  Cellular internalization of nanoparticles requires the full wrapping of the
nanoparticles by the cell membrane. This wrapping process can occur
spontaneously if the adhesive interactions between the nanoparticles and the
membranes are sufficiently strong to compensate for the cost of membrane
bending. In this article, we show that the membrane curvature prior to wrapping
plays a key role for the wrapping process, besides the size and shape of the
nanoparticles that have been investigated in recent years. For membrane
segments that initially bulge away from nanoparticles by having a mean
curvature of the same sign as the mean curvature of the particle surface, we
find strongly stable partially wrapped states that can prevent full wrapping.
For membrane segments that initially bulge towards the nanoparticles, in
contrast, partially wrapped states can constitute a significant energetic
barrier for the wrapping process.
