Protein inclusion in lipid membranes: A theory based on the hypernetted chain integral equation

A theory for describing the structure of the hydrocarbon chains around a pr otein inclusion embedded in a lipid bilayer is developed on the basis of th e hypernetted chain integral equation formalism for liquids. The exact late ral density-density response function of the hydrocarbon core, which is ext racted from a molecular dynamics simulation of a pure lipid bilayer, is use d as input to the theory. Numerical calculations show that the average lipi d order is perturbed over a distance of 25 to 30 Angstrom around a hard rep ulsive cylinder of 5 Angstrom radius representing an alpha-helical polyleuc ine protein inclusion. The lipid-mediated protein-protein interaction is ca lculated and is shown to be non-monotonic, being repulsive at an intermedia te range but attractive at short range. It is found that the lipid matrix c ontributes a free energy well of 8 k(B)T to the association of two cylindri cal inclusions.