Self-Association, Cooperativity and Supercooperativity of Oxygen Binding by Hemoglobins

Hemoglobins that bind ligands cooperatively are widely distributed in organisms from bacteria to mammals. Hill (1913) was the first to deduce the essential feature of cooperativity: the binding of the first ligand makes it easier to bind a second one. Although the mechanisms for cooperative oxygen binding within tetrameric vertebrate Hbs have been extensively studied for almost a century and are now relatively well-understood (Perutz et al. 1987; Perutz, 1989; Ackers et al. 1992; for a recent discussion of the issues, see also Ackers et al. 1997), it is now clear that different mechanisms are dominant in Hbs of non-vertebrates. Indeed, the mechanisms established in vertebrates have not so far been found in any non-vertebrate Hb. Cooperativity in tetrameric α₂β₂ Hbs of mammals depends on oxygenation-dependent changes in the iron-proximal histidine bond that produce a chain of conformational perturbations that lead to a weakening shift of the α1β2 interface between two dimers the subunits of which are joined together at the α1β1 interface. However, this interface does not change appreciably during the oxygenation of mammalian Hbs. Oxygenation-dependent weakening of both these interfaces occurs frequently in the Hbs of reptiles and amphibians so that the oxygenated species often include an equilibrium mixture of tetramers, dimers and monomers (reviewed by Brittain, 1991). The Hbs of most birds and of some reptiles and amphibians are characterized by a further deoxygenation-dependent self-association of tetramers. These tetramer–tetramer complexes have a greatly lowered oxygen affinity. Partial oxygenation results in dissociation to tetramers of higher oxygen affinity. This oxygenation-dependent increase in oxygen affinity is a second mechanism of cooperativity that is superimposed on the cooperativity of O₂ binding within the tetramer. It is this phenomenon that we term ‘supercooperativity’. Such self-association of deoxygenated tetramers should be greatly enhanced by the molecular crowding and the excluded-volume effect within red cells (Zimmerman and Minton, 1993). Such enhancement should result in a further increase in the supercooperativity of O₂ binding within red cells and an increased value of the Hill coefficient. This coefficient, n_H, commonly used as an overall measure of cooperativity, is proportional to the statistical variance of the distribution of ligands among the various species of Hb (Edsall and Gutfreund, 1983). Thus, the higher the Hill coefficient, the more non-random is the distribution. The concentration of Hb in the solvent available to it within a mammalian red cell is approximately 335 g l⁻¹ or 5 mmol l⁻¹ tetramer. The molecules, almost in contact and close to the limit of solubility, occupy a volume fraction similar to that in a crystal (Perutz, 1946). Under these crowded conditions, the excluded volume effect has major consequences. The apparent lack of self-association of tetramers of mammalian Hbs has led to the suggestion (Riggs, 1976) that there should be a general selective advantage against Hbs having complementary surfaces unless the interaction leads to an advantageous change in physiological properties. Although the evidence for supercooperativity is compelling, many of the early results are difficult to interpret because spurious apparent supercooperativity can be produced by incomplete oxygenation.

The homodimeric structures of deoxy and oxy Hbs in the circulating erythrocytes of the clam Scapharca inaequivalvis show a cooperative mechanism that is completely different from that of vertebrate Hbs (Royer et al. 1990). The subunit contacts in vertebrate Hbs are dominated by contacts involving the C, G and H helices, whereas the E and F helices are on the external surface of the tetramer (Perutz et al. 1987). In contrast, the subunit contacts in the dimeric Scapharca Hb involve the E and F helices, so that the hemes are in almost direct contact. The cooperative mechanism in this Hb involves only small changes in the local environment of hemes, and the global conformational changes that characterize vertebrate Hbs are completely absent.

