Mechanistic Modeling of Size and Surface Charge Changes of Gold and Silver Nanoparticles during In Vitro Nanoparticle Protein Corona Formation

The formation of protein corona around nanoparticles fundamentally alters their physicochemical properties and biological identity, yet quantitative predictive models for this complex process remain limited. Here, we present novel mechanistic models that predict the temporal evolution of both hydrodynamic size and ζ-potential during nanoparticle–protein corona formation for gold (AuNPs) and silver nanoparticles (AgNPs) interacting with human serum albumin (HSA) and bovine serum albumin (BSA). Our mathematical framework incorporates protein binding affinities, cooperative effects, and surface saturation phenomena through differential rate equations with experimentally derived parameters. The size evolution models demonstrated excellent predictive capability with R2 values of 0.998 (AuNP-HSA), 0.981 (AuNP-BSA), 0.919 (AgNP-HSA), and 0.947 (AgNP-BSA). ζ-potential models achieved R2 values of 0.907 (AuNP-HSA) and 0.865 (AgNP-HSA), revealing asymmetric charge neutralization behaviors between positively and negatively charged surfaces. The models successfully captured distinct kinetic profiles across different nanoparticle–protein systems, providing quantitative insights into nanoparticle–protein corona formation mechanisms. This framework supports rational design of nanomaterials with tailored biological interactions and bridges the critical gap between laboratory characterization and in vivo nanomedicine behavior.