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Protein-DNA interactions are central to the control of gene expression across all forms of life. The development of approaches to rigorously model such interactions has often been hindered both by a lack of quantitative binding data and by the difficulty in accounting for parameters relevant to the intracellular situation, such as DNA looping and thermodynamic non-ideality. Here, we review these considerations by developing a thermodynamically based mathematical model that attempts to simulate the functioning of an Escherichia coli expression system incorporating two of the best characterised prokaryotic DNA binding proteins, Lac repressor and lambda CI repressor. The key aim was to reproduce experimentally observed reporter gene activities arising from the expression of either wild-type CI repressor or one of three positive-control CI mutants. The model considers the role of several potentially important, but sometimes neglected, biochemical features, including DNA looping, macromolecular crowding and non-specific binding, and allowed us to obtain association constants for the binding of CI and its variants to a specific operator sequence.

The complete binding cascade of human hemoglobin consists of a series of partially ligated intermediates. The individual intermediate binding constants cannot be distinguished in O(2) binding curves, however, each constant can be determined from the O(2)-induced change in assembly constant for the α(2)β(2) tetramer from its constituent αβ dimers. The characterization of these O(2) binding constants has shown the Hb cascade to be asymmetric in nature, with binding dependent upon the specific distribution of O(2) among the four hemesites. A stopped-flow approach to measuring the dissociation constant of a key doubly ligated intermediate, that in which one dimer is oxygenated and the other is not, is described. The intermediate is transiently formed in the absence of O(2) and then allowed to dissociate in the presence of O(2). The free dimers thus released are trapped by the plasma protein haptoglobin, the rate limiting step being that of tetramer dissociation. The kinetic constant observed for the dissociation of this intermediate confirms the value for its equilibrium O(2) binding constant, previously determined under equilibrium conditions by subzero isoelectric focusing.

The Hill coefficient nH is a dimensionless parameter that has long been used as a measure of the extent of cooperativity. Originally derived from the oxygen-binding curve of human hemoglobin (Hb) by A. V. Hill in 1910, and reinvented by J. Wyman several decades later, nH is indexed to the stoichiometry of ligation and is indirectly related to the overall cooperative free energy for binding all four oxygen ligands. However, the overall cooperative free energy of Hb ligation can be measured directly by experimental methods. The microscopic cooperative free energies that relate to energetic coupling between specific subunit pairs can also be experimentally determined, while the Hill coefficient is, by its nature, a macroscopic parameter that cannot detect differences among specific subunit-subunit couplings. Its continued use in studies of the mechanism of cooperativity in Hb is therefore of increasingly limited value.

The complete binding cascade of human hemoglobin consists of eight partially ligated intermediates and 16 binding constants. Each intermediate binding constant can be evaluated via dimer-tetramer assembly when ligand configurations within the tetramer are fixed through the use of hemesite analogs. The Zn/Fe analog, in which the nonbinding Zn2+ heme substitutes for deoxy Fe2+ heme, also permits direct measurement of O2 binding to the remaining Fe2+ hemesites within the symmetrically ligated Hb tetramers. Measurement of O2 binding over a range of Zn/Fe Hb concentrations to both alpha-subunits (species 23) or to both beta-subunits (species 24) shows noncooperative binding and incomplete saturation of the available Fe2+ hemesites. In contrast, the asymmetrically ligated Zn/FeO2 species 21, in which both oxygens are bound to one of the dimers within the tetramer, exhibits positive cooperativity and >90% ligation under atmospheric conditions. These properties are confirmed in the present study by measurement of the rate constant for tetramer dissociation to free dimer. The binding constants thus derived for these partially ligated intermediates are consistent with the stoichiometric constants measured for native hemoglobin by standard O2 binding techniques, providing additional evidence that Zn2+-heme substitution provides an excellent deoxy hemoglobin analog. There is no evidence that Zn-substitution stabilizes a low-affinity form of the tetramer, as previously suggested. These characterizations demonstrate distinct, nonadditive physical properties of the doubly ligated tetrameric species, yielding an asymmetric distribution of cooperativity within the cascade of O2 binding by human hemoglobin.

Stepwise cooperative free energies and intermediate Hill coefficients are used to assess the presence of noncooperative sequences in the database of binding free energies previously obtained for the eight partially ligated intermediates of human hemoglobin, encompassing a variety of hemesite analog substitutions. This analysis is prompted by the observed noncooperative binding of two ligands to hemoglobins that are partially substituted with Zn2+-heme, an analog of deoxy Fe2+-heme (Holt et al. (2005) Biochemistry 44, XXXXX). The results show that noncooperative binding sequences are observed in all hemesite analog studied to date. The noncooperative binding observed in (alpha2Znbeta2FeO2) and (alpha2FeO2beta2Zn) is therefore not a Zn-specific substitution artifact. One of several binding sequences from singly to triply ligated hemoglobin is also observed to occur with little or no positive cooperativity. These results demonstrate the variability possible among different ligation pathways in a highly cooperative multi-subunit system such as hemoglobin. As a direct consequence of this variability, differences among ligation pathways are not always detectable using cooperativity functions based on statistical distributions, such as the Hill coefficient n(H). The limitations of Hill coefficient analysis in evaluating cooperativity in intermediates of complex systems is contrasted with the utility of the stepwise binding parameters.

Ligand photodissociation experiments are used to measure the prephotolysis equilibria between doubly liganded R and T quaternary conformers of the symmetric Fe-Co HbCO hybrids, (alpha(FeCO)beta(Co))(2) and (alpha(Co)beta(FeCO))(2). The free energies obtained from these data are used to calculate the cooperative free energies of the (alpha(FeCO)beta(Fe))(2) and (alpha(Fe)beta(FeCO))(2) intermediate CO-ligation states of normal hemoglobin in the T conformation, quantities important to the evaluation of current models of cooperativity. The symmetry rule model, incorporating sequential cooperativity of T-state ligand binding within an alphabeta dimer in addition to the traditional two-state cooperativity of the tetramer, predicts a larger free energy penalty for disturbing both dimers in a doubly liganded T tetramer than would be expected in the two-state model as currently formulated. (Cooperative energy penalties are simply proportional to the number of tetramer-bound ligands in the traditional two-state model.) The value found here for the energies of doubly liganded T microstates in which both dimers are perturbed, 7.9 +/- 0.3 kcal/mol, is consistent with the symmetry rule model but significantly higher than that expected (5-6 kcal/mol) in the two-state model of cooperativity.

