Hemoglobin-oxygen equilibria: retrospective and phenomenological perspective

The origin of the concept of a molecular complex between oxygen and hemoglobin can be traced to Stokes, a century and a half ago. Subsequently, physicochemical concepts of equilibria provided a path to quantitative formulations of these ligand–receptor interactions. Then, it took a quarter of a century before a proper format was prepared in terms of four stoichiometric equilibria and their associated binding constants. Since then, experimental measurements of these stoichiometric binding constants have consistently disclosed that successive values of K₁ to K₄ are accentuated above those expected if every subunit of hemoglobin maintained the same, intrinsic, unchanging affinity for oxygen. An alternative analysis of the observed cooperative interactions has been obtained by extracting the roots of the polynomial of the stoichiometric binding equation and deriving an alternative binding equation containing constants that for O₂–Hb are complex numbers. These constants have the dimensions and properties of equilibrium constants. They provide some novel phenomenological insights into ligand–receptor equilibria.     

Ligand binding systems at equilibrium: specificity, heterogeneity, cross-reactivity, and site-site interactions

The simplest ligand binding model that can account for systems which consist of heterogeneous receptors that show site-site interactions and can react with several types of ligands was presented. This model was based on the grand canonical partition function whose properties and potentialities for obtaining binding functions are briefly illustrated. A computer simulation of this model was carried out in order to examine the contributions of site-site interactions on the shape of binding isotherms and on specificity curves. The shape of the binding isotherms was shown to be independent regardless of whether the path of binding was considered. However, the shape of the specificity curves was strongly dependent on site-site interactions and on the particular sequence of ligand-receptor configurations formed during the ligand binding process, leading to the conclusion that site-site interactions may influence the specificity of a system more than even very strong cross-reactions. A method based on the Ising model of statistical mechanics was also described and was used for obtaining binding functions applicable to infinite lattices which show site-site interactions and competitive binding. The results presented here point out possible errors that can arise if standard statistical methods are used to fit binding data in order to prove a given binding model.     

Asymmetric distribution of cooperativity in the binding cascade of normal human hemoglobin. 1. Cooperative and noncooperative oxygen binding in Zn-substituted hemoglobin

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.     

Mutagenic dissection of hemoglobin cooperativity: effects of amino acid alteration on subunit assembly of oxy and deoxy tetramers.

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.     

The linkage between the four-step binding of oxygen and the binding of heterotropic anionic ligands in hemoglobin

The linkage between the four-step binding of oxygen and the binding of heterotropic anionic ligands in hemoglobin was investigated by accurately measuring and analyzing the oxygen equilibrium curves of human adult hemoglobin in the presence and absence of various concentrations of one or two of the following materials: chloride (Cl-), 2,3-diphosphoglycerate (DPG), and inositol hexaphosphate (IHP). Each equilibrium curve was analyzed according to the Adair equation to evaluate the four-step oxygen equilibrium constants (Adair constants) and the median oxygen pressure. The binding constants of the anions for the molecular species of hemoglobin carrying j oxygen molecules, Hb(O2)j(j=0,1,...,4), were evaluated from the dependences of the Adair constants and the median oxygen pressure on the anion concentration by introducing a model which takes the competitive binding of Cl- and DPG or IHP into account. Assumptions made in the model are: (a) the hemoglobin molecule has two oxygen-linked binding sites for Cl- which are equivalent and independent and (b) no Cl- can be bound to hemoglobin to which DPG or IHP is already bound and vice versa. Thus, we could obtain values for the intrinsic binding constants of Cl- and DPG, i.e., the constants in the absence of other competitive anions. For IHP, only the binding constants and apparent binding constants for Hb and Hb(O2)2 were obtained. Values of the Cl- binding constants and apparent binding constants for DPG and IHP, i.e., the binding constants in the presence of Cl- for Hb and Hb(O2)4, were in reasonable agreement with literature values. From the binding constants we calculated anion binding curves for Hb(O2)j(J=0,1,...,4), the number of anions bound to Hb(O2)J, And the relationship between fractional anion saturation of hemoglobin and fractional oxygen saturation. The numbers of released anions are not uniform with respect to oxygenation step. This non-uniformity is the reason for the changes in the shape of the oxygen equilibrium curve with anion concentration changes and for the non-uniform dependences of the Adair constants on anion concentration, and also results in non-linear relations between anion saturation and oxygen saturation. The anion binding constants and various binding properties of the anions derived from those constants are consistent with those observed by other investigators using different techniques, indicating that the present model describes the oxygen-linked competitive anion binding well.     

