  The assembly of curved protein rods on fluid membranes is studied using
implicit-solvent meshless membrane simulations. As the rod curvature increases,
the rods on a membrane tube assemble along the azimuthal direction first and
subsequently along the longitudinal direction. Here, we show that both
transition curvatures decrease with increasing rod stiffness. For comparison,
curvature-inducing isotropic inclusions are also simulated. When the isotropic
inclusions have the same bending rigidity as the other membrane regions, the
inclusions are uniformly distributed on the membrane tubes and vesicles even
for large spontaneous curvature of the inclusions. However, the isotropic
inclusions with much larger bending rigidity induce shape deformation and are
concentrated on the region of a preferred curvature. For high rod density, high
rod stiffness, and/or low line tension of the membrane edge, the rod assembly
induces vesicle rupture, resulting in the formation of a high-genus vesicle. A
gradual change in the curvature suppresses this rupture. Hence, large stress,
compared to the edge tension, induced by the rod assembly is the key factor
determining rupture. For rod curvature with the opposite sign to the vesicle
curvature, membrane rupture induces inversion of the membrane, leading to
division into multiple vesicles as well as formation of a high-genus vesicle.
