The Bohr Effect of Hemoglobin Intermediates and the Role of Salt Bridges in the Tertiary/Quaternary Transitions*

Understanding mechanisms in cooperative proteins requires the analysis of the intermediate ligation states. The release of hydrogen ions at the intermediate states of native and chemically modified hemoglobin, known as the Bohr effect, is an indicator of the protein tertiary/quaternary transitions, useful for testing models of cooperativity. The Bohr effects due to ligation of one subunit of a dimer and two subunits across the dimer interface are not additive. The reductions of the Bohr effect due to the chemical modification of a Bohr group of one and two α or β subunits are additive. The Bohr effects of monoliganded chemically modified hemoglobins indicate the additivity of the effects of ligation and chemical modification with the possible exception of ligation and chemical modification of the α subunits. These observations suggest that ligation of a subunit brings about a tertiary structure change of hemoglobin in the T quaternary structure, which breaks some salt bridges, releases hydrogen ions, and is signaled across the dimer interface in such a way that ligation of a second subunit in the adjacent dimer promotes the switch from the T to the R quaternary structure. The rupture of the salt bridges per se does not drive the transition.


Understanding mechanisms in cooperative proteins requires the analysis of the intermediate ligation states.
The release of hydrogen ions at the intermediate states of native and chemically modified hemoglobin, known as the Bohr effect, is an indicator of the protein tertiary/ quaternary transitions, useful for testing models of cooperativity. The Bohr effects due to ligation of one subunit of a dimer and two subunits across the dimer interface are not additive. The reductions of the Bohr effect due to the chemical modification of a Bohr group of one and two ␣ or ␤ subunits are additive. The Bohr effects of monoliganded chemically modified hemoglobins indicate the additivity of the effects of ligation and chemical modification with the possible exception of ligation and chemical modification of the ␣ subunits. These observations suggest that ligation of a subunit brings about a tertiary structure change of hemoglobin in the T quaternary structure, which breaks some salt bridges, releases hydrogen ions, and is signaled across the dimer interface in such a way that ligation of a second subunit in the adjacent dimer promotes the switch from the T to the R quaternary structure. The rupture of the salt bridges per se does not drive the transition.
A vast amount of data on the structure/function of human hemoglobin in solution apparently supports the mechanism of a concerted transition between two quaternary structural states in the course of ligand binding, in agreement with the Monod-Wyman-Changeaux model (1). Due to cooperativity, the end states largely prevail on species in a partial state of ligation under equilibrium conditions, masking the functional properties of the intermediate species. This is demonstrated by the close agreement between the isotherms of CO binding calculated from the experimental distributions of the CO ligation intermediates according to the Monod-Wyman-Changeaux model and the alternative Koshland-Nemethy-Filmer model, which assumes transitions through intermediate structural/ functional states (2), as shown by Perrella and Di Cera (3). The functional/structural studies of the intermediates still provide the most critical test for any model of cooperativity. Such studies are difficult because of the high rates of the dissociation and association reactions of the physiological ligand, the com-plexity of the intermediate ligation states Fig. 1, and the instability of tetrameric hemoglobin. The partially liganded hemoglobin tetramers reversibly dissociate into dimers faster than the rate of resolution of the separation techniques (4), and dimer rearrangement reactions occur under nonequilibrium conditions, as depicted in Fig. 2. In a previous study of the Bohr effect of the intermediate ligation states (5), the problem of the ligand mobility was circumvented by using cyanide bound to the ferric subunits to mimic ligation and a cryogenic technique to determine the proportion of any asymmetrical hybrid species in equilibrium with the respective symmetrical parental species (6). This information was needed to calculate the contribution of each species from the total Bohr effect of a mixture of hybrid and parental species. The study of the pH dependence of the Bohr effects of the mono-and diliganded intermediates revealed the absence of additivity of the effects, an important clue to the mechanism of tertiary/quaternary transitions in ligand binding to hemoglobin. However, the discovery by Shibayama et al. (7) that the cyanomet intermediates undergo valency exchange has made such studies questionable. We have now repeated the measurement of the Bohr effect of the mono-and some diliganded species under conditions of slight or negligible valency exchange, confirming the results of the previous study.
Using the same technical approach we have measured the decrease in Bohr hydrogen ions in hemoglobin derivatives in which either one or both Bohr groups of the ␣ and ␤ subunits of deoxy hemoglobin and of the deoxy/cyanomet intermediates were chemically modified by carbamoylation (8) and by the NEM 1 reaction of cysteine F␤93 (9). We found that the functional effects of the single and double chemical modifications were additive, as were the combined effects of ligation and chemical modification, with just one possible exception. These findings help define the role of the salt bridges with regard to the stabilization of the hemoglobin T quaternary structure, which was described by Perutz in his stereochemical mechanism of cooperativity (10).

