Eaton Review - fisica ufmg

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review

Is cooperative oxygen binding by hemoglobin really understood? William A. Eaton1, Eric. R. Henry1, James Hofrichter1 and Andrea Mozzarelli2


The enormous success of structural biology challenges the physical scientist. Can biophysical studies provide a truly deeper understanding of how a protein works than can be obtained from static structures and qualitative analysis of biochemical data? We address this question in a case study by presenting the key concepts and experimental results that have led to our current understanding of cooperative oxygen binding by hemoglobin, the paradigm of structure function relations in multisubunit proteins. We conclude that the underlying simplicity of the two-state allosteric mechanism could not have been demonstrated without novel physical experiments and a rigorous quantitative analysis.

There are many levels at which a scientific question can be answered. An answer that is quite satisfying to a scientist from one discipline may be totally unsatisfactory to a scientist from another. This has become an increasingly important issue in research on biological problems as scientists from different disciplines ask what appear to be the very same questions. For proteins, the most common questions are: what does a protein look like, what does it do, and how does it do it? Although a threedimensional structure at atomic resolution provides a clear answer to the first, the latter questions concerning protein function may be quite problematic. Part of the problem is describing just what is meant by understanding protein function. A genome scientist, faced with trying to determine the role of tens of thousands of proteins, may consider understanding a protein’s function to be a brief descriptor of what it does in a cell, such as ‘bind ligand x’, or ‘oxidize protein y’, or ‘phosphorylate protein z’. To a molecular biologist the problem of understanding the ligandbinding function of a protein, for example, may be solved once the binding site has been identified in the three-dimensional structure. To a physical scientist, solution of the structure and the identification of a binding site mark just the first, albeit absolutely essential, step in understanding the function of this protein. At the very least the physical scientist would like to have a complete thermodynamic and kinetic description of the binddeoxy, T

ing process and a quantitative explanation of the experimental data in terms of a (statistical mechanical) model. It is, however, an interesting challenge for the physical scientist to demonstrate that such studies provide a truly deeper understanding of protein function than is already apparent from the beautiful, static color pictures of the structural biologist and qualitative analysis of biochemical data. We address this issue by describing the key findings in the evolution of our understanding of cooperative ligand binding by a single protein, hemoglobin (Hb), the paradigm of structure– function relations in multisubunit proteins (Fig. 1). Even though this history spans almost a century1, it is quite relevant to current protein research. With today’s technology comparable results on a newly discovered protein would be obtained in a much shorter time, but the conceptual approach would be very similar. From Bohr to Perutz The physiologically important and physically interesting property of hemoglobin and other so-called allosteric proteins is that they exhibit cooperative interactions in binding ligands to sites that are distant from each other in the structure. The initial critical observation was made by the physiologist, Christian Bohr, father of the atomic physicist Niels Bohr1,2. Bohr’s careful measurements of hemoglobin oxygenation showed that the binding oxy, R

Fig. 1 Schematic structures of hemoglobin (adapted from ref. 42). The two views on the right are looking down the pseudo two-fold x axis. The quaternary conformational change consists of a rotation of the symmetrically related αβ dimers by ~15° relative to each other and a translation of ~0.1 nm along the rotation axis.

Laboratory of Chemical Physics, Building 5, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520, USA. 2Institute of Biochemical Sciences and National Institute of the Physics of Matter, University of Parma, 43100 Parma, Italy.

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Correspondence should be addressed to W.A.E. email: [email protected] nature structural biology • volume 6 number 4 • april 1999

