Linkage between ligand binding and the dimer-tetramer equilibrium in the Monod-Wyman-Changeux model of hemoglobin

G. Weber [(1984) Proc. Natl. Acad. Sci. USA 81, 7098-7102] has inferred that the Monod-Wyman-Changeux (MWC) model for ligand binding by hemoglobin would require (contrary to experimental evidence) that increased ligand binding must promote stabilization of alpha 2 beta 2 tetramers with respect to dissociation into alpha beta dimers. Reexamination of the MWC model, however, in the light of general linkage principles and the specific analysis by G. K. Ackers and M. L. Johnson [(1981) J. Mol. Biol. 147, 559-582] shows that the opposite relation must hold, in agreement with experiment. The T form of the tetramer, with low ligand affinity, must be destabilized and progressively dissociates into the high-affinity dimers, designated D, as ligand binding increases. Each ligand molecule bound shifts the standard Gibbs free energy delta G2T for the D-T equilibrium by approximately 3 kcal/mol in favor of the dimer. Thus, T must exist in (at least) five delta G levels of cooperative free energy as it becomes progressively destabilized by successive binding of ligand molecules. Dissociation of the R tetramer to dimers, in contrast, is independent of the amount of ligand bound, so long as dimers and R-state tetramers possess the same (high) affinity for ligand. While the intrinsic ligand-binding constants of the T and R states (KT and KR) remain unchanged throughout by the postulates of the model, the model should not be regarded as a strictly two-state system in view of the multiple free-energy levels indicated above. The present analysis gives approximate, though not precise, agreement with experimental findings on the dimer-tetramer equilibrium considered by Weber and provides a rationale for interpreting other recent experiments concerning this equilibrium.