  Membrane budding and wrapping of particles, such as viruses and
nano-particles, play a key role in intracellular transport and have been
studied for a variety of biological and soft matter systems. We study
nano-particle wrapping by numerical minimization of bending, surface tension,
and adhesion energies. We calculate deformation and adhesion energies as a
function of membrane elastic parameters and adhesion strength to obtain
wrapping diagrams. We predict unwrapped, partially-wrapped, and
completely-wrapped states for prolate and oblate ellipsoids for various aspect
ratios and particle sizes. In contrast to spherical particles, where
partially-wrapped states exist only for finite surface tensions,
partially-wrapped states for ellipsoids occur already for tensionless
membranes. In addition, the partially-wrapped states are long-lived, because of
an increased energy cost for wrapping of the highly-curved tips. Our results
suggest a lower uptake rate of ellipsoidal particles by cells and thereby a
higher virulence of tubular viruses compared with icosahedral viruses, as well
as co-operative budding of ellipsoidal particles on membranes.
