Two-state Allosteric Model Research Articles

Kinetic and cooperative mechanisms of ligand binding to hemoglobin.

The reactions of 13 isonitriles with deoxyhemoglobin have been examined and characterized at pH 7, 20 degrees C. Kinetic studies have shown that these ligands can be divided into two mechanistic classes based on their size and stereochemistry. The larger and branched compounds (isopropyl, all butyl isomers, n-pentyl, n-hexyl, cyclohexyl, and benzyl isocyanides) exhibit biphasic time courses at all ligand concentrations as a result of intrinsic differences between the reactivities of the alpha and beta subunits. In contrast, the smaller isonitriles (methyl, ethyl, and n-propyl isocyanides) exhibit monophasic, and often accelerating, time courses at high ligand concentrations. At low concentrations, the smaller isonitriles also exhibit biphasic time courses; however, in this case, the two phases are due to marked differences between the dissociation rate constants of the high and low affinity quaternary conformations of the protein. Sets of equilibrium and kinetic data for the binding of 11 of the isonitriles were fitted to an expanded version of the two-state allosteric model first described by Monad, Wyman, and Changeux (Monod, J., Wyman, J., and Changeux, J.-P. (1965) J. Mol. 12, 108 118). The resultant rate and equilibrium constants for the R (high affinity) and T (low affinity) states were used to calculate chemical potentials for ligand molecules bound to the heme iron and for the kinetic barriers experienced by these compounds during the binding process. For the beta subunits, both the difference between the bound chemical potentials for the R and T states and the differences between the barrier potentials for the two protein conformations are independent of ligand length and stereochemistry. Thus, it would appear that steric interactions are not a major factor in the expression of cooperativity by these subunits. For alpha chains, a 30% decrease in the difference between the bound R and T state potentials is observed in going from methyl to n-hexyl isocyanide. In addition, a marked increase in the height of the T state, alpha chain kinetic barrier is observed with increasing length of the alkyl side chain. Thus, steric hindrance between the bound ligand molecule and protein residues at the sixth coordination position of the heme iron atom does appear to play a significant role in the expression of cooperativity by the alpha subunits, at least for the larger alkyl isocyanides.

Temperature perturbation of the allosteric equilibrium in trout hemoglobin.

The carbon monoxide binding kinetics of the isolated trout Hb I has been investigated by flash photolysis at various temperatures, from approximately 20 degrees to 72 degrees C. The time course of recombination has been quantitatively analyzed with a simple two-state allosteric model, making use of the thermodynamic data previously obtained. These new experiments and their analysis show that a simple two-state kinetic model is adequate, in the case of trout Hb I, to describe quantitatively the time course of CO binding at all temperatures. Moreover, we show that temperature can be used to perturb the quaternary conformational equilibrium, the high affinity state of the molecule (R) being progressively more populated at higher temperatures.

Ligand binding and the gelation of sickle cell hemoglobin

The solubility equilibrium between monomer and polymer which has been shown to exist in deoxyhemoglobin S solutions is examined in solutions partially saturated with carbon monoxide. The total solubility is found to increase monotonically with increasing fractional saturation. At low fractional saturations the increase is nearly linear, amounting roughly to an increase of 0.01 g cm −3 in solubility for each 10% increase in fractional saturation. Linear dichroism measurements on the spontaneously aligned polymer phase are used to examine the composition of the polymer as a function of the fractional saturation of the corresponding solution phase. The dichroism experiments show that the polymer phase contains less than 5% of CO-liganded hemes even at supernatant fractional saturations in excess of 70%. The polymer selects against totally liganded hemoglobin molecules by a minimum factor of 65 and against singly liganded molecules by a factor of at least 2.5. Consequently, polymerized hemoglobin S has a ligand affinity which is significantly lower than that of monomeric hemoglobin S in the deoxy quaternary structure. The kinetics of the polymerization reaction in the presence of CO are similar to those observed in pure deoxyhemoglobin S solutions. The polymerization is preceded by a pronounced delay, the duration of which, t d, is proportional roughly to the 30th power of the solubility. At low fractional saturations, this amounts to a tenfold increase in t d for each 10% increase in the fractional saturation. These results show that the polymerization reaction is nearly specific for deoxyhemoglobin. Models for the dependence of the solubility and the polymer saturation on ligand partial pressure demonstrate the importance of solution phase non-ideality in determining the solubility of mixtures. The results require selection against partially liganded species which is significantly greater than is predicted by the two-state allosteric model. The data are compatible with either sequential or allosteric models in which the major polymerized component is the unliganded hemoglobin molecule.

