A calibration model on dynamic measurements of nanoparticles endocytosis

Recent advances in force tracing technique have revealed that cellular uptake of nanoparticle (NP) is a time-, force- and energy-dependent and cytoskeleton associated process. However, as it remains largely elusive on the role that cytoskeleton remodeling plays during the NP internalization, there are still no existing calibration models that are able to quantitatively relate the experimentally measured driving forces to associated endocytic processes. In this study, we have established a viscoelastic model on the dynamics of NP internalization by accounting contributions of binding energy released from ligand-receptor complexes, viscoelastic deformation of cytoskeleton, and elastic deformations of cell membrane and probe system. Based on this model, we have analytically identified the engulfing driving force associated with the endocytic process, which are found in good agreement with recent experimental measurements through advanced force tracing techniques. This fact confirms that the proposed model can be used to calibrate endocytosis experiments on NPs, and the endocytic dynamics of NPs is indeed regulated by the creep behaviour associated with cytoskeleton remodeling