The model of Monod, Wyman, and Changeux generates two sets of parameters when applied to oxygen binding in hemoglobin

The model of Monod, Wyman and Changeux is applied to binding phenomena where the Mass Law and its expansion are employed. In this communication the model of Monod, Wyman and Changeux (MWC) is applied to analyze the oxygen binding reaction in hemoglobin. The symmetrical structure of the MWC model with its three parameters is such that two sets of these parameters, rather than one, fit experimental data for the binding of oxygen to hemoglobin.     

The Nernst equation applied to oxidation-reduction reactions in myoglobin and hemoglobin. Evaluation of the parameters

Analyses of the binding of oxygen to monomers such as myoglobin employ the Mass Action equation. The Mass Action equation, as such, is not directly applicable for the analysis of the binding of oxygen to oligomers such as hemoglobin. When the binding of oxygen to hemoglobin is analyzed, models incorporating extensions of mass action are employed. Oxidation-reduction reactions of the heme group in myoglobin and hemoglobin involve the binding and dissociation of electrons. This reaction is described with the Nernst equation. The Nernst equation is applicable only to a monomeric species even if the number of electrons involved is greater than unity. To analyze the oxidation-reduction reaction in a molecule such as hemoglobin a model is required which incorporates extensions of the Nernst equation. This communication develops models employing the Nernst equation for oxidation-reduction reactions analogous to those employed for hemoglobin in the analysis of the oxygenation (binding of oxygen) reaction.     

Temperature and domain size dependence of sickle cell hemoglobin polymer melting in high concentration phosphate buffer.

Deoxygenated sickle cell hemoglobin (Hb S) in 1.8 M phosphate buffer, and carbon monoxide (CO) saturated buffer were rapidly mixed using a stopped-flow apparatus. The binding of the CO to the Hb S polymers and the polymer melting was measured by time resolved optical spectroscopy. Polymer melting was associated with decreased turbidity, and CO binding to deoxy-Hb S was monitored by observation of changes in the absorption profile. The reaction temperature was varied from 20 degrees C to 35 degrees C. Polymer domain size at 20 degrees C was also varied. The data for mixtures involving normal adult hemoglobin (Hb A) fit well to a single exponential process whereas it was necessary to include a second process when fitting data involving Hb S. The overall Hb S-CO reaction rate decreased with increasing temperature from 20 degrees C to 35 degrees C, and increased with decreasing domain size. In comparison, Hb A-CO reaction rates increased uniformly with increasing temperature. Two competing reaction channels in the Hb S-CO reaction are proposed, one involving CO binding directly to the polymer and the other involving CO only binding to Hb molecules in the solution phase. The temperature dependence of the contribution of each pathway is discussed.     

Statistical analysis of data pertaining to complex state systems by stepwise regression with reformulated parameters; Application to spectroscopically monitored hemoglobin oxygen binding data

A method is described for the statistical analysis of data pertaining to complex state systems, based on the concept of reformulating the parameters describing the system as a hierarchy of interactions, and this method demonstrated on the analysis of spectroscopically monitored hemoglobin oxygen binding data [K. Imai, Biophys. Chem. 37 (1990) 197-210]. The concept of reformulation was first extended to state parameters other than ΔG°s, such as the extinction coefficients (εs) associated with different ligation states during hemoglobin oxygen binding. The reformulated parameters are incrementally allowed to vary in the data fitting procedure, and the statistical significance of the added parameters tested by F and Kolmogorov-Smirnov tests. The result of this method is the minimal set of statistically significant parameters required to describe the data. The hierarchical nature of reformulated parameters allows the physical significance of the subset of statistically significant parameters to be discussed even when all reformulated terms may not be statistically significant. Applying this method to hemoglobin oxygen binding data with the reformulated Adair model demonstrated that at least two, and at most three, of the four reformulated Adair constants are statistically significant. A reformulated square model was found to give a statistically indistinguishable fit from the Adair model, with the statistically significant thermodynamic terms essentially those proposed by Linus Pauling in 1935. A change in Δ ε with subsequent oxygen binding events was found to be significant in both models. These results are consistent with a model for hemoglobin oxygen binding where a subunit changes its conformation upon oxygen binding, and affects the conformation of adjacent subunits.     