MATERIALS AND METHODS
Hemoglobin Purification-HbA 0 was obtained from normal adult blood and HbS from heterozygous donors. The hemoglobins were purified by ion exchange chromatography on CM-52 cellulose, as previously described (5), equilibrated with 0.2 M KCl, and stored in liquid nitrogen at a concentration of 6 mM in heme.
Preparation of NES Hemoglobin-Samples (4.5 g) of HbO 2 were reacted with a 5-fold excess of NEM at 4°C and pH 7.3 for 2 h (11). The reactants were gel-filtered on Sephadex G-25 equilibrated with 5 mM potassium phosphate, 0.5 mM Na 2 EDTA, pH 6.8, and loaded onto a column (8 ϫ 27 cm) of CM-52-cellulose equilibrated with the same buffer. Elution with 7.5 mM potassium phosphate, 0.5 mM Na 2 EDTA, pH 7.3, at 300 ml/h was continued until a good resolution of NES Hb was achieved. The resin-bound derivative was collected and eluted in a batch procedure with 20 mM Tris-HCl, 50 mM KCl, pH 7.5. Titration with p-chloromercurybenzoate was carried out to check for the absence of free thiol groups in the product (11).
Preparation of Hemoglobin Carbamoylated at the ␣-Amino Groups of the ␣ Subunits, (␣ C ␤)(␣ C ␤)-Hb samples (4.5 g) were reacted anaerobically at 20°for 1 h with a 50-fold molar excess of KCNO in the presence of a 10 mM excess of inositol hexaphosphate at pH 6.5. The carbamoylation reaction was stopped by anaerobic gel filtration of the protein at pH 6.5, and the excess inositol hexaphosphate was removed by aerobic gel filtration using 50 mM potassium phosphate, pH 8 (12). Most of the protein carbamoylated at the ⑀-amino groups of the lysines was removed by ion exchange chromatography on a DEAE-cellulose column (8 ϫ 30 cm) equilibrated with 50 mM Tris-HCl, pH 8.1, using a pH gradient of the same buffer (pH 8.1 3 7.6). Finally (␣ C ␤)(␣ C ␤) was purified by chromatography on a CM-52 column as for the purification of HbA 0 . The product obtained by this method had the same chromatographic properties as the carbamoylated hemoglobin prepared by the procedure of Williams et al. (13) and the same isoelectric point as the ␣ chain carbamoylated hemoglobin prepared by the chain separation and recombination method (8,14).
Hemoglobin Incubations-HbO 2 solutions were deoxygenated by N 2 tonometry and transferred into thermostatted vials for the anaerobic incubation at 20°C using a flow of humidified N 2 . The Hb stability over 60-h periods was checked by measuring the spectra of undiluted oxygenated samples using a 0.2-mm optical path flow cell. When the amount of Hb ϩ raised above the initial value of 2-3% because of the presence of O 2 traces in the gas flow, N 2 was purged through an alkaline solution of sodium pyrogallate. The same procedure was used for the anaerobic incubation of solutions containing CNHb. The excess of cyanide (5 mM) added to the solutions was enough to compensate for the cyanide loss due to evaporation (5). The absence of free Hb ϩ due to cyanide evaporation was checked routinely by measuring the spectra of the oxygenated solutions after incubation. Alternatively, to keep the cyanide concentration during long incubations of the solutions constant, N 2 was flown over a 5 mM solution of cyanide before reaching the incubation vial. Oxygen scavenging enzymes, catalase and superoxide dismutase, were not used.
Measurement of the BE-Samples (1 ml) of 6 mM Hb were transferred into an anaerobic vessel thermostatted at 20°for pH measurement. The solution was exposed to O 2 and the pH was titrated back to the value of the anaerobic sample using carbonate-free 20 mM NaOH (15).