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review that increased their affinity. One parameter was taken as the interaction parameter and the other as the intrinsic binding constant. Since fitting the binding curve required observed only a single interaction parameter Pauling reasoned that hemoglobin possesses either a tetrahedral or square symmetric arrangement of the hemes. He preferred the latter, oxygen pressure (torr) because he could then saturation explain the change in Fig. 2 MWC description of hemoglobin oxygenation. a, The observed binding curve (green) and the corresponding hyperbolic (noncooperative) binding curves for the R and T quaternary structures (red and blue, respectively). affinity as somehow resultBinding begins at low oxygen pressure along the T-state binding curve and ends at high pressure along the R-state ing from a resonance elecbinding curve. As successive oxygen molecules bind, the equilibrium between the two quaternary structures shifts tronic interaction between toward R. The sigmoidal shape of the observed curve and its shift to the right by acid and carbon dioxide facilitate loading of oxygen in the lungs and unloading in the tissues. b, Population of 10 tetrameric species as a function of adjacent hemes. (For realigand saturation for a two-state MWC allosteric model with four identical binding sites 40. Each curve is labeled by sons that are not clear, quaternary state (T or R) with a subscript to indicate the number of ligands bound. The populations of T2, T3, T4, R0, Pauling assumed that the R1, and R2 are not visible on this scale. hemes were on the surface of the molecule and with this arrangement tetrahecurve is sigmoidal instead of hyperbolic, as would occur with a dral symmetry would place them too far away for the direct HbO2 equilibrium. The binding of oxygen by interaction he thought necessary.) It was 1935. Hemoglobin was simple Hb + O2 hemoglobin is therefore cooperative. That is, as the number of known to contain four hemes that serve as binding sites for oxybound oxygen molecules increases in the association reaction, gen; its cooperative behavior could be explained by a sequential the apparent binding affinity increases (Fig. 2). In the same study model in which binding to one heme raises the affinity of its Bohr also discovered that carbon dioxide lowers the oxygen neighbors through a direct heme–heme interaction. Would a affinity. (The necessary reciprocal effect of increased affinity for modern-day biologist want more of an explanation? The answer carbon dioxide and protons as the oxygen pressure is lowered is almost certainly yes, because the biologist would like to ‘see’ was measured much later.) These properties make hemoglobin hemoglobin. A three-dimensional structure would be essential an efficient transporter of oxygen from the lungs to the tissues to explain the alteration in hemoglobin’s function produced by and of carbon dioxide from the tissues to the lungs (Fig. 2a). By mutations, particularly those that cause disease, such as sickle the year 1904 both the protein and its physiological function had been clearly identified, and the functional significance of cooperative binding had been explained. How much more would a genome scientist want to know? We are of course at the very beginning of the subject, and a fundamental question remains: how does hemoglobin exhibit this cooperative behavior? Another physiologist, Gilbert Adair, took the next major step. He made extremely precise osmotic pressure measurements from which he determined the molecular weight of hemoglobin to be 67,000 g mol–1 (refs. 1,3). At that time it was known that ~17,000 g of protein contained one mole of iron atoms, so Adair had discovered that Fig. 3 Simplified schematic of the MWC/Perutz mechanism7,9,14. Open symbols designate hemoglobin contained four binding sites. He then unliganded subunits and filled symbols liganded subunits. Arrows connecting subunits repformulated binding in terms of four successive resent salt bridges—the quaternary bonds of MWC theory that constrain and stabilize the T binding constants, which increased with the addi- quaternary structure. There are actually six intersubunit salt bridges in the T quaternary (each arrow between α subunits represents a pair of salt bridges) that are not tion of each oxygen molecule, the fourth oxygen structure present in the R quaternary structure and two intrasubunit salt bridges (not shown) in the molecule binding with an affinity much greater β subunits. Four of the eight salt bridges contain ionizable groups, and their breakage produces a change in pK of the participating residues that leads to a net release of protons. than the first. The legendary chemist Linus Pauling suggested Proton release upon binding to the T quaternary structure is called the ‘tertiary Bohr effect’, while proton release upon the change of quaternary structure is called the ‘quaterthe first structural explanation of cooperative nary Bohr effect’. Ligand binding to a subunit in the T quaternary structure breaks the salt binding4. He discovered that he could reproduce bridge originating from that subunit, while the change from the T to R quaternary structhe oxygen-binding curve with a two-parameter ture at any ligation state breaks all four salt bridges. Ligand binding to the T quaternary structure occurs with an association constant (KT) that is simply the R-state association conmodel in which binding oxygen to one heme stant (KR) reduced by a factor that is proportional to the strength of the salt bridge (c). The caused an interaction with neighboring hemes quaternary equilibrium constant between the zero-liganded tetramers is defined as L.


