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 NPs behavior depends on the NP valence, size, and the non-electrostatic interaction parameters.
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