Ab initio quantification of the oxygen-hemoglobin dissociation curve

Uptake of oxygen by hemoglobin (Hb), described by the oxygen-Hb dissociation curve, is obviously important for the existence of all vertebrates. Its sigmoidal curve shape indicates that oxygen binds more tightly if sites already are occupied, commonly referred to as the cooperative effect. The effect has been challenging to understand and quantify ever since its experimental demonstration in 1904. Here, we derive an ab initio analytical expression for the dissociation curve based on the fundamental principle of uniform oxygen chemical potential and absolute activity throughout the system at equilibrium using the grand partition function. The resulting analytical dissociation expression therefore only has four molecular oxygen-Hb binding energies as free variables, which are determined by fitting the analytical expression to measured data. The corresponding resulting negative reaction enthalpies identified in increasing magnitude are, $$, $$, $$, $$, in the range observed experimentally. The difference between $$ and $$ is $$, smaller than the maximum enthalpy difference measured experimentally, $$. Hence, the cooperative effect can therefore be explained, from an energy point of view, as caused by the reaction enthalpy difference between $$ and the three subsequent enthalpy values. No impact of Hb's spatial and structural properties is assumed. The finding highlights the importance of identifying the ligand-receptor molecular binding energies, and thereby the reaction enthalpies, under different conditions as a way for calculating not only the oxygen-Hb but ligand-receptor dissociation curves in general under various conditions, a priori, since the procedure for determining these curves ab initio has been established.