Membrane-mediated interactions between arc-shaped particles adsorbed on vesicles

Membrane-bound curved proteins and scaffolds remodel lipid membranes by imposing local curvature and interacting through membrane-mediated elastic forces. Although collective morphologies induced by arc-shaped scaffolds have been studied extensively, the elementary pair interaction between two isolated arc-shaped particles on a closed vesicle remains less well characterized. Here, we determine the membrane-mediated pair-interaction free energy between two rigid arc-shaped particles adsorbed on a fluid triangulated vesicle. Using umbrella-sampling Monte Carlo simulations and weighted histogram analysis, we reconstruct the potential of mean force as a function of the center-to-center distance between the particles. Direct attractive interactions are not included, and the adhesion strength is chosen such that the particles remain strongly bound to the membrane. We systematically vary the particle radius of curvature and arc angle, which control the curvature mismatch with the vesicle and the membrane-bound footprint. The free-energy profiles show a robust membrane-mediated attraction that becomes stronger for larger arc angles and smaller particle radii. Interaction maps further reveal that the total attraction is controlled by both footprint and curvature, while area-normalized interactions demonstrate that curvature mismatch is an intrinsic driver of the attraction. These results provide a two-body free-energy basis for understanding how arc-shaped curvature-generating particles assemble on vesicles and contribute to collective membrane remodeling.