Biochemistry & Analytical Biochemistry

Abstract

Rate and Equilibrium Constants of O₂-Binding and O₂ Release: ?The Forward and Reverse Steps for the ^TState ? ^RState Change for Human Hb₄/BPG, Under Standard Conditions?

Francis Knowles*, Samantha Doyle and Douglas Magde

Three unknown quantities describe the O₂-equilibrium binding curve for fractional saturation of human hemoglobin in red blood cells, under standard conditions: K_α, the O₂-binding constant of equivalent ^Tstate α-chains; K_Δ, the equilibrium constant for the ^Tstate → ^Rstate transition; K_β, the O₂-binding constant of equivalent ^Rstate β-chains. The model for formulation of the equation of state is a 3-stage ordered sequence of reactions.

Values of K_α, K_Δ and K_β were established by determination of rate constants for the oxygenation reaction and the dithionite-mediated de-oxygenation reaction. The rate law for the forward reaction in the presence of excess O₂ yields k_α, k_Δ, k_-Δ, and k_β. The rate law yields k_-β, k_-Δ, k_Δ, and k_-α for the dithionite-mediated deoxygenation reaction. Rate constants for binding O₂ are pseudo 1^st-order. Rate constants for release of O₂ are 1^st-order. Reactions involving O₂: I→II, II→I, III→IV; are 2-step ordered sequences of equivalent subunits: α_α, β_β. Progress curves for a 2-step ordered sequence of equivalent chains collapse to a first order reaction. K_α=k_α/ k_-α=8.53 × 103 L/mol; K_β=k_β/k_-β=2.38 × 105 L/mol. Progress curves for both oxygenation and dithionitemediated de-oxygenation reactions return K_Δ. K_Δ is 0.0580 for the oxygenation reaction and 0.0358 for the dithionite-mediated de-oxygenation reaction. The corresponding values from the O₂-equilibrium binding curve are: K_α=15.09 × 103 l/mol; K_β=3.94 × 105 L/mol: K_Δ=0.02602. Values of K_α, K_Δ, and K_β determined from rate constants of progress curves for oxygenation and dithionite-mediated de-oxygenation reactions are close to values determined by fitting of the O₂-equilibrium binding curve for whole blood, under standard conditions, to the Perutz/Adair equation. Data for the dithionite mediated de-oxygenation reaction may be most reliable insofar as errors in knowledge of the concentration of di-oxygen do not enter into consideration.

Keypoints points

• The manuscript examines rate equations based on the model expressed by the Perutz/Adair equation

• Rate equations are presented for: (i) the reaction of DHb₄/BPG with O₂ and (ii) the reaction of (HbO₂)₄/ BPG with dithionite.

• Rate constants obtained from progress curves for these reactions can be used to predict equilibrium constants defining K_α, K_β and K_Δ. These results confirm the values for K_α, K_β and K_Δ obtained by fitting O₂-equilibrium binding data for whole blood, under standard conditions, to the Perutz/Adair equation.

Published Date: 2023-08-22; Received Date: 2023-07-20