BE of the Singly Modified Hemoglobins-Hemoglobin species chemically modified at a Bohr group of one ␣ or one ␤ subunit cannot be studied in a pure form. Because of the tetramer dissociation reaction, they disproportionate into the parental species, i.e. unmodified and doubly modified hemoglobin, as shown in Fig. 2. The BE of the singly modified species was measured by the same approach used to study the asymmetrical deoxy/cyanomet analogs of the intermediates (5). Since HbS differs from HbA 0 for the surface charge but is otherwise functionally equivalent, a one to one mixture of two parent species, e.g. HbS and NES HbA 0 , was incubated anaerobically until the equilibrium with the asymmetrical species modified by NEM at just one ␤ subunit was reached. The total BE of the mixture was measured, and the contributions to the BE of the fractions of HbS and NES HbA 0 at equilibrium were subtracted from the total. The fractions of the three species at equilibrium were measured using a cryogenic separation method, as follows. A sample of the anaerobic mixture was quenched into a hydroorganic solvent at Ϫ30°C to stop the tetramer dissociation reactions, the mixture was resolved by cryofocusing at Ϫ25°C, and the three fractions were assayed by the pyridine hemochromogen method (16). The data on the rate of equilibration at 20°C in 0.2 M KCl, pH 7, of an equimolar mixture of HbS and (␣ C ␤)(␣ C ␤) plotted in Fig. 3

indicate that equilibrium was reached after a 20-h incubation.
Valency Exchange Controls-Valency exchange was measured by a procedure similar to that used by Shibayama et al. (7). At the end of each anaerobic incubation of mixtures of deoxy-HbS and cyanomet HbA 0 , (␣ ϩCNϪ ␤)(␣ ϩCNϪ ␤) or (␣ ␤ ϩCNϪ )(␣ ␤ ϩCNϪ ) valency exchange was stopped by exposure to O 2 , and the two hemoglobin species, oxy/cyanomet HbS and oxy/cyanomet HbA 0 , were separated by ion exchange chromatography using small CM-52 columns equilibrated with buffer containing cyanide. The proportion of oxy versus cyanomet hemoglobin in each separated fraction, determined by a spectral analysis of the samples in the 450 -600-nm range, yielded the amount of valency exchange. The proportions of each component were obtained by fitting the spectra of the mixtures with the spectra of pure HbO 2 , CNHb, and Hb ϩ using a Matlab 5.3 program. The error was 1-2% of the total. Similar spectral analyses of the undiluted oxygenated samples before chromatography allowed a check for the absence of free Hb ϩ due to cyanide evaporation and for any increase in the total CNHb concentration due to Hb oxidation by O 2 leaking in during the anaerobic incubations.
BE of the Deoxy/Cyanomet Analogs of the Intermediates-In the The dashed lines indicate the ␣ 1 ␤ 2 and ␣ 2 ␤ 1 contacts that dissociate under physiological conditions. Symmetrical tetramers dissociate into identical dimers that re-associate to yield the original tetramer. These species can be studied in a pure form. Asymmetrical tetramers dissociate into different dimers that re-associate, yielding two symmetrical parental species in addition to the asymmetrical species. absence of valency exchange, the anaerobic incubation of HbA 0 and species (␣ ϩCNϪ ␤)(␣ ϩCNϪ ␤) or (␣ ␤ ϩCNϪ )(␣ ␤ ϩCNϪ ) should yield the monoliganded intermediates 11 or 12, respectively (Fig. 1). As shown in Fig.  3, the incubation for 3 h at neutral pH of a 1 to 1 mixture of HbS and species (␣ ϩCNϪ ␤)(␣ ϩCNϪ ␤) or (␣ ␤ ϩCNϪ )(␣ ␤ ϩCNϪ ) yielded an amount of hybrid comparable with that observed by incubating under the same conditions HbS and (␣ C ␤)(␣ C ␤). The proportion of hybrid was approximately that predicted by the kinetics of the Hb tetramer-dimer reactions (4). A higher proportion of hybrid was obtained when the mixture was pre-incubated under aerobic conditions before deoxygenation (1/2 h) and anaerobic incubation (2 h). Under these conditions the valency exchange was negligible at neutral or alkaline pH and slight (Յ5%) at the most acidic pH values. 2 The valency exchange, proportion of hybrid, and BE were measured using the same anaerobic mixtures.
Data Analysis-The concentration of hydrogen ions released per tetramer of asymmetrical hybrid in mixture with the parental species was calculated as follows.
where subscripts refer to the hybrid, parental species 1 and 2, and their mixture with the hybrid, and f is the fraction of the three species determined by the cryogenic technique. The calculations were carried out on the individual data points or using polynomials fitting the data points. Hence the results presented in the form of bands are calculated interpolations of the original data. The amplitude of the band indicates the error. The difference between the total Bohr hydrogen ions released by HbA 0 and the residual Bohr hydrogen ions released by the chemically modified hemoglobins represents the hydrogen ions lost because of the chemical modification. Similarly the difference between the total Bohr hydrogen ions released by HbA 0 and the residual Bohr hydrogen ions released by the vacant sites of the liganded species represents the putative hydrogen ions released in the change of the subunit state from deoxy to cyanomet. In such a case the difference is defined as the BE of the ligation intermediate (5).