A novel model linking the thermodynamics and kinetics of hemoglobin's allosteric (R --> T) and ligand binding reactions is applied to photolysis data for human HbCO. To describe hemoglobin's kinetics at the microscopic level of structural transitions and ligand-binding events for individual [ij]-ligation microstates ((ij)R --> (ij)T, (ij)R + CO --> ((i)(+1))(k)R, and (ij)T + CO --> ((i)(+1))(k)T), the model calculates activation energies, (ij)DeltaG(++), from previously measured cooperative free energies of the equilibrium microstates (Huang, Y., and Ackers, G. K. (1996) Biochemistry 35, 704-718) by using linear free energy relations ((ij)DeltaG(++) - (01)DeltaG(++) = alpha[(ij)DeltaG - (01)DeltaG], where the parameter alpha, describing the variation of activation energy with reaction energy perturbation, can depend on the natures of both the reaction and the perturbation). The alpha value measured here for the allosteric dynamics, 0.21 +/- 0.03, corresponds closely to values observed previously, strongly suggesting that the thermodynamic microstate energies directly underlie the allosteric kinetics (as opposed to the alpha((ij)DeltaG(RT)) serving merely as arbitrary fitting parameters). Besides systematizing the study of hemoglobin kinetics, the utility of the microstate linear free energy model lies in the ability to test microscopic aspects of allosteric dynamics such as the "symmetry rule" for quaternary change deduced previously from thermodynamic evidence (Ackers, G. K., et al. (1992) Science 255, 54-63). Reflecting a remarkably detailed correspondence between thermodynamics and kinetics, we find that a kinetic model that includes the large free energy splitting between doubly ligated T microstates implied by the symmetry rule fits the data significantly better than one that does not.

The mechanism of cooperativity in the human hemoglobin tetramer (a dimer of alpha beta dimers) has historically been modeled as a simple two-state system in which a low-affinity structural form (T) switches, on ligation, to a high-affinity form (R), yielding a net loss of hydrogen bonds and salt bridges in the dimer-dimer interface. Modifications that weaken these cross-dimer contacts destabilize the quaternary T tetramer, leading to decreased cooperativity and enhanced ligand affinity, as demonstrated in many studies on symmetric double modifications, i.e., a residue site modified in both alpha- or both beta-subunits. In this work, hybrid tetramers have been prepared with only one modified residue, yielding molecules composed of a wild-type dimer and a modified dimer. It is observed that the cooperative free energy of ligation to the modified dimer is perturbed to the same extent whether in the hybrid tetramer or in the doubly modified tetramer. The cooperative free energy of ligation to the wild-type dimer is unperturbed, even in the hybrid tetramer, and despite the overall destabilization of the T tetramer by the modification. This asymmetric response by the two dimers within the same tetramer shows that loss of dimer-dimer contacts is not communicated across the dimer-dimer interface, but is transmitted through the dimer that bears the modified residue. These observations are interpreted in terms of a previously proposed dimer-based model of cooperativity with an additional quaternary (T/R) component.

For the treatment of beta-globin gene defects, a homologous recombination-mediated gene correction approach would provide advantages over random integration-based gene therapy strategies. However, "neighborhood effects" from retained selectable marker genes in the targeted locus are among the key issues that must be taken into consideration for any attempt to use this strategy for gene correction. An Ala-to-Ile mutation was created in the beta6 position of the mouse beta-major globin gene (beta(6I)) as a step toward the development of a murine model system that could serve as a platform for therapeutic gene correction studies. The marked beta-major gene can be tracked at the level of DNA, RNA, and protein, allowing investigation of the impact of a retained phosphoglycerate kinase (PGK)-neo cassette located between the mutant beta-major and beta-minor globin genes on expression of these 2 neighboring genes. Although the PGK-neo cassette was expressed at high levels in adult erythroid cells, the abundance of the beta(6I) mRNA was indistinguishable from that of the wild-type counterpart in bone marrow cells. Similarly, the output from the beta-minor globin gene was also normal. Therefore, in this specific location, the retained, transcriptionally active PGK-neo cassette does not disrupt the regulated expression of the adult beta-globin genes. (Blood. 2001;98:65-73)

The bacteriophage lambda relies on interactions of the cI and cro repressors which self assemble and bind the two operators (O(R) and O(L)) of the phage genome to control the lysogenic to lytic switch. While the self assembly and O(R) binding of cI have been investigated in detail, a more complete understanding of gene regulation by phage lambda also requires detailed knowledge of the role of cro repressor as it dimerizes and binds at O(R) sites. Since dimerization and operator binding are coupled processes, a full elucidation of the regulatory energetics in this system requires that the equilibrium constants for dimerization and cooperative binding be determined. The dimerization constant for cro has been measured as a prelude to these binding studies. Here, the energetics of cro binding to O(R) are evaluated using quantitative DNaseI footprint titration techniques. Binding data for wild-type and modified O(R) site combinations have been simultaneously analyzed in concert with the dimerization energetics to obtain both the intrinsic and cooperative DNA binding energies for cro with the three O(R) sites. Binding of cro dimers is strongest to O(R)3, then O(R)1 and lastly, O(R)2. Adjacently bound repressors exhibit positive cooperativity ranging from -0.6 to -1.0 kcal/mol. Implications of these, newly resolved, energetics are discussed in the framework of a dynamic model for gene regulation. This characterization of the DNA-binding properties of cro repressor establishes the foundation on which the system can be explored for other, more complex, regulatory elements such as cI-cro cooperativity., (Copyright 2000 Academic Press.)

The cro repressor from bacteriophage lambda is an important and classical transcription regulatory protein that binds DNA operator sites as a dimer. Therefore, a complete understanding of gene regulation by cro requires knowledge of the coupled energetics of its protein dimerization and site-specific DNA binding. A method is described by which cro repressor can be labeled in vivo with [(35)S]methionine to a specific activity of 2 x 10(15) cpm/mol. As a prelude to binding studies, the association equilibrium of cro was determined over the range 10(-)(9)-10(-)(3) M using large-zone analytical gel chromatography with radiolabeled repressor. The data are best described by a monomer-dimer stoichiometry with an equilibrium constant of 3.07 (+/-1.08) x 10(6) M(-)(1) total cro monomer. Stokes radii for monomers and dimers were evaluated from the resolved gel partition coefficients. Under the conditions employed in this study (10 mM Bis-Tris, 200 mM KCl, 2.5 mM MgCl(2), 1 mM CaCl(2), 100 microg/mL BSA, pH 7.0, 20 degrees C), self-association of cro to species with assembly states greater than dimers is not observed.

The contribution of the alpha(1)beta(1)half-oxygenated tetramer [alphabeta:alphaO(2)betaO(2)] (species 21) to human hemoglobin cooperativity was evaluated using cryogenic isoelectric focusing. The cooperative free energy of binding, reflecting O(2)-driven protein structure changes, was measured as (21)DeltaG(c) = 5.1 +/- 0. 3 kcal for the Zn/FeO(2) analog. For the Fe/FeCN analog, (21)DeltaG(c) was estimated as 4.0 kcal after correction for a CN ligand rearrangement artifact, demonstrating that ligand rearrangement does not invalidate previous conclusions regarding this species. In the context of the entire Hb cooperativity cascade, which includes eight intermediate species, the 21 tetramer is highly abundant relative to the other doubly-ligated species, providing strong support for the previously determined consensus partition function of O(2) binding and for the Symmetry Rule model of hemoglobin cooperativity (Ackers et al., Science 1992;255:54-63). Cooperativity of normal human hemoglobin is shown to depend on site-configuration, and not solely the number of O(2) bound, nor the occupancy of alpha vs. beta subunits. Verification of a unique contribution from the alpha(1)beta(1)doubly-oxygenated species to the equilibrium O(2) binding curve strongly reinforces the Symmetry Rule interpretation that the alpha(1)beta(1)dimer acts both as a structural and functional element in cooperative O(2) binding.

