Measures of cooperativity in the binding of ligands to proteins and their relation to non-additivity in protein-protein interactions

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Abstract
The analogy between cooperativity in the binding of ligands to proteins and non-additivity in protein-protein interactions is demonstrated and discussed in terms of the Wong and the Hill coefficients. A measure of non-additivity, the interaction constant, is rigorously derived for four thermodynamic cycles, involving the binding of small molecules to proteins and protein association. It is the reciprocal of the ''defect factor'' of Laskowski et al. in Proteinase inhibitors: medical and biological aspects (ed. N. Katunuma et al.), pp. 55-68 (1983), and its logarithm is the Wong measure of cooperativity. These three measures are thus here given a common theoretical basis. The Hill coefficient for an asymetric dimer that binds two different ligands which do not compete for the same site, at 50% saturation of each site, is derived. It is shown to be a function of the interaction constant and of the fraction of protein to which ligand is bound at both sites. These relations for protein-ligand interactions are then discussed in the context of non-additivity in protein-protein interactions.