Two-state Allosteric Model Research Articles

Modulation of Allosteric Control and Evolution of Hemoglobin.

Allostery arises when a ligand-induced change in shape of a binding site of a protein is coupled to a tertiary/quaternary conformational change with a consequent modulation of functional properties. The two-state allosteric model of Monod, Wyman and Changeux [J. Mol. Biol. 1965; 12, 88-118] is an elegant and effective theory to account for protein regulation and control. Tetrameric hemoglobin (Hb), the oxygen transporter of all vertebrates, has been for decades the ideal system to test for the validity of the MWC theory. The small ligands affecting Hb's behavior (organic phosphates, protons, bicarbonate) are produced by the red blood cell during metabolism. By binding to specific sites, these messengers make Hb sensing the environment and reacting consequently. HbI and HbIV from trout and human HbA are classical cooperative models, being similar yet different. They share many fundamental features, starting with the globin fold and the quaternary assembly, and reversible cooperative O2 binding. Nevertheless, they differ in ligand affinity, binding of allosteric effectors, and stability of the quaternary assembly. Here, we recollect essential functional properties and correlate them to the tertiary and quaternary structures available in the protein databank to infer on the molecular basis of the evolution of oxygen transporters.

Allosteric control of hemoglobin S fiber formation by oxygen and its relation to the pathophysiology of sickle cell disease

The pathology of sickle cell disease is caused by polymerization of the abnormal hemoglobin S upon deoxygenation in the tissues to form fibers in red cells, causing them to deform and occlude the circulation. Drugs that allosterically shift the quaternary equilibrium from the polymerizing T quaternary structure to the nonpolymerizing R quaternary structure are now being developed. Here we update our understanding on the allosteric control of fiber formation at equilibrium by showing how the simplest extension of the classic quaternary two-state allosteric model of Monod, Wyman, and Changeux to include tertiary conformational changes provides a better quantitative description. We also show that if fiber formation is at equilibrium in vivo, the vast majority of cells in most tissues would contain fibers, indicating that it is unlikely that the disease would be survivable once the nonpolymerizing fetal hemoglobin has been replaced by adult hemoglobin S at about 1 y after birth. Calculations of sickling times, based on a recently discovered universal relation between the delay time prior to fiber formation and supersaturation, show that in vivo fiber formation is very far from equilibrium. Our analysis indicates that patients survive because the delay period allows the majority of cells to escape the small vessels of the tissues before fibers form. The enormous sensitivity of the duration of the delay period to intracellular hemoglobin composition also explains why sickle trait, the heterozygous condition, and the compound heterozygous condition of hemoglobin S with pancellular hereditary persistence of fetal hemoglobin are both relatively benign conditions.

Allosteric Antagonism of the A2A Adenosine Receptor by a Series of Bitopic Ligands.

Allosteric antagonism by bitopic ligands, as reported for many receptors, is a distinct modulatory mechanism. Although several bitopic A2A adenosine receptor (A2AAR) ligand classes were reported as pharmacological tools, their receptor binding and functional antagonism patterns, i.e., allosteric or competitive, were not well characterized. Therefore, here we systematically characterized A2AAR binding and functional antagonism of two distinct antagonist chemical classes. i.e., fluorescent conjugates of xanthine amine congener (XAC) and SCH442416. Bitopic ligands were potent, weak, competitive or allosteric, based on the combination of pharmacophore, linker and fluorophore. Among antagonists tested, XAC, XAC245, XAC488, SCH442416, MRS7352 showed Ki binding values consistent with KB values from functional antagonism. Interestingly, MRS7396, XAC-X-BY630 (XAC630) and 5-(N,N-hexamethylene)amiloride (HMA) were 9–100 times weaker in displacing fluorescent MRS7416 binding than radioligand binding. XAC245, XAC630, MRS7396, MRS7416 and MRS7322 behaved as allosteric A2AAR antagonists, whereas XAC488 and MRS7395 antagonized competitively. Schild analysis showed antagonism slopes of 0.42 and 0.47 for MRS7396 and XAC630, respectively. Allosteric antagonists HMA and MRS7396 were more potent in displacing [3H]ZM241385 binding than MRS7416 binding. Sodium site D52N mutation increased and decreased affinity of HMA and MRS7396, respectively, suggesting possible preference for different A2AAR conformations. The allosteric binding properties of some bitopic ligands were rationalized and analyzed using the Hall two-state allosteric model. Thus, fluorophore tethering to an orthosteric ligand is not neutral pharmacologically and may confer unexpected properties to the conjugate.

