Statistical Modeling of Ligand-Mediated Multimeric Nanoparticle Assembly

Understanding and controlling nanoparticle (NP) assembly have tremendous importance and impact in nanoscience, materials science, physical sciences, and nanobiotechnology. Although NP assembly has been heavily studied and used, a general model that describes the NP assembly process from a monomer to a multimer supported by experimental data has not been established. In this study, we developed a statistical model [NP self-assembly statistical estimation model with blocking and linking efficiency (NSSEMBLE)] to quantitatively describe multimeric NP assembly and provide directional information for forming, analyzing, and utilizing desired assembled nanostructures. The proposed approach is a straightforward probabilistic model considering the distribution of the ligands on NPs, ligand-linking efficiency, and excluded area based on the steric effect between NPs. As a proof of concept, we demonstrated the multimeric assembly of DNA-modified gold NPs that follows the NSSEMBLE-guided behavior. Moreover, using the results of electron microscopy-based experimental analysis, a set of parameters such as the ligand-linking efficiency (epsilon(1))and section number (s) could be estimated by a fitting process. We found that the estimated model could explain and predict the distribution of multimeric NP clusters in terms of the ligand-linking efficiency and steric effect. Importantly, based on zeta potential measurement data, we have shown that the parameter values (epsilon(1,s)) from the NSSEMBLE not only enable the prediction of the NP assembly distribution and yield but also provide physical, chemical, and mechanistic insights for multimeric NP assembly. The model provides quantitative and analytical information and insight into not only the formation of assembled nanostructures but also the molecular features of the ligands on the NPs during the dynamic binding process.