The goal of this brief review is to evaluate these diverse processes of ligand-dependent dissocation/association found in the hemoglobins of many organisms. There are two key questions to be addressed. First, how widespread is the ‘Scapharca’ mechanism among non-vertebrate Hbs? Second, how important are the tetramer–tetramer interactions responsible for ‘supercooperativity’?

Expression of the homodimeric Hb of the bacterium Vitreoscilla sp., first called cytochrome o, increases some 50-fold when the culture is made hypoxic (⁠ ≤ 15 mmHg; 1 mmHg=0.1333 kPa) (Tyree and Webster, 1978; Wakabayashi et al. 1986). The X-ray structure of the homodimer reveals that the intersubunit contacts between parts of the E and H helices are very different from those of other known oligomeric Hbs (Tarricone et al. 1997). The Hb has been reported to bind CO with high cooperativity (Hill coefficient, n_H≈2). Cytochrome o (=Hb) from Acetobacter suboxydans has also been reported to bind CO cooperatively (Hill n_H≈1.9) (Daniel, 1970). However, the quantitative importance of cooperative intracellular Hbs in O₂ delivery has not yet been assessed. It could be that a primary function of some microbial Hbs is not in oxygen delivery but rather in sensing oxygen stress (Bunn and Poyton, 1996) or as a terminal oxidase (Wittenberg and Wittenberg, 1990).

It should be mentioned here that CO-equilibrium measurements can give a spurious cooperativity under some conditions if a gas phase is present. Thus, beef heart cytochrome oxidase has been reported to bind CO cooperatively with a Hill coefficient of 1.26 (Wald and Allen, 1957), but this appears to be an artifact that resulted from the lack of sufficient time for equilibration. Measurement of CO binding by soybean legHb using exactly the same tonometry revealed an apparent Hill coefficient of 2.0, but this value was shown to be the result of an inadequate 10 min equilibration time; 60–120 min was required because the rate of transfer of the introduced CO from gas phase to solution is limited by the very low P_CO used in the experiments (Imamura et al. 1972).

Although most Mbs are non-cooperative monomers, the radular muscles of several gastropods and chitons contain cooperative dimeric Mbs (Manwell, 1958; Terwilliger and Read, 1971; Geraci et al. 1977; Smith et al. 1988) with Hill coefficients of 1.2–1.6. None of these dimers has been reported to undergo ligand-dependent subunit dissociation. In contrast, the notonectid diving beetles have cooperative Hbs that do have this property. The Hb of the notonectid backswimmer Anisops assimilis self-associates extensively upon deoxygenation (Wells et al. 1981), from largely monomeric (approximately 17 kDa) HbO₂ to an equilibrium mixture of dimers, trimers, tetramers and hexamers at 75% deoxygenation. The overall effect of this ligand-dependent association is that the O₂ equilibrium changes from being non-cooperative at low concentrations to highly cooperative at 300 mg ml⁻¹, with a maximal n_H value near 6.0. Oxygen released from the Hb into a gas bubble provides a mechanism by which the buoyant density is regulated (Miller, 1966).

The nemertean worm Cerebratulus lacteus has Hb in circulating red cells, in neural tissue and in the body wall muscles (T. L. Vandergon, C. K. Riggs, T. A. Gorr, J. M. Colacino and A. F. Riggs, in preparation). Although the red cell Hb has not yet been studied, both the neural and body wall Hbs bind O₂ with high cooperativity in vivo and in vitro (neural Hb n_H≈2.6–3.0, body wall Hb n_H≈2.1–2.2) even though the ligated Hbs are monomeric. This finding indicates deoxygenation-dependent self-association, probably at least to tetramers. Calculations show that the neural Hb, present at 2–3 mmol l⁻¹ heme concentration, could function as an oxygen store to prolong the activity of this predator in anoxic muds where it searches for prey. Even under normoxic conditions, the neural and body wall Hbs could augment O₂ delivery during bursts of activity.