The binding of activated Gαq to phospholipase C-β exhibits anomalous affinity

Upon activation by the Gq family of Gα subunits, Gβγ subunits, and some Rho family GTPases, phospholipase C-β (PLC-β) isoforms hydrolyze phosphatidylinositol 4,5-bisphosphate to the second messengers inositol 1,4,5-trisphosphate and diacylglycerol. PLC-β isoforms also function as GTPase-activating proteins, potentiating Gq deactivation. To elucidate the mechanism of this mutual regulation, we measured the thermodynamics and kinetics of PLC-β3 binding to Gαq FRET and fluorescence correlation spectroscopy, two physically distinct methods, both yielded Kd values of about 200 nm for PLC-β3-Gαq binding. This Kd is 50-100 times greater than the EC50 for Gαq-mediated PLC-β3 activation and for the Gαq GTPase-activating protein activity of PLC-β. The measured Kd was not altered either by the presence of phospholipid vesicles, phosphatidylinositol 4,5-bisphosphate and Ca2+, or by the identity of the fluorescent labels. FRET-based kinetic measurements were also consistent with a Kd of 200 nm We determined that PLC-β3 hysteresis, whereby PLC-β3 remains active for some time following either Gαq-PLC-β3 dissociation or PLC-β3-potentiated Gαq deactivation, is not sufficient to explain the observed discrepancy between EC50 and Kd These results indicate that the mechanism by which Gαq and PLC-β3 mutually regulate each other is far more complex than a simple, two-state allosteric model and instead is probably kinetically determined.

An Exclusive α/β Code Directs Allostery in TetR–Peptide Complexes

The allosteric mechanism of one of the best characterized bacterial transcription regulators, tetracycline repressor (TetR), has recently been questioned. Tetracycline binding induces cooperative folding of TetR, as suggested by recent unfolding studies, rather than switching between two defined conformational states, namely a DNA-binding-competent conformation and a non-DNA-binding conformation. Upon ligand binding, a host of near-native multiconformational structures collapse into a single, highly stabilized protein conformation that is no longer able to bind DNA. Here, structure–function studies performed with four synthetic peptides that bind to TetR and mimic the function of low-molecular-weight effectors, such as tetracyclines, provide new means to discriminate between different allosteric models. Whereas two inducing peptides bind in an extended β-like conformation, two anti-inducing peptides form an α-helix in the effector binding site of TetR. This exclusive bimodal interaction mode coincides with two distinct overall conformations of TetR, namely one that is identical with induced TetR and one that mirrors the DNA-bound state of TetR. Urea-induced unfolding studies show no increase in thermodynamic stability for any of the peptide complexes, although fluorescence measurements demonstrate peptide binding to TetR. This strongly suggests that, at least for these peptide effectors, a classical two-state allosteric model best describes TetR function.

Probing Pore Constriction in a Ligand-gated Ion Channel by Trapping a Metal Ion in the Pore upon Agonist Dissociation

Eukaryotic pentameric ligand-gated ion channels (pLGICs) are receptors activated by neurotransmitters to rapidly transport ions across cell membranes, down their electrochemical gradients. Recent crystal structures of two prokaryotic pLGICs were interpreted to imply that the extracellular side of the transmembrane pore constricts to close the channel (Hilf, R. J., and Dutzler, R. (2009) Nature 457, 115-118; Bocquet, N., Nury, H., Baaden, M., Le Poupon, C., Changeux, J. P., Delarue, M., and Corringer, P. J. (2009) Nature 457, 111-114). Here, we utilized a eukaryotic acetylcholine (ACh)-serotonin chimeric pLGIC that was engineered with histidines to coordinate a metal ion within the channel pore, at its cytoplasmic side. In a previous study, the access of Zn(2+) ions to the engineered histidines had been explored when the channel was either at rest (closed) or active (open) (Paas, Y., Gibor, G., Grailhe, R., Savatier-Duclert, N., Dufresne, V., Sunesen, M., de Carvalho, L. P., Changeux, J. P., and Attali, B. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 15877-15882). In this study, the interactions of Zn(2+) with the pore were probed upon agonist (ACh) dissociation that triggers the transition of the receptor from the active conformation to the resting conformation (i.e. during deactivation). Application of Zn(2+) onto ACh-bound open receptors obstructed their pore and prevented ionic flow. Removing ACh from its extracellular binding sites to trigger deactivation while Zn(2+) is still bound led to tight trapping of Zn(2+) within the pore. Together with single-channel recordings, made to explore single pore-blocking events, we show that dissociation of ACh causes the gate to shut on a Zn(2+) ion that effectively acts as a "foot in the door." We infer that, upon deactivation, the cytoplasmic side of the pore of the ACh-serotonin receptor chimera constricts to close the channel.