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cell anemia (the first example of a ‘molecular disease’, also discovered by Pauling5). The problem was taken up by Max Perutz. After almost three decades of pioneering work on developing the X-ray crystallographic method for proteins, Perutz solved the three-dimensional structure of hemoglobin. A comparison of the structures of oxy- and deoxyhemoglobin at low resolution produced one of his first major results: the β subunits move closer together upon oxygenation6. This experimental fact helped motivate a completely different and powerful theory on the origin of cooperative interactions, not only for hemoglobin oxygenation but for multisubunit proteins in general. Jacques Monod and Jean-Pierre Changeux observed that many enzymes are activated and inhibited by substrates and ligands in a cooperative fashion, and that such enzymes contain more than one protein subunit. They saw the analogy to hemoglobin (where the ‘substrate’ is now oxygen), and together with Jeffries Wyman they developed a theoretical model that would apply to all types of multisubunit proteins7. Their model was very different from Pauling’s, later elaborated by Daniel Koshland and coworkers (KNF)8. In the MWC model, cooperativity arises from an equilibrium between two structures having different arrangements of the subunits, so-called quaternary structures (Fig.1). The ‘tense’ or T quaternary structure has a low affinity for ligands, while the ‘relaxed’ or R quaternary structure has a high affinity for ligands. Cooperativity in the MWC model arises from a shift in the population from the low-affinity T quaternary structure to the high-affinity R quaternary structure with increasing oxygen pressure, as required by Le Chatelier’s principle (Fig. 2a). Each quaternary structure, however, binds statistinature structural biology • volume 6 number 4 • april 1999

Fig. 4 Oxygen binding to a single crystal of hemoglobin in the T quaternary structure. a, Projection of four hemes onto the (ac) crystal face of the optical measurements. b, Absorption spectra of a crystal at nine oxygen pressures between 0 and 760 torr with light linearly polarized parallel to either the a (blue) or c (red) crystal axes. c, Hill plot of fractional saturation with oxygen (y) versus oxygen pressure from spectra measured with linearly polarized light parallel to the a crystal axis. The circles are for increasing oxygen pressure, while the squares are for decreasing oxygen pressure. Binding is perfectly reversible and noncooperative. The p50 (oxygen pressure at 50% saturation) measured from the a-axis data is 155 ± 1 torr and 141 ± 1 torr from the c-axis data; absorption of light polarized parallel to the c-axis has a greater contribution from the α-hemes, indicating an intrinsically higher affinity for the α-subunits20. d, Binding curves for the separate α and β subunits calculated using the polarized absorption spectra and the heme orientations derived from the X-ray structures28.

cally, so that the intrinsic oxygen affinity of each heme in either R or T is independent of the number of oxygen molecules already bound (Fig. 2). MWC called cooperative interaction between identical ligands ‘homotropic’, while the cooperative interaction between unlike ligands, such as oxygen and protons (or substrate and allosteric inhibitor in the case of enzymes) was called ‘heterotropic’. What was the relation between the MWC model and the structure of hemoglobin? Perutz took a bold approach that went far beyond simply identifying the R and T quaternary structures of the MWC model with the structures of oxy- and deoxyhemoglobin, and describing them in detail (Fig. 1). In a tour de force he saw through the complexity of his atomic models and developed a structural explanation for exactly how hemoglobin worked—his ‘stereochemical mechanism’9,10. The key finding was a set of salt bridges at the subunit interfaces that are present in the T quaternary structure but absent in R. Perutz described how oxygen binding to the heme in the T quaternary structure with its associated iron displacement could move a helix, break a salt bridge, release a proton, and destabilize the structure at the subunit interface between αβ dimers of the tetramer, thereby biasing the quaternary equilibrium toward the R state (Figs 1, 3). In Perutz’s mechanism the salt bridges play three roles: they stabilize the T quaternary structure relative to R, lower the oxygen affinity in T because of the energy required to break them upon oxygen binding, and release protons upon breakage, explaining why the overall affinity is lowered when the pH decreases (the Bohr effect). He viewed the mechanism as a combination of the MWC and KNF models, because in the KNF model ligand binding induces conformational changes in the protein (the KNF model ignores 353


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log time (s) Fig. 5 Kinetics of hemoglobin following nanosecond photodissociation of carbon monoxide complex40. a, Ligand rebinding kinetics obtained from the average deoxy minus carbonmonoxy difference spectrum (inset). Geminate rebinding (rebinding of dissociated ligands before they escape from the protein) to R is followed by bimolecular rebinding to R and then to molecules that have switched from R to T. b, Protein conformational changes obtained from the change in the deoxyhemoglobin spectrum (inset). In both (a) and (b) the points are experimental, and the dotted curves are calculated from the extended MWC model of Henry et al.40. Because the deoxyheme spectral change is more than 10-fold smaller than the spectral change due to ligand binding (as indicated by the relative amplitudes in the insets), the deviations between the data and the fit in (b) represent less than 1% of the total spectral amplitude, and may not be significant.

