Non-additivity in interactions between three membrane-wrapped colloidal spheres

Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that these proteins induce. While the pairwise interaction potential of two membrane deforming spheres has recently been measured, membrane-deformation induced interactions have been predicted to be non-additive and hence their collective behavior cannot be deduced from this measurement. We here employ a colloidal model system consisting of adhesive spheres and giant unilamellar vesicles to test these predictions by measuring the interaction potential of the simplest case of three membrane-deforming spherical particles. We quantify their interactions and arrangements and for the first time experimentally confirm and quantify the non-additive nature of membrane-deformation induced interactions. We furthermore conclude that there exist two favorable configurations on the membrane: (1) a linear, and (2) a triangular arrangement of the three spheres. Using Monte Carlo simulations we corroborate the experimentally observed energy minima and identify a lowering of the membrane deformation as the cause for the observed configurations. The high symmetry of the preferred arrangements for three particles suggests that arrangements of many membrane-deforming objects might follow simple rules.