Review Article. Spectroscopic Contributions to the Understanding of Hemoglobin Function: Implications for Structural Biology

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1 IUBMB Life, 51: , 2001 Copyright c 2001 IUBMB /01 $ Review Article Spectroscopic Contributions to the Understanding of Hemoglobin Function: Implications for Structural Biology Robert G. Shulman Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut, 06510, USA Summary Structural biology is based on the assumption that structural determinations will explain macromolecular function. To examine the basis of these proposals, the structure/function connections in hemoglobin have been examined. Presently the Monod, Wyman, Changeux (MWC) model of hemoglobin function has great validity. In this model, ligand-binding af nities are linked to quaternary structure, and it has been shown that the model describes the function accurately to a high rst approximation. To see how this understanding developed, we review two sets of experimental studies in that supported the applicability of MWC to hemoglobin oxygen binding. One set of data from NMR and ligand binding kinetics supported the quaternary-linked nature of binding required by the MWC model. The other approach, by Perutz, proposed a structural basis for MWC, by suggesting that in one quaternary structure the binding of oxygen broke a salt bridge that caused a lowered quaternary-linked af nity. However, experiments since that time, mostly by X-ray crystallography of deoxygenated hemoglobin, have failed to show salt bridges breaking upon ligation, whereas af nities have remained low. This pattern of results shows that the small energies responsible for ligand-binding af nities and reaction rates have not been identi ed by discrete structural features. Rather, thermodynamic and kinetic data from a variety of spectroscopic studies have played the central role in establishing the MWC model for hemoglobin. IUBMB Life, 51: , 2001 Keywords Hemoglobin; Monod-Wyman-Chageuk; NMR; X-ray structure. INTRODUCTION Hemoglobin is a physical scientists dream molecule. It has contributed toevery signi cant advance inbiophysical chemistry Received 3 July 2001; revised 21 August 2001; accepted 21 August Address correspondence to Robert G. Shulman. since Christian Bohr s measurements in 1904 of the cooperative nature of oxygen af nity and its ph dependence. Thermodynamical evaluations of linked functions and optical spectroscopy were the frontier methods starting in the 1920s, then application of kinetics followed rapidly. The rst great advance in macromolecular X-ray structures by Perutz continued this tradition and did it gloriously because it subsequently presented not only the rst structure at atomic resolution of such a large molecule, but also set the goals and standards for structural biology. Appropriately, while X-ray crystallographers moved rapidly to apply and extend Perutz s methods to thousands of proteins, the structural studies of hemoglobin have had the most prominent position in the eld (1, 2). All modern studies of hemoglobin are undertaken and interpreted within the frame of reference offered by the available structural information. This dependence on structure for understanding Hb properties, supported and extended by analogous structural studies of macromolecules, has been so successful that it has been generalized into a eld structural biology. This eld has been at the cutting edge of biophysical studies for decades, and with its recent move into proteomics it shows no signs of fading (3). The linkage of structure to function satis es a basic goal of physical/chemical studies of biological molecules. X-ray structures of macromolecules describe these complex entities in terms of their component atoms, bonds, and substructures. For these components, physics and chemistry provide understanding in terms of statistical and quantum mechanics so that our understanding of these parts is enhanced by their tractability to the laws of energy and mass. Furthermore, when this reduction of complex molecules into structural components has been accomplished, the information has generally provided a novel understanding of function at the more complex level. This ful- llment of Descartes method has led to the acceptance of the structure/function relationship as the ruling paradigm in biology 351

2 352 SHULMAN at the molecular level. The paradigm is simply the extension, by these great advances in macromolecular structure, of structureenergy explanations that earlier had been responsible for advances in the chemical and physical understanding of small molecules (4). In view of the dominant role played by structural information, biophysicists have recently asked in a quantitative review of hemoglobin function, whether their thermodynamic and kinetic studies provide a truly deeper understanding of protein function than is already apparent from the beautiful, static color pictures of the structural biologists (5). Eaton et al. answered this challenge af rmatively by extending the validity of the Monod, Wyman, Changeux (MWC) (6) model thermodynamically by the analysis of recent apparently contradictory data and kinetically by showing how this model could simultaneously t the kinetics of the quaternary switch and of ligand binding and release. Have biophysical