Kinetics of subcellular distribution of multiply ionizable compounds: A mathematical description and its use in QSAR

An explicit mathematical model describing the distribution and, in some cases, also biological activity of anthropogenic chemicals capable of multiple ionization in biological systems during the elimination period has been constructed. The biological system is represented by a catenary chain of alternating aqueous phases (with proteins and other macromolecular and low-molecular-weight cell constituents) and membranes. Pseudo-equilibrium distribution of the compounds before the start of elimination is a key assumption which has led to a substantial simplification of the mathematical description. Substitution of the model parameters by their appropriate relations to physicochemical properties of the compounds (the reference partition coefficients and dissociation constants) converts the model to the quantitative structure-activity relationship. The resulting expression satisfactorily describes the published data on growth inhibitory activity of phenol derivatives, against the ciliate Tetrahymena pyriformis, as a function of their hydrophobicity and acidity. The model can be used in drug design for description of the distribution of compounds in biological test systems or in environmental sciences to predict the fate of anthropogenic chemicals in ecological systems.