Analysis of hemoglobin oxygenation from combined equilibrium and kinetic data. Is quaternary enhancement necessary?

An experimental approach based on four independent techniques, in which kinetic and equilibrium measurements of subunit assembly reactions are combined with concentration-dependent oxygen-binding curves, has previously been used to resolve parameters of the linkage system for human hemoglobin over a wide range of conditions [(G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A. 71 (1974) 4312; F.C. Mills et al., Biochemistry 15 (1976) 1093; M.L. Johnson et al., Biochemistry 15 (1976) 5363). Throughout this extensive body of results it has been found that the affinity for binding oxygen to tetramers at the fourth step exceeds the mean affinity of dissociated dimers. The existence of this "quaternary enhancement" effect has recently been questioned by Gibson and Edelstein (J. Biol. Chem. 262 (1987) 516) and by Philo and Lary (J. Biol. Chem. 265 (1990) 139) on the basis of kinetically derived oxygen-binding constants that do not exhibit quaternary enhancement. These authors have also suggested that quaternary enhancement might not be necessary to explain the oxygen-binding data mentioned above. In this study, we have explored the effect of constraining the numerical analysis of oxygen-binding data against the new kinetically derived binding constants. It is found that the sets of linkage constants which are compatible with both the oxygen-binding data and the new kinetically derived dimer binding constant require both quaternary enhancement and substantial dimer cooperativity. Increasing the dimer cooperativity to compensate completely for quaternary enhancement requires both dimeric and tetrameric binding constants that disagree with the kinetically derived values. Thus, the quaternary enhancement effect cannot be eliminated by readjustment of the remaining constants of the linkage system. Possible sources of the discrepancy between the kinetically derived binding constants and the otherwise self-consistent data from the other four techniques are discussed.