Two techniques for evaluating small molecule-macromolecule binding in complex system

Two techniques are proposed for the evaluation of multiple binding in complex systems. These techniques can be applied to reactions where more than one class of binding sites is present or where there are interactions between equivalent sites. The first technique employs a Klotz or Scatchard plot to evaluate three stoichiometric binding constants and the total number of sites. Furthermore the individual site binding parameters can be determined for several very important systems such as a macromolecule with two classes of independent sites or a macromolecule with three sites that are equivalent but not independent. For a system with many classes of independent sites, a second technique employs a continuous distribution of binding constants to analyze the reaction. This method does not require the assumption of a functional form for the distribution or a knowledge of the number of classes.     

Stoichiometric noncovalent interaction in molecular imprinting

In this review article the function of the binding site monomers in the molecular imprinting procedure is discussed. Especially, new developments towards stoichiometric noncovalent interactions are highlighted. In stoichiometric noncovalent interactions template and binding site monomer in an 1:1 molar ratio are nearly completely bound to each other. This is only possible if the association constants are considerably high (K _ass < 900 M^–1). Using this type of interaction in molecular imprinting no excess of binding sites is necessary and binding sites are only located inside the imprinted cavity. Since all cavities can be reloaded these polymers show high capacity (e.g., for preparative application) and are especially suited for the synthesis of catalytically active imprinted polymers. Discussed are binding site interactions based on amidines (and guanidines), multiple hydrogen bonding, charge-transfer interactions, and host–guest inclusion. The systematic investigation of the underlying binding reaction is described in detail. With low-molecular weight model substances the thermodynamics of the association can be conveniently investigated, e.g., by NMR spectroscopy.     

Chromatographic analysis of allosteric effects between ibuprofen and benzodiazepines on human serum albumin

The effects of (R)- and (S)-ibuprofen on the binding of benzodiazepines to human serum albumin (HSA) were examined by biointeraction chromatography. The displacement of benzodiazepines from HSA by (R)- and (S)-ibuprofen was found to involve negative allosteric interactions (or possible direct competition) for most (R)-benzodiazepines. However, (S)-benzodiazepines gave positive or negative allosteric effects and direct competition when displaced by (R)- or (S)-ibuprofen. Association equilibrium constants and coupling constants measured for these effects indicated that they involved two classes of ibuprofen binding regions (i.e., low- and high-affinity sites). Based on these results, a model was proposed to explain the binding of benzodiazepines to HSA and their interactions with ibuprofen. This model gave good agreement with previous reports examining the binding of benzodiazepines to HSA.     

Direct measurement of equilibrium constants for high-affinity hemoglobins

The biological functions of heme proteins are linked to their rate and affinity constants for ligand binding. Kinetic experiments are commonly used to measure equilibrium constants for traditional hemoglobins comprised of pentacoordinate ligand binding sites and simple bimolecular reaction schemes. However, kinetic methods do not always yield reliable equilibrium constants with more complex hemoglobins for which reaction mechanisms are not clearly understood. Furthermore, even where reaction mechanisms are clearly understood, it is very difficult to directly measure equilibrium constants for oxygen and carbon monoxide binding to high-affinity (K(D) < 1 micro M) hemoglobins. This work presents a method for direct measurement of equilibrium constants for high-affinity hemoglobins that utilizes a competition for ligands between the "target" protein and an array of "scavenger" hemoglobins with known affinities. This method is described for oxygen and carbon monoxide binding to two hexacoordinate hemoglobins: rice nonsymbiotic hemoglobin and Synechocystis hemoglobin. Our results demonstrate that although these proteins have different mechanisms for ligand binding, their affinities for oxygen and carbon monoxide are similar. Their large affinity constants for oxygen, 285 and approximately 100 micro M(-1) respectively, indicate that they are not capable of facilitating oxygen transport.     

