Analysis of teleost hemoglobin by Adair and Monod-Wyman-Changeux models

Summary The allosteric effects of the erythrocytic nucleoside triphosphates (NTP) and of proton concentrations were investigated by precise measurement of Hb–O₂ equilibria of tench hemoglobin (including extreme, high and low saturation ranges) and analysed in terms of the MWC two state model and the Adair four step oxygenation theory.At low concentrations (NTP/Hb ratio=1.0, and pH>7.3) ATP, GTP and protons decrease Hb–O₂ affinity by increasing the allosteric constantL and reducingK _T, the association constant¹ of the deoxy, tense state of the Hb, without significantly affecting that (K _R) of the oxy state, increasing the free energy of cooperativity (G). High concentrations of these effectors, however, also reduceK _R. The greater sensitivity of the half-saturation O₂ tension (P ₅₀) of the Hb to GTP than to ATP at the same concentration, correlates with greater effects of GTP on bothK _T andK _R. The pH and NTP dependence of the four Adair association constants and the calculated fractional populations of Hb molecules in different stages of oxygenation show that the autochthonous NTP effectors and protons stabilize the T structure and postpone the TR transition basic to cooperativity in fish Hb.The possible implications of the findings for aquatic respiration are discussed.Abbreviations ATP adenosine triphosphate - DPG 2,3-diphosphoglycerate (glycerate-2,3-bisphosphate) - GTP guanosine triphosphate - IHP inositol hexaphosphate - NTP nucleoside triphosphates In this paperK _T andK _R are defined as theassociation equilibrium constants instead of dissociation constants (as originally defined by Monod et al. 1965) to facilitate comparison with the Adair constants     

PH dependence of the Adair constants of human hemoglobin. Nonuniform contribution of successive oxygen bindings to the alkaline Bohr effect.

In order to solve the problem of an apparent discrepancy between the pH variance of oxygen equilibrium curve and the linear relation between the number of released Bohr protons and the degree of ligation, precise oxygen equilibrium curves of human hemoglobin were determined at a number of pH values from 6.5 to 8.8. From the equilibrium data individual steps (Adair constants), ki (i equals 1, 2, 3, 4), were obtained and the number of Bohr protons (deltaHi+) released on the ith stage of oxygenation was estimated. The pH dependence of k4 was very small, while the other ks strongly depended on pH over the pH range examined. As a consequence, the contribution of each step of oxygen binding to the alkaline Bohr effect nonuniform: deltaH4 was very small compared with deltaH1+, deltaH2+, and deltaH3+. In spite of this, calcuation has shown that the fractional number of released protons is essentially proportional to fractional oxygen saturation because of cooperative effects in hemoglobin. Thus, the present study indicates that the linear relationship between the fractional number of released protons and the degree of ligation, as obtained from titration experiments, is not necessarily incompatible with the pH variance of the shape of the oxygen equilibrium curve. The nonuniform pH depencence of the Adair constants implies that the two-state allosteric model of Monod, J., Wyman, J., and Changeus, J.P. (1965) J. Mol. Biol. 12, 88-118 is not adequate to describe the heterotropic effect caused by protons.     

Use of dual wavelength spectrophotometry and continuous enzymatic depletion of oxygen for determination of the oxygen binding constants of hemoglobin

A small stopped-flow cuvette was built into a computer-controlled Cary 210 spectrophotometer. The enzymatic depletion of oxygen in solutions of hemoglobin and myoglobin was initiated by flowing the hemeproteins with the enzyme against a solution of the hemeproteins containing the appropriate substrate. The deoxygenation was homogeneous throughout the solution. Oxygen activity was calculated at each instant of time from the fractional saturation of Mb, determined from observations at the Hb/HbO2 isosbestic wavelength. Fractional saturation of Hb was determined from absorbances at the Mb/MbO2 isosbestic wavelength. The spectrophotometer cycled between these two wavelengths during the deoxygenation. The deoxygenation of HbO2 was largely complete in 20-25 min, whereas the deoxygenation of MbO2 was allowed to proceed for about 1 h. This procedure eliminates equilibration of Hb solutions with a gas phase and replaces oxygen electrode readings with spectrophotometric sensing by Mb, providing essentially instantaneous determinations of oxygen activity and hence 250-500 or more independent data points per run. The Mb and Hb data vectors require several manipulations to correct for small relative displacements in time and for small non-isosbestic effects. Detailed consideration of the enzyme kinetics allowed oxygen activities to be determined in regions where Mb is a poor sensor. Studies of HbO2 deoxygenation as a function of wavelength show that the determination of the four Adair constants requires in addition the determination of three spectroscopic parameters. Values of the apparent Adair constants, determined without these spectroscopic parameters, depend strongly on the monitoring wavelength.     

