Size-Dependent Endocytosis of Nanoparticles.

Adv. Mater. 2009, 21, 419–424 2009 WILEY-VCH Verlag Gm IC A T IO N Recent advances in nanotechnology have stimulated novel applications in biomedicine where nanoparticles (NPs) are used to achieve drug delivery and photodynamic therapy. In chemotherapeutic cancer treatment, tumor-specific drug delivery is a topic of considerable research interest for achieving enhanced therapeutic efficacy and for mitigating adverse side effects. Most anticancer agents are incapable of distinguishing between benign and malignant cells, and consequently cause systematic toxicity during cancer treatment. Owing to their small size, ligand-coated NPs can be efficiently directed toward, and subsequently internalized by tumor cells through ligand–receptor recognition and interaction (see Fig. 1), thereby offering an effective approach for specific targeting of tumor cells. For example, branching dendrimers have recently been identified as potential candidates for site-specific drug carriers. NPs have also been exploited in other biomedical applications such as bioimaging and biosensing. It has been demonstrated that florescent quantum dots are efficient in tumor cell imaging, recognition, and tracking, and that gold NPs are capable of detecting small proteins. To enable rational design of such NP-based agents, it is essential to understand the underlying mechanisms that govern the transmembrane transport and invagination of NPs in biological cells. In this communication, we present a thermodynamic model for receptor-mediated endocytosis of ligandcoated NPs. We identify an optimal NP radius at which the cellular uptake reaches a maximum of several thousand at physiologically relevant parameters, and we show that the cellular uptake of NPs is regulated by membrane tension, and can be elaborately controlled by particle size. The optimal NP radius for endocytosis is on the order of 25–30 nm, which is in good agreement with prior estimates. Theoretical models have provided insights into the dynamics of receptor-mediated endocytosis based on energetic and kinetic considerations, primarily in the context of virus budding. Lerner et al. argued that the discreteness of membrane wrapping via ligand-receptor binding results in a corrugated energy landscape for NP wrapping, which governs the kinetics of endocytosis. In contrast, Gao et al. proposed that the endocytic rate is limited by the diffusion of receptors toward the NP. They predicted that NPs with a radius of approximately 25 nm have the shortest internalization time of about 20 minutes, which appears to be consistent with certain experimental data. The aforementioned models have attempted to rationalize the mechanisms of receptor-mediated endocytosis from a kinetic point of view and have sought to address the question of ‘‘how fast’’ a single NP can be transported into the cell. In this work, we address an equally important question to the realization of NP-based cell type-specific targeting units, namely, ‘‘how many’’ NPs can be endocytosed in a sufficiently long period? The question is important for a range of medical and biological applications of NPs, including the maximum numbers of proteins tagged when NPs are used to protein targeting, and the maximum drug-delivery capability when NPs are used to internalize drug molecules. We approach the problem from a different viewpoint by invoking thermodynamic arguments. In order to develop a quantitative framework for this problem, we consider a cell immersed in a solution with dispersed ligandcoated NPs. Driven by the chemical potential difference of the adherent and suspended NPs, the many-NP-cell system reaches a thermodynamic equilibrium at which a certain number of NPs are endocytosed. The existence of the thermodynamic equilibrium is suggested by recent experiments where the cellular uptake of NPs increases at the initial stage of cell incubation, and