The red cells of the arcid clam Scapharca inaequivalvis have two Hbs, homodimeric Hb I and heterotetrameric Hb II, both of which bind O₂ cooperatively by mechanisms completely different from those used by the α₂β₂ tetrameric Hbs of vertebrates (Chiancone et al. 1981; Ikeda-Saito et al. 1983). The essential features of the Scapharca mechanism will be summarized here because of the finding that some of the properties are shared by many Hbs in organisms of diverse phyla. Royer et al. (1990) have shown that the subunit interface of the homodimeric Hb I is formed by the E and F helices so that the two hemes are in direct contact via their propionic acid groups through a set of 17 symmetrically ordered water molecules (Royer et al. 1996, 1997). Ligand binding to the heme causes the iron atom to move into the heme plane, as it does in vertebrate Hbs. Associated changes in heme shape squeeze a phenylalanine (residue 97) out of the heme pocket into the interface to contact the other subunit. These changes disrupt the 17 ordered water molecules, and six are released. The hemes move further into the pocket so that the propionic acid groups of each subunit move away from those of the other subunit. These local changes in the heme pocket and the adjacent interface are the processes that are responsible for cooperative O₂ binding. The importance of water molecules in the mechanism is underlined by the finding that mutation of interface residue Thr72→Val causes a 40-fold increase in O₂ affinity, although the change involves the loss of only two hydrogen bonds and two water molecules (Royer et al. 1996). The crystal structure of the heterotetrameric Hb II of Scapharca (Royer et al. 1995) shows that the structure of the heterodimers within the tetramer is very similar to that of the homodimeric Hb I, suggesting that O₂ binding to the heterodimer within the tetramer is also cooperative. Oxygen binding by Hb I is characterized by a Hill coefficient, n_H, of 1.5. The higher cooperativity of O₂ binding by the tetrameric Hb II (n_H=2.1) reflects either the additional interactions across the dimer–dimer interface or the association of deoxygenated tetramers. A striking difference between Hbs I and II is that O₂ binding by Hb I has no heterotropic effects, i.e. the equilibrium is unaffected by allosteric factors such as protons or anions. In contrast, tetrameric Hb II self-associates upon deoxygenation, probably to tetramers of tetramers (Chiancone et al. 1981), a process that is pH-dependent and linked to anion binding (Boffi et al. 1990).

Although ferrous dimeric Hb I and tetrameric Hb II do not dissociate appreciably, oxidation results in dissociation of Hb I to monomers and of Hb II to dimers (Spagnuolo et al. 1988). These dissociations are marked by hemichrome formation in which the sixth coordination position of the iron is occupied by an endogenous ligand, presumably the distal histidine. The dissociation is reversed by addition of ligands such as NO₂− to the ferric iron. Thus, the association states of Hbs I and II are both valence- and ligand-state-dependent. This property, initially thought to be unique to Scapharca, turns out to be widespread and occurs in the Hbs of animals in at least five phyla including the chordates. Examples are discussed below.

Zhu et al. (1996b), following the earlier work of Ascoli et al. (1978), have shown that the extracellular Hb of the annelid Lumbricus terrestris behaves upon oxidation exactly as described for the Hb of the mollusc Scapharca. Lumbricus Hb has four major kinds of globin chains: chains a, b and c (forming a disulfide-linked trimer) and chain d. The CO–ferrous trimer self-associates extensively to assemblages as large as (abc)₁₀, and CO chain d is largely tetrameric (d₄),but oxidation causes the trimer assemblages to dissociate completely to (abc)₂ and d₄ to dissociate to d₂. Addition of CN⁻ reverses these dissociations completely. The abc trimer and chain d associate to form (abcd)₄, a principal subunit, which, together with non-globin structural units (‘linkers’), form the 4.1 MDa, approximately 200 polypeptide, assemblage of the Hb. Partial oxidation causes the Hb to shed subunits, a property that accounts for the wide variation in reports of the molecular mass. Just as in Scapharca Hb, the oxidation of the heme causes a conformational change of the E helix that results in hemichrome formation. This shift is associated with a weakening of a critical subunit interface that results in dissociation.

