarded as a regular solution of gel and fluid lipids with distinct inter- and intralayer interactions plus the interaction of the core with the inner layer. It is required that both the inner and the outer surfaces of the bilayer are perfectly covered with lipids, with the gel and fluid lipids having different areas/lipid. The equilibrium state is found by minimizing the free energy as a function of the fractions of fluid lipids in the inner and outer layers. The transition has been studied extensively for lamellar membranes in the thermodynamic limit. LNP have significant curvature and are not in the thermodynamic limit. The increase of the gel energy with curvature, identified in our previous work as its most important effect, is included. The focus of the paper is the dependence of the transition on the core radius, R, controlling curvature, and the core-lipid interaction. With decreasing R, trends found in experiment are reproduced in a model calculation: (1) decrease of the transition temperature, T_m, (2) decoupling of the transitions in the inner and outer layers, and (3) possibility of lower T_m in the inner layer. The disruption of gel packing by curvature and the interaction of the core with the inner layer are highlighted as the most important determinants of deviation from bulk behavior.