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Background  Nanoparticle-protein corona complex formation involves absorption of protein molecules onto nanoparticle surfaces in a physiological environment. Understanding the corona formation process is crucial in predicting nanoparticle behavior in biological systems, including applications of nanotoxicology and development of nano drug delivery platforms.    Method  This paper extends the modeling work in to derive a mathematical model describing the dynamics of nanoparticle corona complex formation from population balance equations. We apply nonlinear dynamics techniques to derive analytical results for the composition of nanoparticle-protein corona complex, and validate our results through numerical simulations.    Results  The model presented in this paper exhibits two phases of corona complex dynamics. In the first phase, proteins rapidly bind to the free surface of nanoparticles, leading to a  metastable composition . During the second phase, continuous association and dissociation of protein molecules with nanoparticles slowly changes the composition of the corona complex. Given sufficient time, composition of the corona complex reaches an equilibrium state of  stable composition . We find analytical approximate formulae for metastable and stable compositions of corona complex. Our formulae are very well-structured to clearly identify important parameters determining corona composition.    Conclusion  The dynamics of biocorona formation constitute vital aspect of interactions between nanoparticles and living organisms. Our results further understanding of these dynamics through quantitation of experimental conditions, modeling results for  in vitro  systems to better predict behavior for  in vivo  systems. One potential application would involve a single cell culture medium related to a complex protein medium, such as blood or tissue fluid.

Dynamics of Nanoparticle-Protein Corona Complex Formation: Analytical Results from Population Balance Equations