methods, for example, NMR and kinetics, merely deepened and supported structural explanations of functions, which for hemoglobin means the MWC model, or have they, in fact, been responsible for this functional explanation? In formulating these contributions retrospectively, we start with the present understanding of Hb function as delineated in the Eaton review, which supported the widely accepted MWC view of Hb function. This consensus position is that the two quaternary states of Hb correspond to the two states postulated by MWC in that one, of completely ligated Hb, is identi ed with the R state in which all four subunits have identical high af nity for ligands, while the other quaternary state, found in completely unligated Hb, is called T, with low af n- ity. It is generally considered that this functional description of hemoglobin oxygenation was established by Perutz s interpretation of the crystal structures of ligated and unligated Hb. This interpretation in proposed a structural basis for the energetics of an MWC model (7 9). To the extent that this structural proposal is still considered as having identi ed the functional MWC behavior of hemoglobin, it has been the basis of a larger achievement it has set the standards for macromolecular function the standards for the structural determination of function. However, it is my contention that although the correct functional conclusion was reached from Pertuz s structural proposal, (that is, the MWC model does describe hemoglobin oxygenation), the speci cs of the structural explanation have not been supported by 30 years of experimentation. Furthermore, I show that the energetic functional results that have established our present understanding of hemoglobin function were based on NMR and kinetic experiments that were performed simultaneously with, and independently of, the crystallography (10 13). To support these points, I contrast what was published in with what we know now, after 30 years of study. The structural studies of hemoglobin that often are credited with elucidating the pathways and mechanisms of oxygen binding have resulted in what is often referred to as the Perutz-MWC model. This attribution consolidates the assumption that structural studies, particularly the ligand-linked salt bridge breakage, did not just propose a mechanism that could assign the low binding af nities to the deoxy quaternary structure, but that this structural proposal actually established that the low af nity was linked to that particular quaternary structure. If Perutz s bold proposal about ligand-linked salt bridge breakage had been supported by subsequent experiments, it would have extended the functional consequences of structural features that could be determined at crystallographic resolution. It would justify the con dence in structure/function explanations assumed by contemporary scienti c planning. For this reason, it is important to have a realistic retrospective assessment of the contributions that macromolecules structural determinations have made to our understanding of hemoglobin. It is important to determine the extent to which other biophysical approaches, utilizing diverse spectroscopies, and explicit measurements of kinetics and energetics, have not only built on structural ndings but have, in fact, played early, central, roles in determining the functional mechanisms. Spectroscopic Contributions Since 1969 In the late 1960s, the Hb world was wrestling with the choice between the MWC and Koshland-Nemethy-Filmer (KNF) (10) models of cooperative oxygen binding. High-quality data of fraction bound versus PO 2 were available from Roughton s experiments (11), whereas good Hb samples and tested experimental methods were widely available (12), mainly through the creative oversight of the University of Rome group (under the leadership of Eraldo Antonini, seconded by Maurizio Brunori and advised by Jeffries Wyman) who provided splendid Italian venues for discussions of hemoglobin research. The spirit of these meetings was of courteous exchanges of information, and the goal was to share scienti c knowledge. The cooperative binding and the Bohr effect were the obvious Hb phenomena in need of explanation. Most participants held to explanations of one or both. But these theories the dimer model, inequivalence, local exible regions, MWC, or KNF were rarely addressed directly rather, data were presented to speak for the experimentalist s guiding theory. For Hb, the MWC and KNF models were well understood to be contradictory. A choice clearly existed between models where the af nities were either quaternary linked, as in MWC, or tertiary linked, only depending on the number of ligands already bound, as in KNF. The clean separation of dependence, although not necessarily the - nal explanation, presented a clear start. Both models were able to explain the cooperative oxygenation data to within the experimental accuracy, so that binding data could not distinguish between them. At Bell Telephone Laboratories, we had been studying Hb by high resolution NMR and our results encouraged us to contribute to this problem by distinguishing between these two models (13). The KNF model had suggested that oxygen-binding energies at a heme were increased by binding to another heme. This hypothesis was our rst point of attack.