Human hemoglobin produced in the Escherichia coli coexpression system of Hernan et al. [(1992) Biochemistry 31, 8619-8628] has been transformed into a functionally homogeneous protein whose properties closely approximate those of normal hemoglobin A. Both of the alpha and beta chains of this hemoglobin contain a valine-methionine substitution at position 1 in order to accommodate the difference in specificity of the protein-processing enzymes of procaryotes. Despite extensive purification, functional homogeneity of the E. coli expressed hemoglobin was achieved only by the complete disassembly of the hemoglobin into its component alpha and beta globins and their reassembly in the presence of hemin. The kinetics of CO combination and the thermodynamics of O2 binding and cooperativity of the reassembled alphaV1M-betaV1M hemoglobin closely approximate those of HbA. The alpha globin obtained from the E. coli expressed hemoglobin was also combined with normal human beta chains and hemin to form the alphaV1M variant. The alpha+M variant of HbA, in which the normal N-terminal valine of the alpha chains is preceded by a methionine residue, was prepared by the same procedure. The kinetics of the reactions of CO with the alphaV1M and alpha+M variants are similar to those for HbA. The equilibria of oxygen binding to alphaV1M and HbA are similar whereas alpha+M exhibits a significantly higher oxygen affinity. The three-dimensional structures of alphaV1M and alpha+M offer an explanation for the latter affinity difference. Although the structures of alphaV1M and HbA, which have been determined by X-ray crystallography, are virtually indistinguishable except at the N-terminal residues, that of alpha+M indicates the displacement of a solvent molecule, possibly a chloride ion, from arginine 141alpha. Such an alteration in an anion binding site could result in increased oxygen affinity.

Relationships between dimerization and site-specific binding have been characterized previously for wild-type and mutant cI repressors at the right operator (OR) of bacteriophage lambda DNA. However, the roles of higher-order oligomers (tetramers and octamers) that are also formed from these cI molecules have remained elusive. In this study, a clear correlation has been established between repressor oligomerization and non-specific DNA-binding activity. A modification of the quantitative DNase I footprint titration technique has been used to evaluate the degree of saturation of non-specific, OR-flanking lambda DNA by cI repressor oligomers. With the exception of one mutant, only those repressors capable of octamerizing were found to exhibit non-specific DNA-binding activity. The non-specific interaction was accurately modeled using either a one-dimensional, univalent, site-specific Ising lattice approximation, or a more traditional, multivalent lattice approach. It was found that non-specific DNA-binding by repressor oligomers is highly cooperative and energetically independent from site-specific binding at OR. Furthermore, the coupling free energy resolved for non-specific binding was similar to that of site-specific binding for each repressor, suggesting that similar structural elements may mediate the cooperative component of both binding processes. It is proposed that the state of assembly of the repressor molecule modulates its relative affinity for specific and non-specific DNA sequences. These specificities are allosterically regulated by the transmission of assembly-state information from the C-terminal domain, which mediates self-association and cooperativity, to the N-terminal domain, which primarily mediates DNA-binding. While dimers have a high affinity for their cognate sites within OR, tetramers and octamers may preferentially recognize non-specific DNA sequences. The concepts and findings developed in this study may facilitate quantitative characterization of the relationships between specific, and non-specific binding in other systems that utilize multiple modes of DNA-binding cooperativity., (Copyright 1998 Academic Press.)

A cryogenic gel mobility shift technique was developed in which a mixture of protein and DNA samples at equilibrium is rapidly quenched and electrophoresed at -40 degrees C. The rapid and sustained drop in temperature results in almost complete stabilization of the equilibrium species distribution. Autoradiogram analysis of relative abundances for the bound and free DNA sites is carried out over a range of initial binding ratios to yield the binding curve and equilibrium constant as in the usual gel-shift assay. Validity of this technique for determining equilibrium populations of the interacting species is based upon two testable assumptions: (i) The equilibrium species distribution does not change during the cryogenic quench procedure. (ii) This equilibrium distribution is also constant during electrophoresis of the sample. Evidence supporting these assumptions was obtained using lambda cI repressor and a 570-bp DNA fragment containing the repressor binding site OR1. The resolved free energy for this interaction (delta G1) was shown to be independent of the quench procedure, duration of the quench stage, residence time in the gel wells, and duration of low-temperature electrophoresis. The technique yielded a free energy that was in close agreement with those from filter binding and DNAse footprint titration methods. This cryogenic version of the gel-shift method may prove especially useful in cases like that of lambda cI/OR1 binding, for which conventional gel-shift methodology has not been feasible.

In human hemoglobin (Hb) the beta37 tryptophan residue (betaW37), located at the hinge region of the alpha1beta2 interface, forms many contacts with alpha subunit residues of the opposite dimer, in both the T and R quaternary structures. We have carried out equilibrium O2 binding studies on a series of recombinant Hbs that have mutations at this residue site: betaW37Y, betaW37A, betaW37G, and betaW37E. Binding isotherms measured at high concentrations of these mutants were found to be shifted toward increased affinity and decreased cooperativity from that of the normal HbA0 tetramer. Analysis of these binding isotherms indicated that amino acid substitutions at the beta37 position could both destabilize the tetrameric form of the mutants relative to their constituent dimers and also alter cooperativity of the intact tetrameric species. These alterations from wild-type function are dependent on the particular side chain substituted, with the magnitude of change increasing as Trp is substituted by Tyr, Ala, Gly, and Glu. The dimer to tetramer assembly free energy of deoxy-betaW37E, the most perturbed mutant in the series, was measured using analytical gel chromatography to be 9 kcal/tetramer less favorable than that of deoxy HbA0. Stabilizing the betaW37E tetramer by addition of IHP, or by cross-linking at the alphaK99 positions, does not restore normal O2 binding behavior. Thermodynamic parameters of all the mutants were found to correlate with their CO binding rates and with their high-resolution X-ray crystal structures (see accompanying papers: Kwiatkowski et al. (1998) Biochemistry 37, 4325-4335; Peterson & Friedman (1998) Biochemistry 37, 4346-4357; Kavanaugh et al. (1998) Biochemistry 37, 4358-4373].