Kinetics of ligand binding and quaternary conformational change in the homodimeric hemoglobin from Scapharca inaequivalvis

The kinetics of the reaction with oxygen and carbon monoxide of the homodimeric hemoglobin from the bivalve mollusc Scapharca inaequivalvis has been extensively investigated by flash and dye-laser photolysis, temperature jump relaxation, and stopped flow methods. The results indicate that cooperativity in ligand binding, already observed for oxygen at equilibrium, finds its kinetic counterpart in a large decrease of the oxygen dissociation velocity in the second step of the binding reaction. In the case of carbon monoxide, cooperativity is clearly evident in the increase of the combination velocity constant as the reaction proceeds. Therefore, the ligand-binding kinetics of this dimeric hemoglobin shows the characteristic features of the corresponding reactions of tetrameric hemoglobins. Analysis of the data in terms of the allosteric model proposed by Monod et al. (Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88-118) has shown that the values of the allosteric parameters cannot be fixed uniquely for a dimeric hemoglobin. The rapid changes in absorbance observed at the isosbestic points of unliganded and liganded hemoglobin following laser photolysis provided a value of 7 X 10(4) S-1 at 20 degrees C for the rate of the ligand-free quarternary conformational change, postulated on the basis of cooperative ligand binding. Comparison of the rapid absorbance changes observed during ligand rebinding in this hemoglobin with those observed in tuna hemoglobin indicate that, at full photolysis, binding to the T state is followed by further binding and conversion to the liganded R state; at partial photolysis, population of the liganded T state occurs immediately and is followed by a decay to the liganded R state upon further ligand binding. These new results, in conjunction with previous equilibrium data on the same system, show unequivocally that the presence of two different types of chain is not an absolute prerequisite for cooperativity in hemoglobins, contrary to currently accepted ideas.     

The relation between carbon monoxide binding and the conformational change of hemoglobin.

The spectral difference between normal and rapidly reacting deoxyhemoglobin (Sawicki and Gibson (1976), J. Biol Chem. 251:1533-1542) is used to study the relationship between CO binding to hemoglobin and the conformational changes to the rapidly reacting form in a combined flow-laser flash experiment. In both pH 7 phosphate buffer and pH 7 bis(2-hydroxy-ethyl)imino-tris (hydroxymethyl)methane buffer (bis-Tris) with 500 muM 2,3-diphosphoglycerate (DPG), the conformational change lags far behind CO binding; rapidly reacting hemoglobin is not observed until more than 10% of the hemoglobin is liganded. In pH 9 borate buffer the formation of rapidly reacting hemoglobin leads CO binding by a significant amount. A simple two-state allosteric model (Monod et. al. (1965), J. Mol. Biol. 12:88-118) which assumed equivalence of the hemoglobin subunits in their reaction with CO was used to simulate the experimental results. In terms of the model, the conformational change lead observed at pH 9 suggests that significant conformational change has occurred after binding of only one CO molecule per tetramer. In the presence of phosphates good agreement between experimental results and simulations is obtained using parameter values suggested by previous experimental studies. The simulations suggest that the conformational change occurs after binding of three CO molecules.     

Validation and estimation of parameters for a general probabilistic model of the PCR process.

Earlier work rigorously derived a general probabilistic model for the PCR process that includes as a special case the Velikanov-Kapral model where all nucleotide reaction rates are the same. In this model, the probability of binding of deoxy-nucleoside triphosphate (dNTP) molecules with template strands is derived from the microscopic chemical kinetics. A recursive solution for the probability function of binding of dNTPs is developed for a single cycle and is used to calculate expected yield for a multicycle PCR. The model is able to reproduce important features of the PCR amplification process quantitatively.With a set of favorable reaction conditions, the amplification of the target sequence is fast enough to rapidly outnumber all side products. Furthermore, the final yield of the target sequence in a multicycle PCR run always approaches an asymptotic limit that is less than one. The amplification process itself is highly sensitive to initial concentrations and the reaction rates of addition to the template strand of each type of dNTP in the solution. This paper extends the earlier Saha model with a physics based model of the dependence of the reaction rates on temperature, and estimates parameters in this new model by nonlinear regression. The calibrated model is validated using RT-PCR data.     

