Abstract
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.
Highlights
In the case of receptordiffusion-mediated endocytosis of NPs, we have previously examined the effect of ligand distribution on wrapping cylindrical NPs by cell membrane and determined an almost uniform ligand distribution as the optimal distribution associated with the highest cellular uptake efficiency [35]
We propose a coupled elasticity–diffusion statistical dynamic model to investigate the influence of ligand distribution on the cellular uptake of ellipsoidal NPs, where we assume that the uptake process is driven by the binding energy between diffusive receptors on the cell membrane and ligands on the NP surface to overcome resistances from membrane deformation, cytoskeleton deformation, and changes in the configuration entropy of receptors
We provide a detailed description on the dependence of the optimal ligand distribution on the NP shape and cytoskeleton stiffness, we have treated the NPs as a rigid body
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. A thorough understanding of the interaction between nanoparticles (NPs) and cells is of significant interest. The effective design of NPs with penetration capability in target drug delivery systems is expected, and the safety and toxicity in extensive applications of industrial NPs [1,2,3] should be of considerable concern. Given the prevalent assumption that ligands are uniformly distributed, an open question about how ligand distribution may affect the internalization of NPs into cells is raised, despite the considerable progress mentioned above
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