  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 simulation 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.
