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Understanding the cell membrane penetration process of biomedical nanosystems and its dependence on nanomaterial properties and surface functionalization is crucial for the rational design of safe and efficient cellular internalization strategies. Computer simulations are powerful tools to evaluate the thermodynamic aspects of the process and to elucidate its underlying molecular mechanisms. In this work, the interaction between uncoated or polymer-coated graphene oxide (GO) dots and lipid bilayer models is investigated by coarse-grained (CG) molecular dynamics (MD) simulations. We first validate the coarse-grained model against all-atom MD simulations (AAMD). Then, we perform CGMD simulations and free energy calculations to assess the effect of the polymeric coating and of its features (grafting density, polymer end-group charge and polymer hydrophilic/hydrophobic character) on the interaction between GO dots of realistic size and lipid membranes. We find that the membrane penetration of GO dots is spontaneous when coated with a low-density polyethylene glycol (PEG) layer, while a high-density PEG coating prevents the penetration, and a mixed PEG/polyethylene (PE) coating excessively stabilizes the nanosystem in the inner membrane region. These findings will help to fine-tune how GO dots interact with cellular membranes.