Multiple 10 nm-sized anionic nanoparticles complexed with plasma proteins (human serum albumin (SA) or immunoglobulin gamma-1 (IgG)) at different ratios are simulated using all-atom and coarse-grained models. Coarse-grained simulations show much larger hydrodynamic radii of individual particles at a low protein concentration (a protein-to-particle ratio of 1) than at high protein concentrations or without proteins, indicating particle aggregation only at such a low protein concentration, in agreement with experiments. This particle aggregation is attributed to both electrostatic and hydrophobic particle-protein interactions, to an extent dependent on different proteins. In all-atom simulations, IgG proteins induce particle aggregation with and without salt, while SA proteins promote particle aggregation only in the presence of salt that can weaken the electrostatic repulsion between anionic particles closely linked via SA that is smaller than IgG, which also agree well with experiments. Besides charge interactions, hydrophobic interactions between particles and proteins are also important especially at the high salt concentration, leading to the increased particle-protein contact area. These findings help explain experimental observations regarding that the effects of protein concentration and ionic strength on particle aggregation depend on different plasma proteins, which are interpreted by binding free energies, electrostatic, and hydrophobic interactions between particles and proteins.