Correlations between the energetics of cooperativity and quaternary structural probes have recently been made for the intermediate ligation states of Hb [Daugherty et al. (1991) Proc. Natl. Acad. Sci. US 88, 1110-1114]. This has led to a "molecular code" which translates configurations of the 10 ligation states into switch points of quaternary transition according to a "symmetry rule"; T-->R quaternary structure change is governed by the presence of at least one heme-site ligand on each of the alpha beta dimeric half-molecules within the tetramer [see Ackers et al. (1992) Science 255, 54-63, for summary]. In order to further explore this and other features of the cooperative mechanism, we have used oxygen binding to probe the energetics and cooperativities for the vacant sites of the cyanomet ligation species. We have also probed structural aspects of all eight cyanomet ligation intermediates by means of sulfhydryl reaction kinetics. Our oxygen binding results, obtained from a combination of direct and indirect methods, demonstrate the same combinatorial aspect to cooperativity that is predicted by the symmetry rule. Overall oxygen affinities of the two singly-ligated species (alpha +CN beta)(alpha beta) and (alpha beta +CN)(alpha beta) were found to be identical (pmedian = 2.4 Torr). In contrast, the doubly-ligated species exhibited two distinct patterns of oxygen equilibria: the asymmetric species (alpha +CN beta +CN)(alpha beta) showed very high cooperativity (nmax = 1.94) and low affinity (pmedian = 6.0 Torr), while the other three doubly-ligated species showed diminished cooperativity (nmax = 1.23) and considerably higher oxygen affinity (pmedian = 0.4 Torr). Extremely high oxygen affinities were found for the triply-ligated species (alpha +CN beta +CN)(alpha beta +CN) and (alpha +CN beta +CN)(alpha +CN beta) (pmedian = 0.2 Torr). Their oxygen binding free energies are considerably more favorable than those of the alpha and beta subunits within the dissociated alpha beta dimer, demonstrating directly the quaternary enhancement effect, i.e., enhanced oxygen affinity at the last binding step of tetramer relative to the dissociated protomers. Oxygen binding free energies measured for the alpha subunit within the isolated (alpha beta +CN) dimer and for the beta subunit within the isolated (alpha +CN beta) dimer sum to the free energy for binding two oxygens to normal hemoglobin dimers (-16.3 +/- 0.2 versus -16.7 +/- 0.2, respectively), arguing against cooperativity in the isolated dimer. Correlations were established between cooperative free energies of the 10 cyanomet ligation microstates and the kinetics for reacting their free sulfhydryl groups.(ABSTRACT TRUNCATED AT 400 WORDS)