Statistical thermodynamics of association colloids. III. The gel to liquid phase transition of lipid bilayer membranes

Abstract

A new theory is introduced to model the lipid membrane structure and stability both above and below the gel to liquid phase transition temperature. Recently, we elaborated a self-consistent-field (SCF) theory, in which the full set of conformations was generated in a rotational isomeric state scheme and Boltzmann statistics was used to determine the statistical weight per conformation. In the present paper we also take into account that the anisotropic distribution of the molecules on the lattice induce a self-consistent anisotropic molecular field. This field, which is a function of the bond orientations, leads to an extra factor in the statistical weight of each conformation and is based on a generalization of Flory’s and Di Marzio’s analysis of systems with rigid rods. This elegant refinement follows from elementary statistics, is free of new adjustable parameters, and significantly improves details of the structure of the model membranes. To examine the properties of the SCAF (self-consistent anisotropic field) theory we use a model membrane built up by lecithin-like molecules composed of apolar and polar segments. The model has three nearest-neighbor interaction parameters of the Flory–Huggins type, namely for the interaction between apolar segments and water, that between polar segments and water, and that between polar and apolar segments. A fourth parameter is the dihedral trans/gauche energy difference. The theory predicts a first order gel to liquid phase transition for the model membranes. Depending on the membrane concentration, both an intercalated (in the dilute regime) and a nonintercalated (in the concentrated regime) gel phase are observed. Detailed information on the various membrane phases is obtained. Order parameter and segment density profiles are given.