Advances in the understanding of nanomaterial-biomembrane interactions and their mathematical and numerical modeling.

The widespread application of nanomaterials (NMs), which has accompanied advances in nanotechnology, has increased their chances of entering an organism, for example, via the respiratory system, skin absorption or intravenous injection. Although accumulating experimental evidence has indicated the important role of NM-biomembrane interaction in these processes, the underlying mechanisms remain unclear. Computational techniques, as an alternative to experimental efforts, are effective tools to simulate complicated biological behaviors. Computer simulations can investigate NM-biomembrane interactions at the nanoscale, providing fundamental insights into dynamic processes that are challenging to experimental observation. This paper reviews the current understanding of NM-biomembrane interactions, and existing mathematical and numerical modeling methods. We highlight the advantages and limitations of each method, and also discuss the future perspectives in this field. Better understanding of NM-biomembrane interactions can benefit various fields, including nanomedicine and diagnosis.