The software program, HINT (Hydropathic INTeractions), which characterizes non-polar-non-polar, polar-polar, and non-polar-polar interactions, has been used to examine subunit interface associations involved in the hemoglobin allosteric transition at a residue and atomic level. HINT differs from many other computational programs in that it is based not on a statistical method or a force-field but employs parameters experimentally determined from solvent transfer experiments. The main focus of this study is to compare HINT scores that are based upon experimentally and thermodynamically derived measurements with experimentally determined thermodynamic results. The HINT analysis yields a good first-order approximation of experimentally measured energies for these interactions as determined by free energies of dimer-tetramer assembly for mutant hemoglobins. The results provide a framework for understanding subunit stabilities based upon individual atom interactions and repulsions. HINT, in agreement with previous analyses, indicates that: (1) the alpha1beta1 and alpha2beta2 subunit contacts are stabilized via several polar and many hydrophobic interactions with few repulsive contact areas in both the T (deoxyhemoglobin) and R (oxyhemoglobin) structures; (2) the alpha1alpha2 subunit contacts are primarily stabilized by polar salt bridge linkages in both T and R states; and (3) the alpha1beta2 and alpha2beta1 contacts have both strong positive and negative interactions in both T and R states with few hydrophobic interactions. The HINT scoring methodology provides a quantitative characterization of the major role of the alpha1beta2 and alpha2beta1 interfaces in the T-->R quaternary transition. HINT also confirms the stronger hydrogen bond formation in mutant Hb Rothschild (Trp 37beta-->Arg) with Asp94alpha1 that gives rise to a low-affinity (deoxy) hemoglobin. HINT shows that the stabilization of the alpha1beta2 interface with mutant Hb Ypsilanti (Asp99alpha-->Tyr) produces a high-affinity (oxy) hemoglobin by reducing hydrophobic-polar contacts in the R state. HINT interaction maps also identified specific sites for mutagenesis at the alpha1beta2 interface that can be explored to shift the allosteric equilibrium in either direction. In addition, the HINT program provides useful diagnostic data for checking the quality of refined crystallographic structures., (Copyright 1997 Academic Press Limited.)

Free energy contributions to cooperativity by the eight ligation intermediates of human hemoglobin (Hb) have been characterized extensively using six oxygenation analogs [cf. Huang et al. (1996) Biophys. J. 71, 2094-2105, Table 2]. These unprecedented data bses have strongly supported the molecular code mechanism of Hb cooperativity [Ackers et al. (1992) science 255, 54-83]. The present study addresses a recent argument against this work [Shibayama et al. (1997) Biochemistry 36, 4375-4381] based on "free energy" determinations for a doubly-ligated species of the CN-met analog. Shibayama et al. (1997) have claimed that, in the hybridization experiments that have been used to determine free energy of the asymmetric "species[21]" tetramer, a portion of the bound cyanide is allegedly released from CN-met Hb during the incubation with deoxy Hb that is used to achieve hybrid equilibrium. These authors have claimed that cyanide release has resulted in extensive electron exchange between heme sites of the hybridizing sample, leading to incorrect evaluation of the equilibrium species population by the cryogenic techniques that have been employed. In this report, we demonstrate that neither appreciable cyanide loss nor electron exchange occurs with the methods that have been used extensively by our two laboratories for these equilibrium determinations [Perrella et al. (1990) Biophys. Chem. 35, 97-103; Daugherty et al. (1991) Proc. Natl. Acad. Sci. U.S.A. 88, 1110-1114]. An alternative experiment, which Shibayama et al. (1997) have carried out to illustrate their claim, does not evaluate a thermodynamic equilibrium property of the species [21] hybrid. The relevance of their newly-estimated "free energy" is therefore unclear. Nevertheless, Shibayama et al. (1997) have claimed that their proposed "free energy" (which is approximately 1.3 kcal more positive than the free energy of -11.4 kcal found independently by our two laboratories) renders invalid the molecular code mechanism of hemoglobin cooperativity. This representation is utterly without foundation since a free energy even more positive than suggested by Shibayama et al. (1997) would be fully consistent with the molecular code mechanism.

The Gibbs conference on biothermodynamics arose in the late 1980's as a 'self-organized' endeavor by researchers at eleven institutions of the US. Over a period of 10 years these annual conferences have grown steadily in size. They have fostered the development of new thermodynamic approaches and their applications in biochemistry. By emphasizing participation by students and postdoctoral fellows they have contributed significantly to the career development of young scientists in this field.

Oxygen binding by human hemoglobin (Hb) and the coupled reactions of dimer-tetramer assembly were studied over a range of NaCl concentrations (from 0.08 M to 1.4 M) at pH 7.4 and 21.5 degrees C. A strategy of multi-dimensional analysis was employed [G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A., 91, (1974) 4312] to optimize the resolution of the contributions to cooperativity and their heterotropic salt linkages at each stoichiometric degree of O2 binding. A wide range of Hb concentration was utilized at each [NaCl] in which O2-linked subunit assembly reactions contributed significantly to the positions and shapes of the binding isotherms. Kinetic determinations yielded forward and reverse rate constants for assembly of the unligated species. Amplitudes for the assembly rate data had concentration dependences in agreement with the independently determined dimer-tetramer assembly constants of oxyhemoglobin. Concentration-dependent binding isotherms were analyzed, in combination with the kinetically determined equilibrium constants, to yield salt-linked components of cooperativity at the four stages of oxygenation. The principal results of this study were as follows. (i) Assembly of fully oxygenated Hb tetramers is opposed by NaCl: the dimer-to-tetramer equilibrium constant becomes two orders of magnitude less favorable over the [NaCl] range 0.08 M to 1.4 M. By contrast, for deoxy-Hb the assembly equilibrium constant is reduced only two-fold. (ii) Oxygen binding to dimers is non-cooperative over the entire salt range, whereas dimer affinity is slightly favored by increasing the NaCl concentration. (iii) Overall affinity of tetramers for O2 is opposed by NaCl, becoming an order of magnitude less favorable over the range employed. Most of this decrease occurs at the fourth binding step, which shows a large, salt-mediated quaternary enhancement effect; i.e., the assembly of dimers into tetramers at 0.08 M NaCl is accompanied by an eight-fold increase in O2 affinity. (iv) The quaternary enhancement effect at the last O2-binding step is titrated progressively by salt until it reaches a negligible value near the highest [NaCl] of this study. The lowest [NaCl] condition (0.08 M) elicits the greatest tetramer cooperativity with the largest maximal Hill coefficient and the greatest suppression of intermediates. Possible origins and mechanistic implications of these phenomena are considered.

