Curvature-mediated cooperative wrapping of multiple nanoparticles at the same and opposite membrane sides

Cell membrane interactions with nanoparticles (NPs) are essential to cellular functioning and mostly accompanied by membrane curvature generation and sensing. Multiple NPs inducing curvature from one side of a membrane are believed to be wrapped cooperatively by the membrane through curvature-mediated interactions. However, little is known about another biologically ubiquitous and important case, i.e., NPs binding to opposite membrane sides induce a curved bend of different directions. Combining coarse-grained molecular dynamics and theoretical analysis, here we systematically investigate the cooperative effect in the wrapping of multiple adhesive NPs at the same and opposite membrane sides and demonstrate the importance of the magnitude and direction of the membrane bend in regulating curvature-mediated NP interactions. Effects of the NP size, size difference, initial distance, number, and strength of adhesion with the membrane on the wrapping cooperativity and wrapping states are analyzed. For NPs binding to the same membrane side, rich membrane wrapping and NP aggregation states are observed, and the curvature-mediated interactions could be either attractive or repulsive, depending on the initial NP distance and the competition between the membrane bending, NP binding and membrane protrusion. In sharp contrast, the interaction between two NPs binding to opposite membrane sides is always attractive and the cooperative wrapping of NPs is promoted, as the curved membrane regions induced by the NPs are shared in a manner that the NP-membrane contact is increased and the energy cost of membrane bending is reduced. Owing to the ubiquity and heterogeneity of membrane shaping proteins in biology, our results enrich the cutting-edge knowledge on the curvature-mediated interaction of NPs for better and profound understanding on high-order cooperative assemblies of NPs or proteins in numerous biological processes.