Evolution of allosteric models for hemoglobin

We compare various allosteric models that have been proposed to explain cooperative oxygen binding to hemoglobin, including the two-state allosteric model of Monod, Wyman, and Changeux (MWC), the Cooperon model of Brunori, the model of Szabo and Karplus (SK) based on the stereochemical mechanism of Perutz, the generalization of the SK model by Lee and Karplus (SKL), and the Tertiary Two-State (TTS) model of Henry, Bettati, Hofrichter and Eaton. The preponderance of experimental evidence favors the TTS model which postulates an equilibrium between high (r)- and low (t)-affinity tertiary conformations that are present in both the T and R quaternary structures. Cooperative oxygenation in this model arises from the shift of T to R, as in MWC, but with a significant population of both r and t conformations in the liganded T and in the unliganded R quaternary structures. The TTS model may be considered a combination of the SK and SKL models, and these models provide a framework for a structural interpretation of the TTS parameters. The most compelling evidence in favor of the TTS model is the nanosecond - millisecond carbon monoxide (CO) rebinding kinetics in photodissociation experiments on hemoglobin encapsulated in silica gels. The polymeric network of the gel prevents any tertiary or quaternary conformational changes on the sub-second time scale, thereby permitting the subunit conformations prior to CO photodissociation to be determined from their ligand rebinding kinetics. These experiments show that a large fraction of liganded subunits in the T quaternary structure have the same functional conformation as liganded subunits in the R quaternary structure, an experimental finding inconsistent with the MWC, Cooperon, SK, and SKL models, but readily explained by the TTS model as rebinding to r subunits in T. We propose an additional experiment to test another key prediction of the TTS model, namely that a fraction of subunits in the unliganded R quaternary structure has the same functional conformation (t) as unliganded subunits in the T quaternary structure.

Allosteric Effectors Influence the Tetramer Stability of Both R- and T-states of Hemoglobin A

The contribution of heterotropic effectors to hemoglobin allostery is still not completely understood. With the recently proposed global allostery model, this question acquires crucial significance, because it relates tertiary conformational changes to effector binding in both the R- and T-states. In this context, an important question is how far the induced conformational changes propagate from the binding site(s) of the allosteric effectors. We present a study in which we monitored the interdimeric interface when the effectors such as Cl-, 2,3-diphosphoglycerate, inositol hexaphosphate, and bezafibrate were bound. We studied oxy-Hb and a hybrid form (alphaFeO2)2-(betaZn)2 as the T-state analogue by monitoring heme absorption and Trp intrinsic fluorescence under hydrostatic pressure. We observed a pressure-dependent change in the intrinsic fluorescence, which we attribute to a pressure-induced tetramer to dimer transition with characteristic pressures in the 70-200-megapascal range. The transition is sensitive to the binding of allosteric effectors. We fitted the data with a simple model for the tetramer-dimer transition and determined the dissociation constants at atmospheric pressure. In the R-state, we observed a stabilizing effect by the allosteric effectors, although in the T-analogue a stronger destabilizing effect was seen. The order of efficiency was the same in both states, but with the opposite trend as inositol hexaphosphate > 2,3-diphosphoglycerate > Cl-. We detected intrinsic fluorescence from bound bezafibrate that introduced uncertainty in the comparison with other effectors. The results support the global allostery model by showing that conformational changes propagate from the effector binding site to the interdimeric interfaces in both quaternary states.