The intracellular Hbs of Caudina arenicola (Bonaventura and Kitto, 1973; Mitchell et al. 1995) are dimeric as oxy Hbs and associate to tetramers and larger assemblages upon deoxygenation. The ligand-linked dissociation appears to be completely responsible for the observed cooperativity. The Hbs dissociate to monomeric hemichromes upon oxidation, just as in Scapharca, and cyanide causes reassociation. The crystal structures of Caudina Hbs (Mitchell et al. 1995) reveal that the interface in the dimer is similar to that in Scapharca, although the contact residues differ.

The ligated intracellular Hbs of Phoronopsis viridis are completely dimeric, but dissociate to monomers upon oxidation and reassociate to dimers upon cyanide addition (Garlick et al. 1979). The oxygen equilibrium has low cooperativity (n_H=1.2) at a Hb concentration of 125 μmol l⁻¹ heme.

The lampreys and hagfish are the most primitive living vertebrates, and their Hbs have properties that sharply distinguish them from those of all other vertebrates. Although cooperative O₂ binding (n_H=1.2) was found in lamprey Hb by Wald and Riggs (1951), it was not recognized because it was thought that the Hb was always monomeric. The Hbs of lampreys are monomeric at pH 7 when ligated with CO or O₂, but self-associate to dimers and tetramers upon deoxygenation (Briehl, 1963; Behlke and Scheler, 1970; Andersen, 1971; Andersen and Gibson, 1971; Dohi et al. 1973; Brittain et al. 1989). The ligand-dependent dissociation from dimers and tetramers with low O₂ affinity to high-affinity monomers is responsible for the cooperativity (n_H=1.2–1.4). The release of protons accompanying the dissociation accounts completely for the pH-dependence of O₂ binding. Oxidized Hbs of the lampreys Lampetra fluviatilis (Behlke and Scheler, 1970) and Petromyzon marinus (Qiu, 1997) are monomeric, but addition of metHb ligands causes reassociation to dimers at low pH, as in many invertebrate Hbs.

The pH-dependent dissociation of lamprey Hb within red cells will increase the osmotic pressure and alter the acid–base balance. These topics are reviewed in detail by Nikinmaa et al. (1995).

Hagfish Hbs also self-associate upon deoxygenation, but the level of cooperativity is lower than in lamprey Hbs. Bannai et al. (1972) found that none of the isolated components of the Hb of the hagfish Eptatretus burgeri showed significant cooperativity, but discovered that upon deoxygenation two components formed a hybrid tetramer that exhibited significant cooperativity. Evidence for such subunit interaction has also been shown for the Hb of the hagfish Myxine glutinosa (Fago and Weber, 1995). The combination of unlike chains to produce a cooperative complex might be thought of as a precursor of the cooperative α₂β₂ tetramers of higher vertebrates, but there is no structural evidence that the interfaces are similar. If the interfaces resemble those suggested for the lamprey, the cooperative mechanism would be totally different.

In conclusion, oligomeric Hbs have been identified in five phyla (chordates, echinoderms, phoronids, molluscs and annelids) that dissociate upon oxidation and reassociate with the addition of a ferric heme ligand. This finding points to a common mechanism that links oxidation of the heme iron to the weakening of a critical subunit interface. We suggest that the same pathway is used for communication between heme and the subunit interface during cooperative O₂ binding. The crystal structures of both Caudina and Scapharca Hbs reveal that the E/F helices form the dimer interface. We infer that the critical interface is likely to be similar, although not identical, in all these Hbs. This phylogenetic perspective suggests that the most common cooperative mechanism in the animal kingdom may be that of Scapharca Hb.

