  Experiments show that cellular uptake of nanoparticles, via receptor-mediated
endocytosis, strongly depends on nanoparticle size. There is an optimal size,
approximately 50 nm in diameter, at which cellular uptake is the highest. In
addition, there is a maximum size, approximately 200 nm, beyond which uptake
via receptor-mediated endocytosis does not occur. By comparing results from
different experiments, we found that these sizes weakly depend on the type of
cells, nanoparticles, and ligands used in the experiments. Here, we argue that
these observations are consequences of the energetics and assembly dynamics of
the protein coat that forms on the cytoplasmic side of the outer cell membrane
during receptor-mediated endocytosis. Specifically, we show that the energetics
of coat formation imposes an upper bound on the size of the nanoparticles that
can be internalized, whereas the nanoparticle-size-dependent dynamics of coat
assembly results in the optimal nanoparticle size. The weak dependence of the
optimal and maximum sizes on cell-nanoparticle-ligand type also follows
naturally from our analysis.
