Kinetics of receptor-mediated endocytosis of elastic nanoparticles

It is now widely recognized that mechanical properties play critical roles in the cell uptake of nanomaterials. Here we conduct a theoretical study on the kinetics of receptor-mediated endocytosis of elastic nanoparticles that is limited by receptor diffusion, specifically focusing on how the uptake rate depends on the nanoparticle stiffness and size, membrane tension and binding strength between membrane receptors and ligands grafted on the nanoparticle surface. It is shown that, while soft nanoparticles are energetically less prone to full wrapping than stiff ones, the wrapping of the former is kinetically faster than that of the latter. Spherical and cylindrical elastic nanoparticles show dramatic differences in the effect of stiffness on the uptake rate. Additional theoretical analysis is performed to investigate the role of the stochastic receptor-ligand binding in the endocytosis of elastic nanoparticles. The relation between the uptake efficiency and uptake proneness is discussed. This study provides new insight into the elasticity effects on cell uptake and may serve as a design guideline for the controlled endocytosis and diagnostics delivery.