Multi-random binding molecular interactions: a general kinetic model

A kinetic model is suggested to account for the interactions of several ligands with a target whose molecule possesses several independent equivalent receptor sites for each ligand (multiligand multisite model). To analyse the problem, we shall derive solutions for three elementary situations: (a) interactions of a ligand with a mono-receptor site target molecule (monosite model); (b) interactions of several ligands with a target whose molecule possesses one receptor site for each ligand involved (multiligand model); (c) interactions of a ligand with a target whose molecule possesses several receptor sites of the same kind for this ligand (multisite model). Throughout this study, every ligand molecule is assumed to offer one binding site to the target. The main implications of the corresponding analytical solutions are discussed from a molecular point of view. The results cover a great many well-known aspects of the molecular interactions in various fields such as enzymology, endocrinology, radio-immunology and saturation analysis. As suggested by the inhibition patterns obtained, this model may therefore provide a new point of view to interpret the relevant phenomena. Furthermore, a kinetic approach to the generalized mass action law can be deduced from this model, and experimental conditions in which the isotopic dilution law applies are examined.