The Sweet Taste of Losing One's Inhibition

Although sodium saccharin (Na-saccharin) is used as a sweetener, high concentrations taste mostly bitter--especially with consecutive exposures. Rinsing the bitter taste from your mouth leads to a sort of taste "after-image," so that the water tastes sweet, in what is referred to as a sweet "water-taste." Galindo-Cuspinera et al. found that, when mixed with sweet substances, various compounds that elicit sweet water-tastes, including lactisole, MgSO 4 , high concentrations of Na-saccharin, and acesulfame-K, inhibited sweetness. Sweeteners that do not elicit a sweet water-taste, such as Na-cyclamate, did not inhibit the sweetness of other sweet substances. Using calcium imaging to monitor the responses of human embryonic kidney cells transfected with the heteromeric human sweet taste receptor hTAS1R2-hTAS1R3, the authors found that responses to increasing concentrations of Na-saccharin or acesulfame-K peaked and declined in a manner that paralleled the loss of sweetness perceived by human tasters. Similarly, single-cell calcium imaging revealed that high concentrations of Na-saccharin inhibited the response to other sweeteners and that both Na-saccharin and acesulfame-K produced an off-response when rinsed from the cells (that is, the receptors were stimulated when the ligand was removed; this is analogous to the perceptual sweet water-taste). The authors interpret these data in terms of a two-state allosteric model for the sweetness receptor, with substances such as Na-saccharin or acesulfame-K binding to a high-affinity activating site at low concentrations and binding to a lower affinity site that shifts receptor equilibrium toward an inactive conformation at higher concentrations. In this model, rinsing leads to the preferential loss of these substances from the low-affinity inhibitory site and thus to a rebound perception of sweetness. V. Galindo-Cuspinera, M. Winnig, B. Bufe, W. Meyerhof, P. A. S. Breslin, A TAS1R receptor-based explanation of sweet "water-taste." Nature 441 , 354-357 (2006). [PubMed]

New insights into allosteric mechanisms from trapping unstable protein conformations in silica gels.

To understand why the classical two-state allosteric model of Monod, Wyman, and Changeux explains cooperative oxygen binding by hemoglobin but does not explain changes in oxygen affinity by allosteric inhibitors, we have investigated the kinetic properties of unstable conformations transiently trapped by encapsulation in silica gels. Conformational trapping reveals that after nanosecond photodissociation of carbon monoxide a large fraction of the subunits of the T quaternary structure has kinetic properties almost identical to those of subunits of the R quaternary structure. Addition of allosteric inhibitors reduces both the fraction of R-like subunits and the oxygen affinity of the T quaternary structure. These kinetic and equilibrium results are readily explained by a recently proposed generalization of the Monod-Wyman-Changeux model in which a pre-equilibrium between two functionally different tertiary, rather than quaternary, conformations plays the central role.

A Two-State Allosteric Model for Autoinhibition Rationalizes WASP Signal Integration and Targeting

Remodeling of the actin cytoskeleton is controlled by signaling pathways that include the Wiskott–Aldrich syndrome protein (WASP). WASP is regulated by autoinhibition, and the intramolecular contacts that inactivate the protein can be relieved through binding to the Rho-family GTPase Cdc42. Here, we show that the allosteric regulation of WASP can be quantitatively described by a two-state equilibrium between an active, largely unfolded conformation that is able to stimulate the Arp2/3 complex, and an inactive, folded conformation. The model is parameterized by the stability of WASP against unfolding and by the Cdc42 affinities of WASP constructs that mimic the unfolded and folded conformations. The model is consistent with NMR spectra of GTPase-bound WASP, and accurately predicts changes of amide hydrogen exchange behavior and Cdc42 affinity as a function of WASP stability. The results provide a thermodynamic rationale for the GTPase-independent recruitment of WASP and other autoinhibited effectors to their sites of activity. They also explain how basal activity is suppressed and confirm that WASP needs to integrate multiple cooperative inputs for maximal activation. Our analysis suggests that, in general, simple modulation of a two-state equilibrium may determine several regulatory functions, allowing the generation of complex signaling behavior in vivo.

Allosteric determinants in guanine nucleotide-binding proteins.

Members of the G protein superfamily contain nucleotide-dependent switches that dictate the specificity of their interactions with binding partners. Using a sequence-based method termed statistical coupling analysis (SCA), we have attempted to identify the allosteric core of these proteins, the network of amino acid residues that couples the domains responsible for nucleotide binding and protein-protein interactions. One-third of the 38 residues identified by SCA were mutated in the G protein Gs alpha, and the interactions of guanosine 5'-3-O-(thio)triphosphate- and GDP-bound mutant proteins were tested with both adenylyl cyclase (preferential binding to GTP-Gs alpha) and the G protein beta gamma subunit complex (preferential binding to GDP-Gs alpha). A two-state allosteric model predicts that mutation of residues that control the equilibrium between GDP- and GTP-bound conformations of the protein will cause the ratio of affinities of these species for adenylyl cyclase and G beta gamma to vary in a reciprocal fashion. Observed results were consistent with this prediction. The network of residues identified by the SCA appears to comprise a core allosteric mechanism conferring nucleotide-dependent switching; the specific features of different G protein family members are built on this core.

