Nonadditivity in\nMany-Body Interactions between Membrane-Deforming\nSpheres Increases Disorder

Membrane-induced interactions play an important role\nin organizing\nmembrane proteins. Measurements of the interactions between two and\nthree membrane deforming objects have revealed their nonadditive nature.\nThey are thought to lead to complex many-body effects, however, experimental\nevidence is lacking. We here present an experimental method to measure\nmany-body effects in membrane-mediated interactions using colloidal\nspheres placed between a deflated giant unilamellar vesicles and a\nplanar substrate. The confined colloidal particles cause a large deformation\nof the membrane while not being physicochemically attached to it and\ninteract through it. Two particles attract with a maximum force of\n0.2 pN. For three particles, compact equilateral triangles were preferred\nover linear arrangements. We use numerical energy minimization to\nestablish that the attraction stems from a reduction in the membrane-deformation\nenergy caused by the particles. Confining up to 36 particles, we find\na preference for hexagonally close packed clusters. However, with\nincreasing number of particles the order of the confined particles\ndecreases, at the same time, diffusivity of the particles increases.\nOur experiments show that the nonadditive nature of membrane-mediated\ninteractions affects the interactions and arrangements and ultimately\nleads to spherical aggregates with liquid-like order of potential\nimportance for cellular processes.