Chelate effect and cooperativity effect in metal-ligand and macromolecule-ligand equilibria. I. Chemical potential changes and cooperativity-chelation parameters

Abstract

Chelate and cooperativity effects both in the field of complexes formed in solution by metal ion with ligands and in the field of binding between protein and ligands were examined on the basis of thermodynamic arguments. The analysis was carried out by means of the formation function n = ∂ ln Σ M/∂ ln[A] where Σ M is a partition function having free metal or macro-molecule as basis reference level and A is a ligand. The chemical potential changes due to cooperativity and chelation are calculated from differences between areas of the diagram n = f(ln[A]). The chemical potentials are: Δμ° γ = -RT ln K γ (homotropic co-operativity), Δμ° γ′ = -RT ln K γ′ (heterotropic co-operativity), Δμ° ϵ = -RT ln K ϵ (homotropic chelation), Δμ° ϵ′ = -RT ln K ϵ′ (heterotropic chelation). The cooperativity and chelation parameters K γ, K γ′, K ϵ, K ϵ′ are related to each other by other parameters K η = K ϵ·K γ and K η′= K ϵ′·K γ′. All these dimensionless parameters are derived as ratios of experimental equilibrium constants. Therefore a corresponding consistent chemical potential scale can be obtained from experimental data for all these effects, leading to quantitative comparisons between cooperative and chelate effects, either homotropic or heterotropic. Thermodynamic function changes in metal-ligand complexes can also be compared on this same scale with the energetic changes in protein-ligand complexes.