  The point-curvature model for membrane protein inclusions is shown to capture
multibody interactions very well. Using this model, we find that the interplay
between membrane tension and multibody interactions results in a collective
attraction of oppositely curved inclusions tending to form antiferromagnetic
structures with a square lattice. This attraction can produce a phase
separation between curved and non-curved proteins, resulting in the clustering
of curved proteins. We also show that the many-body repulsion between identical
curved proteins is enhanced by membrane tension. This can lead to the
dissolution of clusters stabilized by short-range forces when the tension is
increased. These new phenomena are biologically relevant and could be
investigated experimentally