A tertiary two-state allosteric model for hemoglobin

The two-state allosteric model of Monod, Wyman, and Changeux (MWC) provides an excellent description of homotropic effects in a vast array of equilibrium and kinetic measurements on cooperative ligand binding by hemoglobin. However, in contrast to experimental observations, the model does not allow for alteration of the ligand affinity of the T quaternary structure by allosteric effectors. This failure to explain heterotropic effects has been appreciated for over 30 years, and it has been generally assumed to result from tertiary conformational changes in the absence of a quaternary change. Here we explore a model that preserves the essential MWC idea that binding without a quaternary conformational change is non-cooperative, but where tertiary conformations of individual subunits play the primary role instead of the quaternary conformations. In this model, which we call the ‘tertiary two-state (TTS) model’, the two affinity states correspond to two tertiary conformations of individual subunits rather than the two quaternary conformations of the MWC two-state allosteric model. Ligation and the R quaternary structure bias the subunit population toward the high affinity tertiary conformation, while deligation and the T quaternary structure favor the low affinity tertiary conformation. We show that the model is successful in quantitatively explaining a demanding set of kinetic data from nanosecond carbon monoxide photodissociation experiments at times longer than ∼1 μs. Better agreement between the model and the submicrosecond kinetic data may result from detailed considerations of the distribution and dynamics of conformational substates of the two tertiary conformations. The model is consistent with the results of solution, gel, and single crystal oxygen binding studies, but underestimates the population of doubly-liganded molecules determined in low-temperature electrophoresis experiments.

Control of heme reactivity by diffusion: structural basis and functional characterization in hemoglobin mutants.

The effect of mutagenesis on O(2), CO, and NO binding to mutants of human hemoglobin, designed to modify some features of the reactivity that hinder use of hemoglobin solutions as blood substitute, has been extensively investigated. The kinetics may be interpreted in the framework of the Monod-Wyman-Changeux two-state allosteric model, based on the high-resolution crystallographic structures of the mutants and taking into account the control of heme reactivity by the distal side mutations. The mutations involve residues at topological position B10 and E7, i.e., Leu (B10) to Tyr and His (E7) to Gln, on either the alpha chains alone (yielding the hybrid tetramer Hbalpha(YQ)), the beta chains alone (hybrid tetramer Hbbeta(YQ)), or both types of chains (Hb(YQ)). Our data indicate that the two mutations affect ligand diffusion into the pocket, leading to proteins with low affinity for O(2) and CO, and especially with reduced reactivity toward NO, a difficult goal to achieve. The observed kinetic heterogeneity between the alpha(YQ) and beta(YQ) chains in Hb(YQ) has been rationalized on the basis of the three-dimensional structure of the active site. Furthermore, we report for the first time an experiment of partial CO binding, selective for the beta chains, to high salt crystals of the mutant Hb(YQ) in the T-state; these crystallographic data may be interpreted as "snapshots" of the initial events possibly occurring on ligand binding to the T-allosteric state of this peculiar mutant Hb.

Modulation of ligand binding in engineered human hemoglobin distal pocket

Functional and structural studies on hemoglobin and myoglobin from different animals and engineered variants have enlightened the great importance of the physico-chemical properties of the side-chains at topological position B10 and E7. These residues proved to be crucial to the discrimination and stabilisation of gaseous ligands. In view of the data obtained on the high oxygen affinity hemoglobin from Ascaris worms and a new mutant of sperm whale myoglobin, we selected the two mutations Leu B10 → Tyr and His E7 → Gln as potentially relevant to control ligand binding parameters in the α and β-chains of human hemoglobin. Here, we present an investigation of three new mutants: HbαYQ (α 2 YQβ 2 A), HbβYQ (α 2 Aβ 2 YQ) and HbαβYQ (α 2 YQβ 2 YQ). They are characterised by a very low reactivity for NO, O 2 and CO, and a reduced cooperativity. Their functional properties are not inconsistent with the behaviour expected for a two-state allosteric model. Proteins with these substitutions may be considered as candidates for the synthesis of a possible “blood substitute”, which should yield an O 2 adduct stable to autoxidation and slowly reacting with NO. The mutant HbαβYQ is particularly interesting because the rate of reaction of NO with the oxy and deoxy derivatives is reduced. A structural interpretation of our data is presented based on the 3D structure of deoxy HbαβYQ determined by crystallography at 1.8 Å resolution.