3 UNDERSTANDING HEMOGLOBIN FUNCTION 353 The early crystal structures of Hb had shown (14) that the four hemes were widely separated by 35 ÊA. This eliminated single-bond connections between the hemes and made any direct heme-to-heme effect unlikely. However, the free energy of cooperativity was only 3 kcal/mole, a small fraction of bond energies, so that the direct mechanism could not be eliminated until quantitative energetic limits were put on localized hemeheme interactions. This was done in 1969 in our article entitled, The Absence of Heme-Heme Interaction in Hemoglobin (13). This article mainly reported NMR results in the mixed state hybrids of the form [ Fe C3 CN; Fe C2 O 2 ] 2. My colleagues Seiji Ogawa, Kurt Wuthrich, Dinshaw Patel, and Brian Sheard had been doing high-resolution NMR experiments of Hb and Mb since In one type of experiment, they measured NMR shifts of protons of the porphyrin ring in paramagnetic Fe C3 CN forms of the macromolecules. The proton resonances were shifted by hyper ne interactions with the delocalized unpaired electrons, providing a measure of the unpaired electron density at numerous positions around the ring. These experimental electron densities provided a basis for calculating electronic binding energies of the iron ligand bond. Calculations of the heme energetics in the cyanoferric heme resonances upon oxygenating and deoxygenating the Fe 2C, were made from the data. The spectral changes were small and from model system studies, where bond energies had been calibrated in terms of the heme proton resonance positions, it was concluded that direct effects of oxygenating the neighbor were less than several percent of the 3 kcal/mole energy of cooperativity. In the absence of heme-heme interaction, it was said (14) that one must look for changes in the protein : : : for example in the different subunit interfaces. It concluded: When the structure of deoxy hemoglobin is obtained by Perutz : : : that will be the time to ask just what speci c ligand-induced conformational changes within the subunits, might be responsible for the changes extending to the interfaces : : : NMR and The MWC Model The choice between the MWC and KNF models depended on being able to determine whether the ligand af nities were linked to the quaternary structure in the (MWC) model or to the number of ligands bound, independent of the quaternary structure as in the KNF model. This choice in our minds was not a con ict of abstractions, but a meaningful question, whose answer would describe the pathways of ligation and that would decide where the structural basis of energetics would be found. With this background, Seiji Ogawa extended the experiments on purely half-ligated hemoglobin (15 17). These compounds had been prepared by separating Hb tetramers into their constituent and chains. The Fe C3 subunits of one type, for example the chains, were oxidized and ligated with CN-keeping the chains in the reduced Fe 2C form. Recombining the chains to form [ Fe C3 CN; Fe C2 ] 2 at low ambient oxygen tension produced a solution of Hb with two ligands, in which the chains were ligated, by CN, whereas the two chains were not ligated. The alternate hybrids with oxidized chains were also prepared. Ogawa s experiment consisted of changing the energies of the T quaternary structure by changing solution conditions and measuring effects on the half-ligated Hb molecule. As shown in reference 15, in a solution stripped of phosphates, the energy of T2 > R2, whereas the introduction of inositol hexaphosphate (IHP) lowered energies of the T quaternary structure so that T2 < R2. As a result, the IHP binding switched the quaternary state (because the molecules minimized their energy), yet the number of oxygens bound remained constant. The quaternary state, with and without IHP, was identi ed by using the NMR markers of quaternary structure in solution that had previously been established (18). Most of these resonances were distant from the heme and had been observed in either the fully ligated or fully unligated Hb molecules, yet some were heme resonances. These markers of quaternary state, in solution, showed in Ogawa s experiment (15) that IHP induced the R!T switch that was reversed when IHP was removed. This switched the quaternary structure at constant ligation, which had not been possible earlier in the fully ligated (R4) and fully unligated (T0) states because the quaternary energies were too widely separated to be inverted by merely changing solution conditions. The experiments showed that an intermediate degree of ligation such as T2 or R2 could facilitate the switch (16 19). In the MWC quaternary-linked model, the ligand af nity should switch with state. It was well established at that time, mainly from experiments by Quentin Gibson (20), that the last ligand to be bound which was a state of high af nity had rapid binding rates, whereas the rst ligand to bind, in a state