Avian Hbs and bloods have been the most extensively studied. Many studies of chicken blood have reported very steep O₂ binding curves with Hill coefficients above 4 at high levels of oxygenation (for references, see Cobb et al. 1992; Vorger, 1994). Examples of such equilibria (Lapennas and Reeves, 1983a,b) are shown in Fig. 1. These data show that embryonic red cells of the chicken have steeper O₂ equilibria than those of the adult; both are much steeper than that of human red cells. In contrast, most in vitro studies of Hb solutions do not exhibit this property. This puzzling difference has not been fully resolved, but may depend in part on differences in concentration and allosteric factors. Such data can be produced by deoxygenation-dependent self-association of tetramers. However, erroneously high Hill coefficients can also result from incomplete saturation with oxygen, as emphasized by Lapennas et al. (1981) and Vorger (1987, 1994). The superposition of the artifactual effects of incomplete saturation on the real effects of tetramer–tetramer self-association makes analysis of some of the early data difficult. Nevertheless, the evidence for tetramer–tetramer interactions is compelling. We will consider first the general consequences of linkage (Wyman, 1964; Wyman and Gill, 1990) between oxygenation and dissociation of tetramer–tetramer complexes. We neglect the dissociation of tetramers to dimers in the discussion, but one should recognize that real data do exhibit ligand-dependent dissociation of tetramer to dimer at low concentrations as well. The deoxygenation-linked self-association of tetramers can be described in terms of a thermodynamic cycle (Fig. 2)

A striking feature of the O₂ equilibria in Fig. 3 is that the curves, appear biphasic in the presence of IHP but not in its absence. Could the elevated Hill coefficients at high degrees of oxygenation in Fig. 3 be merely the artifactual consequence of the low oxygen affinity resulting from IHP binding? This might result in less than 100% saturation being taken as full saturation. Fig. 4 shows simulated Hill plots on the assumption that the value n_H is either 2.0 or 3.0 and that 89% oxygenation, corresponding to 102 mmHg (Hb D data), is used as if it were 100% oxygenation. Although the data of Fig. 4 resemble those of Isaacks et al. (1976) (Fig. 3), a major difference is apparent: the lack of saturation produces only a 1.5-fold increase in the mean Hill coefficient between the lower and upper parts of the curves in the simulated data, whereas Fig. 3 shows a 2.8-to 3.5-fold increase. The maximal used in the experiments was 265 mmHg, indicating that the high n_H values cannot be attributed completely to inadequate saturation and therefore must reflect the known presence of dimers of tetramers in deoxy chicken Hb D (Cobb et al. 1992).

Vorger (1994) has made very careful O₂ binding studies of both blood and Hb from the pigeon, which has only component A whereas most birds possess both components A and D. The oxygen equilibria for blood and Hb solutions were very similar and showed no evidence for supercooperativity: the maximal Hill coefficient of 3.35 (pigeon blood) is close to the maximal value of 3.38 obtained for human Hb (Doyle et al. 1992). Vorger (1994) suggests that supercooperativity is absent in pigeon blood because it requires two different components. However, the data of Isaacks et al. (1976) (see Fig. 3) show evidence for high cooperativity in isolated single components of chicken Hb. The measurements of solutions of pigeon Hb were made at too great a dilution to ensure detection of supercooperativity were it present. The lack of n_H values greater than 4 in pigeon blood, however, is strong evidence against the presence of supercooperativity. This result might conceivably have arisen from depletion of the organic phosphates within the red cells either before or during the measurements.

The data of Baumann et al. (1987) in Table 1 are not consistent with those of Isaacks et al. (1976). The data of Baumann et al. (1987) were obtained at a protein concentration of 200 mg ml⁻¹ so that virtually all of the deoxy Hb should have been associated to dimers of tetramers, but the n_H values do not show this. Two possible reasons for this can be suggested: (1) the lengthy technique used generates up to 25% metHb (Baumann et al. 1982), which would decrease n_H, and (2) Isaacks et al. (1976) used a of 40 mmHg, whereas Baumann et al. (1987) used no CO₂. The known preferential binding of CO₂ to T-state Hb would increase the amount of both Hb_T and (Hb_T)₂ so that n_H should be elevated. The discrepancy between the two sets of data underlines the need to re-examine this system to define the conditions required for supercooperativity.

