Protein corona impact on nanoparticle-cell interactions: toward an energy-based model of endocytosis.

Upon incubation of nanoparticles in biological fluids, a new layer called the protein corona is formed on their surface affecting the interactions between nanoparticles and targeted cells during the endocytosis process. In the present study, a mathematical model based on the diffusion of membrane mobile receptors is proposed. Opposing the endocytosis proceeding, membrane bending and tension energies are named as resistant energy. Also, the binding energy and free-energy associated with the configurational entropy are collectively termed promoter energy. Utilizing this model, endocytosis of gold nanoparticle (GNP) is simulated to explore the biological media effect. The results reveal that there exists a nanoparticle size of 60 nm at which, the endocytosis time is at a minimum. It has been illustrated that, although for sufficiently small particles of diameter 30nm, membrane tension has a negligible contribution (<10%) in the resistant energy, it noticeably increases the endocytosis processing time for large particles. Therefore, we report several parametric studies to provide a better insight into the effects of biological media on the ingestion of nanoparticles. Through a detailed analysis of the engulfment of the nanoparticles, it is shown that the nanoparticle radius corresponding to the quickest possible ingestion time is affected in the presence of corona. Moreover, it is found that the formation of this layer does not only affect the endocytosis time but also can lead to incomplete engulfment by decreasing the ligand density on the nanoparticle surface. Use of the proposed model can play a significant role in advancing the design of nanoparticles in targeted drug delivery applications.