Non-additivity in many-body interactions between membrane-deforming spheres increases disorder

Membrane-induced interactions have been predicted to be important for the organization of membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their non-additive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking to date. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The thus confined colloidal particles cause a large deformation of the membrane while not being physochemically attached to it and interact through it. Two particles are found to attract with a maximum force of 0.2~pN. For three particles, we observe a preference for forming compact equilateral triangles over a linear arrangement. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, while at the same time, diffusivity of the particles increases. Our experiments for the first time show that the non-additive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.