Cooperativity in Associating Proteins. Monomer-Dimer Equilibrium Coupled to Ligand Binding

The cooperativity due to ligand binding to a protein monomer and a protein dimer in equilibrium was studied. The system is: E + E ⇌ E₂(K₁); E + S ⇌ ES (K₂): ES + E ⇌ E₂S (K₃); and ES + ES ⇌ E₂S₂(K₄). Using a computer and a plotter, Hill plots for differenct combinations of the parameters K₁, K₂, K₃, and K₄ were constructed. It was found that high ratios of K₄/K₂ with moderate K₁ and K₂ ensure high positive cooperativity. In such cases the species E₂, ES, and E₂S never accumulate to significant concentrations throughout the titration. High K₄/K₂ ratios or high K₄ alone does not ensure binding of ligand. The monomer must have a finite affinity toward the ligand in order for the whole binding process to occur. Ratios of K₄/K₂ lower than 10³ generate negative cooperativity and the transient accumulation of E₂S in the proteinligand mixture. The possible physiological significance of positive cooperativity due to protein aggregation is discussed.