Orientation and interaction of oblique cylindrical inclusions embedded in a lipid monolayer: a theoretical model for viral fusion peptides

We consider the elastic behavior of flat lipid monolayer embedding cylindrical inclusions oriented obliquely with respect to the monolayer plane. An oblique inclusion models a fusion peptide, a part of a specialized protein capable of inducing merger of biological membranes in the course of fundamental cellular processes. Although the crucial importance of the fusion peptides for membrane merger is well established, the molecular mechanism of their action remains unknown. This analysis is aimed at revealing mechanical deformations and stresses of lipid monolayers induced by the fusion peptides, which, potentially, can destabilize the monolayer structure and enhance membrane fusion. We calculate the deformation of a monolayer embedding a single oblique inclusion and subject to a lateral tension. We analyze the membrane-mediated interactions between two inclusions, taking into account bending of the monolayer and tilt of the hydrocarbon chains with respect to the surface normal. In contrast to a straightforward prediction that the oblique inclusions should induce tilt of the lipid chains, our analysis shows that the monolayer accommodates the oblique inclusion solely by bending. We find that the interaction between two inclusions varies nonmonotonically with the interinclusion distance and decays at large separations as square of the distance, similar to the electrostatic interaction between two electric dipoles in two dimensions. This long-range interaction is predicted to dominate the other interactions previously considered in the literature.