Effects of particle size and ligand density on the kinetics of receptor-mediated endocytosis of nanoparticles

We elucidate, from thermodynamic arguments, the governing factors of receptor-mediated endocytosis of nanoparticles (NPs). We show that the endocytic energetics specifies a minimal particle size and a minimal ligand density below which endocytosis is not possible. Due to the entropic penalty involved in ligand-receptor binding, endocytosis may occur with a large fraction of ligands unbound with receptors. Our analyses suggest that the endocytic time depends interrelatedly on the particle size and ligand density. There exists an optimal condition at which the endocytic time minimizes. These findings may provide valuable guidance to the rational designs of NP-based biomarkers and anticancer bioagents.