Oxygen Binding and Aggregation of Hemoglobin from the Common European Frog, Rana temporaria

The hemoglobin from the European frog, Rana temporaria, consists of one major and three minor components. The tetramers aggregate upon deoxygenation notably at pH 7.3. Aggregation due to formation of disulphide bridges, as occurs in related species, was observed only in polyacrylamide gels. The hemolysate showed a pronounced Bohr effect. Oxygen affinity decreased with increasing hemoglobin concentration, indicating that aggregation affects the functional properties of the hemolysate. Oxygen binding equilibria of unfractionated hemolysate are insensitive to chloride and show low sensitivity to ATP. Analysis of oxygen equilibrium curves in terms of the two-state allosteric model (MWC) showed that pH change exerted a greater effect on the association constant of the oxygenated state (KR) than that of the deoxy state (KT). The number of interacting binding sites (q) increased with hemoglobin concentration. Cooperativity of oxygen binding, evaluated as Hill coefficient n, never exceeded the value of 3.0. Earlier studies on hemoglobin and blood from this and related species, report significantly higher n values at high O2 saturation. Molecular adaptive aspects are discussed.

Can a two-state MWC allosteric model explain hemoglobin kinetics?

We have analyzed the nanosecond-millisecond kinetics of ligand binding and conformational changes in hemoglobin. The kinetics were determined from measurements of precise time-resolved optical spectra following nanosecond photodissociation of the heme-carbon monoxide complex. To fit the data, it was necessary to extend the two-state allosteric model of Monod, Wyman, and Changeux (MWC) to include geminate ligand rebinding and nonexponential tertiary relaxation within the R quaternary structure. Considerable simplification of the model is obtained by using a linear free energy relation for the rates of quaternary transitions, and by incorporating concepts from recent studies on the physics of geminate rebinding and conformational changes in myoglobin. The model, described by 85 coupled differential equations, quantitatively explains a demanding set of complex kinetic data. Moreover, with the same set of kinetic parameters it simultaneously fits the equilibrium data on ligand binding and the distribution of ligation states. The present results, together with those from single-crystal oxygen binding studies, indicate that the two-state MWC allosteric model has survived its most critical tests.

Allosteric effectors do not alter the oxygen affinity of hemoglobin crystals.

In solution, the oxygen affinity of hemoglobin in the T quaternary structure is decreased in the presence of allosteric effectors such as protons and organic phosphates. To explain these effects, as well as the absence of the Bohr effect and the lower oxygen affinity of T-state hemoglobin in the crystal compared to solution, Rivetti C et al. (1993a, Biochemistry 32:2888-2906) suggested that there are high- and low-affinity subunit conformations of T, associated with broken and unbroken intersubunit salt bridges. In this model, the crystal of T-state hemoglobin has the lowest possible oxygen affinity because the salt bridges remain intact upon oxygenation. Binding of allosteric effectors in the crystal should therefore not influence the oxygen affinity. To test this hypothesis, we used polarized absorption spectroscopy to measure oxygen binding curves of single crystals of hemoglobin in the T quaternary structure in the presence of the "strong" allosteric effectors, inositol hexaphosphate and bezafibrate. In solution, these effectors reduce the oxygen affinity of the T state by 10-30-fold. We find no change in affinity (< 10%) of the crystal. The crystal binding curve, moreover, is noncooperative, which is consistent with the essential feature of the two-state allosteric model of Monod J, Wyman J, and Changeux JP (1965, J Mol Biol 12:88-118) that cooperative binding requires a change in quaternary structure. Noncooperative binding by the crystal is not caused by cooperative interactions being masked by fortuitous compensation from a difference in the affinity of the alpha and beta subunits. This was shown by calculating the separate alpha and beta subunit binding curves from the two sets of polarized optical spectra using geometric factors from the X-ray structures of deoxygenated and fully oxygenated T-state molecules determined by Paoli M et al. (1996, J Mol Biol 256:775-792).