Solubilization and assay of an hepatic receptor for the haptoglobin-hemoglobin complex

Hemoglobin released into the bloodstream is tightly bound by haptoglobin. The resulting complex (HpHb) is promptly cleared from the circulation and accumulates in the liver. A binding protein with a high affinity for HpHb has been solubilized from an acetone powder of rat liver and freed from an endogenous inhibitor by passage over a column of immobilized hemoglobin. An assay procedure has been developed whereby the bound HpHb is selectively precipitated by polyethylene glycol 6000. Employing this assay, the binding reaction was shown to be linear and saturable with respect to the ligand. In contrast to several previously described receptors for glycoproteins, the carbohydrate moiety of haptoglobin did not appear to participate in the binding of HpHb by the soluble receptor.     

Membrane chromatographic immunoassay method for rapid quantitative analysis of specific serum antibodies

This paper discusses a membrane chromatographic immunoassay method for rapid detection and quantitative analysis of specific serum antibodies. A type of polyvinylidine fluoride (PVDF) microfiltration membrane was used in the method for its ability to reversibly and specifically bind IgG antibodies from antiserum samples by hydrophobic interaction. Using this form of selective antibody binding and enrichment an affinity membrane with antigen binding ability was obtained in-situ. This was done by passing a pulse of diluted antiserum sample through a stack of microporous PVDF membranes. The affinity membrane thus formed was challenged with a pulse of antigen solution and the amount of antigen bound was accurately determined using chromatographic methods. The antigen binding correlated well with the antibody loading on the membrane. This method is direct, rapid and accurate, does not involve any chemical reaction, and uses very few reagents. Moreover, the same membrane could be repeatedly used for sequential immunoassays on account of the reversible nature of the antibody binding. Proof of concept of this method is provided using human hemoglobin as model antigen and rabbit antiserum against human hemoglobin as the antibody source.     

Linked functions in allosteric proteins: Extension of the concerted (MWC) model for ligand-linked subunit assembly and its application to human hemoglobins

The allosteric model of Monod et al. (1965) (MWC) has been extended to take into account the effects of subunit dissociation. The problem is formulated theoretically in terms of a general model for two allosteric species (dimers and tetramers) linked by a polymerization reaction. Relationships are presented for interpreting the dimer-tetramer association constants in terms of allosteric model parameters.Sub-cases of the general model were tested against recent experimental data on the oxygenation-linked dimer-tetramer equilibria in normal human hemoglobin and in the variant hemoglobin Kansas (β₁₀₂, Asp → Thr). The objectives of these analyses were: (1) to find the simplest models capable of describing the linked dimer-tetramer equilibria in the two hemoglobin systems, and (2) to evaluate the corresponding model parameters so that allosteric properties of the two hemoglobins may be compared.In the simplest version of the model, the dimer is half of an R-state tetramer. This model was found to be excluded unequivocally by the data for both normal hemoglobin and hemoglobin Kansas when the α and β chains have equal binding affinities. When this two-state model was modified to permit non-equivalent affinities for the chains, the model could be fitted to hemoglobin Kansas, but not to hemoglobin A. A model, in which the dimers are allowed to exist in a state different from the tetramer R state, was found to be consistent with the data for hemoglobin A, with equivalent binding by the α and β chains. For hemoglobin A, the unliganded R-state tetramers have a different subunit dissociation energy from that of fully liganded R-state tetramers. The simplest model capable of describing both hemoglobin A and hemoglobin Kansas was obtained by extending this three-state model to permit (but not require) functional non-equivalence of the α and β chains. For these MWC models, unique estimates were obtained for the model parameters.The allosteric constants for tetrameric hemoglobins A and Kansas are approximately equal. The value obtained from hemoglobin A is similar to previous estimates, whereas the value for hemoglobin Kansas is lower than previously estimated (Edelstein, 1971) by approximately two orders of magnitude. The low affinity of hemoglobin Kansas tetramer does not arise from an unusually high allosteric constant favoring the T-state species. It is largely the consequence of a greatly reduced oxygen affinity of β chains in the T state, and reduced values for the ratio between affinities in the R and T states.     

Linkage between cooperative oxygenation and subunit assembly of cobaltous human hemoglobin.