Heterotropic effects of NaCl were studied using CN-met hemoglobin, which has been found to follow the same rules of homotropic cooperativity as CO-Hb and O2-Hb [Huang and Ackers, Biochemistry, 35 (1996) 704; Huang et al., Biophys. J., 71 (1996) 2094]. Modulation of heme site cooperativity by NaCl was determined in this study for all partially ligated CN-met intermediates by measuring their dimer-to-tetramer assembly free energies as a function of NaCl concentration (0.08-1.4 M; pH 7.4, T = 21.5 degrees C). Thermodynamic linkage analysis yielded the contributions to heme site binding cooperativity for all 16 reactions of the binding cascade, and also their apparent changes in bound salt. The principal findings were as follows: (i) At each [NaCl] the ten tetrameric species exhibited three discrete cooperative free energy levels; (ii) positional isomers of the doubly ligated tetramers were distributed among two of these levels according to their specific configurations of ligated sites, in conformity with the symmetry rule mechanism of hemoglobin cooperativity [Ackers et al., Science 255 (1992) 54]; (iii) the apparent moles of NaCl release followed the same configuration-specific distribution as that of heme site cooperativity, i.e., this parameter was synchronized according to the same response clusters. The system thus manifests both a "tertiary chloride effect" and a "quaternary chloride effect", which parallel the tertiary and quaternary Bohr effects [Daugherty et al., Biochemistry, 33 (1994) 10345; Perrella et al., Biochemistry, 33 (1994) 10358] and the tertiary and quaternary enthalpy effects [Huang and Ackers, Biochemistry, 34 (1995) 6316]. Comparison with findings on the stoichiometric O2-binding linkages over an identical range of conditions [Doyle et al., Biophys. Chem., 64 (1997)] revealed that the overall NaCl release upon ligating all four hemes is identical for O2 and CN-met, whereas the detailed distributions of apparent chloride release showed variations between the two ligands, i.e., CN-met Hb showed only a negligible quaternary enhancement at all [NaCl] conditions and a larger tertiary chloride effect compared with O2-Hb. Possible origins of these variations are considered.

Hemoglobin tetramers [Zn/FeO(2)] containing oxygenated subunits (FeO(2)), in combination with unligated subunits containing zinc-substituted hemes (Zn), were analyzed to determine their contributions to the cooperativity of oxygen binding at the Fe sites. Energetic consequences of possible perturbation by zinc substitution were evaluated in all combinations of unligated Zn/Fe hybrid tetramers. A general thermodynamic strategy that corrects for the energetic effects of substituting a second metal for Fe showed the perturbations of Zn substitution to be negligible. This permitted cooperativity parameters of the native Fe/FeO(2) intermediates to be calculated from data on the corresponding Zn/FeO(2) molecules. These parameters, determined explicitly for all eight oxygen-binding intermediates (Fe/FeO(2)), were found to be identical to those predicted earlier from analyzing the O(2) binding data of normal hemoglobin according to the "molecular code" of hemoglobin allostery. The cooperativity parameters determined for this system showed the same distribution pattern found previously for five other oxygen analog systems (Fe/FeCN, FE/Mn(3+), Co/FECO, Co/FeCN, and Fe/FeCO).

Dimer-tetramer assembly reactions of the 10 CN-met ligation microstates of hemoglobin (Hb) were analyzed as a function of NaCl concentration while maintaining constant water activity by the addition of compensating sucrose. The assembly free energy for fully ligated cyanomet Hb and for fully oxygenated Hb becomes less favorable by 1.8 kcal when [NaCl] is increased from 0.08 to 0.7 M, whereas that of unligated Hb is practically insensitive to changes in [NaCl]. Values of 1.6 and 0.3 mol chloride release were found for the assembly of fully ligated and deoxy Hb, respectively; i.e., a net release of 1.3 mol chloride is coupled to the ligation of tetramers for both oxygen and cyanomet ligation. The ligation-linked salt component at constant water activity was evaluated to be 1.0 mol for the full oxygenation of the Hb tetramer in agreement with the overall value previously reported. When the detailed salt linkages accompanying all 16 stepwise cyanomet ligation reactions were experimentally resolved, only two "chloride" effects were found. The first chloride effect correlates with the ligation steps, which create tertiary constraint, and the second effect is coupled to the six switchpoints of quaternary T-->R transition. The distribution of these chloride effects agrees closely with predictions of the "symmetry rule mechanism." The total chloride release for CN-met ligation is in good agreement with that for oxygenation. Free energy contributions to assembly and cooperativity arising from the osmotic effects of chloride were found to be small for all ligation species.

Hybridization experiments between normal Hb tetramers (Fe2+ Hb) and those with four metal-substituted hemes (i.e., replacement of Fe2+ by Co2+, Mg2+, Mn2+, Mn3+, Ni2+, or Zn2+) have revealed unexpected behavior. These homometallic Hbs have previously served as models that mimic the deoxy or oxy properties of normal Fe2+ Hb. In this study, hybrids were composed of one alpha 1 beta 1 dimer that is metal-substituted at both hemes, in association with a second dimer alpha 2 beta 2 that has normal Fe2+ hemes. Both metal-substituted subunits are unligated, whereas the two Fe2+ subunits either are both unligated or both ligated with O2, CO, or CN. It was found that four of the metal-substituted Hbs (Mg2+ Hb, Mn2+ Hb, Ni2+ Hb, and Zn2+ Hb) did not form detectable amounts of heterometallic hybrids with normal Fe2+ Hb even though (i) their homometallic parents formed tight tetrameric complexes with stabilities similar to that of Fe2+ Hb and (ii) hybrids with metal substitution at both alpha sites or both beta sites are known to form readily. This striking positional effect was independent of whether the normal Fe2+ hemes were ligated and of which ligand was used. These findings indicate that surprisingly large changes in tetramer behavior can arise from small and subtle perturbations at the heme sites. Possible origins of these effects are considered.

Analytical ultracentrifugation was used to study higher order self-assembly of lambda cI repressors, including eight mutants whose monomer to dimer reactions were recently characterized [Burz et al. (1994) Biochemistry 33, 8399]. Six of the mutants were found to remain dimeric up to 50 microM total protein; the remaining mutants (EK102 and PT158) were found to undergo higher order oligomerization, as does wild-type cI. For these three repressors, we determined the stoichiometries and energetics of higher order assembly over the temperature range 5-40 degrees C. Weak dimerization exhibited by two other mutants, SN228 and SR228, was also evaluated by sedimentation equilibrium over this same temperature range. The end-state for higher order assembly of wild-type cI was determined to be octameric, in agreement with Senear et al. [(1993) Biochemistry 32, 6179-6189]. The assembly free energies resolved by the sedimentation analysis program NONLIN [Johnson, M. L., et al. (1981) Biophys. J. 36, 575-588] leads to the prediction that tetramers may contribute significantly to the intermediate populations during assembly. This analysis of the species populations is in accord with recent conclusions from fluorescence anisotropy studies [Banik et al. (1993) J. Biol. Chem. 268, 3938]. It was found that two of the mutant repressors (EK102 and PTI58) assemble into octamers, but with differing possible intermediates. PT158 satisfies the stoichiometry 8M1 <--> 2M4 <--> M8, while the EK102 data conforms to a 4M2 <--> 2M4 <--> M8 model, similar to WT (both the EK102 and WT data could also be described by a dimer-octamer model with no intermediates). Of the six repressors found in this study to remain dimeric, three exhibit non-cooperative DNA binding (GD147, KN192, YH210), two express intermediate cooperativity (EK188, SR228), and one is fully cooperative (SN228). The three octamerizing repressors are fully cooperative [Burz & Ackers (1994) Biochemistry 33, 8399], suggesting a correlation between their ability to form higher order assemblies and to engage in cooperative DNA binding. Linear van't Hoff plots were obtained for overall assembly of wild-type and EK102 dimers, while that of PT158 monomers was curved, indicating a negative heat capacity change. The van't Hoff analyses of dimerization constants for SN228 and SR228 were distinctly different from each other and also from that of wild type; such differences might be related to the disparate cooperative behavior found previously for these mutants (Burz & Ackers, 1994).

