Monod, Wyman, and Changeux (MWC) explained allostery in multisubunit proteins with a widely applied theoretical model in which binding of small molecules, so-called allosteric effectors, affects reactivity by altering the equilibrium between more reactive (R) and less reactive (T) quaternary structures. In their model, each quaternary structure has a single reactivity. Here, we use silica gels to trap protein conformations and a new kind of laser photolysis experiment to show that hemoglobin, the paradigm of allostery, exhibits two ligand binding phases with the same fast and slow rates in both R and T quaternary structures. Allosteric effectors change the fraction of each phase but not the rates. These surprising results are readily explained by the simplest possible extension of the MWC model to include a preequilibrium between two tertiary conformations that have the same functional properties within each quaternary structure. They also have important implications for the long-standing question of a structural explanation for the difference in hemoglobin oxygen affinity of the two quaternary structures.S mall molecules can regulate protein reactivity by binding to residues distant from the active site, a phenomenon known as allostery. The classic theoretical model proposed by Monod, Wyman, and Changeux (MWC) (1, 2) for explaining this phenomenon considered only proteins with multiple subunits, and the two-state allosteric model of MWC was originally used by them to explain the functional properties of the hemoglobin tetramer, the "honorary enzyme" (1, 3). This famous model has since been applied to a wide variety of other systems in biology, including ligand-gated ion channels, G-protein-coupled receptors, nuclear receptors, and supramolecular assemblies such as chaperonins (4-7). In the case of hemoglobin, the paradigm of allostery, MWC makes two key postulates that have been extensively tested by experiments. Oxygen binding to the deoxy quaternary structure (T) is noncooperative; cooperativity arises from a shift in the population from the low-affinity T quaternary structure to the high-affinity R quaternary structure as the oxygen concentration is increased. The second postulate is that allosteric effectors regulate oxygen affinity by altering only the R ⇄ T preequilibrium. Investigations of hemoglobin focused primarily on the first postulate, which was finally confirmed by single-crystal oxygen-binding measurements that ruled out a sequential model (8) and ended a 25-y controversy (9-12). The second is of more general interest because it applies to all multisubunit proteins exhibiting allosteric behavior and has been known for many years to be inconsistent with the fact that allosteric effectors markedly affect oxygen affinity without changing the quaternary preequilibrium [see data summaries by Imai, Yonetani, and coworkers (13,14)]. The change in oxygen affinity constants, K T and K R , with conditions was interpreted as indicating that tertiary conformations must be affected or that more than two quat...