of low af nity, had slow binding rates. Using these rates as measures of af nity, we performed stopped- ow kinetic experiments with Cassoly and Gibson (21) of the rates of ligand binding in each half-ligated hemoglobins in the two quaternary structures as identi ed by the NMR markers. The results showed that the rates and their associated af nities depended upon the quaternary state, as in the MWC model, and were independent of the number ligands already bound. These results were extended with John Hop eld (19) by re-interpreting the extensive data available on hemoglobin kinetics, showing that to a satisfactory rst approximation all the data were consistent with a pure MWC model. With the kinetic data supporting the NMR switch, we stated at the 1971 Cold Spring Harbor symposium (16): In conclusion the MWC model gives a very satisfactory rst order explanation of the NMR and ligand binding data, in which the two quaternary states determine the ligand binding properties. The Perutz MWC Model In late 1970, from the crystal structure data, Perutz proposed that the MWC model was the correct description of Hb function (7). A structural mechanism was proposed as an explanation for low af nity in the deoxy quaternary structure (T), which was not available in the oxy quaternary structure (R). This mechanism,

4 354 SHULMAN the well-known, ligand-linked breakage of salt bridges at the 1-2 interface in the T structure, was used in a second paper to explain the alkaline Bohr effect (8). The rst paper started with a preliminary discussion of the known aspects of cooperativity followed by structural ndings that in deoxy Hb, the Fe was well out of the plane. From a variety of structural information, Perutz proposed that the reaction with oxygen should be accompanied by a substantial movement of the iron atom relative to the porphyrin ring and that this could lead to cooperative movements in the protein framework. The structures further showed that the C terminal residues of all four chains had complete freedom of rotation in oxy Hb while in deoxy Hb each of the C-terminal residues is doubly anchored by salt-bridges (7). From experiments in Perutz s laboratory at that time (7), and in many cases afterwards, there was strong evidence that the salt bridges stabilized the T structure. This stabilization has the structural consequence of affecting the relative stability of two quaternary structures but the importance of the salt bridges was the proposal that they identi ed a structural basis for the low af nity of the deoxy quaternary structure. In his papers of that time (7 9), it is said clearly that binding of oxygen to a subunit in the deoxy quaternary structure breaks the salt bridges at the C-terminus of that subunit (9). Reaction of Fe with oxygen causes Tyrosine HC2(140) 1 to be expelled from its pocket and the links between arginine HC3(141) 1, and the 2 subunit to be broken, with the release of Bohr protons (7). This proposed mechanism of salt-bridge breaking became the basis for explaining the nature of the interaction energy of cooperativity that earlier had been identi ed as the difference in binding energy of the rst and fourth oxygen molecules (11, 12), and was 3 kcal/iron. Perutz than continued by stating about the interaction energy (7): Where in this large molecule should one look for that energy? Conceivably the reaction of one haem with oxygen might exercise a direct steric effect which raises the oxygen af nity of its neighbors. Nuclear magnetic resonance spectra offer an extremely sensitive probe for small changes in the environment of one haem caused by the binding of oxygen to another. Studies with mixed hybrids show no evidence that such changes occur unless there is a change in quaternary structure, which led Shulman and his colleagues to suggest that the energy of interaction arises at the boundaries between the subunits. This statement was attributed to references 25 and 36 in Perutz s paper (7). Reference 36 was our 1969 Science paper on The Absence of Heme-Heme Interactions in Hemoglobin where, as described previously, we showed that the energy changes upon ligation did not appear at the neighboring heme but at some intermediate point (14). Reference 25 was to a paper by Ogawa and Shulman, identi ed as in the press, one that appeared in January 1971 entitled Observation of Allosteric Transition in Hemoglobin (15). In that paper, it was shown that half-ligated hemoglobins could be switched between the two quaternary states by altering solution conditions, as described above. Continuing, Perutz s paper (7) said that because the salt bridges between the subunits had a total interaction energy of between 6 and 12 kcal/mol of hemoglobin, that is, a value of the same order as the observed interaction energy of 12 kcal/mole, the next question was If it is only the salt bridges which constrain the deoxy tetramer, then part of the energy released by the action