The thermodynamic linkage between cooperative oxygenation and dimer-tetramer subunit assembly has been determined for cobaltous human hemoglobin in which iron(II) protoporphyrin IX is replaced by cobalt(II) protoporphyrin IX. The equilibrium parameters of the linkage system were determined by global nonlinear least-squares regression of oxygenation isotherms measured over a range of hemoglobin concentrations together with the deoxygenated dimer-tetramer assembly free energy determined independently from forward and reverse reaction rates. The total cooperative free energy of tetrameric cobalt hemoglobin (over all four binding steps) is found to be 1.84 (±0.13) kcal, compared with the native ferrous hemoglobin value of 6.30 (±0.14) kcal. Detailed investigation of stepwise cooperativity effects shows the following: (1) The largest change occurs at the first ligation step and is determined on model-independent grounds by knowledge of the intermediate subunit assembly free energies. (2) Cooperativity in the shape of the tetrameric isotherm occurs mainly during the middle two steps and is concomitant with the release of quaternary constraints. (3) Although evaluation of the pure tetrameric isotherm portrays identical binding affinity between the last two steps, this apparent noncooperativity is the result of a “hidden” oxygen affinity enhancement at the last step of 0.48 (±0.12) kcal. This quaternary enhancement energy is revealed by the difference in subunit assembly free energies of the triply and fully ligated species and is manifested visually by the oxygenation isotherms at high versus low hemoglobin concentration. (4) Cobaltous hemoglobin dimers exhibit apparent anticooperativity of 0.49 (±0.16) kcal (presumed to arise from heterogeneity of subunit affinities). The distribution of cooperative switching effects found in this study is compared with those of ferrous hemoglobin oxygenation and the cobaltous hemoglobin iron-carbon monoxide ligand analogue system [Speros, P. C., Licata, V. J., Yonetani, T., & Ackers, G. K. (1991) Biochemistry (preceding paper in this issue)]. The three systems exhibit a common pattern of cooperative switching effects.
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