the important structural finding of two quaternary structures). Although oxygen binding results in conformational changes, there appeared to be no structural mechanism for transmitting these changes to the heme of the neighboring subunits other than through a change in quaternary structure. For homotropic effects Perutz’s stereochemical mechanism appeared, therefore, to be pure MWC in that the intrinsic affinity of a subunit is solely determined by the quaternary structure. Perutz’s structure and mechanism were also successful in qualitatively rationalizing the altered behavior of mutant hemoglobins. The site of the sickle cell mutation (β6 Glu to Val), for example, is found on the molecular surface, creating a sticky hydrophobic patch that causes polymerization to form a solid fiber of 14 intertwined helical strands, a structure solved by Stuart Edelstein and coworkers11. Moreover, fiber formation in T, but not in R, explains sickling of red cells by deoxygenation in the tissues and unsickling by oxygenation in the lungs12. The structure and mechanism also elegantly explain how substitutions at the subunit interface distant from the heme produce changes in oxygen affinity by altering the quaternary equilibrium13. Overall, Perutz’s analysis of hemoglobin could be viewed as a turning point in the history of proteins. It represented the beginning of an era in which structural changes at the atomic level were being used to explain how a protein functioned and how mutations in a protein caused disease. It was 1970. To structural biologists ‘the hemoglobin problem was solved’, and it was time to move on to other proteins. Would further inquiry by physical scientists lead to a truly deeper understanding of how hemoglobin functions? After the structure Perutz’s work aroused the interest of many physical scientists, both theorists and experimentalists, and stimulated an enormous amount of research. His mechanism qualitatively explained a vast array of experimental facts, but could it also provide a quantitative explanation? Monod, Wyman, and Changeux had invented a very general model with little structural detail, while Perutz had proposed a detailed structural mechanism 354

which appeared consistent with their model, but contained no prescription for making it quantitative. This important step was taken by Attila Szabo and Martin Karplus, who developed a statistical mechanical formulation of Perutz’s structural mechanism (Fig. 3)14. Szabo and Karplus showed that the Perutz mechanism was consistent with the MWC model for homotropic effects and could indeed provide a quantitative explanation of equilibrium experimental data. They also recognized that the MWC model had to be modified to account for heterotropic effects, particularly the influence of pH on the T-state affinity. This is, however, not a serious criticism of the MWC model. Monod, Wyman, and Changeux clearly recognized that it was unrealistic to expect pH changes to affect the affinity only by altering the quaternary equilibrium, and not also to affect the affinity of R or T for oxygen7. The Szabo and Karplus analysis of heterotropic effects made the interesting prediction that once the salt bridges are completely broken, as in the fully oxygenated molecule, the quaternary equilibrium constant (Lc4, Fig. 3) would be relatively insensitive to solution conditions. Their prediction of Lc4 ≈ constant was dramatically confirmed a decade later15, a fact that has remained largely unrecognized. The most important idea of MWC that the intrinsic affinity depends on the quaternary structure alone, and not on the number of ligands bound per se, was strongly supported by a series of novel spectroscopic studies and insightful analyses by Robert Shulman, John Hopfield, and Seiji Ogawa16. Nevertheless, the applicability of the MWC model remained controversial for several reasons. First, subsequent papers by Perutz and others appeared to contradict the conclusion that his stereochemical mechanism was consistent with the MWC model17. Second, in an investigation of individual ligation intermediates using the cyanide complex of oxidized hemoglobin as an analog of oxyhemoglobin, Gary Ackers and coworkers reported a very large cooperative interaction in ligand binding to the T-state18. Finally, studies of hemoglobin kinetics by Quentin Gibson also appeared inconsistent with the MWC model19. A reinvestigation of the problem was clearly required. To do so required new kinds of experiments. nature structural biology • volume 6 number 4 • april 1999