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.

Thermodynamics of ligand binding and allosteric transition in hemoglobins. Reaction of Hb trout IV with CO

The reaction of hemoglobin trout IV with carbon monoxide has been studied in three parallel sets of experiments comprising: (1) microcalorimetric measurements in different buffers at two pH values (7.1 and 8.5) and two temperatures (20 °C and 5 °C) to determine the overall value of the enthalpy change of ligand binding as well as its point values as a function of fractional saturation with CO; (2) a study of the CO binding curves at three pH values (from 5.7 to 7.4) and at 23 °C and 5 °C in order to explore the pH and temperature dependence of the model-independent binding parameters which describe the system; (3) differential titrations in 0.2 m-sodium chloride at 23 °C and 5 °C of the deoxy and CO saturated forms of the molecule in order to determine the overall CO Bohr effect as a function of temperature. Analysis of the results of these three different sets of experiments at a purely phenomenological level shows that they are in satisfactory agreement. Further analysis in terms of a modified two-state allosteric model shows how the three model parameters k T, k R, and L vary with pH and temperature. From this it appears that the essential feature of the functional behavior of trout IV hemoglobin, which is characteristic of hemoglobins of teleost fish in general, lies in a proton-induced shift in the allosteric equilibrium constant. The data indicate, semiquantitatively, that the apparent enthalpy change corresponding to the allosteric equilibrium constant is pH-dependent and positive.

Three-dimensional structure of an intact human immunoglobulin.

We have examined the low-resolution structure of a complete human IgG1 using known domain coordinates from crystallographic investigations of immunoglobulin fragment structures. Our results indicate that the Fc portion of this molecule has a structure similar to that of an isolated Fc fragment, with the carbohydrate moiety playing a central role as the principal contact between the CH2 domains. Carbohydrate also forms a large part of the interface between the Fc and Fab regions. The relative orientations of the variable and constant portions of the Fab regions are intermediate between those reported previously, emphasizing the flexibility of the switch region. These data do not support a two-state allosteric model such as has been proposed for antibody effector functions.

The enhancement of the alkaline Bohr effect of some fish hemoglobins with adenosine triphosphate

The oxygen equilibria of the hemoglobins of one holostean fish, the spotted gar ( Lepisosteus osculatus), and of four teleost fish, the carpsucker ( Carpiodes carpio), the small mouth buffalo fish ( Ictiobus bubalus), the Rio Grande cichlid ( Cichlasoma cyanoguttatum), and the redear sunfish ( Lepomis microlophus), have been measured as a function of pH in the presence and absence of ATP. The oxygen equilibria of the teleost hemoglobins in the presence of 200 μ m ATP can be superimposed within experimental error upon the data obtained in the absence of ATP by a simple downward shift of the pH scale by 0.5 unit. Thus the effects of proton and ATP binding appear equivalent: Both can be interpreted in terms of a two-state allosteric model in which binding occurs preferentially to the low-affinity T-state. The oxygen affinities of each of the teleost hemoglobins approach asymptotically a maximal value at high pH. Although these high affinities are associated with decreased cooperativity of oxygen binding, as reflected by the Hill coefficient n, the asymptotic value of n never appears lower than 1.2 to 1.4. This indicates that the data cannot be completely described in terms of a single high-affinity R-state in alkaline solution: At least two different conformations are required. The oxygen affinity of the spotted gar hemoglobin, like that of each of the teleost hemoglobins, reaches a maximal value (minimal value of log PO 2 for half-saturation) above pH 8, but unlike teleost hemoglobins, the Hill coefficient reaches maximal values of 2.6 to 2.7 at high pH. The data in the absence of ATP are superimposable on the data in its presence by a downward shift of the pH scale by 0.25 unit. The measurement of the Bohr effect ( Δlog P 30 ΔpH ) in the presence and absence of ATP shows that the Bohr effect in each of the hemoglobins is substantially enhanced by organic phosphates, as it is in mammalian hemoglobins. The extent of the enhancement of the Bohr effect by 200 μ m ATP for each of the hemoglobins is approximately the same in the range pH 6.7 to 7.3 (increase in Δlog P 50 ΔpH ~ 0.3 ). This is a direct consequence of the equivalence of the linked-function relationship to the effects of ATP and proton binding on oxygenation.

