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Hill's plots of oxygen binding isotherms reveal the presence of a transition between two different oxygen affinities at the beginning and end of the isotherm. They correspond to the two conformations anticipated by the MWC model, namely, the T and R conformations at the beginning and end of oxygen binding, when the lower affinity of the T form develops into the higher affinity of the R form. The difference between the binding Gibbs free energy changes of the two affinities (Δ G(L)) is the free energy of binding cooperativity. Notably, Δ G(L) is positive in favor of the T form, which moves to a higher energy level upon oxygen release. Osmotic stress reveals a higher volume/surface ratio of deoxyhemoglobin, with a positive Δ G(W) also in favor of the T form. An increasing protein concentration shifts the isotherms to the right, indicating the formation of intermediate polymeric forms. The enthalpy of the intermediates shows a strong absorption of heat at the third oxygenation step because of polymer formation with quinary, and higher-order, structures. The disassembly of intermediate polymers releases energy with a negative Δ G that compensates and allows the positive values of Δ G(L). High-energy polymers are the barrier preventing the relaxation of the T and R conformations into one another. The MWC allosteric model is the best justification of oxygen binding cooperativity.

Free Energy Changes and Components Implicit in the MWC Allosteric Model for the Cooperative Oxygen Binding of Hemoglobin