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.     

Analysis of oxygen equilibria of the giant hemoglobin from the earthworm Eisenia foetida using the Adair model

Oxygen equilibrium curves of the giant hemoglobin from the earthworm Eisenia foetida were determined at various concentrations of cations. Using the Adair model of 12 oxygenation steps, we succeeded in fitting the data better than the simple concerted model (MWC model). Analysis of the Adair constants (K1 to K12) indicated that the increase in oxygen affinity occurs in the last six steps (K7 to K12) of the oxygen binding and that it is enhanced by increase in Ca2+ concentration. The Hill coefficient (nmax) at pH 7.5 attained a maximum value of 9.76 at 20 mM CaCl2. In the presence of physiological levels of Ca2+ (5 mM), the Bohr effect was similar to that seen in vertebrates. The data were consistent with the release of two Bohr protons being accompanied by the oxygen-linked binding of one Ca2+. Mg2+ and Na+ exerted a similar effect on the hemoglobin, though to a lesser extent. The stoichiometry of Ca2+ binding of the hemoglobin revealed the presence of two classes of binding sites, of which the affinities are high (Ka = 8.8 x 10(3) +/- 103 M-1) and low. The number of high affinity sites per heme was found to be 0.3, comparable to the number of oxygen-linked Ca2+ binding sites.     

Consequences of neglecting the hemoglobin concentration on the determination of Adair binding constants

It is commonly believed that the tetrameric Adair constants for oxygen binding to human hemoglobin can be evaluated from a single oxygenation experiment at 'high' hemoglobin concentration without considering the consequence of the presence of alpha beta dimers. We present examples which demonstrate that this is a very dangerous assumption. Without a knowledge of the complete oxygenation-linked dimer-tetramer association reaction (alpha beta Xi----(alpha beta)2Xj), it is impossible to predict a priori how high of a hemoglobin concentration would be required to make this assumption. Furthermore, without a knowledge of the complete oxygenation-linked dimer-tetramer association reaction, it is impossible to predict a priori the direction and magnitude of the systematic errors which are induced by making this assumption.     

Involvement of Glu G3(101)beta in the function of hemoglobin. Comparative O2 equilibrium studies of human mutant hemoglobins

The glutamyl residue at G3(101)beta of normal hemoglobin (Hb A) is one of the alpha 1 beta 2 subunit contacts which are vital to O2 binding properties of the molecule. The O2 equilibrium properties of the four mutants with different substitutions at this site are studied in order to elucidate the role of this residue. Under stripped conditions with minimum chloride the order of O2 affinity is: Hb A (Glu) much less than Hb Rush (Gln) less than or equal to Hb British Columbia (Lys) less than or equal to Hb Potomac (Asp) less than or equal to Hb Alberta (Gly). The first Adair constants, K1, for the mutant hemoglobins are greater than that for Hb A whereas the fourth, K4, are similar, indicating that the allosteric constants (L) of these mutants are greatly reduced. Therefore, the G3(101)beta residue contributes intrinsically to the strengthening of the structural constraints that are imposed upon the deoxy (T) forms but not the oxy (R) form. On addition of 0.1 M Cl- and further addition of 2,3-diphosphoglycerate or inositol hexaphosphate, their O2 affinities and cooperativities are altered, reflecting different responses to anionic ligands. Hb Rush exhibits a stronger chloride effect than Hb A and the other variants and, as a result, an increased Bohr effect and a smaller heat of oxygenation at pH 6.5. These changes are consistent with an increased positive net charge in the central cavity of Hb Rush and subsequent extra anion binding in the deoxy form. The tetramer to dimer dissociation constants are estimated to be greater than normal for Hb British Columbia and less than normal for Hb Alberta. This comparative study of the G3(101)beta mutants indicates that the size and the charge of this residue may influence the switching of two neighboring interchain hydrogen bonds that occurs during oxygenation of normal hemoglobin.     

The linkage between oxygenation and subunit dissociation in human hemoglobin. Consequences for the analysis of oxygenation curves.