review Hemoglobin in the R quaternary structure binds oxygen with very nearly the same high affinity as the αβ dimer (that is, the half-molecule; Fig. 1), as well as the isolated α and β chains. The question of the relative contribution to cooperativity from the quaternary change versus direct subunit–subunit interaction therefore centers on the binding properties of the low-affinity T quaternary structure. Does cooperativity arise solely from the T to R transition, as in the MWC model, or is there significant cooperativity in binding to T, as in a Pauling/KNF sequential model? To address this question directly, Rivetti et al.20 measured oxygen binding to single crystals of hemoglobin known to remain in the T quaternary structure by X-ray crystallography21. There was now no ambiguity about the quaternary structure, which has always been a source of uncertainty in solution studies, and possible differences between crystal and solution were not an issue. The crystal binding curve was found to be noncooperative, confirming the essential point of the MWC model that the T quaternary structure binds oxygen noncooperatively (Fig. 4). However, a small amount of cooperative binding was detected, which is masked by unequal binding to the α and β subunits (Fig. 4) (see below). Since the X-ray results showed that oxygenation does not break the salt bridges21, the crystal-binding studies also supported a major element of Perutz’s mechanism. According to the Perutz mechanism there should be no pH dependence to the T-state affinity unless the salt bridges break, and none was observed in the crystal20. (The contribution of the salt bridges to the Bohr effect in solution has been studied in detail using nuclear magnetic resonance by Chien Ho and coworkers22.) Removal of two of the six salt bridges, moreover, raises the oxygen affinity of the crystal T-state, but only about threefold23. Factors in addition to the constraints of the salt bridges must therefore contribute to the low affinity of the T-state. One obvious criticism of the crystal studies is that the lattice forces may prevent hemoglobin from undergoing the conformational relaxation that would lead to more significant cooperative binding within the T quaternary structure and a pH-dependent affinity. Strong evidence against this argument has recently been obtained by showing that deoxyhemoglobin encapsulated in a silica gel is trapped in the T quaternary structure, binds oxygen noncooperatively24, has the same affinity as T-state hemoglobin in solution (about fourfold higher than the crystal)25, and exhibits most of the solution T-state Bohr effect25. An important question regarding equilibrium properties remains. How can the MWC model be reconciled with the results of Ackers? Using chemical analogs to investigate the properties of singly, doubly, and triply liganded molecules, normally present at very low population (Fig. 2b), Ackers and coworkers made an extensive series of measurements of the free energy of dissociation of the tetramer into two αβ dimers for all 10 ligation microstates26. The new information on ligand binding to the tetramer from this approach is based on thermodynamic linkage, namely that the difference in the tetramer-todimer dissociation free energy for ligation microstates is the same as the difference in the free energy of binding ligands to the tetramers compared to the dissociated dimers. Since the free dimers bind oxygen noncooperatively and have nearly the same affinity as the R-state tetramer, these free energy differences are measures of cooperative interactions associated with liganding each microstate, and are called ‘cooperative free energies’. Using primarily the results from a zinc for iron substitution, Ackers has recently derived these energies for the 10 distinct ligation microstates of unmodified hemoglobin (Table 1)26. Although the discrepancy is now much less than that found earlier using nature structural biology • volume 6 number 4 • april 1999

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Fig. 6 Schematic for ligand rebinding to a single subunit in the R quaternary structure40. A ligand dissociated from the heme or entering the heme pocket from the solvent may either bind or escape into the solvent. The rate of ligand entry and escape is independent of quaternary or tertiary structure, while the bond making and breaking steps at the heme depend on both the tertiary and quaternary structure. Following dissociation the subunit conformation relaxes from r*, the liganded conformation existing before dissociation, to r, the liganded conformation in the relaxed equilibrium R quaternary structure. The rate of the R to T quaternary transition now depends both on the number of ligands bound and the tertiary conformation of the four subunits. An analogous scheme applies to subunits in the T quaternary structure, with the subunits labeled t* and t.

