Nonadditivity in Many-Body Interactions between Membrane-Deforming Spheres Increases Disorder

Membrane-induced interactions play an important role
in organizing
membrane proteins. Measurements of the interactions between two and
three membrane deforming objects have revealed their nonadditive nature.
They are thought to lead to complex many-body effects, however, experimental
evidence is lacking. 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 confined colloidal particles cause a large deformation
of the membrane while not being physicochemically attached to it and
interact through it. Two particles attract with a maximum force of
0.2 pN. For three particles, compact equilateral triangles were preferred
over linear arrangements. 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, at the same time, diffusivity of the particles increases.
Our experiments show that the nonadditive 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.