BE of the Deoxy/Cyanomet-diliganded Intermediates 23 and 24 and Monoliganded
Intermediates 11 and 12-The BE of species 23 and 24 measured after 3 h of anaerobic incubation are compared in Fig. 4, a-b, with the values previously obtained immediately after deoxygenation of the oxygenated species (5). Valency exchange controls were not carried out, but the close agreement with the previous data suggests that the exchange had only minor effects during a 3-h incubation.
The data on the BE of the hybrid monoliganded intermediates, compared in Fig. 4, c-d, with the previously published data (5), were calculated from the titration data of the ternary mixtures of parental species, HbS plus species 23 or 24, and hybrid species incubated under anaerobic conditions for 2 h after deoxygenation (data not shown) and the fractional values of the concentration of hybrid in the mixtures, shown in the inset of Fig. 3. Valency exchange controls carried out at the end of each anaerobic incubation showed negligible exchange at neutral or alkaline pH and a slight exchange (Յ5%) at acidic pH. 2 Such controls carried out after longer periods of incubation (up to 48 h), as in our previous studies (5), indicated a high proportion of valency exchange. 2 The data in Fig. 3 indicate that a high proportion of hybrid was attained after 2-3 h, although not yet at equilibrium. In contrast, the rate of hybridization between HbS and CNHbA 0 , yielding intermediate 21 is slower (17), and valency exchange controls under these conditions indicated a high proportion of exchange, in agreement with the measurements of Shibayama et al. (7). Therefore we could not confirm the data previously published on the BE of species 21 (5). The apparent agreement between the data on the BE of the monoliganded species obtained in the present study under conditions of low valency exchange and the previous data obtained under conditions of extensive valency exchange (5) has two possible explanations. It could be an artifact of the calculation of the BE of the monoliganded species from the total BE of the mixture of monoliganded and parental species. In the previous work, ignoring the valency exchange, it was assumed that only three species were present. Alternatively, it could be due to the mechanism of the exchange reactions. The method of Shibayama et al. (7) measures the global valency exchange but does not provide information on which species are generated in the exchange process.
The curves of the BE in Fig. 4, a-b, and Fig. 4, c-d, are the functional responses of different structures. The bell-shaped curve of the hemoglobin alkaline BE yields the hydrogen ions released in the transition from the T to the R structure due to oxygenation. The bell-shaped curves of the monoliganded intermediates (Fig. 4, c-d) are indicative of the functional effect of a tertiary structural change occurring in the T quaternary structure due to ligation of a subunit. In Fig. 4, c-d, the BE of the vacant sites of the intermediates is measured by the difference between the total BE of Hb and the BE of the monoliganded intermediate. It is clear that these vacant sites released hydrogen ions on oxygenation at all pH values except where the alkaline BE of Hb itself vanishes. The sigmoidal shape of the curves of the BE of the diliganded intermediates (Fig. 4, a-b) are not equal to the sum of the bell-shaped curves of the two monoliganded intermediates, indicating a profound interaction between the ligation sites. The vacant sites of the diliganded intermediates did not release hydrogen ions upon oxygenation at pH values at which the BE of Hb is still significant, Fig. 4, a-b. This is the response of a molecule in the R quaternary structure in which all salt bridges are broken, as described by Perutz (10) Fig. 5a. a, species (␣ ϩCNϪ ␤)(␣ ϩCNϪ ␤). The new data were obtained at 3 h of anaerobic incubation after deoxygenation (1/2 h); the previous data were obtained after deoxygenation. b, species (␣␤ ϩCNϪ )(␣␤ ϩCNϪ ). The new data were obtained at 3 h of anaerobic incubation after deoxygenation; the previous data had no incubation. c, species (␣ ϩCNϪ ␤)(␣␤). The new data were obtained by mixing the oxygenated parental species, 1/2 h of deoxygenation, and 2 h of anaerobic incubation of the mixture; the previous data were obtained after 20 -40 h of anaerobic incubation. d, species (␣␤ ϩCNϪ )(␣␤). The new data were obtained at 2 h of anaerobic incubation after deoxygenation; the previous data were obtained after 20 -40 h of anaerobic incubation after deoxygenation.