Holland and associates have found very high cooperativity of O₂ binding in the red cells of embryonic marsupials (Holland et al. 1988, 1994; Calvert et al. 1994) and rabbits (Holland and Calvert, 1995). They used a Hemo-Scan instrument modified as described by Lapennas and Lutz (1982) to ensure that the recorded accurately corresponded to that of the chamber. They found that full saturation was achieved by air ≈ 150 mmHg); raising the to 400 mmHg did not change the final absorbance significantly (Holland et al. 1994). Furthermore, they measured O₂ binding in both directions: oxygenation and deoxygenation gave indistinguishable results (Holland et al. 1988). Fig. 5 shows the results for the brushtail possum. The overall pattern corresponds closely to that reported by Lapennas and Reeves (1983a,b) for chicken blood (see Fig. 1), which shows a biphasic Hill plot with n_H values greater than 4 above 50% oxygenation. The blood for these studies was obtained from newborn marsupials which at birth are still embryonic, as reflected in the fact that neural connections between eye and brain have not been made. Whole embryonic rabbit blood gave similar biphasic Hill plots with high cooperativity in the upper half of the curves. The increase in the Hill coefficient is approximately 240% between the lower and upper halves of the curve, a result similar to that in the data of Isaacks et al. (1976) for chicken Hb. Hemolysis by addition of distilled water abolished the high cooperativity, but it is unclear why this occurred. Dilution, a decrease in organic phosphate levels and the loss of intracellular buffering could be partly responsible.

The Hb of an elasmobranch, the spiny dogfish Squalus acanthias, is tetrameric only in the deoxy form; it dissociates reversibly to dimers upon oxygenation (Fyhn and Sullivan, 1975). The adult Hb used in these studies was treated with iodoacetamide to prevent irreversible polymerization by disulfide formation. Organic phosphates (ATP and GTP) greatly reduce the O₂ affinity as in other Hbs, and also enhance the cooperativity of O₂ binding (Weber et al. 1983). This is the expected result because organic phosphates bind preferentially to tetrameric deoxy Hbs. Dissociation of the tetramer destroys the binding site for GTP or ATP so that enhanced cooperativity produced by organic phosphates results directly from the decreased tetramer–dimer dissociation in the presence of ATP or GTP.

The tetrameric oxy Hbs of teleost fish, in contrast, are extremely resistant to dissociation to dimers (Edelstein et al. 1976): the tetramer to dimer dissociation constant is 100-fold lower than that of human Hb. However, sedimentation analysis of deoxy carp Hb indicates a weak self-association to dimers of tetramers with a dissociation constant of =22 mg ml⁻¹ (Atha and Riggs, 1982). Deoxy Hb in the red cells should be at least 75% associated on this basis. The in vivo effect of tetramer–tetramer interaction should therefore be substantial. The linked effect of such association on O₂ binding has not yet been investigated.

The Hbs of amphibians display a complex array of dissociation/association processes that change during development. Elli et al. (1970) showed by sedimentation velocity experiments that the Hbs of the frog Rana esculenta and the axolotl Axolotl mexicanum both polymerize reversibly upon deoxygenation. The deoxygenation-linked assembly of axolotl Hb was found to be extremely sensitive to pH: a rise in pH from 6.5 to 7.0 caused almost complete dissociation. This suggests a very large pH-dependence of O₂ binding (Bohr effect), but this linkage has yet to be studied. In contrast, the corresponding assembly of Hb of the frog Rana esculenta is independent of pH, and the Hb of the newt Triturus cristatus does not self-associate at all.