The thermodynamic linkage between cooperative oxygenation and dimer-tetramer subunit assembly has been determined for cobaltous human hemoglobin in which iron(II) protoporphyrin IX is replaced by cobalt(II) protoporphyrin IX. The equilibrium parameters of the linkage system were determined by global nonlinear least-squares regression of oxygenation isotherms measured over a range of hemoglobin concentrations together with the deoxygenated dimer-tetramer assembly free energy determined independently from forward and reverse reaction rates. The total cooperative free energy of tetrameric cobalt hemoglobin (over all four binding steps) is found to be 1.84 (+/- 0.13) kcal, compared with the native ferrous hemoglobin value of 6.30 (+/- 0.14) kcal. Detailed investigation of stepwise cooperativity effects shows the following: (1) The largest change occurs at the first ligation step and is determined on model-independent grounds by knowledge of the intermediate subunit assembly free energies. (2) Cooperativity in the shape of the tetrameric isotherm occurs mainly during the middle two steps and is concomitant with the release of quaternary constraints. (3) Although evaluation of the pure tetrameric isotherm portrays identical binding affinity between the last two steps, this apparent noncooperativity is the result of a "hidden" oxygen affinity enhancement at the last step of 0.48 (+/- 0.12) kcal. This quaternary enhancement energy is revealed by the difference in subunit assembly free energies of the triply and fully ligated species and is manifested visually by the oxygenation isotherms at high versus low hemoglobin concentration. (4) Cobaltous hemoglobin dimers exhibit apparent anticooperativity of 0.49 (+/- 0.16) kcal (presumed to arise from heterogeneity of subunit affinities).(ABSTRACT TRUNCATED AT 250 WORDS)     

A model for ligand binding to hexacoordinate hemoglobins

Hexacoordinate hemoglobins are heme proteins capable of reversible intramolecular coordination of the ligand binding site by an amino acid side chain from within the heme pocket. Examples of these proteins are found in many living organisms ranging from prokaryotes to humans. The nonsymbiotic hemoglobins (nsHbs) are a class of hexacoordinate heme proteins present in all plants. The nsHb from rice (rHb1) has been used as a model system to develop methods for determining rate constants characterizing binding and dissociation of the His residue responsible for hexacoordination. Measurement of these reactions exploits laser flash photolysis to initiate the reaction from the unligated, pentacoordinate form of the heme protein. A model for ligand binding is presented that incorporates the reaction following rapid mixing with the reaction starting from the pentacoordinate hemoglobin (Hb). This model is based on results indicating that ligand binding to hexacoordinate Hbs is not a simple combination of competing first order (hexacoordination) and second order (exogenous ligand binding) reactions. Ligand binding following rapid mixing is a multiphasic reaction displaying time courses ranging from milliseconds to minutes. The new model incorporates a "closed", slow reacting form of the protein that is not at rapid equilibrium with the reactive conformation. It is also demonstrated that formation of the closed protein species is not dependent on hexacoordination.     

Migration of small molecules through the structure of hemoglobin: evidence for gating in a protein electron-transfer reaction

It has previously been shown that the rates and activation energies for migration molecules of different sizes through myoglobin are very similar. The results were interpreted in terms of conformational changes in the protein structure that facilitate the passage of the different molecules to a similar extent. Here we ask whether the quaternary structural changes that accompany the binding of ligands (O2 or CO) to hemoglobin might influence the migration rate from the solution into the protein's binding site. As a model for the R state of hemoglobin, we used the protein in which the Fe protoporphyrin (FePP) in the alpha subunit was substituted by Zn protoporphyrin (ZnPP) and the oxidized heme was ligated by CN-. The T state of hemoglobin was represented by the protein in which all four FePP groups were substituted by ZnPP. The quenching rate of the excited ZnPP triplet state within the hemoglobin by oxygen, methyl viologen, and anthraquinonesulfonate served as a measure of the migration rate through the protein into the binding site. It was found that the activation energies for all three quenchers were very similar and closely resembled those in myoglobin, suggesting that the migration rates are determined by the subunit structure only and that the quaternary configurational changes do not influence the quenching rates. The implications of the results for electron transfer in proteins are briefly discussed.     

