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Cooperative free energies have been determined for the 10 ligation species of human hemoglobin in the Co(II)/Fe(II)-CO system. In this system, subunits containing unligated cobaltous hemes coexist in the same tetramer with naturally occurring ferrous hemes that are ligated with carbon monoxide. Tetramers comprising the 10 structurally unique combinations of ligated and unligated subunits were characterized in terms of their dimer-tetramer assembly free energies. By use of the thermodynamic linkage between assembly and ligation, the experimentally resolved values were used to obtain the corresponding cooperative free energies (i.e., the differences between actual free energies of ligation and the summed contributions of intrinsic values). The results obtained are in general accord with previous findings on this same system (Imai et al., 1980). The present study extends this earlier work by resolving the cooperative properties of each configurational isomer of the doubly ligated tetramers. The 10 ligation species were found to distribute into 5 discrete cooperative free energy levels according to a combinatorial code which includes, as a special case, the code found previously with cyanomethemoglobin and manganese-substituted hemoglobin (Smith et al., 1987; Daugherty et al., 1991). This distribution exhibits additional characteristics found in the oxygenation of normal ferrous hemoglobin including the quaternary enhancement effect (MillsAckers, 1979a,b). These results, and those of the following paper (Doyle et al., 1991), strongly support the premise that a common set of qualitative rules governs the cooperative interactions in hemoglobin irrespective of |