The ligand-dependent dissociation behavior of the Hbs of the tadpole and adult bullfrog Rana catesbeiana have been studied extensively. The adult hemoglobin has two major components, B and C, present in the molar ratio 1:2. Component C polymerizes by forming intermolecular disulfide bonds, but this can be prevented by reaction of available sulfhydryl groups with iodoacetamide. The more interesting association occurs upon deoxygenation of a 1:2 mixture of components B and C which forms a mixed trimer of tetramers, BC₂ (Aggarwal and Riggs, 1969; Tam and Riggs, 1984). Analysis of sedimentation velocity profiles reveals that the association can be satisfactorily described in terms of two steps, B+C⇌BC and BC+C⇌BC₂, in which the second C is bound more tightly than the first, indicating significant cooperativity (Tam et al., 1993). The tightness of the BC₂ assemblage increases strongly with a decrease in temperature, which suggests that the interactions are not primarily hydrophobic but electrostatic, Van der Waals and hydrogen bonding. Model building has suggested a possible explanation for this cooperativity: the first C binds to B at one site, whereas the second C binds to both C and B (Smith et al. 1993). This deoxygenation-linked association is reflected in the strong dependence of the O₂ equilibrium on protein concentration (Tam and Riggs, 1984). Thus, the O₂ affinity decreases and the Hill coefficient increases as the concentration of Hb rises. The n_max values of the separate B and C components are lower than in mammals, but the 1:2 B:C mixture causes n_H to reach values similar to those in mammals. This indicates that BC₂ formation may serve to raise cooperativity close to the value in mammals rather than to create ‘supercooperativity’. The very high Hill coefficients (n_H>4) reported earlier (Tam and Riggs, 1984) may have resulted from incomplete saturation with O₂, as previously discussed.

The formation of BC₂ also makes an important contribution to the Bohr effect because the assembly process is pH-dependent. The dissociation of BC₂ within the red cell would be accompanied by a threefold increase in the osmotic pressure if compensating ionic changes did not occur. These cellular changes have yet to be explored.

The Hbs of the tadpole of the bullfrog Rana catesbeiana display ligand-linked dissociation of tetramers to dimers and to monomers that is strongly pH-dependent (Atha et al. 1979). These dissociations are partly reflected in the pH-dependence of cooperativity. However, the cooperativity as measured by n_H decreases from 2.5 to 1.5 between pH 7 and pH 8, where very little dissociation of the tetramer occurs. So this drop in cooperativity with pH must be intrinsic within the tetramer and not a function of dissociation. Cooperativity of O₂ binding is modulated not only by pH but also by organic phosphates (Watt and Riggs, 1975), which raise the cooperativity because they bind only to tetramers. These studies emphasize the fact that the O₂ equilibria are concentration-dependent and that measuring this dependence is essential for establishing physiologically relevant data.

Bårdgard et al. (1997) have recently made very careful measurements of O₂ binding and aggregation of the adult Hb from the European frog Rana temporaria. A single component accounts for 80–90% of the Hb. This Hb associates upon deoxygenation and the O₂ equilibria are strongly concentration-dependent, as with the Hb of the bullfrog. They obtained data up to a of 760 mmHg and estimated full saturation by extrapolation. The maximal values of the Hill coefficient, n_H, never exceeded 3.0 even at very high Hb concentrations. The data were analyzed in terms of the two-state Monod–Wyman–Changeux model. Deoxygenation-dependent tetramer–tetramer association suggests, however, that the number of states required to describe the system is likely to be greater than two.