Structure-function relationships in EF-hand Ca2+-binding proteins. Protein engineering and biophysical studies of calbindin D9k

Genes encoding the minor A component of bovine calbindins D9k--the smallest protein known with a pair of EF-hand calcium-binding sites--with amino acid substitutions and/or deletions have been synthesized and expressed in Escherichia coli and characterized with different biophysical techniques. The mutations are confined to the N-terminal Ca2+-binding site and constitute Pro-20----Gly (M1), Pro-20----Gly and Asn-21 deleted (M2), Pro-20 deleted (M3), and Tyr-13----Phe (M4). 1H, 43Ca, and 113Cd NMR studies show that the structural changes induced are primarily localized in the modified region, with hardly any effects on the C-terminal Ca2+-binding site. The Ca2+ exchange rate for the N-terminal site changes from 3 s-1 in the wild-type protein (M0) and M4 to 5000 s-1 in M2 and M3, whereas there is no detectable variation in the Ca2+ exchange from the C-terminal site. The macroscopic Ca2+-binding constants have been obtained from equilibration in the presence of the fluorescent chelator 2-[[2-[bis(carboxymethyl)-amino]- 5-methylphenoxy]methyl]-6-methoxy-8-[bis(carboxymethyl)amino]quinoline or by using a Ca2+-selective electrode. The Ca2+ affinity of M4 was similar to that of M0, whereas the largest differences were found for the second stoichiometric step in M2 and M3. Microcalorimetric data show that the enthalpy of Ca2+ binding is negative (-8 to -13 kJ.mol-1) for all sites except the N-terminal site in M2 and M3 (+5 kJ.mol-1). The binding entropy is strongly positive in all cases. Cooperative Ca2+ binding in M0 and M4 was established through the values of the macroscopic Ca2+-binding constants. Through the observed changes in the 1H NMR spectra during Ca2+ titrations we could obtain ratios between site binding constants in M0 and M4. These ratios in combination with the macroscopic binding constants yielded the interaction free energy between the sites delta delta G as -5.1 +/- 0.4 kJ.mol-1 (M0) and less than -3.9 kJ.mol-1 (M4). There is evidence (from 113Cd NMR) for site-site interactions also in M1, M2, and M3, but the magnitude of delta delta G could not be determined because of sequential Ca2+ binding.     

Differences in the binding mechanism of RU486 and progesterone to the progesterone receptor

The binding mechanism of the antagonist RU486 to the progesterone receptor was compared with that of the agonists progesterone and R5020. Both progesterone and RU486 bound to the receptor with a Hill coefficient of 1.2, indicating the binding of each ligand is positive cooperative. However, when each ligand was used to compete with [3H]progesterone for binding to the receptor at receptor concentrations near 8 nM, at which the receptor is likely a dimer, the competition curve for RU486 was significantly steeper than the curves for progesterone and R5020 (p less than 0.001). This indicated that a difference in the binding mechanism of RU486 and progesterone can be detected when both ligands are present. In contrast, at receptor concentrations near 1 nM, at which the receptor is likely a monomer, the competition curves for all three ligands were indistinguishable (p = 0.915). These results indicate that RU486 and agonists have different binding mechanisms for the receptor and further suggest that this difference may be related to site-site interactions within the receptor.     

Analysis of ligand binding curves on basis of mean intrinsic thermodynamic quantities

The mean intrinsic thermodynamic quantity can be defined by considering the relative population of complex species in the solution and the value of intrinsic thermodynamic quantity corresponds to each step of ligation. In the present study a new method is introduced for analysis of experimental ligand binding data on basis of mean intrinsic thermodynamic quantities. In this regard, a deviation parameter was defined by comparing the non-interacting system with the cooperative interactive one. This parameter can be calculated just by estimation of the first binding constant. A set of relations between this deviation parameter and other binding characteristics, such as mean intrinsic Gibbs free energy of binding and mean Gibbs free energy of site-site interaction, have been developed. This model presents binding mechanism in a unified way that is simple, yet stringent, more straightforward, more reliable and informative. This analyzing method has been successfully applied for evaluation of various systems such as oxygen binding to hemoglobin, laurate and warfarin binding to human serum albumin, and reveals some new biological features of these binding systems.     