For human hemoglobin, a pronounced dependence of oxygenation curves upon protein concentration can be demonstrated experimentally in the range between 10(-4) and 2 X 10(-6) M heme. The effects of such protein concentration dependence upon analysis of saturation curves have been explored using a model-independent linkage analysis which incorporates the dissociation of tetramers to dimers. We have carried out stimulations of oxygenation curves representing a variety of energy distributions designed to cover a wide range of values which are relevant to known hemoglobin systems and experimental conditions. The resulting simulated oxygenation curves were analyzed by least-squares minimization procedures in terms of the tetramer binding isotherm to yield the four apparent Adair constants. These derived constants were compared with the originally assumed values used in the simulation in order to assess the extent to which their values may be altered by the presence of dimer. For each energy distribution the analysis has been carried out over a wide range of protein concentration. We have found that the presence of even small amounts of dimer that are necessarily present at the low protein concentrations commonly employed may have a devastating effect upon the reliability of Adair constant determinations. In addition to these simulated cases, we have analyzed two sets of highly precise experimental data from the literature in order to assess the degree to which constants obtained may have been influenced by the presence of dimer.     

Simulation of continuous blood O2 equilibrium curve over physiological pH, DPG, and Pco2 range

We analyzed 56 O2 equilibrium curves of fresh human blood, each from 0 to 150 Torr Po2. The data were collected over ranges of values for the 2,3-diphosphoglyceric acid-to-hemoglobin concentration ratio [DPG]/[Hb] of 0.2-2.7, for pH of 7.0-7.8, and for Pco2 of 7-70 Torr. Each curve was characterized according to the Adair scheme for the stepwise oxygenation of Hb, and the resulting constants (a1, a2, a3, a4) were analyzed to allow the simulation of the entire O2 equilibrium curve under any conditions of [DPG]/[Hb], pH, and Pco2 in the specified range. This analysis provides a powerful tool to study the affinity of Hb for O2 within the red blood cell and to predict the shape of the O2 equilibrium curve in various physiological and pathological states. Other attempts to predict blood O2 affinity have considered only P50 (the Po2 at one-half saturation with O2) or have provided too little data for continuous simulations.     

Influence of anions and protons on the Adair coefficients of haemoglobins A and Cowtown (His HC3(146) beta----Leu)

We have measured the contribution of the alkaline Bohr effect of the C-terminal histidine residues of the beta-chains of haemoglobin A by comparing haemoglobin A with haemoglobin Cowtown in which those histidine residues are replaced by leucine. Oxygenation of a stripped 2.5 mM (haem) solution of haemoglobin A yielded 0.19 H+/haem, while oxygenation of a similar solution of haemoglobin Cowtown produced no change of pH. Oxygen equilibria measured at 60 microM-haem in 0.1 M-Hepes buffer gave an alkaline Bohr effect of -0.21 H+/haem for haemoglobin A and only -0.01 H+/haem for haemoglobin Cowtown, even though its Hill's coefficient was greater than 2 throughout the pH range studied. These results prove that the chloride-independent part of the alkaline Bohr effect is due to the C-terminal histidine residues of the beta-chains. Oxygen equilibria measured in 0.095 M-bis-Tris buffers with minimal chloride or with 0.1 M-chloride showed the contribution of those histidine residues to the alkaline Bohr effect to be about 0.2 H+/haem, independent of chloride concentration. Determination of the individual Adair coefficients in the three different buffers indicated that pH and chloride tend to have their greatest effects at the second or third steps of oxygenation when the change of quaternary structure is most likely to occur; between pH 7 and 9, the fourth Adair coefficient is only very slightly affected by pH and not significantly by chloride.     

A plausible sequence of the conformational changes of hemoglobin induced by oxygenation.

Recent experimental data of oxygen equilibrium constants of human adult hemoglobin, which are measured over a wide range of oxygen pressures, are analyzed successfully from the viewpoint that the change in the molecular structure of hemoglobin induced by oxygenation is considered individually at each stage of oxygenation. Then, a simple phenomenological rule, which explains quantitatively the values of the four Adair constants with only three parameters, is found for hemoglobin under normal physiological conditions. The temperature dependence of these parameters suggests a sequence of the conformational changes such that until the third stage of oxygenation the conformational changes occur within the deoxy quaternary structure and at the fourth stage of oxygenation the deoxy quaternary structure is altered to the oxy one. The effects of pH and phosphate compounds on the Adair constants are discussed, and a possible modification and extension of the rule is suggested. The connection between the rule and the molecular structures of deoxy- and oxyhemoglobin is also discussed.     

Resolvability of adair constants from oxygenation curves measured at low hemoglobin concentration

Analyses of low concentration oxygenation curves for apparent Adair constants in which the effects of dimers is ignored have been explored using recently determined values of the overall energy coupling parameters. For high affinity systems and favorable energy distributions, it is found that the errors in estimated binding free energies may be less than one kcal provided the measurement errors are strictly random and of small magnitude. These errors are nevertheless quite substantial as compared with the differences between values for the successive binding steps.     