Binding of carbon monoxide to hemoglobin Zürich. Proposal for a kinetic model.

When the spectroscopic properties and kinetics of combination with carbon monoxide of hemoglobin Zurich (HbZh) and its isolated abnormal chains with two sulphydryl groups blocked by mercuribenzoate (βZhSHgR) were studied by flash photolysis and rapid-mixing techniques, large differences compared to human hemoglobin (HbA) and normal isolated chains were observed as follows. 1 The position of the absorption maximum and its coefficient in the Soret region is very different for the CO derivatives of βZhSHgR and tetrameric abnormal HbZh from that of normal chains and hemoglobin. 2 Flash photolysis on βZhSHgR chains show they react with a single rate constant of 2.7 × 107 M−1 s−1 compared to 4.5 × 106 M−1 s−1 for isolated α chains; photochemical efficiency of CO dissociation is also less. 3 Kinetic analysis of CO binding to HbZh by the stopped-flow technique gave a second-order rate constant for βZh chains within the tetramer in the deoxy (T) quaternary conformation of 13.4 × 106 M−1 s−1 compared to 4.7 × 106 M−1 s−1 for α chain in the tetramer in its liganded (R) state. 4 Flash photolysis on solutions of fully saturated HbZh reveal a very fast initial phase during recombination with CO with a second-order rate constant comparable to that of βZhSHgR and attributed to βZh in the dimer. At very low levels of saturation there is a single phase only with a rate constant similar to that of βZh chains in the tetramer. Reduction of the intensity of the photodissociating light causes a decrease in the relative amplitude of the intial fast phase. The proposed kinetic scheme, based on a modified two-state (R and T) allosteric model, implies that βZh chains in the tetramer with a deoxy T configuration have a higher affinity for CO than α chains and a very high combination rate constant. However, when the tetramer flops to the liganded R configuration these chains increase their combination velocity to that of βZh chains in the dimer (R state).

The effect of ferric ligands on the oxygen affinity of the ferrous subunits in valency hybrid haemoglobins

Oxygen equilibrium curves of various valency hybrid haemoglobins (cyanide, azide, fluoride, aquomet hybrids) have been measured in the presence of inorganic phosphate or inositol hexaphosphate. All the hybrids showed asymmetric oxygen equilibrium curves which is inconsistent with the presence of only two oxygen binding sites. This inconsistency was found to be due to a small amount of oxidation of the ferrous subunits. Except for α 2 + β 2 combined with inositol hexaphosphate, the oxygen affinity was always lower in high compared to low spin hybrids implying that the deoxy quaternary structure is more stable for high spin derivatives. This result is consistent with the stereochemical interpretation of the co-operative effects proposed by Perutz (1970) . However, in the presence of inositol hexaphosphate, α 2 +CN β 2 and α 2 +F β 2 have similar oxygen affinity, showing that here the effect of spin state is no longer dominant. The reason for this is not yet clear. The oxygen binding parameters of the valency hybrids have been analysed according to the two-state allosteric model ( Monod et al. , 1965 ). This model adequately describes the oxygen binding properties in the presence of inositol hexaphosphate but not in phosphate buffer.

Regulation of hepatic adenylate cyclase by glucagon, GTP, divalent cations, and adenosine.

