Use of activity coefficients for bound and free sites to describe metal–macromolecule complexation

Abstract

A thermodynamic formalism to describe the small molecule–macromolecule complexation equilibrium, based on the concept of free and occupied sites (formal species) is presented. The formalism is particularly useful in systems with a large number of species and allows for the inclusion of either transport phenomena or adsorption on the boundary of the system. The homogeneous and independent complexation behaviour is denoted ideal complexation. All other behaviours of complexation are treated as deviations from such an ideal system by means of their activity coefficients, this allows the definition of a thermodynamical equilibrium constant, K, for any complexation process, written in terms of formal species. Irrespective of the model of complexation considered in the system, the concentration equilibrium relationship for formal species tends to K when the concentration of the small molecule tends to vanish (limit of ligand excess). The experimental recording of activity coefficients is straightforward and there is no need for numerical derivatives of experimental data. The analysis of the activity coefficients vs. the free metal concentration plots allows an easy and general characterization of the complexation process. Two particular cases of non-ideal complexation (interactions between bound sites and the presence of chelates) are selected to illustrate the general characteristics of the activity coefficients, and to relate them to the affinity spectrum. Expressions for the first two moments of the affinity distribution in terms of the characteristics of the activity coefficients are given.