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 th eory 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 [Lague et at., Farad. Discuss. 111:165-172, 1998]. The theo ry 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 dipalmitoylphosph atidylcholine bilayer based on an atomic model, is used as input. For the s ake of simplicity, protein inclusions are modeled as hard repulsive cylinde rs. Numerical calculations were performed with three cylinder sizes: a smal l cylinder of 2.5-Angstrom radius, corresponding roughly to an aliphatic ch ain; a medium cylinder of 5-Angstrom radius, corresponding to a alpha -heli cal polyalanine protein; and a large cylinder of 9-Angstrom radius, represe nting a small protein, such as the gramicidin channel. The calculations sho w that the average hydrocarbon density is perturbed over a distance of 20-2 5 Angstrom 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 repulsiv e at an intermediate range but attractive at short range. At contact, there is a free energy of -2k(B)T for the 2.5-Angstrom -radius cylinder and -9k( B)T for the 5-Angstrom -radius cylinder, indicating that the association of two alpha -helices of both sizes is favored by the lipid matrix. In contra st, the effective interaction is repulsive at all distances in the case of the large cylinder. Results were obtained with two integral equations theor ies: hypernetted chain and Percus-Yevick. For the two theories, all results are qualitatively identical.