the cyanometheme substitution, one of the 10 microstates is still inconsistent with a perfect MWC model. The discrepant microstate is the doubly liganded tetramer with both ligands on the same αβ dimer (Table 1). The most straightforward way of explaining this result is to simply add intradimer cooperativity in the T-state to the MWC model, as was done by Gill et al.27 That is, the second ligand binds to the αβ dimer with a (δ -fold) higher intrinsic affinity than the first, instead of with the same affinity as required by the MWC model. This modified MWC model explains noncooperative binding in the crystal (Hill n = 1.0) as resulting from intradimer cooperativity (1 < δ < 2.5, corresponding to 1 < n < 1.2), exactly compensating for the 2–5 fold higher affinity of the α subunit compared to the β subunit (0.97 > n > 0.85)28. A comparable value of δ = 4 is consistent with the cooperative free energies observed for the microstates (Table 1). Although there is clearly some cooperative binding within the T quaternary structure, it is very small compared to the ~1,000-fold increase in affinity accompanying the change in quaternary structure from T to R (the MWC parameter c in Table 1). The surprise is that this small deviation from the MWC model does not result from a cooperative interaction across the interface between αβ dimers that is known to change with quaternary structure and thereby affect the oxygen affinity. Instead it results from cooperative interaction between subunits of the same αβ dimer. X-ray crystallography detects no change at the interface between these dimers upon either ligand binding or quaternary transition10, so there is as yet no structural explanation for either intradimer cooperativity or why it may be considerably exaggerated in some chemical analogs. The large cooperativity in the T-state found with the cyanometheme substitution (δ ≈ 170) (a result that has recently been challenged on technical grounds10,26,29) prompted Ackers to discard the MWC model prematurely18. With the new results from the crystal, gel, and tetramer–dimer dissociation studies, almost every major element of the equilibrium formulation of the MWC model and Perutz stereochemical mechanism for homotropic effects has been subjected to critical tests, with no major discrepancies between theory and experiments. For 355