Oxygen binding by single crystals of hemoglobin: the problem of cooperativity and inequivalence of alpha and beta subunits.

Oxygen binding by the human hemoglobin tetramer in the T quaternary structure is apparently noncooperative in the crystalline state (Hill n = 1.0), as predicted by the two-state allosteric model of Monod, Wyman, and Changeux (MWC) (Mozzarelli et al., Nature 351:416-419, 1991; Rivetti et al., Biochemistry 32:2888-2906, 1993). However, cooperativity within the tetramer can be masked by a difference in affinity between the alpha and beta subunits. Indeed, analysis of the binding curves derived from absorption of light polarized along two different crystal directions, for which the projections of the alpha and beta hemes are slightly different, revealed an inequivalence in the intrinsic oxygen affinity of the alpha and beta subunits (p50(alpha) approximately 80 torr, p50(beta) approximately 370 torr at 15 degrees C) that compensates a small amount of cooperativity (Rivetti et al., Biochemistry 32:2888-2906, 1993). To further investigate this problem, we have measured oxygen binding curves of single crystals of hemoglobin (in a different lattice) in which the iron in the alpha subunits has been replaced by the non-oxygen-binding nickel(II). The Hill n is 0.90 +/- 0.06, and the p50 is slightly different for light polarized parallel to different crystal directions, indicating a very small difference in affinity between the two crystallographically inequivalent beta subunits. The average crystal p50 is 110 +/- 20 torr at 15 degrees C, close to the p50 of 80 torr observed in solution, but about threefold less than the p50 calculated by Rivetti et al. (Biochemistry 32:2888-2906, 1993) for the beta subunits of the unsubstituted tetramer. These results suggest that Rivetti et al., if anything, overestimated the alpha/beta inequivalence. They therefore did not underestimate the cooperativity within the T quaternary structure, when they concluded that it represents a small deviation from the perfectly noncooperative binding of an MWC allosteric model. Our conclusion of nearly perfect MWC behavior for binding to the T state of unmodified hemoglobin raises the question of the relevance of the large T-state cooperativity inferred for cyanide binding to partially oxidized hemoglobin (Ackers et al., Science 255:54-63, 1992).

Oxygen binding by single crystals of hemoglobin: The problem of cooperativity and inequivalence of alpha and beta subunits

Oxygen binding by the human hemoglobin tetramer in the T quaternary structure is apparently noncooperative in the crystalline state (Hill n = 1.0), as predicted by the two-state allosteric model of Monod, Wyman, and Changeux (MWC) (Mozzarelli et al., Nature 351:416–419, 1991; Rivetti et al., Biochemistry 32:2888–2906, 1993). However, cooperativity within the tetramer can be masked by a difference in affinity between the α and β subunits. Indeed, analysis of the binding curves derived from absorption of light polarized along two different crystal directions, for which the projections of the α and β hemes are slightly different, revealed an inequivalence in the intrinsic oxygen affinity of the α and β subunits (p50(α) ≅ 80 torr, p50(β) ≅ 370 torr at 15°C) that compensates a small amount of cooperativity (Rivetti et al., Biochemistry 32:2888–2906, 1993). To further investigate this problem, we have measured oxygen binding curves of single crystals of hemoglobin (in a different lattice) in which the iron in the α subunits has been replaced by the non-oxygen-binding nickel(II). The Hill n is 0.90 ± 0.06, and the p50 is slightly different for light polarized parallel to different crystal directions, indicating a very small difference in affinity between the two crystallographically inequivalent β subunits. The average crystal p50 is 110 ± 20 torr at 15°C, close to the p50 of 80 torr observed in solution, but about threefold less than the p50 calculated by Rivetti et al. (Biochemistry 32:2888–2906, 1993) for the β subunits of the unsubstituted tetramer. These results suggest that Rivetti et al., if anything, overestimated the α/β inequivalence. They therefore did not underestimate the cooperativity within the T quaternary structure, when they concluded that it represents a small deviation from the perfectly noncooperative binding of an MWC allosteric model. Our conclusion of nearly perfect MWC behavior for binding to the T state of unmodified hemoglobin raises the question of the relevance of the large T-state cooperativity inferred for cyanide binding to partially oxidized hemoglobin (Ackers et al., Science 255:54–63, 1992). © 1996 Wiley-Liss, Inc.