of the haem groups must be expended to break them. After reviewing evidence from modi ed hemoglobins suggesting that the interaction energy of cooperativity required a change in quaternary structure, he continued, which suggests that changes in the free energy of the subunit do seem to account for all the energy of interaction. Perutz s contribution to the MWC model was proposing a structural mechanism for low af nity of the deoxy quaternary structure. It assigned the low af nity to that particular quaternary structure and proposed, on the basis of this mechanism, that the af nity was linked to the quaternary structure and therefore the MWC model described the binding. Do the Salt Bridges Break Upon Ligation? In Perutz s model of 1970, ligand binding breaks the salt bridges in the deoxy quaternary structure. Upon ligation, the iron movement into the heme plane is transmitted by the proximal histidine to the salt bridges at the 1ß2 subunit interface, breaking them. Three functional consequences were proposed (7). 1. The salt bridges were proposed to cause the lower oxygen af nity in the deoxy quaternary state because of the energy required to break them upon ligation. 2. Because the salt bridges existed only in the T quaternary structure they caused this structure to have low af nity. This linkage of quaternary structure with af nity supported the MWC model. 3. When a salt bridge broke, its pk would be lowered and this was proposed to be the structural basis of the alkaline Bohr effect (8). The oxygen-linked salt bridge breakage provided a step-by-step mechanism for the T!R switch upon ligation and thereby explained the previously observed linearity of proton release with oxygenation (12). The basis of the model was the ligand-linked salt bridge breakage, which would explain the low af nity in the T structure. X-ray crystallography had shown that the salt bridge disappeared in the T!R quaternary switch. But did the salt bridges in the T structure break when O 2 bound? Furthermore, if the salt bridges did not break upon ligation and the molecular remained in T, was the oxygen af nity raised to the high-af nity value? Perutz proposed that the answer to these two questions would be yes. However, after 30 years of experiments testing these hypotheses, there is no evidence that the salt bridges break upon ligation in the T quaternary state. Second, numerous structural results show that the ligand af nity in the T structure remained low even though the salt bridges did not break upon ligation (5). There are no reports, to our knowledge, of experiments that showed any of the T state salt bridges breaking upon ligation

5 UNDERSTANDING HEMOGLOBIN FUNCTION 355 while the quaternary state is unchanged. On the other hand, there are several reports where the salt bridges in the T structure did not break under ligation, and the af nity was low. Tests of these proposals have been possible because of the developments of different spectroscopic measurements and the availability of novel crystallizations of Hb. The rst direct structural evidence against the proposed ligand-linked salt bridge breakage came from Anderson s (22) crystal structure of hemoglobin Kansas. This mutant hemoglobin had been shown by Bonaventura and Riggs (23) to have low ligand af nities, low cooperativity, and a weak acid Bohr effect. This mutant Hb seemed particularly well suited for a study of T state bridges because the mutant amino acid Asn 102(G4)ß!Thr was signi cant mainly in the R state where it removed a salt bridge at the 1ß2 interface that only existed in the R state. The loss of a salt bridge destabilized the R state so that in the presence of IHP the T quaternary structure was stabilized (24) without any chemical modi cations at its 1ß2 interface, and with normal salt bridges. NMR and stopped- ow kinetics (24) showed that, in the presence of IHP, fully ligated CO Hb Kansas existed in the T state, that it had low af nity as previously reported, and that crystals of deoxy Hb Kansas with IHP bound did not shatter when CO was added. Anderson then determined the crystal structures of deoxy and CO Hb Kansas and was able to prepare the difference Fourier map. In his words the crystallographic evidence presented here indicates that ligands can combine with haemoglobin Kansas in the T state without breaking the salt bridges (22). The difference Fourier of T state CO-Hb Kansas versus the deoxy form showed that in the haem region a negative density behind the Fe appeared as expected if the iron moves into the haem plane. Although an accurate calculation is impossible, it seems unlikely that this relatively small negative peak could be associated with an iron movement of more than a few tenths of an angstrom unit. This questioned any large movement of ÊA and was, in fact, supported later by a reconciliation (25) of more re ned crystallographic data showing a 0.4 ÊA movement with EXAFS results (26) that gave 