A strategy has been developed for quantitatively "translating" the distributions of cooperative free energy between different oxygenation analogs of hemoglobin (Hb). The method was used to resolve the cooperative free energies of all eight carbon monoxide binding intermediates. These parameters of the FeCOHb system were determined by thermodynamic transformation of corresponding free energies obtained previously for all species of the Co/FeCO system, i.e., where cobalt-substituted hemes comprise the unligated sites [Speros, P. C., et al. (1991) Biochemistry 30, 7254-7262]. Using hybridized combinations of normal and cobalt-substituted Hb, ligation analog systems Co/FeX (X = CO, CN) were constructed and experimentally quantified. Energetics of cobalt-induced structural perturbation were determined for all species of both the "mixed metal" Co/Fe system and also the ligated Co/FeCN system. It was found that major energetic perturbations of the Co/Fe hybrid species originate from a pure cobalt substitution effect on the alpha subunits. These perturbations are transduced to the beta subunit within the same dimeric half-tetramer, resulting in alteration of the free energies for binding at the nonsubstituted (Fe) sites. Using the linkage strategy developed in this study along with the determined energetics of these couplings, the experimental assembly free energies for the Co/FeCO species were transformed into cooperative free energies of the 10 Fe/FeCO species. The resulting values were found to distribute according to predictions of a symmetry rule mechanism proposed previously [Ackers, G. K., et al. (1992) Science 255, 54-63]. Their distribution is consistent with accurate CO binding data of normal Hb [Perrella, M., et al. (1990b) Biophys. Chem. 37, 211-223] and also with accurate O2 binding data obtained under the same conditions [Chu, A. H., et al. (1984) Biochemistry 23, 604-617].

Enthalpies and heat capacities were determined by isothermal titration calorimetry for bacteriophage lambda cI repressor binding to DNA containing various combinations of the three operator sites OR1, OR2, and OR3 (each comprising a consensus half-site and a specific nonconsensus half-site). Differential scanning calorimetry was employed to evaluate the effects of specific DNA binding on thermal melting of the N-terminal and C-terminal repressor domains. Principal findings of this study are as follows: (1) Binding of repressor to each of the DNA operators is dominated by a large negative enthalpy, in agreement with earlier van't Hoff analyses of quantitative footprint titration data [Koblan & Ackers (1992) Biochemistry 31, 57-65]. The calorimetric data also revealed negative heat capacities for cI binding that are of comparable magnitude with many other systems [Spolar & Record (1994) Science 263, 777-784]. However, this feature in combination with the large negative values of binding enthalpies leads to an enthalpic dominance throughout the physiological temperature range. The resulting thermodynamic profile is opposite to the entropically dominated binding observed for many systems, including lambda cro repressor which binds to the same sites as cI and also employs a helix-turn-helix binding domain [Takeda et al. (1992) Proc. Natl. Acad. Sci. U.S.A. 89, 8180-8184]. It is suggested that these thermodynamic differences may arise from interactions of the cI repressor's N-terminal "arm" with the DNA. (2) Repressor monomers do not bind significantly to DNA containing either a consensus half-site or a nonconsensus half-site. Binding affinity to the double-consensus operator is much weaker than to any of the natural full-site operators. The same was found with other combinations of half-sites. A mutant repressor (PT158) which is severely defective in dimerization [Burz et al. (1994) Biochemistry 33, 8399-8405] was also found to bind only full-site operators and showed dimeric stoichiometry. (3) The thermal melting unit for N-terminal domains in the absence of DNA was found to reach values of 6-8 (monomer units) at concentrations where high-order oligomers of wild-type protein are formed [Senear et al. (1993) Biochemistry 32, 6179-6189]. However, in the presence of DNA operator sites, the cooperative unit for thermal unfolding was reduced to precisely two monomers, indicating that the N-terminal domain binds strictly as a dimer. (4) Significant nonadditivity was observed for the repressor binding enthalpies and heat capacities determined with multiple combinations of full-site operators.(ABSTRACT TRUNCATED AT 400 WORDS)

Subunit assembly reactions of hemoglobin's 10 ligation microstates have been studied as a function of temperature to evaluate the enthalpic and entropic components of cooperativity. It is found that the cooperative enthalpies and cooperative entropies distribute in close agreement with predictions of the symmetry rule mechanism (Ackers et al., 1992) previously deduced from the free energy distribution, in combination with structure-sensitive probes (Doyle & Ackers, 1992; LiCata et al., 1993; Daugherty et al., 1994). Principal findings of the present study are as follows: (1) In unligated hemoglobin (quaternary T), dimer-tetramer assembly is driven by a large negative enthalpy, whereas in the fully ligated (quaternary R) species, the driving force for quaternary assembly is entropic. For the eight intermediate ligation species, the switchover from enthalpic to entropic control follows precisely the symmetry rule predictions; i.e., switching from enthalpic to entropic control occurs at each of the six steps that create ligated heme sites on both sides of the dimer-dimer interface. The combinatorial distribution found previously with free energies does not therefore arise from coincidental enthalpy-entropy compensation that masks a more fundamental distribution. (2) The free energy of tertiary constraint delta Gtc, which pays for intradimer cooperativity prior to quaternary switching, contains large enthalpic and entropic components delta Htc and delta Stc. Like delta Gtc, these terms vanish at the second binding step within the T tetramer. It is found that delta Gtc arises from a net enthalpic dominance over an almost equally large T delta Stc. (3) The stepwise enthalpies correlate with stepwise values of Bohr protons and Bohr free energies (Daugherty et al., 1994) throughout the cascade of 16 stepwise reactions; the correlated clusters of these values follow predictions of the symmetry rule mechanism. (4) These results obtained with cyanomethemoglobin are consistent with the corresponding data on oxygenated hemoglobin which has been resolved at each stage of oxygenation.