Comparative least-squares analysis of hemoglobin oxygen equilibrium curves

The oxygen-binding properties of hemoglobin have been studied at 600 microM protein concentration with organic phosphate, and analyzed by a series of different nonlinear least-squares analysis methods to determine whether reports of negligibly small values of the third overall Adair parameter, A3, are consequences of the data or a product of the data analysis. Data from other laboratories were analyzed as well. The single most important factor in creating a measurement that yields a small A3 is the use of equally weighted fitting in the Adair equation, while end-weighted fitting generally yields a larger A3. Endpoint extrapolation is ruled out as a major cause of abnormal A3 values. Monte Carlo simulations of the 600 microM results suggest that, if a small A3 were present, end weighting is at least as sensitive to a small A3 as equal weighting. We conclude that equally weighted fitting of the tetrameric Adair equation is unable to resolve the upper asymptote of the oxygen-binding data, resulting in an unusually small value for A3.     

Nonlinear optical effects in oxygen-binding reactions of hemoglobin A0

Optical spectra have been taken in the Soret band (440-400 nm) under different oxygen partial pressures for hemoglobin (Hb) A0 at pH 7.0, 15 degrees C, 2-3 mM heme, 30 mM inositol hexaphosphate, 0.1 Hepes and 0.1 M NaCl. Application of the matrix method of singular value decomposition (SVD) to the difference spectra for different oxygen pressures shows the presence of at least two distinct optical transitions. From this result one concludes that the optical response to oxygen binding is nonlinear in the Soret band. The degree of nonlinearity has been determined by fitting the data at different wavelengths to the four-step reaction Adair equation with the inclusion of optical parameters that describe the intermediate oxygenated species. It is found that the data are well-represented by two optical parameters at each wavelengths, one which represents the optical change for the addition of the first and second oxygen molecules and the other which corresponds to the change for the addition of the third and fourth oxygen molecules. The ratio of these optical parameters depends only moderately upon wavelength with an average value of 0.8 over the Soret band. Thus, there is an approx. 20% smaller optical response for the first two ligated species than that for the last two ligated species. The overall Adair equilibrium constants are evaluated as follows: beta 1 = 0.081 +/- 0.003 Torr-1, beta 2 = 2.53 x 10(-3) +/- 2.4 x 10(-4) Torr-2, beta 3 = 1.25 x 10(-5) +/- 1.0 x 10(-6) Torr-3, beta 4 = 1.77 x 10(-6) +/- 1.5 x 10(-7) Torr-4.     

Equilibrium oxygen binding to human hemoglobin cross-linked between the alpha chains by bis(3,5-dibromosalicyl) fumarate

Oxygen equilibrium curves of human hemoglobin Ao (HbAo) and human hemoglobin cross-linked between the alpha chains (alpha alpha Hb) by bis(3,5-dibromosalicyl) fumarate were measured as a function of pH and chloride or organic phosphate concentration. Compared to HbAo, the oxygen affinity of alpha alpha Hb was lower, cooperativity was maintained, although slightly reduced, and all heterotropic effects were diminished. The major effect of alpha alpha-cross-linking appears to be a reduction of the oxygen affinity of R-state hemoglobin under all conditions. However, while the oxygen affinity of T-state alpha alpha Hb was slightly reduced at physiologic chloride concentration and in the absence of organic phosphates, KT was the same for both hemoglobins in the presence of 2,3-diphosphoglycerate (or high salt) and higher for alpha alpha Hb in the presence of inositol hexaphosphate. The reduced O2 affinity arises from smaller binding constants for both T- and R-state alpha alpha Hb rather than through stabilization of the low affinity conformation. All four Adair constants could be determined for alpha alpha Hb under most conditions, but a3 could not be resolved for HbAo without constraining a4, suggesting that the cross-link stabilizes triply ligated intermediates of hemoglobin.     

Effect of differences in optical properties of intermediate oxygenated species of hemoglobin A0 on Adair constant determination

Careful evaluation of the so-called isosbestic properties of oxygenated and deoxygenated hemoglobin spectra demonstrates that the spectral changes are not strictly linear with respect to the degree of saturation. In order to quantify the extent of nonlinearity, optical measurements of O2 binding to human hemoglobin were made at different wavelengths in the Soret region approaching the presumed isosbestic point. The results indicate that the extinction coefficient of intermediate oxygenated hemoglobin is 1% less than that of the fully oxygenated hemoglobin, with a resulting 3% (+/- 0.15%) nonlinearity effect on measurements taken at the peak of the oxygenated hemoglobin spectrum (414 nm). The lack of isosbestic conditions allows one to investigate the functional properties of the oxygenated intermediates directly. The small difference in the absorbance of different oxygenated species has practically no influence on the determination of Adair constants at wavelengths removed from the critical isosbestic region.     

