Role of Ligand Distribution in the Cytoskeleton-Associated Endocytosis of Ellipsoidal Nanoparticles

Nanoparticle (NP)–cell interaction mediated by receptor–ligand bonds is a crucial phenomenon in pathology, cellular immunity, and drug delivery systems, and relies strongly on the shape of NPs and the stiffness of the cell. Given this significance, a fundamental question is raised on how the ligand distribution may affect the membrane wrapping of non-spherical NPs under the influence of cytoskeleton deformation. To address this issue, in this work we use a coupled elasticity–diffusion model to systematically investigate the role of ligand distribution in the cytoskeleton-associated endocytosis of ellipsoidal NPs for different NP shapes, sizes, cytoskeleton stiffness, and the initial receptor densities. In this model, we have taken into account the effects of receptor diffusion, receptor–ligand binding, cytoskeleton and membrane deformations, and changes in the configuration entropy of receptors. By solving this model, we find that the uptake process can be significantly influenced by the ligand distribution. Additionally, there exists an optimal state of such a distribution, which corresponds to the fastest uptake efficiency and depends on the NP aspect ratio and cytoskeleton stiffness. We also find that the optimal distribution usually needs local ligand density to be sufficiently high at the large curvature region. Furthermore, the optimal state of NP entry into cells can tolerate slight changes to the corresponding optimal distribution of the ligands. The tolerance to such a change is enhanced as the average receptor density and NP size increase. These results may provide guidelines to control NP–cell interactions and improve the efficiency of target drug delivery systems.