The energetics of hemoglobin cooperativity has been analyzed through the use of stable, partially-ligated intermediates. These studies revealed that the two dimeric halves of the tetramer are autonomous, leading to a Symmetry Rule that governs the relationship between ligand-binding and the T-->R quaternary switch: the R structure is favored over T only when ligands are bound to both dimers within the tetramer. A major feature of the Symmetry Rule mechanism is the generation of cooperative free energy by tertiary conformational constraints, which are formed within one dimeric half of the T-tetramer and released during the quaternary structure change to R. These rules of tertiary and quaternary molecular switching also govern the roles of the heterotropic allosteric effectors (e.g. Bohr protons).

The effects of temperature, protons, and KCl on self-assembly and site-specific binding of lambda cI N-terminal domains with operator sites OR were studied to assess the roles of these domains in DNA binding and cooperativity of the natural system. Domain self-assembly was studied using sedimentation equilibrium while domain-OR interactions were analyzed by quantitative DNase footprint titration. The self-assembly reactions were modeled best as a monomer-dimer-tetramer stoichiometry. Compared with intact cI, the monomer-dimer assembly is energetically weak and is largely independent of pH and KCl. The van't Hoff enthalpy of dimerization was found to be large and positive (+ 10.8 kcal/mol), in sharp contrast to that of intact cI (i.e., -16.1 kcal/mol; Koblan & Ackers, 1991a), indicating that different driving forces dominate the respective assembly processes. The interactions of OR with N-terminal domains were noncooperative under all conditions studied. Binding at each site is accompanied by a negative enthalpy (large at site 1, small at sites 2 and 3). Identical values for salt release and proton absorption were found for the three sites. Comparisons with the analogous thermodynamic parameters from our previous studies indicate that N-terminal domains exhibit different linkages to pH, KCl, and T from those of intact cI-OR interactions. This implies that the domains do not act independently within the intact repressor. Since the linkage differences are dependent upon which site the proteins are binding, the C-terminal domain must play a role in repressor discrimination between specific sites.

Free energies of quaternary assembly (dimers to tetramers) were determined for the 10 ligation species of CN-methemoglobin in the region of the alkaline Bohr effect (pH 7.0-9.5). Analysis of this database yielded the following principal findings: (1) At each pH, the nine CN-met species exhibit two distinct values of Bohr proton release and Bohr free energy. The two Bohr effects are found to distribute in a fashion that coincides with predictions of a symmetry rule (Ackers et al., 1992), i.e., the first value reflects a "tertiary Bohr effect" arising from ligation within the quaternary T tetramer and a second Bohr effect arises from the quaternary transition (T-->R) which occurs when both dimeric half-molecules acquire at least one ligated subunit. (2) The Bohr effects for CN-met ligation are in good agreement with previously-established Bohr effects for stepwise O2 binding under identical conditions (Chu et al., 1984). (3) In combination with recent studies which show that CN-met species [21] has a quaternary T structure (Daugherty et al., 1991; Doyle & Ackers, 1992; LiCata et al., 1993), the present results show that the "tertiary Bohr effect" within quaternary T exceeds the Bohr effect of dissociated dimers, as suggested by Lee and Karplus (1983). (4) The tertiary Bohr effect is found to account for the pH dependence of tertiary constraint energy, delta Gtc, which "pays" for ligand-binding cooperativity prior to the quaternary (T-->R) switchover. Possible origins of the tertiary Bohr effect and its relationship to the quaternary Bohr effect are considered.

Wild-type cI repressor dimers bind with 2.5-3 kcal/mol of cooperative free energy to the tripartite right operator region (OR) of bacteriophage lambda [Johnson, A. D., et al. (1981) Nature 294, 217-223; Brenowitz, M., et al. (1986) Methods Enzymol. 130, 132-181]. Quantitative modeling has suggested that cooperativity is required for maintenance of the lysogenic state and for the efficient switch from lysogenic to lytic growth [Ackers, G. K., et al. (1982) Proc. Natl. Acad. Sci. U.S.A. 79, 1129-1133; Shea, M. A., & Ackers, G. K. (1985) J. Mol. Biol. 181, 211-230]. Cooperativity and self-association are thought to involve protein-protein contacts between C-terminal domains of the repressor molecule [Pabo, C. O., et al. (1979) Proc. Natl. Acad. Sci. U.S.A. 76, 1608-1612]. To address the importance of the C-terminal domain in mediating the cooperativity exhibited by lambda cI repressor, a number of single-site mutant candidates were screened for possible deficiencies in cooperative interactions [Beckett, D., et al. (1993) Biochemistry 32, 9073-9079; Burz, D. S., et al. (1994) Biochemistry 33, 8399-8405]. Since repressor dimerization and binding to operator sites are coupled processes, elucidation of the energetic basis of regulation in this system requires that the equilibrium dimerization constants and the intrinsic and cooperative free energies of binding be measured. In this work we evaluate the interaction of eight mutant repressors with OR DNA: Gly147-->Asp (GD147), Pro158-->Thr (PT158), Glu188-->Lys (EK188), Lys192-->Asn (KN192), Tyr210-->His (YH210), Ser228-->Arg (SR228), and Ser228-->Asn (SN228), each with an amino acid substitution in the C-terminal domain, and Glu102-->Lys (EK102) where the substitution lies in the "linker sequence" between domains. Self-assembly properties of six of these mutant repressors are presented in the preceding paper (Burz et al., 1994). In this work, the binding of mutant cI repressors to OR was examined using quantitative DNAse I footprinting. This technique monitors individual site occupancy concurrent with binding at the other sites within a multisite complex.(ABSTRACT TRUNCATED AT 400 WORDS)

Dimerization of lambda cI repressor monomers is required for high-affinity binding to bacteriophage lambda operator DNA and is known to involve protein-protein contacts between C-terminal domains of the repressor monomers. In order to address the importance of the C-terminal domain in mediating the oligomeric properties of dimerization and cooperative binding to operator DNA, eight single-site mutant repressors were screened for possible deficiencies in cooperative interactions; all but one of the amino acid substitutions are located within the C-terminal domain. As a prelude to binding studies and the complete characterization of cooperativity mutants of lambda cI repressor (Burz, D. S., & Ackers, G. K. (1994) Biochemistry 33, 8406-8416), the thermodynamics of self-assembly of seven of these mutants was examined from 10(-11) to 10(-5) M total repressor using analytical gel chromatography. Results show that the structural perturbation accompanying single amino acid replacement does not significantly affect the monomer-dimer equilibrium with the exception of that accompanying replacements of serine 228; mutations at that site weaken, by 2-4 kcal/mol, the protein-protein interactions responsible for self-association. An additional mutant repressor, Pro158-->Thr, was also examined and found to associate reversibly from monomers to a species with stoichiometry greater than 2. All mutations increase the apparent Stokes radius of the monomeric form by 2-4.5 A and that of dimers by 1 or 3 A.

