Phase transition of triangulated spherical surfaces with elastic skeletons

A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of triangulated surfaces is maintained by skeletons, which have a one-dimensional bending elasticity characterized by the bending rigidity b, and the surfaces has no two-dimensional bending elasticity except at the junctions. The surfaces swell and become spherical at large b and collapse into crumpled at small b. These two phases are separated from each other by the first-order transition. Although both of the surface and the skeleton are allowed to self-intersect and hence phantom, our results indicate a possible phase transition in biological or artificial membranes whose shape is maintained by cytoskeletons.