Lipid-cholesterol interactions in the P beta' phase. Application of a statistical mechanical model

We describe a statistical mechanical model for lipid-cholesterol mixtures in the P beta' (ripple) phase of lipid bilayers. The model is a simple extension of an earlier model for the ripple phase in pure lipid bilayers. The extension consists of adding a degree of freedom to allow for the occupation of underlying lattice sites by cholesterol molecules, and adding a lipid-cholesterol interaction term to the model Hamiltonian. The interaction term was constructed based on numerical calculations of lipid-cholesterol energies for several different packing juxtapositions of the two molecules. Other than the lipid-cholesterol interactions, the extended model uses the same parameter set as the earlier model, so that comparison of the properties of the extended model with experimental data serves as a test of the validity of the original model. Properties of the model were calculated using the Monte Carlo method. Results are displayed as snapshots of the ripple configurations at different cholesterol concentrations. The spacing of the ripples increases with increasing cholesterol concentration and the rate of increase compares very well with experimental data. The success of this model supports the conclusion drawn earlier that frustration arising from anisotropic packing interactions is responsible for the ripple phase in lipid bilayers. In the extended model these packing interactions are responsible for the selective partitioning of cholesterol in the regions between the ripples.