  We use a coarse-grained molecular dynamics simulation to investigate the
interaction between neutral or charged nanoparticles (NPs) and a vesicle
consisting of neutral and negatively charged lipids. We focus on the
interaction strengths of hydrophilic and hydrophobic attraction and
electrostatic interactions between a lipid molecule and an NP. A neutral NP
passes through the lipid membrane when the hydrophobic interaction is
sufficiently strong. As the valence of the positively charged NP increases, the
membrane permeation speed of the NP is increased compared with the neutral NP
and charged lipids are accumulated around the charged NP. A charged NP with a
high valence passes through the lipid membrane via a transient channel formed
by charged lipids or transport-like endocytosis. These permeation processes can
be classified based on analyses of the density correlation function. When the
non-electrostatic interaction parameters are large enough, a negatively charged
NP can be adsorbed on the membrane and a neutral lipid-rich region is formed
directly below the NP. The NP is spontaneously incorporated into the vesicle
under various conditions and the incorporation is mediated by the membrane
curvature. We reveal how the NP's behavior depends on the NP valence, size, and
the non-electrostatic interaction parameters.
