Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such large-scale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvature-mediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvature-mediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarse-grained membrane simulations to show that curvature-inducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvature-mediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.

Particles binding to a fluid lipid membrane can induce bilayer deformations, for instance when these particles are curved. Since the energy of two overlapping warp fields depends on the mutual distance between the two particles creating them, they will experience forces mediated by the curvature of the membrane. If the deformations are sufficiently weak, the associated differential equations for the membrane shape are linear, and the resulting interactions are understood very well; but very little is known for stronger curvature imprint, owing to the highly nonlinear nature of the problem. Here we numerically calculate the magnitude of such membrane-mediated interactions in the case of two axisymmetric particles over a wide range of curvature imprints, deep into the nonlinear regime. We show that over an intermediate distance range the sign of the force reverses beyond a sufficiently strong deformation. These findings are quantitatively confirmed by a simple analytical close-distance expansion. The sign flip can be traced to a change in magnitude between the two principal curvatures midway between the two particles, which can only occur at sufficient particle tilt, a condition which is by construction ruled out in the linearized description. We also show these large perturbation results to agree with coarse-grained molecular dynamics simulations and suggest that a favorable comparison is indeed more likely to hold in the strongly deformed regime.

The authors investigate membrane composition-mediated interactions between proteins adsorbed onto a two-component lipid bilayer close to critical demixing using coarse-grained molecular dynamics simulations and a phenomenological Ginzburg-Landau theory. The simulations consist of three-bead lipids and platelike proteins, which adsorb onto the membrane by binding preferentially to one of the two lipid species. The composition profile around one protein and the pair correlation function between two proteins are measured and compared to the analytical predictions. The theoretical framework is applicable to any scalar field embedded in the membrane, and although in this work the authors treat flat membranes, the methodology extends readily to curved geometries. Neglecting fluctuations, both lipid composition profile and induced protein pair potential are predicted to follow a zeroth order modified Bessel function of the second kind with the same characteristic decay length. These predictions are consistent with our molecular dynamics simulations, except that the interaction range is found to be larger than the single profile correlation length.