Lipid-mediated interactions between intrinsic membrane proteins: a theoretical study based on integral equations.

This study of lipid-mediated interactions between proteins is based on a theory recently developed by the authors for describing the structure of the hydrocarbon chains in the neighborhood of a protein inclusion embedded in a lipid membrane [Lagüe et al., Farad. Discuss. 111:165-172, 1998]. The theory involves the hypernetted chain integral equation formalism for liquids. The exact lateral density-density response function of the hydrocarbon core, extracted from molecular dynamics simulations of a pure dipalmitoylphosphatidylcholine bilayer based on an atomic model, is used as input. For the sake of simplicity, protein inclusions are modeled as hard repulsive cylinders. Numerical calculations were performed with three cylinder sizes: a small cylinder of 2.5-A radius, corresponding roughly to an aliphatic chain; a medium cylinder of 5-A radius, corresponding to a alpha-helical polyalanine protein; and a large cylinder of 9-A radius, representing a small protein, such as the gramicidin channel. The calculations show that the average hydrocarbon density is perturbed over a distance of 20-25 A from the edge of the cylinder for every cylinder size. The lipid-mediated protein-protein effective interaction is calculated and is shown to be nonmonotonic. In the case of the small and the medium cylinders, the lipid-mediated effective interaction of two identical cylinders is repulsive at an intermediate range but attractive at short range. At contact, there is a free energy of -2k(B)T for the 2.5-A-radius cylinder and -9k(B)T for the 5-A-radius cylinder, indicating that the association of two alpha-helices of both sizes is favored by the lipid matrix. In contrast, the effective interaction is repulsive at all distances in the case of the large cylinder. Results were obtained with two integral equations theories: hypernetted chain and Percus-Yevick. For the two theories, all results are qualitatively identical.