Size Limit and Energy Analysis of Nanoparticles during Wrapping Process by Membrane

The wrapping of nanoparticles (NPs) by a membrane is a phenomenon of widespread and generic interest in biology, as well as in a variety of technological applications, such as drug delivery, clinical diagnostics, and biomedical imaging. However, the mechanisms of the interaction between the membrane and NPs are not well understood yet. In this paper, we have presented an analytic thermodynamic model to investigate the wrapping process of NPs by a cell membrane. It is found that the bending energy of the deformed membrane increases nonlinearly with increasing wrapping degree, which leads to a free energy barrier for the wrapping. On the basis of analysis results, the wrapping of NPs can be divided into three types, i.e., impossible wrapping, barrier wrapping, and free wrapping. Furthermore, a phase diagram for the wrapping of NPs has been constructed, which clarifies the interrelated effects of the size and the ligand density of NPs. We hope that this work can provide some help in understanding the physical mechanism of the wrapping of NPs.