Membrane-Mediated Interaction between Strongly Anisotropic Protein Scaffolds

Abstract

Specialized proteins serve as scaffolds sculpting strongly curved membranes of intracellular organelles. Effective membrane shaping requires segregation of these proteins into domains and is, therefore, critically dependent on the protein-protein interaction. Interactions mediated by membrane elastic deformations have been extensively analyzed within approximations of large inter-protein distances, small extents of the protein-mediated membrane bending and small deviations of the protein shapes from isotropic spherical segments. At the same time, important classes of the realistic membrane-shaping proteins have strongly elongated shapes with large and highly anisotropic curvature. Here we investigated, computationally, the membrane mediated interaction between proteins or protein oligomers representing membrane scaffolds with strongly anisotropic curvature, and addressed, quantitatively, a specific case of the scaffold geometrical parameters characterizing BAR domains, which are crucial for membrane shaping in endocytosis. In addition to the previously analyzed contributions to the interaction, we considered a repulsive force stemming from the entropy of the scaffold orientation. We computed this interaction to be of the same order of magnitude as the well-known attractive force related to the entropy of membrane undulations. We demonstrated the scaffold shape anisotropy to cause a mutual aligning of the scaffolds and to generate a strong attractive interaction bringing the scaffolds close to each other to equilibrium distances much smaller than the scaffold size. We computed the energy of interaction between scaffolds of a realistic geometry to constitute tens of kBT, which guarantees a robust segregation of the scaffolds into domains.

A Model for Shaping Membrane Sheets by Protein Scaffolds

“…Previous analysis of the membrane-mediated interaction of two strongly elongated scaffolds, r a [ r b , has shown that for relevant values of the transverse curvature, c b , the scaffolds mutually orient such that their long axes tend to be parallel to each other and perpendicular to the line connecting their centers (26). In addition, the scaffolds exhibit a long-range attraction and short-range repulsion resulting in an equilibrium distance between them, which is comparable to the scaffold dimension (26). While the membrane-mediated forces between multiple scaffolds are not pairwise (28), their qualitative features should be similar to those of the two-scaffold interactions.…”

“…The convergence of the optimization conditions, the error estimations, and the accuracy criteria of the calculations have been described in our previous study of a two-scaffold system (26).…”

“…While such links cannot be generally excluded and may exist between scaffolds formed by lunapark and/or other yet undiscovered edge-generating proteins, structural data argue against direct proteinic connections between reticulons. Another possibility is that the interscaffold distance, L, and the relatively large value of the stretching modulus, k S , are established by the sufficiently strong scaffold-scaffold interactions mediated by membrane deformations (26).…”

Membrane structure formation induced by two types of banana-shaped proteins

“…It was also shown that anisotropic inclusions experience interactions of longer range than isotropic ones and are able to produce complex aggregates [29,30]. To simplify the theoretical calculations, membrane inclusions are usually modelled as non-deformable objects with a fixed curved shape [30][31][32][33]. Owing to their small sizes it is often convenient to treat them as point-like objects [30,31,34].…”

Shape deformation of lipid membranes by banana-shaped protein rods: Comparison with isotropic inclusions and membrane rupture

“…The classical Canham-Helfrich curvature free energy [32,33] has been extended to anisotropic curvatures [34][35][36]. To simplify the interactions, the protein and membrane underneath it have been often modeled together as an undeformable object with a fixed curved shape such as a point-like object with an anisotropic curvature [37,38] and a bent elliptical surface [39]. Furthermore, it has also been clarified that two undeformable parallel rods have an attractive interaction but the interaction is repulsive for a perpendicular orientation.…”