Model-independent link between the macroscopic and microscopic descriptions of multidentate macromolecular binding: relationship between stepwise, intrinsic, and microscopic equilibrium constants.

The binding of ions or other small molecules to macromolecules and surfaces can be macroscopically characterized by means of the stepwise (or stoichiometric) equilibrium constants, which can be obtained experimentally from coverage versus concentration data. The present work presents a novel, simple, and direct interpretation of the stepwise constants in terms of the microscopic, site-specific, stability constants. This formalism can be applied to the most general case, including the heterogeneity of the sites, interactions among them, multicomponent adsorption, and so forth, and, in particular, to chelate complexation. We show that the stepwise equilibrium constants can be expressed as a product of two factors, (i) the average number of free potential sites (per bound ion) of the microscopic species to be complexed (stoichiometric factor) and (ii) the average of the microscopic stability constants of their free potential sites. The latter factor generalizes the concept of the intrinsic equilibrium constant to systems with chelate complexation and reduces to the standard definition for monodentate binding. However, in the case of heterogeneous multidentate complexation, the stoichiometric factor cannot be known a priori, so that the finding of the intrinsic constants is not trivial. One option is to approximate the stoichiometric factor by the value that would correspond to identical active centers. We investigate the accuracy of this assumption by comparing the resulting approximate intrinsic constants to those obtained by Monte Carlo simulation of several binding models. For the cases investigated, it is found that the assumption is quite accurate when no correlated structures (typical of short-range interactions) are formed along the chain. For adsorption of particles attached to a large number of active centers, the formalism presented here leads to the Widom particle insertion method.