  The shape transformations of fluid membranes induced by curved protein rods
are studied using meshless membrane simulations. The rod assembly at low rod
density induces a flat membrane tube and oblate vesicle. It is found that the
polyhedral shapes are stabilized at high rod densities. The discrete shape
transition between triangular and buckled discoidal tubes is obtained and their
curvature energies are analyzed by a simple geometric model. For vesicles,
triangular hosohedron and elliptic-disk shapes are formed in equilibrium,
whereas tetrahedral and triangular prism shapes are obtained as metastable
states.