0.4 ÊA as a maximum iron movement. This small iron movement also had the consequence in Hb Kansas that the F helix shows no interpretable bulk movement (22). Therefore, this difference Fourier showed very de nitely no salt bridge breakage nor was the proposed pathway for this break detected in the globin. Other hemoglobin crystals have subsequently shown similar results in the vicinity of the salt bridges. In the past 10 years, ithas become possible to crystallize Hb under conditions where the crystals do not shatter upon changing the degree of ligation. In this method, deoxygenated Hb A was crystallized from solutions of polyethylene glycol (28, 29) and the X-ray crystal structures showed that the molecules remained in the T state and that the salt bridges remained intact over the full range of oxygen tension from 9 to 700 Torr. The crystallographic results surprisingly showed that only the chains were ligated even at the high oxygen pressure. These studies were followed by polarized microspectrometric studies of Hb crystals prepared in the same way (30). The degrees of saturation of the and ß chains were separately determined from the absorption over the entire visible spectrum using linearly polarized light and disentangling the and ß contributions by using their orientation in the structure. The oxygen binding was of low af nity and effectively noncooperative for these crystals in which the molecules remained in the deoxygenated quaternary state over the entire range of ligation under similar crystallization conditions as in the X-ray studies (30). The X-ray results had not observed ligation of the ß hemes. However, the full ligation of these hemes, as detected by the resolved absorption spectrum, led Rivetti et al. to suggest that the different O 2 orientations had weakened its X-ray scattering and that the molecule was close to completely ligated at the high oxygen tension (5, 30). Two optical measurements supported the existence of a fully ligated T structure. The polarization ratio for the fully oxygenated T structure, and the ts of the spectral absorption were both consistent with a T quaternary structure. The quality of the optical spectra made it possible to measure ß inequivalence with the subunits having a ve-fold higher af nity. This was approximately cancelled by a small amount of cooperative binding in the ß dimer, which explained the essentially noncooperative low-af nity binding (5). In several additional experiments, crystals of metal hybrids, which remained intact upon full ligation in the T quaternary structure, were prepared and the crystal structures determined by X-ray crystallography (31 34). In all these crystals, the salt bridges were observed to be intact and to remain so upon ligation while the af nity remained low. In summary, in all the crystals where the molecules remained in the T quaternary structures upon ligation the af nities, when measured, were close to the rst ligand binding to HbA in solution and the salt bridges did not break. DISCUSSION What do we understand about the oxygenation of hemoglobin and how did we get here? The evidence is consistent to rst order with an MWC model in which the ligand af nity is quaternary linked. Early support for this model came from the switch of quaternary state, accompanied by a switch of af nity, which was independent of the number of ligands. This experiment disproved the KNF dependence of af nity upon number of ligands. The earlier NMR experiment on the absence of direct heme-heme interaction (13), combined with the NMR-determined switch of quaternary structure with constant ligation (15 17 ), were the acknowledged background for Perutz s ligand-linked salt bridge model, which proposed a structural explanation of the quaternary linked binding energies. As we have shown, subsequent evidence for this structural basis of low T state af nity has not been found. However, the MWC model has survived as explaining the function. The correlation between quaternary

6 356 SHULMAN state and af nity continues to support the MWC model and it has been reported in many chemically modi ed hemoglobins, in mutants, and in partially ligated molecules (2). In addition, there is abundant structural information about the relative energetics of the quaternary states including information about salt bridge stabilization, and effector binding. Contributions to the establishment of the MWC model made by X-ray crystallography and NMR have been emphasized in this report because these experiments originally and simultaneously suggested this model. But other physical measurements, which include kinetics, optical spectroscopy, polarized optical absorption, Raman spectroscopy, EXAFS, and temperaturedependent kinetics have also supported the rst order MWC model (2, 5). In the idealized symmetric MWC model, all subunits would be identical. Many observed departures from this idealized state have justi ed Wyman s concern