Two-dimensional convex-molecule fluid model for surface adsorption of proteins: effect of soft interaction on adsorption equilibria

Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube

Curvature induced sorting of lipid membrane bound proteins has been widely studied through experiments that induce curvature variation in a giant unilamellar lipid-bilayer vesicle with adsorbed proteins by pulling thin cylindrical tethers. In the theoretical space, this has been supplemented with models that capture curvature dependent interaction between membrane and idealized protein particles, through free energy contributions. Many membrane proteins such as the BAR domain proteins are known to have extremely anisotropic shapes and soft interacting potentials, whereas the idealizations of protein particles explored in models have only assumed them as hard disk-like particles with curvature anisotropy. Here, we present a model of sorting of the proteins while including the effects of softness in their interaction potentials, shape anisotropy in the protein structure, and curvature anisotropy in the interactions with the membrane. This is based on a clean separation of free energy contributions from non-ideal fluid behavior of soft anisotropic particles and curvature interactions between proteins and membranes. We probe the behavior of the sorting function under limiting conditions and show that it converges to the previously derived models. In addition to this, we present a comparison of the variation in sorting ratio due to the observed variation in the shape parameter values in known membrane proteins. Finally, using published experimental data for membrane proteins, we perform fitting and derive model parameters. We observe that shape anisotropy adversely affects the sorting of proteins to a high curvature region, whereas curvature anisotropy and softer interaction between proteins favor sorting.

Sorting of integral membrane proteins mediated by curvature-dependent protein-lipid bilayer interaction

Cell membrane proteins, both bound and integral, are known to preferentially accumulate at membrane locations with curvatures favorable to their shape. This is mainly due to the curvature dependent interaction between membrane proteins and their lipid environment. Here, we analyze the effects of the protein-lipid bilayer interaction energy due to mismatch between the protein shape and the principal curvatures of the surrounding bilayer. The role of different macroscopic parameters that define the interaction energy term is elucidated in relation to recent experiment in which the lateral distribution of a membrane embedded protein potassium channel KvAP is measured on a giant unilamellar lipid vesicle (reservoir) and a narrow tubular extension - a tether - kept at constant length. The dependence of the sorting ratio, defined as the ratio between the areal density of the protein on the tether and on the vesicle, on the inverse tether radius is influenced by the strength of the interaction, the intrinsic shape of the membrane embedded protein, and its abundance in the reservoir. It is described how the values of these constants can be extracted from experiments. The intrinsic principal curvatures of a protein are related to the tether radius at which the sorting ratio attains its maximum value. The estimate of the principal intrinsic curvature of the protein KvAP, obtained by comparing the experimental and theoretical sorting behavior, is consistent with the available information on its structure.