The effect of temperature on oxygen equilibrium curves of trout blood (Salmo gairdnerii)

• 1.1. Oxygen equilibrium curves were measured on trout red blood cell suspensions at pH 7.8 and 8.4 at 15, 20 and 25 C. Normal red cells and red cells that had been depleted of their ATP content were used.
• 2.2. The equilibrium data were fitted to the Adair's model and the enthalpy (ΔH) and entropy (ΔS) changes for the first and fourth steps of oxygenation and for overall oxygenation were calculated from the temperature dependencies of the Adair constants.
• 3.3. For normal red blood cells, the apparent heat for the first oxygenation step, δh₁, is close to zero.
• 4.4. Temperature insensitivity of this step at physiological pH, combined with a large pH dependence, probably denotes a property of Hb4, the Root effect Hb of trout blood.
• 5.5. At pH 7.8, ΔH₄ is about —4kcal/mol, a small value which may be attributed to the large release of Bohr protons that occurs at the last oxygenation step and corresponds to an endothermic process which opposes to the exothermic oxygenation of the haem.
• 6.6. The ΔH₄ value appears to have a large influence on the enthalpy for overall oxygenation.
• 7.7. Results for ATP-free red cells are consistent with a mere increase in the intracellular pH and suggest that ATP has no specific effect at and above pH_i ~ 7.7.
• 8.8. Effects of temperature and pH on trout red blood cell isotherms emphasize the primary importance of the major component of trout blood, namely Hb4, in trout blood functional properties.

     

Evaluation of Adair binding constants from experimental data obtained with an Imai cell. Statistical weighting functions

One group of laboratories uses an 'even-weighted', or unweighted, nonlinear least-squares method for the analysis of experimental oxygen binding data obtained with an Imai oxygenation apparatus. Another group uses an 'end-weighted' nonlinear least-squares analysis. With end weighting each observation is assigned a statistical weight which is proportional to Y(1-Y), where Y is the fractional saturation. In this work we discuss statistical weighting functions as applied to the Imai oxygenation apparatus and then determined what are the best weighting factors for an actual series of published experiments. Based on these calculations, it is concluded that the 'best' weighting for the Imai oxygenation apparatus is a very small amount of end weighting. Furthermore, the amount of end weighting is so small that even weighting, or no weighting at all, is also appropriate.     

The binding of hemoglobin to red cell membrane lowers its oxygen affinity

The mode of interaction of human hemoglobin (Hb) with the red cell membrane was investigated with special reference to the effect on oxygen binding properties and Hb-membrane binding constants. Compared to free native Hb, the membrane-bound native Hb showed a strikingly lowered oxygen affinity and smaller response to organic phosphates such as 2,3-diphosphoglycerate and inositol hexaphosphate. Similar effects of membrane binding were also observed for intermediately cooperative Hbs such as N-ethylmaleimide-treated Hb (NES-Hb) and iodoacetamide-treated Hb (AA-Hb), but very small effects were observed for non-cooperative Hb, i.e., carboxypeptidase A-treated Hb (des-His-Tyr Hb). The magnitude of the affinity lowering was in the order: NES-Hb greater than native Hb greater than AA-Hb much greater than des-His-Tyr Hb. In the presence of inositol hexaphosphate, the three chemically modified Hbs showed an increased oxygen affinity when bound to the red cell membrane, probably due to partial replacement of bound inositol hexaphosphate by membrane. The binding to membrane caused a slight decrease in cooperativity for native Hb, but no distinct change in cooperativity was observed for the three modified Hbs. These results imply: a) the red cell membrane binds to deoxyHb more strongly than to oxyHb; b) the difference in membrane binding affinity between oxyHb and deoxyHb is closely related to the quaternary structure change in the Hb molecule occurring upon oxygenation. The higher affinity of the membrane for deoxyHb than for oxyHb apparently disagrees with the conclusion drawn by earlier investigators. However, the present binding experiments by means of ultrafiltration proved that the red cell membrane actually binds to deoxyHb much more strongly than to oxyHb, validating the present conclusion based on oxygenation experiments. Our results are consistent with those obtained recently by other investigators using a synthetic peptide or the cytoplasmic fragment of red cell membrane band 3.