The Nuclear Pore Complex (NPC) is a large protein complex that controls the flow of ions, small biomolecules, proteins and mRNA into and out of the nuclei of eukaryotic cells. A major component of the NPC consists of natively unfolded nucleoporin (nup) proteins, which are anchored on the inside of a cylindrical pore scaffold. They form a polymer brush that assists in the regulation of cargo flow from nucleus to cytoplasm. Large molecules that enter/leave the nucleus must attach themselves to special receptor proteins that ferry the cargo molecules in/out of nucleus. Via hydrophobic contacts between the receptor protein and the nup filaments, the receptor proteins bind weakly and reversibly to the nup filaments and make their way through the pore, via a mechanism which is at present unknown. The complexity of the in vivo NPC motivates construction of coarse-grained models which can capture some of its essential features while retaining computational tractability. We have developed such a model, focusing particularly on the interactions of this polymer brush with solution phase nanoparticles that are attractive to brush monomers (mimicking the attraction of receptor proteins to hydrophobic segments of nup filaments in the NPC). These attractions cause the nanoparticles to infiltrate into the polymer brush and alter its brush morphology. We have developed a Self-Consistent Field Theory (SCFT) model to analyze the equilibrium properties of the brush-nanoparticle system in an approximate but computationally efficient manner. In addition, we have performed large scale coarse-grained Molecular/Langevin Dynamics simulations to explore the same properties. A variety of results pertaining to collapse/expansion of the brush upon nanoparticle infiltration will be presented. Their relevance to the in vivo mechanism of NPC operation will be stressed.