Nitric oxide formation from the reaction of nitrite with carp and rabbit hemoglobin at intermediate oxygen saturations

The nitrite reductase activity of deoxyhemoglobin has received much recent interest because the nitric oxide produced in this reaction may participate in blood flow regulation during hypoxia. The present study used spectral deconvolution to characterize the reaction of nitrite with carp and rabbit hemoglobin at different constant oxygen tensions that generate the full range of physiological relevant oxygen saturations. Carp is a hypoxia-tolerant species with very high hemoglobin oxygen affinity, and the high R-state character and low redox potential of the hemoglobin is hypothesized to promote NO generation from nitrite. The reaction of nitrite with deoxyhemoglobin leads to a 1 : 1 formation of nitrosylhemoglobin and methemoglobin in both species. At intermediate oxygen saturations, the reaction with deoxyhemoglobin is clearly favored over that with oxyhemoglobin, and the oxyhemoglobin reaction and its autocatalysis are inhibited by nitrosylhemoglobin from the deoxyhemoglobin reaction. The production of NO and nitrosylhemoglobin is faster and higher in carp hemoglobin with high O(2) affinity than in rabbit hemoglobin with lower O(2) affinity, and it correlates inversely with oxygen saturation. In carp, NO formation remains substantial even at high oxygen saturations. When oxygen affinity is decreased by T-state stabilization of carp hemoglobin with ATP, the reaction rates decrease and NO production is lowered, but the deoxyhemoglobin reaction continues to dominate. The data show that the reaction of nitrite with hemoglobin is dynamically influenced by oxygen affinity and the allosteric equilibrium between the T and R states, and that a high O(2) affinity increases the nitrite reductase capability of hemoglobin.     

Nitric oxide binding to oxygenated hemoglobin under physiological conditions.

We have added nitric oxide (NO) to hemoglobin in 0.1 M and 0.01 M phosphate buffers as well as to whole blood, all as a function of hemoglobin oxygen saturation. We found that in all these conditions, the amount of nitrosyl hemoglobin (HbNO) formed follows a model where the rates of HbNO formation and methemoglobin (metHb) formation (via hemoglobin oxidation) are independent of oxygen saturation. These results contradict those of an earlier report where, at least in 0.01 M phosphate, an elevated amount of HbNO was formed at high oxygen saturations. A radical rethink of the reaction of oxyhemoglobin with NO under physiological conditions was called for based on this previous proposition that the primary product is HbNO rather than metHb and nitrate. Our results indicate that no such radical rethink is called for.     

Nitric oxide binding to oxygenated hemoglobin under physiological conditions

We have added nitric oxide (NO) to hemoglobin in 0.1 M and 0.01 M phosphate buffers as well as to whole blood, all as a function of hemoglobin oxygen saturation. We found that in all these conditions, the amount of nitrosyl hemoglobin (HbNO) formed follows a model where the rates of HbNO formation and methemoglobin (metHb) formation (via hemoglobin oxidation) are independent of oxygen saturation. These results contradict those of an earlier report where, at least in 0.01 M phosphate, an elevated amount of HbNO was formed at high oxygen saturations. A radical rethink of the reaction of oxyhemoglobin with NO under physiological conditions was called for based on this previous proposition that the primary product is HbNO rather than metHb and nitrate. Our results indicate that no such radical rethink is called for.     

The kinetics of the diffusion-controlled reaction of the binding of carbon monoxide to hemoglobin in glycerol-water mixtures of high viscosity

The kinetics of the binding of carbon monoxide to human hemoglobin and to ferrous horseradish peroxidase (HRP) have been studied by flash photolysis in mixtures of glycerol and water over a wide range of temperature and solvent viscosities. This was done in order that the influence of diffusion-control on the association rates could be determined. The binding of CO to HRP which is much slower than binding to Hb was devoid of diffusion effects. By contrast, the fast and slow phases of binding to Hb in the high viscosity solvents both displayed curved Arrhenius plots, consistent with a change from a chemical activationcontrolled process in the high temperature region to a diffusion-controlled process in the low temperature region. Analyses of the curved Arrhenius plots indicated that in the low temperature diffusion-controlled region, the activation enthalpy is similar to the activation energy of viscosity of the solvent, as might be expected for a diffusion-controlled reaction.Curve fitting of rate-temperature-viscosity data, assuming simultaneous chemical activation and diffusion-control, yielded factors by which the diffusion rate constants differ from that for reaction between uniformly reactive spheres of equal radii. For the fast Hb reaction, observed upon partial photolysis, this factor varies from 0.02 to 1.1, depending upon the solvent composition. For the slow Hb reaction, observed upon higher degrees of photolysis, this factor was 0.03 and 0.04. These factors were rationalized in terms of fractional surface reactivities and of a maximum allowable solid angle of entry of reactant to the binding site. It was concluded that the steric hindrance of T-state Hb (slow reaction) is much greater than R-state Hb (fast reaction).     