comparable or even less than the amount released by the three vacant sites in the monoliganded species. If the quaternary structures of these diliganded species were in T/R equilibrium, the molecules in T structure should have an additive BE twice as large as the BE of the monoliganded species, and the molecules in R structure should have a BE similar to that observed at alkaline pH. Such a hypothesis is not consistent with the experimental data. Instead the sigmoidal curve of the diliganded intermediates is consistent with the hypothesis that the quaternary structures of diliganded species 23 and 24 have switched to the R conformation at all pH values. The hydrogen ions released on oxygenation by the unliganded subunits of these species would then be the functional effects of tertiary structure changes modulated by pH. It is not known whether such effects are associated with the R2 structure discovered in studying the crystals of carboxy hemoglobin crystallized under low salt (0.1 M Cl Ϫ ) and acidic (pH 5.8) conditions (18). However, the crystallographic studies indicate the possible existence of alternative R quaternary structures.
Our interpretation of the correlation between the observed functional effects of mono-and diligation and the tertiary/ quaternary structures of the protein is consistent with the interpretation of the energetics of the same species provided by Ackers et al. (19). The cooperative free energy of ligand binding, ⌬G C , can be measured from the difference between the free energy changes for the dimer-tetramer assembly of ligation intermediate ij and Hb, assumed as the reference state, ⌬G C (01 3 ij) ϭ ⌬G ij Ϫ ⌬G 01 (20). At neutral pH the ⌬G C value for the first ligation step in the deoxy/cyanomet analogs is 50% of the value for the transition to CNHb (4). A similar value was calculated from the distributions of the CO ligation intermediates reported by Perrella et al. (6,21) under similar conditions. At alkaline pH the ⌬G C values remain intermediate (22). The observation of an intermediate ⌬G C value for the first ligation step is consistent with a two state concerted model (23) and has been interpreted as the energy of destabilization of the T quaternary structure due to the binding of one ligand (19). In contrast, the ⌬G C values for the symmetrical diliganded intermediates are the same as for the transition to CNHb in the range from neutral to alkaline pH. This indicates that these species are in the R quaternary structure under these conditions and that ⌬G C is not significantly modulated by the effects of pH on the tertiary structure of the unliganded subunits. Such effects were observed in our functional studies since the curve of BE versus pH was sigmoidal in shape (Fig. 4). Sigmoidal curves of the BE were also observed in the study of the triply liganded intermediates (5). The present study is partly consistent with the symmetry rule model for hemoglobin cooperativity proposed by Ackers et al. (19). Important features of this model are the energetic and other functional properties of the diliganded intermediate 21 (Fig. 1), which have been re-cently confirmed to be different from those of the diliganded species 22, 23, and 24 (24). As discussed above, the low rate of formation of intermediate 21 from the parental species Hb and CNHb together with the high rate of valency exchange have precluded our study of the BE of this key intermediate.
BE of (␣ C ␤)(␣ C ␤) and NES HbA 0 -The experimental values of the hydrogen ions released on oxygenation per tetramer of HbA 0 and its doubly modified derivatives at 20°C in 0.2 M KCl in the pH range of the alkaline BE are shown in Fig. 5, a-c.
The NEM reaction of Cys␤93 causes a modification of the tertiary structure of the ␤ subunit that disrupts a network of salt bridges at the ␣ 1 ␤ 2 interface with the participation of His␤146, as observed in the Hb crystal structure (9, 10). Carbamoylation of Val1␣ breaks a chloride ion-mediated salt bridge within the structure of the ␣ subunit (25,26). The data in Fig. 5, a-c, indicate that the chemical modification reduced significantly the BE in each derivative, in qualitative agreement with the values at physiological pH reported by several authors (8,9). The loss of Bohr hydrogen ions observed in NES HbA 0 , i.e. the difference between the BE of native and chemically modified hemoglobin, in a range of pH values is compared in Fig. 6a with the differential titration curve of His146␤, assuming the values pK deoxy ϭ 8.1 and pK oxy ϭ 7.2 (27). The loss of Bohr hydrogen ions in (␣ C ␤)(␣ C ␤) is compared in Fig. 6b with the differential titration curve of Val1␣, assuming the values pK deoxy ϭ 8.0 and pK oxy ϭ 7.25 (28). Also shown in Fig.  6b is the differential titration curve corrected on the assumption that carbamoylation of Val1␣ perturbs His122␣ (26). The differential titration curve of His122␣ required for the correction was calculated assuming the values pK deoxy ϭ 6.1 and pK oxy ϭ 6.6 (29). The simulations in Fig. 6, a and b, indicate the strict correlation between the rupture of the salt bridges inferred from the crystal structures of deoxy and oxy hemoglobin and the functional effects we have measured in the chemically modified protein.
