Intrinsic curvature in normal and inverted lipid structures and in membranes

The intrinsic or spontaneous radius of curvature, R(o), of lipid monolayer assemblies is expressed in terms of a lipid molecular packing parameter, V/A/, for various geometries. It is shown that the equivalent lipid length, I, in inverted hexagonal (H-parallel to) phases, defined by a cylindrical shell of equal total lipid volume, yields an expression for R(o) identical to that for inverted cylindrical micelles (or, equivalently, H-parallel to phases in the presence of excess hydrocarbon), This identity is used to obtain values of the effective packing parameter for various phosphatidylethanolamines. The temperature dependence of the intrinsic radius of curvature is predicted to be negative and to be considerably greater than that for the lipid length in nearly all cases. The thermal expansion coefficient is not constant but is found to vary, depending on the value of the lipid packing parameter. A possible addition rule is constructed for the intrinsic radius of curvature of lipid mixtures, based on the linear additivity of the effective molecular volumes, V, and molecular areas, A. This relation is found to hold for mixtures of dioleoyl phosphatidylcholine (DOPC) with dioleoyl phosphatidylethanolamine, and a value of R(o) of greater than or equal to 95 Angstrom (V/A/ = 1.08) is obtained for DOPC. The energetics of the intrinsic curvature and lamellar-nonlamellar transitions are also discussed within the framework of the model.