that the requirement of symmetry was too limiting. A functional de nition of the MWC model requires that only the ligand binding energetics be determined exclusively by the quaternary state. Departures from the symmetric MWC model are discussed in the Appendix where they are shown to be small. X-ray determination of the quaternary structures of Hb have led the way into a general understanding of the roles played by quaternary structures and other intermolecular interactions in macromolecular function. Certain speci c structural features can be quantitatively linked to functional energetics and kinetics; for example, steric hindrance can block a binding site, difference Fouriers can show the binding of small molecules such as DPG to hemoglobin, and salt bridges among other features of quaternary structure, can be identi ed. However, in the absence of large scale changes with direct energetic consequences, structural studies are dependent on energetic and kinetic properties being measured by other methodologies. The unsolved problems facing structure/function relationships are illustrated by the unexplained structural basis of low binding energies in a particular quaternary state. The use of spectroscopic methods particularly optical absorptions and NMR to follow these smaller, subtler functional properties has been emphasized in this report. To the extent that ligand-binding energetics and kinetics are not determined by localized single bonds in macromolecules, as seems to be the case in Hb, spectroscopic studies have played a valuable role in determining the functional mechanism. In the absence of speci c ligand-linked localized bond changes such as the proposed salt bridge breaking, many have suggested that delocalized strain energies are responsible for low af nity in the T structure. Hop eld (35) has carried this general idea forward by describing criteria that could allow experiments to distinguish between distributed strain energies (and thereby supported by small displacements, linear with energy), and energies localized to speci c bonds, which would require large displacements. Because experiments have not identi ed speci c bonds responsible for the low af nity in T, perhaps more experiments should seek to test and quantify delocalization of strain energies within the and ß subunits. This kind of experiment may extend the determination of macromolecular function beyond the present spatial resolutions available from X-ray crystallography or high resolution NMR. APPENDIX Factors that have been shown to affect the binding and thereby to depart from the functional MWC model are: 1) allosteric effectors, 2) inequivalence, and 3) cooperativity within a quaternary structure. With time the effects of all three of these symmetry-breaking contributions have been identi ed and quantitated. All have been shown to perturb the functional MWC model, but their effects upon af nity have been very small compared to the effect of quaternary structure. These three factors are brie y reviewed as follows: 1. The effects of ph and IHP on the af nity in T state was shown by Minton and Imai (36) to require a three-state model, basically with and without the allosteric effectors. However, this was shown (18) to add a small additional term to the MWC model, which could readily be treated as a perturbation. 2. The small effect of inequivalence within the T structure has been shown (37 ) to introduce a factor somewhat less than 5 in which the units bind more strongly than the. 3. Measurements made by linearly polarized absorption spectroscopy of T state crystals showed that the Hill coef- cient of 1.0 in the crystals resulted from the inequivalence (which would produce anti-cooperativity) being compensated by an approximately equal amount of positive cooperativity within the dimer in the T state (37 ). These departures from a pure MWC model are small; the inequivalence being 5 or less, and the dimer inequivalence being 2% at the quaternary-linked binding strengths and cooperativity. These perturbations of the perfectly symmetric MWC model have been shown by Eaton et al. (5) to provide an explanation of the detailed thermodynamic studies by Ackers and colleagues (38) of numerous half ligated hemoglobin, which had been interpreted as disproving the quaternary-linked MWC model. Once again these additional studies have only required a small departure from a pure quaternary-linked model. These studies, showing the effects of small structural departures from perfect symmetry upon the energetics, emphasize the importance of spectroscopic results for understanding protein function. ACKNOWLEDGEMENT I thank Chien Ho for clarifying conversations. REFERENCES 1. Perutz, M. F., Wilkinson, A. J., Paoli, M., and Dodson, G. G. (1998) The stereochemical mechanism of the cooperative effects in hemoglobin. Ann. Rev. Biophys. Biomol. Structure 27, 1 34.

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