Allosteric free energy changes at the alpha 1 beta 2 interface of human hemoglobin probed by proton exchange of Trp beta 37

The energetic changes that occur on ligand binding in human hemoglobin have been investigated by measurements of the exchange rates of the indole proton of Trpbeta37(C3). The Trpbeta37 residues are located in helices C of the beta-subunits and are involved in contacts with the segments FG of the alpha-subunits at the interdimeric alpha1beta2 and alpha2beta1 interfaces of the hemoglobin tetramer. In the quaternary structure change that accompanies ligand binding to hemoglobin, these contacts undergo minimal changes in relative orientation and in packing, thereby acting as hinges, or flexible joints. The exchange rates of the indole proton of Trpbeta37(C3) were measured by nuclear magnetic resonance spectroscopy, in both deoxygenated and ligated hemoglobin. The results indicate that, at 15 degrees C, the exchange rate is increased from 9.0. 10(-6) to 3.3. 10(-4) s(-1) upon ligand binding to hemoglobin. This change suggests that the structural units at the hinge regions of the alpha1beta2/alpha2beta1 interfaces containing Trpbeta37(C3) are specifically stabilized in unligated hemoglobin, and experience a change in structural free energy of approximately 4 kcal/(mol tetramer) upon ligand binding. Therefore, the hinge regions of the alpha1beta2/alpha2beta1 interfaces could play a role in the transmission of free energy through the hemoglobin molecule during its allosteric transition.     

Nitric oxide transport on sickle cell hemoglobin: Where does it bind?

We have recently reported that nitric oxide inhalation in individuals with sickle cell anemia increases the level of NO bound to hemoglobin, with the development of an arterial-venous gradient, suggesting delivery to the tissues. A recent model suggests that nitric oxide, in addition to its well-known reaction with heme groups, reacts with the β-globin chain cysteine 93 to form S-nitrosohemoglobin (SNO-Hb) and that SNO-Hb would preferentially release nitric oxide in the tissues and thus modulate blood flow. However, we have also recently determined that the primary NO hemoglobin adduct formed during NO breathing in normal (hemoglobin A) individuals is nitrosyl (heme)hemoglobin (HbFe^IINO), with only a small amount of SNO-Hb formation. To determine whether the NO is transported as HbFe^IINO or SNO-Hb in sickle cell individuals, which would have very different effects on sickle hemoglobin polymerization, we measured these two hemoglobin species in three sickle cell volunteers before and during a dose escalation of inhaled NO (40, 60, and 80 ppm). Similar to our previous observations in normal individuals, the predominant species formed was HbFe^IINO, with a significant arterial-venous gradient. Minimal SNO-Hb was formed during NO breathing, a finding inconsistent with significant transport of NO using this pathway, but suggesting that this pathway exists. These results suggest that NO binding to heme groups is physiologically a rapidly reversible process, supporting a revised model of hemoglobin delivery of NO in the peripheral circulation and consistent with the possibility that NO delivery by hemoglobin may be therapeutically useful in sickle cell disease.     

Reaction of nitric oxide with heme proteins and model compounds of hemoglobin

Rates for the reaction of nitric oxide with several ferric heme proteins and model compounds have been measured. The NO combination rates are markedly affected by the presence or absence of distal histidine. Elephant myoglobin in which the E7 distal histidine has been replaced by glutamine reacts with NO 500-1000 times faster than do the native hemoglobins or myoglobins. By contrast, there is no difference in the CO combination rate constants of sperm whale and elephant myoglobins. Studies on ferric model compounds for the R and T states of hemoglobin indicate that their NO combination rate constants are similar to those observed for the combination of CO with the corresponding ferro derivatives. The last observation suggests that the presence of an axial water molecule at the ligand binding site of ferric hemoglobin A prevents it from exhibiting significant cooperativity in its reactions with NO.