F ~OR T H E PAST SEVERAL YEARS we have been investigating the properties of the glucagon-sensitive adenylate cyclase system in rat liver plasma membranes (see RodbelP for recent review). The system as it is known today contains at least three components: a specific receptor for glucagon, a nucleotide regulatory component containing sites specific for GTP, and the catalytic component which, in the presence of a divalent cation (Mg 2+ or Mn2+), converts ATP to cyclic AMP, the so-called second messenger of glucagon action. Although the molecular basis for their action remains obscure, glucagon and GTP appear to activate the system in a concerted fashion) A simple two-state (inactive and active) allosteric model has been proposed 3 which suggests that GTP and glucagon bind preferentially with the active state (approximately fiveto nine-fold preference over the inactive state) which, by mass action, results in a shift to higher concentrations of the active form of the enzyme. Gpp(NH)p , an analog of GTP resistant to hydrolysis by nucleotide phosphohydrolases, binds to the active state with 100-fold preference over the inactive state and essentially fully converts the enzyme to the active form at a rate which is enhanced by glucagon. 3 Although GTP and glucagon are required to obtain the active configuration of the enzyme, expression of enzyme activity requires, in addition to the metal ion complex of ATP, occupation of a metal ion site by magnesium or manganous ions. 4 Mn 2+ has at least a tenfold higher affinity for this site than does Mg 2+, such that addition of a low concentrat ion of Mn 2+ along with Mg 2+ resuits in marked stimulation of basal, Gpp(NH)por hormone-stimulated activities. These findings and others 4 have ruled out previous models ~'6 which suggested that the stimulatory effects of divalent cations resulted from a lowering of the concentration of free or protonated forms of ATP, which were thought to act as potent inhibitors of the enzyme. Our tentative conclusion is that the metal ions, like GTP and glucagon, have a higher affinity for the active conformation of the enzyme system. Thus, by mass action, any combination of the positive effectors (metal ions, glucagon, GTP) will shift the equilibrium toward higher concentrations of the active state of the enzyme with resultant increases in enzyme activity. While the two-state allosteric model provides a satisfactory explanation for

Kinetic studies on the binding affinity of human hemoglobin for the 4th carbon monoxide molecule, L4.

L4, the affinity of hemoglobin for the 4th CO molecule, has been determined for human adult hemoglobin (HbA) as a function of pH and the presence of organic phosphates by measuring the kinetic parameters for the reaction. l'4, the rate of combination of CO with the triliganded molecule, was measured by flash photolysis while l4, the rate of CO dissociation for the ligand-saturated molecule, was measured by ligand replacement. L4 is pH-dependent and affected by 2,3-diphosphoglycerate. Additionally, this pH dependence of the high affinity state is largely eliminated by carboxypeptidase A digestion. L4 for human fetal hemoglobin (HbF) in phosphate buffers was also determined and found to be pH-dependent. These results cannot be reconciled within the framework of the two-state allosteric model. Additional structures in the conformational equilibrium due to either intermediates in the T to R transition or two or more R states must exist.

Linearity of the hemoglobin oxidation bohr effect.

The hemoglobin oxidation Bohr effect below pH 7 is essentially proportional to the fraction of hemes oxidized, just as the ligation Bohr effect is proportional to fractional heme ligation. The reported nonlinear proton release during oxidation [(1965) J. Biol. Chem. 240, 3317-3324] is shown to be an artifact resulting from the use of ferricyanide as oxidant. Published forms of the two-state allosteric transition model for hemoglobin function have used several proton linkage schemes, and none are compatible with a linear proton release upon oxidation.

Co-operative regulation mechanism of muscle contraction: Inter-tropomyosin co-operation model

A new model is presented on the basis of our experimental data and the “tropomyosin-blocking theory” of muscle relaxation to explain the regulation of certain characteristics of muscle contraction, namely that the relation of contraction to pCa is co-operative while calcium-binding is essentially non-cooperative. Our experiments show that end-to-end interactions between adjacent tropomyosin molecules in the groove of the actin helix are essential for the co-operative regulation. The blocking theory says that the tropomyosin molecule in relaxed muscle sterically blocks the myosin attachment site on actin, whereas in contracting muscle it moves to a position away from the attachment site. In this model a concerted movement of tropomyosin molecules, brought about by their end-to-end interactions, is considered to be the essential mechanism of co-operative regulation, and it is assumed that the positional changes of tropomyosin occur primarily when the four calcium binding sites of troponin on the tropomyosin are saturated with calcium. Theoretical analysis of the model, based upon the two-state allosteric model, leads to a Michaelis-Menten equation for the Ca-binding function together with a co-operative equation for the state function, proportional to the contraction or ATPase activity. These two functions fit well the experimental data. With cardiac muscle the slope of the contraction versus pCa curve is slightly less steep than that obtained with skeletal muscle. This difference can be explained by the difference in the number of Ca-binding sites of troponins.

