The theory of oxygen hemoglobin association

We develop a theory of oxygen hemoglobin association and derive the oxygen hemoglobin association equation and determine the values of the four association constants by curve fitting four commonly accepted data points that relate oxygen saturation and oxygen partial pressure (PO2) in the blood using mathematical reasoning and chemical kinetics. The four association constants come from the progression of oxygen binding to each of the four subunits on the hemoglobin molecule in a cooperative manner. The binding of oxygen alters the affinity of subsequent binding of additional oxygen molecules, which is reflected in changing magnitudes of the association constants. We also demonstrate rather surprisingly that the value of the third association constant is significantly smaller than all other association constants and offer some conjecture about this puzzling finding. With our equation, we can compute the distributions of all five oxyhemoglobin species at various PO2 levels that are published for the first time in the history of hemoglobin research. After examining the distributions, we find the triply bound oxyhemoglobin exists in very low concentration, consistent with the small third association constant. In addition, we present the oxygen levels where maximal concentrations of various oxyhemoglobin species occur, another unexpected finding that was never published before. Finally, we determine the inflection point of the hemoglobin association curve, a defining property to a specific sigmoid curve, representing the steepest portion of the curve.