Order of free energy couplings between ligand binding and protein subunit association in hemoglobin

The number of protein subunits that must be liganded to effect changes in subunit interaction may be characterized by defining an order for the free energy couplings between these two processes. From available data on the chemical equilibrium of stripped hemoglobin A with oxygen, I show that couplings are unequivocally of first order. The two-state model of cooperative binding is shown to be incompatible with the results of this analysis, as the Monod-Wyman-Changeux parameters derived from the same experimental data demand free energy couplings of an order higher than the second.