The patterns of energetic response elicited by single-site hemoglobin mutations and chemical modifications have been determined in order to probe the dimer-dimer interface of the half-ligated tetramer (species [21]) that was previously shown to behave as allosterically distinct from both the unligated and fully ligated molecules. In this study the free energies of quaternary assembly (dimers to tetramers) were determined for a series of 24 tetrameric species in which one dimeric half-molecule is ligated (cyanomet hemes) while the adjacent alpha beta dimer is unligated and contains a single amino acid modification. Assembly energies have also been determined for tetramers bearing the same amino acid modifications but where the hemesites were completely vacant and additionally where they were fully occupied. A total of 72 molecular species were thus characterized. It was found that mutationally induced perturbations to the free energy of quaternary assembly were identical for the half-ligated tetramers and the unligated tetramers over the entire spatial distribution of altered sites, but exhibited a radically different pattern from that of the fully ligated molecules. These results indicate that the dimer-dimer interface of the half-ligated tetramer (species [21]) has the same quaternary structure as that of the unligated molecule, i.e., "quaternary T." This quaternary structure assignment of species [21] strongly supports the operation of a Symmetry Rule which translates changes in hemesite ligation into six T-->R quaternary switchpoints. Analysis of the observed Symmetry Rule behavior in relation to the measured distribution of cooperative free energies for the partially ligated species reveals significant cooperativity between alpha and beta subunits of the dimeric half-tetramer within quaternary T. The mutational results indicate that these interactions are not "paid for" by breaking or making noncovalent bonds at the dimer-dimer interface (alpha 1 beta 2). They arise from structural and energetic changes that are "internal" to the ligated dimer even though its association with the unligated dimer is required for the cooperativity to occur. Free energy of "tertiary constraint" is thus generated by the first binding step and is propagated to the second hemesite while the dimer-dimer interface alpha 1 beta 2 serves as a constraint. The "sequential" cooperativity that occurs within the half-molecule is thus preconditioned by the constraint of a quaternary T interface; release of this constraint by dissociation produces only noncooperative dimers.(ABSTRACT TRUNCATED AT 400 WORDS)

Hemoglobin is a tetrameric molecule consisting of two identical alpha beta dimers which assemble into either of two quaternary structures, T or R. Recent studies on mutant and partially ligated hemoglobins have revealed that cooperativity exists between the alpha and the beta hemes of each dimeric half-molecule and have led to a symmetry rule for quaternary T-->R switching: the quaternary R structure is energetically favored over the T structure when each dimeric half-molecule contains at least one ligated subunit.

A hybrid operator-promoter region was designed to aid in a screen for cooperativity mutants of the lambda repressor. In this system, lambda repressor mutants with defects in pairwise cooperative binding are unable to act as efficient transcriptional repressors. Four single amino acid substitutions in the C-terminal domain of the repressor were isolated. Studies of the DNA binding properties of the purified mutant proteins show that a repressor bearing the Gly147-->Asp mutation binds with normal affinity to single operator sites but is defective in pairwise cooperative site binding. Quantitative footprinting studies show that the free energy of interaction between repressor dimers bound at operator sites OR1 and OR2 is reduced from -2.4 kcal/mol for the wild-type repressor to 0 kcal/mol for the GD147 mutant.

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)

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.

Recent crystallographic studies on the mutant human hemoglobin Ypsilanti (beta 99 Asp-->Tyr) have revealed a previously unknown quaternary structure called "quaternary Y" and suggested that the new structure may represent an important intermediate in the cooperative oxygenation pathway of normal hemoglobin. Here we measure the oxygenation and subunit assembly properties of hemoglobin Ypsilanti and five additional beta 99 mutants (Asp beta 99-->Val, Gly, Asn, Ala, His) to test for consistency between their energetics and those of the intermediate species of normal hemoglobin. Overall regulation of oxygen affinity in hemoglobin Ypsilanti is found to originate entirely from 2.6 kcal of quaternary enhancement, such that the tetramer oxygenation affinity is 85-fold higher than for binding to the dissociated dimers. Equal partitioning of this regulatory energy among the four tetrameric binding steps (0.65 kcal per oxygen) leads to a noncooperative isotherm with extremely high affinity (pmedian = .14 torr). Temperature and pH studies of dimer-tetramer assembly and sulfhydryl reaction kinetics suggest that oxygenation-dependent structural changes in hemoglobin Ypsilanti are small. These properties are quite different from the recently characterized allosteric intermediate, which has two ligands bound on the same side of the alpha 1 beta 2 interface (see ref. 1 for review). The combined results do, however, support the view that quaternary Y may represent the intermediate cooperativity state of normal hemoglobin that binds the last oxygen.

The previous and following articles in this issue describe the recombinant synthesis of three mutant beta-globins (beta 1 Val----Ala, beta 1 Val----Met, and the addition mutation beta 1 + Met), their assembly with heme and natural alpha chains into alpha 2 beta 2 tetramers, and their X-ray crystallographic structures. Here we have measured the equilibrium and kinetic allosteric properties of these hemoglobins. Our objective has been to evaluate their utility as surrogates of normal hemoglobin from which further mutants can be made for structure-function studies. The thermodynamic linkages between cooperative oxygenation and dimer-tetramer assembly were determined from global regression analysis of multiple oxygenation isotherms measured over a range of hemoglobin concentration. Oxygen binding to the tetramers was found to be highly cooperative (maximum Hill slopes from 3.1 to 3.2), and similar patterns of O2-linked subunit assembly free energies indicated a common mode of cooperative switching at the alpha 1 beta 2 interface. The dimers were found to exhibit the same noncooperative O2 equilibrium binding properties as normal hemoglobin. The most obvious difference in oxygen equilibria between the mutant recombinant and normal hemoglobins was a slightly lowered O2 affinity. The kinetics of CO binding and O2 dissociation were measured by stopped-flow and flash photolysis techniques. Parallel studies were carried out with the mutant and normal hemoglobins in the presence and absence of organic phosphates to assess their allosteric response to phosphates. In the absence of organic phosphates, the CO-binding and O2 dissociation kinetic properties of the mutant dimers and tetramers were found to be nearly identical to those of normal hemoglobin. However, the effects of organic phosphates on CO-binding kinetic properties of the mutants were not uniform: the beta 1 + Met mutant was found to deviate somewhat from normalcy, while the beta 1 Val----Met mutant reproduced the native allosteric response. Further characterization of the allosteric properties of the beta 1 Val----Met mutant was made by measuring the pH dependence of its overall oxygen affinity by tonometry. Regulation of oxygen affinity by protons was found to be nearly identical to normal hemoglobin from pH 5.8 to 9.3 (0.52 +/- 0.07 protons released per oxygen bound at pH 7.4). The present study demonstrates that the equilibrium and kinetic functional properties of the recombinant beta 1 Val----Met mutant mimic reasonably well those of normal hemoglobin. We conclude that this mutant is well-suited to serve as a surrogate system of normal hemoglobin in the production of mutants for structure-function studies.