Although cooperative oxygenation of human adult hemoglobin (HbA) 1 has been studied extensively as a paradigm for regulatory actions of allosteric proteins, the functional and structural properties of its eight partially oxygenated intermediates remain elusive. This is mostly due to the strong cooperativity of Hb, which suppresses relative abundance of the intermediates, precluding direct study. One of the most specific methods for studying the oxygenation intermediates has been to substitute the heme in one or more of four subunits with another metalloprotoporphyrin IX, which does not bind O 2 while mimicking either normal deoxyheme or oxyheme (1-6). However, there has been a limitation to this approach: Six asymmetric forms cannot be studied in isolation, because the asymmetric hybrid tetramers dissociate into dimers, which then reassociate to form not only the former asymmetric tetramers but also symmetric ones (i.e. dimer rearrangement).Ackers and his colleagues (7) have partly circumvented this difficulty by measuring the dimer-tetramer equilibrium constants for asymmetric hybrid species in the presence of the symmetric parental species. In 1985, this methodology was first applied to resolution of the tetramer stabilities of all ten ligation intermediates of the deoxy-cyanomet [Fe(II)/ Fe(III)-CN Ϫ ] hybrid system, in which cyanometheme mimics a fixed oxyheme (8). The most striking finding was that the dimer-tetramer association equilibrium constant for (␣ ϩCNϪ  ϩCNϪ )(␣) was about 170 times that of the other three doubly liganded species at pH 7.4, which implies a hypercooperativity in specific ligation steps in the ␣11 dimer within the tetramer (i.e. a 170-fold affinity change). Subsequently, the effects of pH, temperature, and single-site mutations on the dimer-tetramer equilibrium of (␣ ϩCNϪ  ϩCNϪ )(␣) were studied (7, 9, 10). It was suggested that this key intermediate assumes a form of the deoxy-Tquaternary structure as judged from the nature of the dimerdimer interface.Based on the hyperthermodynamic stability and T quaternary structure of (␣ ϩCNϪ  ϩCNϪ )(␣), Ackers' group proposed a new framework for Hb cooperativity, called a symmetry rule (SR), in 1991 (9). The key features of the SR model are: (i) The two ligation steps leading to the asymmetric ␣11 half-liganded intermediate show distinctly favorable cooperativity while those leading to the other three doubly liganded intermediates exhibit no favorable cooperativity; (ii) The asymmetric ␣11 half-liganded intermediate assumes a deoxy-T-quaternary structure while the other three doubly liganded intermediates exhibit an oxy-R-quaternary structure.Recently, we showed that both the published hyperstability and T structure assignment for (␣ ϩCNϪ  ϩCNϪ )(␣) were artifacts arising from valency exchange between the deoxy and cyanometheme sites during the long deoxy incubation that had been used routinely in the laboratory of Ackers (11,12). Ackers et al. (13) have now accepted the valency exchange artifacts in their previous studies using de...