The interplay between curvature and composition in binary mixture lipid bilayers

In this work we investigate, via computer simulations with an implicit-solvent coarse-grained model, the interplay between curvature and composition in self- assembled lipid structures comprised by two lipid species with different spontaneous curvatures. The different structures considered in this study are: i) planar bilayers with thermally induced shape fluctuations, which allow the investigation of low curvature regimes, ii) cylindrical bilayers with different mid- plane radius of curvature and iii) inverted-monolayer tubes immersed in an hydrophobic solvent. Beside these different self-assembled morphologies and curvature regimes, this study also considers different degrees of segregation between unlike lipid species. To analyze the results from simulations with planar and cylindrical bilayers, a phenomenological model describing the thermodynamics of mixing in the two monolayers of lipid membranes was proposed. The novelty of this model is that beside incorporating contributions from the free energy of mixing on the two membrane leaflets, it also accounts for their difference in curvature. The later contribution becomes particularly important for membranes whose local curvature modulations are comparable to the inverse bilayer thickness. A salient prediction of the model is the existence of a saturation curvature for which the composition difference between the apposing leaflets becomes maximal. The occurrence of this saturation curvature will depend on system segregation. In particular, for low incompatibility between lipid species, the saturation curvature may lie beyond the inverse bilayer thickness, which sets a limit on the curvatures that are physically accessible to the system. In contrast, for high incompatibility the saturation curvature may be comparable to the thermally-induced curvature fluctuations observed in planar bilayers. Another advantage of the proposed model is that many of its parameters can be directly measured from easily accessible experimental quantities, such as the power spectra of shape and composition fluctuations. Furthermore, the two parameters to fit from measurements of the local curvature and composition asymmetry across the bilayer, are directly related to the intrinsic curvature of the constituting lipids.Finally, spontaneous curvatures from the analysis with bilayer membranes were in good agreement with those obtained from a common experimental technique, where lipids with unknown curvature are inserted into an inverted structure whose self-assembled and spontaneous curvatures coincide. It has been seen, however, that this technique may only be used under low segregation conditions and that the anisotropy of this inverted structures together with the change of lipid conformations due to the interdigitation of the hydrophobic solvent inside of the tail region may induce errors in the determination of the spontaneous curvature of the guest lipids