Blood and Hbs of two species of garter snake Thamnophis sp. have been reported to bind O₂ with high cooperativity, with n_H>4 (Berner and Ingermann, 1988; Sode, 1991). Could this finding have resulted from their use of air to achieve full saturation? If their reports of n_H values of approximately 5 reflect the true properties of the oxygen equilibrium, then close to full saturation could be reached with air; if it is wholly an artifact, then full saturation would not have been reached. The analysis given for chicken Hb is applicable here (see Fig. 3). The Sode data show a Hill coefficient ratio (n_upper/n_lower) of approximately 4 for whole blood. Comparison with the simulation in Fig. 3 suggests that the whole-blood data do reflect the presence of supercooperativity that disappears upon hemolysis. This difference is not clearly evident in the data of Berner and Ingermann (1988), where the rise in n_H with oxygenation is only slightly greater than that shown in the simulations in Fig. 4. We conclude that supercooperativity may be present in whole snake blood, but its presence in Hb solutions is uncertain.

Extensive studies by Focesi and associates on the Hb of the Brazilian water snake Liophis miliaris are of particular interest here because oxygenation is accompanied by a large increase in the tetramer to dimer dissociation constant in the presence but not in the absence of ATP (Matsuura et al. 1987; Focesi et al. 1990). The deoxy Hb is an equilibrium mixture of dimers and tetramers in the absence of ATP. These data indicate that ATP shifts the equilibrium to mostly tetramers because it binds only to them. Cooperativity of O₂ binding is low (n_H≈1.0–1.2) in the absence of ATP, but in its presence cooperativity is pronounced (n_H≈1.9–2.0). Amino acid sequence analysis (Matsuura et al. 1989) indicates that the α1β2 dimer–dimer contacts are weakened by two β chain substitutions which eliminate two electrostatic interactions: Glu(G3)→Val and Glu(CD2)→Thr.

Many tetrameric turtle Hbs dissociate readily not only to dimers but also to monomers with dilution (Sullivan and Riggs, 1967; Reischl et al. 1984). An example of the concentration-dependence of the molecular mass is shown in Fig. 6. Hill plots of oxygen binding data are biphasic, with n_H increasing from 1.8 to 2.8. This shift must reflect the pronounced dissociation properties shown in Fig. 6, but it may also include a contribution from incomplete oxygenation. The quantitative linkage between dissociation and oxygenation has not yet been investigated.

This brief survey attempts to answer the two questions asked in the Introduction: how widespread is the Scapharca mechanism among non-vertebrate Hbs, and how important are tetramer–tetramer interactions in vertebrate Hbs? The conclusion is reached that the Scapharca mechanism may be the predominant process in invertebrate Hbs. Surprisingly, it may also occur in a primitive vertebrate, the lamprey. Thus, lamprey Hb may be considered as an invertebrate Hb in a vertebrate.

Ligand-linked subunit dissociation/association processes occur in many diverse Hbs. Although, mammalian Hbs usually dissociate only to dimers, Hbs of numerous lower vertebrates dissociate to both dimers and monomers. Strong evidence for tetramer–tetramer association of some deoxy Hbs has been presented. The overall linked relationships for a dimer–tetramer–octamer system required for a complete description of chicken Hb are shown in Fig. 7. The Monod–Wyman–Changeux (MWC) two-state model has been used extensively to describe the cooperative processes within the tetramer (from α₂β₂ to α₂β₂X₄ in Fig. 7). Ackers et al. (1992, 1997) have been able to determine the detailed linkage relationships for the dimer–tetramer system in human Hb, but addition of tetramer–tetramer interactions adds a daunting new complexity. However, determination of the weight-average molecular mass as a function of the degree of oxygenation would make the task tractable. The X-ray structure of deoxy chicken Hb will be needed for understanding the process. For some of the systems that exhibit tetramer–tetramer interactions, the gain in cooperativity may well be not to create ‘supercooperativity’ (i.e. Hill coefficients greater than 4), but rather to raise an intrinsically low cooperativity of tetrameric Hbs.

The author is grateful to Yang Qiu and James Knapp for valuable discussions. I thank Russell Isaacks for making available the original data used for the construction of Fig. 3. Current work in the author’s laboratory has been supported by NSF grant MCB-9723825.