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 protein inclusion embedded in a lipid bilayer is developed on the basis of the hypernetted chain integral equation formalism for liquids. The exact lateral density-density response function of the hydrocarbon core, which is extracted from a molecular dynamics simulation of a pure lipid bilayer, is used as input to the theory. Numerical calculations show that the average lipid order is perturbed over a distance of 25 to 30 A around a hard repulsive cylinder of 5 A radius representing an alpha-helical polyleucine protein inclusion. The lipid-mediated protein-protein interaction is calculated and is shown to be non-monotonic, being repulsive at an intermediate range but attractive at short range. It is found that the lipid matrix contributes a free energy well of 8 kBT to the association of two cylindrical inclusions.