Architecture of Allosteric Structure. Equation of State Containing Three Unknown Quantities for Fractional Saturation of whole Human Blood with O2: Formatting the Adair Equation to Accommodate Ordered Equivalent Sequences of O2-Binding Reactions and a Single Conformation Change Not Concerted with O2 Binding
O2-Equilibrium binding data of hemoglobin in whole blood under standard conditions (Kernohan JC. & Roughton FJW (1972) in Oxygen Affinity of Hemoglobin and Red Cell Acid Base Status, ed Rorth and Astrup, Copenhagen, Munksgaard, pp 65-72; Severinghaus JW in ibid pp. xx-xx) was fitted to an equation of state comprised of three unknown quantities: Kα, the equilibrium constant for binding O2 by equivalent low affinity α-chains; KΔC, a dimensionless equilibrium constant describing the conformation change between low- and high-affinity conformations of hemoglobin, Tstate and Rstate; Kβ, the equilibrium constant for binding O2 by equivalent high affinity β-chains, the Perutz/Adair Equation. Values of the unknown quantities at pH 7.4 and 37oC are: Kα = 15,090 L/mol; KΔC = 0.0260; Kβ = 393,900 L/mol.
A graph of predicted versus observed values of fractional saturation, F, is linear: FPRE = 0.9998 FOBS – 0.0005, r2 =0.9997. The Perutz/Adair equation of state is defined as such insofar as all aspects of the stereochemical model (Perutz MF (1970) Nature London 228, 726-739) are imposed on the earlier sequential binding model of Adair (1925) JBC 63, 493-545.