review deoxyhemoglobin optical spectrum produced immediately after the flash is different from that of deoxyhemoglobin at Ligation microstate1 Cooperative free energy (kcal mol–1)2 equilibrium, and suggested that this ‘fast3 4 5 6 Expt. MWC Modified MWC x in [-RT ln (x/1+L)] reacting’ deoxyhemoglobin has a different α 1α 2β 1β 2 0 0 0 1+L structure. This work was followed by a α 1O 2α 2β 1β 2 2.8 ± 0.3 3.3 3.3 ε (1 + Lc) series of innovative kinetic experiments α 1α 2β 1O 2β 2 2.8 ± 0.3 3.3 3.3 ε (1 + Lc) using rapid mixing and flash photolysis α 1O 2α 2β 1O 2β 2 5.0 ± 0.87 6.5 5.8 ε2 (1 + Lc2δ) methods by Gibson, Eraldo Antonini and 2 2 α 1O 2α 2β 1β 2O 2 6.7 ± 0.4 6.5 6.6 ε (1 + Lc ) Maurizio Brunori, summarized in the α 1O 2α 2O 2β 1β 2 6.8 ± 0.2 6.5 6.6 ε2 (1 + Lc2) now classic book by Antonini and α 1α 2β 1O 2β 2O 2 6.6 ± 0.2 6.5 6.6 ε2 (1 + Lc2) Brunori31. The connection of the kinetics 3 3 α 1O 2α 2β 1O 2β 2O 2 6.9 ± 0.3 7.0 7.0 ε (1 + Lc δ) to the MWC model was made by Hopfield, α 1O 2α 2O 2β 1O 2β 2 6.9 ± 0.3 7.0 7.0 ε3 (1 + Lc3δ) Shulman, and Ogawa32. They identified 4 4 2 α1O2α2O2β1O2β2O2 6.3 ± 0.1 6.3 6.3 ε (1 + Lc δ ) fast-reacting hemoglobin with hemoglo1There are 16 ligation microstates. Because of the two-fold rotation axis of symmetry that interbin that had not yet switched from the R to changes the α1β1 dimer with the α2β2 dimer (Fig. 1), 10 of the 16 are distinct and are shown here. T quaternary structure after ligand pho2Defined as the free energy change upon dissociating the fully deoxygenated tetramer into two αβ todissociation. These investigators also dimers minus the free energy of dissociation for the microstate (omitting the statistical factors). 3From Table 1 of Ackers26. Experimental uncertainties from Huang et al.43 provided at least a semiquantitative expla4Calculated from -RT ln (x/1+L) with δ = 1 (that is, no cooperative binding to the T-state), ε = 3.1 (the nation of almost all of the kinetic experi44 ratio of the intrinsic R-state affinity to the dimer affinity; Doyle et al. reported ε = 4 (+4,-2)) and MWC 6 parameters (L = 4.4 x 10 , c = KT/KR = 0.0015, and KT = 1/(77 torr)) which simultaneously fit the cooper- ments on both ligand association and ative free energies (weighted by the uncertainties) and the oxygen-binding curve under identical dissociation with a kinetic version of the solution conditions (Fig. 17 in ref. 26). MWC model. In this model there are only 5Same as footnote 4, except δ fixed at 4 (that is, cooperative binding to the αβ dimer in the T-state 6 tetramer), ε = 3.4, L = 6.4 x 10 , c = 0.001, KT = 1/(109 torr). Allowing δ to vary in the minimization yields two pairs of binding and dissociation cooperative free energies of 0, 3.3, 3.3, 4.9, 6.6, 6.6, 6.6, 7.0, 7.0, 6.3 with δ = 21, ε = 3.7, L = 8.8 x 106, rates, one for T and one for R, and all quac =9.2 x 10–4, KT = 1/(110 torr), but decreases the sum of squares by only 15%. However, such a large δ is ternary rates are assumed to be fast relanot possible. For equal α and β affinities it would result in a Hill n of 1.6, compared to the value of n < 1 tive to ligand binding or dissociation. observed in gels25. Furthermore, to produce a Hill n of 1.0 consistent with δ = 21, the ratio of α to β There was still a crucial missing piece to affinities would be greater than 80 (for n = 1, δ = (q+1)2/4q, where q ≡ Kα/Kβ)20, inconsistent with the approximately equal affinities observed for the microstates. the story. In spite of the importance of the 6These expressions are the same as those in Gill et al.27, except that they contain the quaternary quaternary conformational changes, their enhancement factor ε not considered by Gill et al. They are also the same as those given in Table 4 of Ackers45 with cα = cβ, δα = δβ≡ ε, and δαβ ≡ δ. One difference is that Ackers’ expressions45 assume that R and kinetics had not yet been observed. This T exhibit identical intradimer cooperativity. The expressions above can be obtained from the partition prompted Gibson to take advantage of the functions: deoxyheme spectral changes to measure the microsecond-millisecond kinetics of conformational changes in photolysis experiments19. He was, however, unable to use an MWC model to fit the ligand rebinding α β α β with KR = KR , and KT = KT . 7The value reported for this ligation microstate with cyanide bound to the two oxidized hemes as kinetics at neutral pH simultaneously with analogs for oxyhemes is 3.1 kcal mol–1 yielding δ ≈ 170, but as mentioned in the text this value could be the conformational kinetics, which he the result of experimental artifacts10,26,29. attributed to R T quaternary structural changes. Gibson concluded that the experimental results are inconsistent with the most biochemists cooperative oxygen binding by hemoglobin is MWC model19. This of course presented a serious problem, and, as not only well understood, but far better understood than any other mentioned earlier, was a major source of the controversy concernmultisubunit protein. There was, however, a large body of work on ing the applicability of the MWC model. the complex kinetics of hemoglobin to be explained. Kinetics make Several key ingredients went into solving this problem. First, far greater demands on mechanism, and are particularly important nanosecond-resolved spectroscopy showed that the spectral for the hemoglobin mechanism where there is a large number of changes of the deoxyhemes observed by Gibson begin much earliintermediate species with low equilibrium populations (Figs 2b er than a microsecond, and extend from less than a nanosecond and 3). In kinetic experiments large populations of these interme- to milliseconds (Fig. 5)33. Conformational changes before ~1 µs were shown to be purely tertiary, while those occurring later diates can be generated transiently and interrogated. include quaternary changes as well. A second key element was the Hemoglobin kinetics realization that the tertiary relaxation is a single extended process. Gibson made the critical observation for understanding cooper- This view was motivated by the experiments of Philip Anfinrud ativity in hemoglobin kinetics 30. Gibson discovered that follow- on myoglobin34 which showed that, as in glassy systems35, the ing photodissociation by an intense light pulse the bimolecular time course of conformational relaxation could be closely rate of carbon monoxide rebinding is more than 20 times faster approximated by a stretched exponential function (that is, exp[than the initial rate obtained by mixing deoxyhemoglobin with (kt)β], β ≈ 0.1) extending from hundreds of femtoseconds to carbon monoxide. His result suggested that the rate of ligand almost a microsecond. A third ingredient was the idea of Noam binding, and therefore the ligand affinity, is not determined by Agmon and Hopfield that conformational relaxation in myoglothe number of ligands already bound. This is consistent with the bin slows geminate rebinding (that is, rebinding of dissociated MWC model (formulated several years later) but not with a ligands before they escape from the protein) of carbon monoxPauling/KNF sequential model. Gibson also discovered that the ide36. This proposal was most directly confirmed in experiments


Table 1 Comparison of cooperative free energies obtained from tetramer–dimer dissociation experiments with predictions of MWC and modified MWC models

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review on myoglobin embedded in a glass of the sugar trehalose at room temperature37. As in a low-temperature (