Model of complexation between C$_{60}$ fullerenes and biologically active compounds

Various model approaches for describing the equilibrium complexation of aromatic biologically active compounds with fullerene $\mathrm{C}_{60}$ molecules are proposed. Equilibrium constants of complexation for structurally different biologically active compounds in the aquatic environment were obtained based on these approaches. Models of continuous and discrete aggregation of $\mathrm{C}_{60}$ molecules are proposed, taking into account the polydisperse nature of fullerene solutions. The model of continuous aggregation considers the sequential growth of aggregates upon addition of $\mathrm{C}_{60}$ fullerene monomers to the already existing aggregates, with the equilibrium self-association constant of fullerene $K_F$ being the same for all stages of aggregation. The discrete model takes into account the presence of separate stable aggregates and fractal type of the higher aggregates formation from $\mathrm{C}_{60}$ fullerene aggregates. It is achieved by using the simplest two-level hierarchy of clusters distribution in the fractal series $1$–$4$–$7$–$13$, known from the literature data. The model of continuous aggregation represents the classical approach used throughout to describe the aggregation of small molecules, while the discrete aggregation model can only be applied to fullerenes. The results obtained in this study lead to the conclusion that fullerene $\mathrm{C}_{60}$ can form stable complexes with aromatic antitumor drugs, which open the possibility of using these substrates in the future in cancer therapy.