Ligand-dependent aggregation and cooperativity: a critique

Ligand-dependent site-site (or subunit-subunit) interactions provide the basis for explaining cooperativity in chemical reactions. Even in the simplest possible nonaggregating system, interpretation of the interactions in terms of structural details requires an explicit assumption (or model) for the binding of the ligand to the sites when there are no interactions. This paper develops in detail the processes by which aggregation will yield ligand-dependent cooperativity. Two conceptually distinct free energy differences may contribute to cooperativity in an aggregation reaction. One is the free energy difference in ligand binding between the monomer and the aggregate. The other is derived from ligand-dependent interactions between the sites of the aggregate. In this analysis an explicit distinction is made between the experimentally accessible constants and those derived from assumed models. Experimental measurements of an aggregation cycle in which all of the species in equilibrium are defined do not allow for an evaluation of the energies of interaction without some model (or assumption). In the analysis presented, an explicit assumption is employed relating the constant for binding of the ligand to the isolated monomer and the constant for the binding of the ligand to aggregate under conditions where there are no ligand-dependent interactions.     

Anion binding characteristics of the band 3 / 4,4-dibenzamidostilbene-2,2-disulfonate binary complex: evidence for both steric and allosteric interactions.

A novel kinetic approach was used to measure monovalent anion binding to better define the mechanistic basis for competition between stilbenedisulfonates and transportable anions on band 3. An anion-induced acceleration in the release of 4,4'-dibenzamidostilbene-2,2'-disulfonate (DBDS) from its complex with band 3 was measured using monovalent anions of various size and relative affinity for the transport site. The K1/2 values for anion binding were determined and correlated with transport site affinity constants obtained from the literature and the dehydrated radius of each anion. The results show that anions with ionic radii of 120-200 pm fall on a well-defined correlation line where the ranking of the K1/2 values matched the ranking of the transport site affinity constants (thiocyanate < nitrate approximately bromide < chloride < fluoride). The K1/2 values for the anions on this line were about 4-fold larger than expected for anion binding to inhibitor-free band 3. Such a lowered affinity can be explained in terms of allosteric site-site interactions, since the K1/2 values decreased with increasing anionic size. In contrast, iodide, with an ionic radius of about 212 pm, had a 10-fold lower affinity than predicted by the correlation line established by the smaller monovalent anions. These results indicate that smaller monovalent anions have unobstructed access to the transport site within the band 3 / DBDS binary complex, while iodide experiences significant steric hindrance when binding. The observation of steric hindrance in iodide binding to the band 3 / DBDS binary complex, but not in the binding of smaller monovalent anions, suggests that the stilbenedisulfonate binding site is located at the outer surface of an access channel leading to the transport site.     

The insulin-receptor interaction: is the kinetic approach for inferring negative-cooperative site-site interactions valid?

The dissociation of insulin from its receptor is reportedly enhanced when the dissociation is induced by dilution in the presence of insulin. This experiment is frequently conducted when curvilinear Scatchard plots of insulin binding are observed in order to infer negative cooperative site-site interactions amongst insulin receptors. However, when insulin binding to purified liver plasma membranes was measured at 15 degrees C in 50 mM Tris, pH 7.5 containing 0.1% bovine serum albumin and 100 U/ml bacitracin, the insulin binding data was characterised by a linear Scatchard plot and a Hill plot with a slope equal to unity. Thus, under the conditions of this binding assay, insulin apparently bound to a single non-interacting class of homogeneous binding sites. But, despite the apparent absence of cooperative interactions under these specific conditions, the dissociation of receptor-bound insulin was still enhanced when the dissociation of insulin from its receptor was induced by dilution in the presence of insulin. This result cast serious doubt on the validity of inferring negative-cooperative site-site interactions amongst insulin receptors based solely on the observation that the dissociation of receptor-bound insulin is enhanced by dilution in the presence of insulin.     

Asymmetric distribution of cooperativity in the binding cascade of normal human hemoglobin. 2. Stepwise cooperative free energy

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.     

Conformation-specific antibodies to the alpha chain COOH terminus of hemoglobin A0.

