To investigate the role of protons in the cooperative mechanism of human hemoglobin, the thermodynamic linkage between stepwise oxygen binding and dimer-tetramer assembly was studied over the pH range 7.4-9.5 at 21.5 OC. At each pH, oxygen binding isotherms were measured at a series of protein concentrations. These data were analyzed for microscopic free energies of the constituent reactions according to a model-independent thermodynamic treatment [Ackers, G. K., & Halvorson, H. R. (1974) Proc. Natl. Acad. Sci. U.S.A. 74,43 12-43 161. The analysis incorporated equilibrium constants for the assembly of unliganded and fully oxygenated species that were independently determined under identical conditions [Chu, A. H., & Ackers, G. K. (1981) J. Biol. Chem. 256, 1 199-1 2051.From the pH dependencies of the derived equilibrium constants of the linkage system, we have calculated the apparent changes in proton binding that accompany all the reactions of subunit assembly and oxygen binding. The tetramer Bohr effect was also analyzed according to a thermodynamic treatment based on integral relationships between the linked functions. Principal results are as follows: (1) At x e human hemoglobin molecule changes its affinity for protons and oxygen at each successive oxygenation step. A major goal of hemoglobin research is to understand the molecular mechanism of these coupled self-regulatory processes. Since hemoglobin operates essentially as an equilibrium thermodynamic system in vivo, the problem of delineating its structure-function relationships becomes one of establishing relationships between changes in thermodynamic and structural properties that accompany the molecule's functional cycle of oxygenation-deoxygenation. Detailed knowledge of the relationships between the energetic transitions and functional events (e.g., O2 binding, proton binding) provides important constraints on all mechanistic theories of hemoglobin action.The self-regulation properties of hemoglobin are mediated through interactions at the intersubunit contacts of the tetrameric molecule. Subunit dissociation has therefore proven to be a powerful quantitative tool for probing the regulatory energy changes that accompany the molecule's functional cycle. The rationale for this approach is as follows: (1) Interactions within the tetrameric molecule which are responsible for cooperativity can be decoupled by dissociation of the tetramers into noncooperative dimers. (2) The difference between energies of dimer-tetramer assembly at any two stages of oxygenation provides a measure of how much the all pH values, a major fraction of the intersubunit interaction energy, which "pays" for cooperativity in oxygen binding, is "spent" at the first oxygenation step. Changes occur at every pH in the intersubunit contact energy between four stages of oxygenation: unliganded, singly, triply, and fully oxygenated.(2) The quaternary enhancement effect, previously found at pH 7.4 over a wide temperature range [Mills, F. C., & Ackers, G. K. (1979) J . Biol. Chem. 254,2881-...

Free energies of oxygen-linked subunit assembly and cooperative interaction have been determined for 34 molecular species of human hemoglobin, which differ by amino acid alterations as a result of mutation or chemical modification at specific sites. These studies required the development of extensions to our earlier methodology. In combination with previous results they comprise a data base of 60 hemoglobin species, characterized under the same conditions. The data base was analyzed in terms of the five following issues. (1) Range and sensitivity to site modifications. Deoxy tetramers showed greater average energetic response to structural modifications than the oxy species, but the ranges are similar for the two ligation forms. (2) Structural localization of cooperative free energy. Difference free energies of dimer-tetramer assembly (oxy minus deoxy) yielded delta Gc for each hemoglobin, i.e., the free energy used for modulation of oxygen affinity over all four binding steps. A structure-energy map constructed from these results shows that the alpha 1 beta 2 interface is a unique structural location of the noncovalent bonding interactions that are energetically coupled to cooperativity. (3) Relationship of cooperativity to intrinsic binding. Oxygen binding energetics for dissociated dimers of mutants strongly indicates that cooperativity and intrinsic binding are completely decoupled by tetramer to dimer dissociation. (4) Additivity, site-site coupling and adventitious perturbations. All these are exhibited by individual-site modifications of this study. Large nonadditivity may be correlated with global (quaternary) structure change. (5) Residue position vs. chemical nature. Functional response is solely dictated by structural location for a subset of the sites, but varies with side-chain type at other sites. The current data base provides a unique framework for further analyses and modeling of fundamental issues in the structural chemistry of proteins and allosteric mechanisms.

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The sites of energy transduction within the human hemoglobin molecule for the regulation of oxygen affinity have been determined by an extensive study of the molecule's energetic response to structural alteration at individual amino acid residues. For 22 mutant and chemically modified hemoglobins we have determined the total free energy used by the tetrameric molecule for alteration ofoxygen affinity at the four binding steps. The results imply that the regulation of oxygen binding affinity is due to energy changes which are mostly localized at the a'(32 interface. They also indicate a high degree of "internal cooperativity" within this contact region-i.e., the structural perturbations at individual residue sites are energetically coupled. Cooperativity in ligand binding is thus a reflection of cooperativity at a deeper level-that of the protein-protein interactions within the al(92-interfacial domain.A fundamental problem of protein structure and function is the issue ofhow "local" properties ofindividual amino acid residues are related to "system" properties which reflect behavior ofthe molecule as a whole. Well-known manifestations ofthis problem include (a) the acid-base titration behavior of proteins, (b) the cooperative folding of tertiary structures, (c) the nucleated polymerization of self-assembling aggregates, and (d) the cooperative binding ofligands in allosteric systems. A large number of studies, including both experimental and theoretical work, have provided insights into the nature of these problems (cf. refs. 1-15).One strategy for the exploration ofstructure-energy coupling and its role in biological function lies in perturbing a protein molecule through alteration of individual amino acid residues (i.e., deletion, substitution, or chemical modification) and determining the effects of these alterations upon appropriately selected system properties. By studying the effects on the system properties ofa series of such changes, distributed throughout the molecular structure, one can determine which regions of the molecule are especially sensitive to structural perturbation. The power of this approach will be maximized when the system properties chosen reflect the energy states of the molecule as a whole and are at the same time directly related to its biological functions.In this paper we present results of such a study with human hemoglobin. Using 23 different hemoglobins we have determined the effects of structural perturbation upon the energy invested by-the molecule in altering the affinity at successive oxygenation steps. The results provide a structural "map" of energetic sensitivity related to the regulation of function.The problem of structure-energy correlation in the human hemoglobin molecule is centered on the classic problem of resolving the cooperative mechanism of oxygen binding. A complete understanding of this problem must include (a) the structural and energetic changes at the heme site that accompany the binding of oxygen, (b) the changes of tertiary structure and energy ...