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.

Functional Properties of Hemoglobin Kempsey

Abstract Functional studies have been performed on hemoglobin Kempsey (α2β299 asp→asn), a variant associated with familial erythrocytosis. In most experiments, the properties of hemoglobin Kempsey were compared to those of hemoglobin A, isolated from the same chromatography column. Hemoglobin Kempsey had high oxygen affinity (p50 at pH 7.2 was 10% that of hemoglobin A) and nearly absent subunit cooperativity. Its alkaline Bohr effect was less than one-half normal. The addition of organic phosphates (2, 3-diphosphoglycerate and inositol hexaphosphate) resulted in a lowering of oxygen affinity and an increase in subunit cooperativity. The dissociation of oxygen from partially saturated intermediates of hemoglobin Kempsey was slow and monophasic with no wavelength dependency indicative of subunit heterogeneity. The combination of carbon monoxide with deoxyhemoglobin Kempsey in a solution of low ionic strength was explained best by the presence of three hemoglobin species in equilibrium: one slowly reacting form which was probably hemoglobin in the T state and comprised 10% of the total; and two rapidly reacting forms, hemoglobin dimer and tetrameric hemoglobin in the R state. The dimer-tetramer equilibrium is shifted to favor the tetramer by inositol hexaphosphate which also converts the rapidly reacting deoxytetramer to a slowly reacting form. The existence of a substantial proportion of deoxyhemoglobin Kempsey in the form of a dimer was supported by the following experiments. (a) The change in absorbance (430 nm) following the addition of inositol hexaphosphate to deoxyhemoglobin Kempsey was dependent upon hemoglobin concentration, and indicated a tetramer to dimer dissociation constant (K4, 2) of about 5 µm. (b) Haptoglobin bound to deoxyhemoglobin Kempsey about as rapidly as to oxyhemoglobin A. The former reaction was inhibited strongly by inositol hexaphosphate. (c) The rapid component in the reaction of deoxyhemoglobin Kempsey with carbon monoxide and inositol hexaphosphate (in the same syringe) was increased at low hemoglobin concentration. (d) The hybrid hemoglobin α2βaβKempsey was relatively less stable than α2βaβs. Deoxyhemoglobin Kempsey resembled oxyhemoglobin A in reacting rapidly with p-mercuribenzoate. However after the addition of inositol hexaphosphate, this reaction was slowed 30-fold, indicating a partial transition to the T state. These results support the general conclusion that p-mercuribenzoate reactivity is a probe of over-all quaternary conformation. The interaction of hemoglobin Kempsey with ligands is consistent with a two-state allosteric model. Its functional abnormalities can be explained by a shift in the conformational equilibrium toward the R state. In contrast to hemoglobin A, the transition between conformers occurs at an earlier stage in ligand binding and is relatively slow in solutions of low ionic strength.

Relationship between ligand binding and conformational change of macromolecules in the two-state allosteric model

The relationship between the binding function Y and the state function R of an oligomeric protein has been analysed for the general two-state allosteric model. It is shown that this relation is determined by the numerical values of the inherent parameters of the model. The shape of the function Y = f ( R) can therefore be strictly concave, strictly convex or inverse sigmoidal according to the conditions. In the two-state allosteric model only a dimeric protein can display a linear relationship between Y and R . In the paper general criteria for the estimation of the state function R from experimentally obtained conformational parameters are discussed.

Comments on extensions of the allosteric model for haemoglobin.

RECENTLY Edelstein1 has concluded on the basis of a numerical analysis that the sequential model as formulated by Koshland, Nemethy and Filmer (KNF)2 describes the oxygen binding curves of a number of species of human haemoglobin less well than does the two-state allosteric model of Monod, Wyman and Changeux (MWC)3. This communication demonstrates that Edelstein's analysis is incomplete and that extension of his analysis reveals that no such conclusion can be drawn from the data considered.