An anti-hemoglobin antiserum obtained from a sheep immunized with human carboxyhemoglobin A0 demonstrated little difference in its reactivity with deoxy- or carboxyhemoglobin A0. However, a subpopulation of this antiserum isolated by synthetic peptide affinity chromatography clearly distinguished between these two hemoglobin species. This subpopulation, designated alpha(129-141) anti-hemoglobin antibodies, represents less than 1% of the total anti-hemoglobin antibodies. They are nonprecipitating by Ouchterlony analysis, and fluorescence-quenching studies demonstrate the interaction of a single antibody binding site per hemoglobin dimer. These antibodies bind preferentially to carboxyhemoglobin with a median affinity constant of 5 X 10(8) M-1 compared to binding to deoxyhemoglobin with a binding affinity of less than 1 X 10(8) M-1. Furthermore, the presence of these antibodies in stoichiometric amounts increases the oxygen affinity of hemoglobin, and thus antibody and oxygen binding to hemoglobin can be considered as a linked function.     

Role of magnesium ion in the interaction between chromomycin A3 and DNA: binding of chromomycin A3-Mg2+ complexes with DNA.

Chromomycin A3 is an antitumor antibiotic which blocks macromolecular synthesis via reversible interaction with DNA template only in the presence of divalent metal ions such as Mg2+. The role of Mg2+ in this antibiotic-DNA interaction is not well understood. We approached the problem in two steps via studies on the interaction of (i) chromomycin A3 and Mg2+ and (ii) chromomycin A3-Mg2+ complex(es) and DNA. Spectroscopic techniques such as absorption, fluorescence, and CD were employed for this purpose. The results could be summed up in two parts. Absorption, fluorescence, and CD spectra of the antibiotic change upon addition of Mg2+ due to complex formation between them. Analysis of the quantitative dependence of change in absorbance of chromomycin A3 (at 440 nm) upon input concentration of Mg2+ indicates formation of two types of complexes with different stoichiometries and formation constants. Trends in change of fluorescence and CD spectroscopic features of the antibiotic in the presence of Mg2+ at different concentrations further corroborate this result. The two complexes are referred to as complex I (with 1:1 stoichiometry in terms of chromomycin A3:Mg2+) and complex II (with 2:1 stoichiometry in terms of chromomycin A3:Mg2+), respectively, in future discussions. The interactions of these complexes with calf thymus DNA were examined to check whether they bind differently to the same DNA. Evaluation of binding parameters, intrinsic binding constants, and binding stoichiometry, by means of spectrophotometric and fluorescence titrations, shows that they are different. Distinctive spectroscopic features of complexes I and II, when they are bound to DNA, also support that they bind differently to the above DNA. Measurement of thermodynamic parameters characterizing their interactions with calf thymus DNA shows that complex I-DNA interaction is exothermic, in contrast to complex II-DNA interaction, which is endothermic. This feature implies a difference in the molecular nature of the interactions between the complexes and calf thymus DNA. These observations are novel and significant to understand the antitumor property of the antibiotic. They are also discussed to provide explanations for the earlier reports that in some cases appeared to be contradictory.     

The mismatch in distributions of vertebrates and the plants that they disperse

Little is known about how mutualistic interactions affect the distribution of species richness on broad geographic scales. Because mutualism positively affects the fitness of all species involved in the interaction, one hypothesis is that the richness of species involved should be positively correlated across their range, especially for obligate relationships. Alternatively, if mutualisms involve multiple mutualistic partners, the distribution of mutualists should not necessarily be related, and patterns in species distributions might be more strongly correlated with environmental factors. In this study, we compared the distributions of plants and vertebrate animals involved in seed‐dispersal mutualisms across the United States and Canada. We compiled geographic distributions of plants dispersed by frugivores and scatter‐hoarding animals, and compared their distribution of richness to the distribution in disperser richness. We found that the distribution of animal dispersers shows a negative relationship to the distribution of the plants that they disperse, and this is true whether the plants dispersed by frugivores or scatter‐hoarders are considered separately or combined. In fact, the mismatch in species richness between plants and the animals that disperse their seeds is dramatic, with plants species richness greatest in the in the eastern United States and the animal species richness greatest in the southwest United States. Environmental factors were corelated with the difference in the distribution of plants and their animal mutualists and likely are more important in the distribution of both plants and animals. This study is the first to describe the broad‐scale distribution of seed‐dispersing vertebrates and compare the distributions to the plants they disperse. With these data, we can now identify locations that warrant further study to understand the factors that influence the distribution of the plants and animals involved in these mutualisms.