Larger nanoparticles
can act as a cross-linking agent to cluster receptors and induce uptake. Thermodynamically, a
40–50-nm nanoparticle is capable of recruiting and binding enough receptors to successfully produce
membrane wrapping. Above 50 nm, nanoparticles bind such a large number of receptors
that uptake is limited by the redistribution of receptors on the cell membrane via diffusion to
compensate for local depletion. Nanoparticles larger than 50 nm bind with high affinity to a great
number of receptors and may limit the binding of additional nanoparticles. Mathematical modeling
of this phenomenon has demonstrated that optimal endocytosis occurs when there is no
ligand shortage on the nanoparticle and no localized receptor shortage on the cell surface