BE of the Mixtures of Parental Species, HbS plus (␣ C ␤)(␣ C ␤) and HbS plus NES HbA 0 , and Hybrid Species-The experimental titration data are shown in Fig. 7, a-b. The fractions of BE due to the hybrid species (not shown) were calculated from the data in Fig. 7, a-b, using the values of the fraction of hybrid species in the mixture shown in Fig. 7, c-d.
BE Loss in the Doubly and Singly Chemically Modified Hemoglobins-The Bohr hydrogen ions lost in NES HbA 0 and (␣ C ␤)(␣ C ␤) (Fig. 6, a-b) are compared in Fig. 8, a-b, with those lost in the singly modified derivatives calculated from the data in Fig. 7. Within the experimental error, the effects on function of both types of chemical modification were additive. The additivity observed in this study of the NEM-modified hemoglobins parallels the additivity observed in the study of the energetics of the same species by Ackers and co-workers (30 -32). The modification by NEM of the Bohr group on 1 ␤ subunit results in a 1.4-kcal/mol increase in free energy for the dimertetramer assembly, one-half the amount observed with a double modification (31,32), indicating that the two sites are independent of one another with regard to their effect on function despite the destabilization of the quaternary structure brought about by the chemical modification. A measure of such a destabilization is obtained by comparing the change in free energy from Hb to NES Hb, 2.8 kcal/mol, with the free energy change of 5.8 kcal/mol for the transition from Hb to NES HbO 2 (32).
BE of the Chemically Modified Deoxy/Cyanomet-monoliganded Intermediates- Fig. 9, a-d, shows the BE of intermediates (␣␤ ϩCNϪ )(␣ C ␤), (␣␤ ϩCNϪ )(␣␤ NEM ), (␣ ϩCNϪ ␤)(␣␤ NEM ), and (␣ ϩCNϪ ␤)(␣ C ␤). The fraction of hybrid and parental species were determined by the cryogenic technique using mixtures of HbS and species 23 and 24 carbamoylated at the ␣-amino groups of the ␣ subunits or NES HbS (data not shown). The putative hydrogen ions released upon ligation of one ␣ or ␤ subunit in a dimer and the Bohr hydrogen ions lost because of the chemical modification of one ␣ or ␤ subunit in the adjacent dimer were in most cases roughly additive, as shown in Fig. 9, a-c. This indicates that the signal of ligand binding is not mediated by a tertiary structural change in the adjacent subunits involving the rupture of a salt bridge. A possible exception was species (␣ ϩCNϪ ␤)(␣ C ␤) (Fig. 9d). The BE of this species, i.e. the difference between the total BE of hemoglobin and the residual BE of its vacant, normal and chemically modified sites (shaded area in Fig. 9d) was significantly greater than the sum of the BE of the mono-liganded species and the hydrogen ions lost because of the chemical modification of one ␣ subunit (continuous line in Fig. 9d).
Role of the Salt Bridges in the Ternary/Quaternary Transitions-From the above information we can draw the following overall picture of the tertiary and quaternary transitions in the process of hemoglobin ligation. Hydrogen ions are released upon ligation of a subunit because ligation perturbs the tertiary structure of the ligated subunit in such a way as to break some salt bridge and/or hydrogen bond in agreement with the Perutz stereochemical mechanism (10). However, ligation is also signaled to the neighboring subunits, since a second ligation step promotes a dramatic change from the T to the R structure, as monitored by the different characteristics and nonadditivity of the BE of the mono-and diliganded interme-FIG. 6. BE of chemically modified HbA 0 . a, experimental data on the hydrogen ions lost by NES HbA 0 (shaded band) compared with the theoretical curve calculated assuming, for His146␤, pK deoxy ϭ 8.1 and pK oxy ϭ 7.2 (27) (solid line). b, experimental data on the hydrogen ions lost by (␣ C ␤)(␣ C ␤) (shaded band) compared with the theoretical curve calculated assuming, for Val1␣, pK deoxy ϭ 8.0 and pK oxy ϭ 7.25 (28) (solid line) and, in addition to the same pK values for Val1␣, pK deoxy ϭ 6.1 and pK oxy ϭ 6.6 for His122␣ (29) (broken line). diates (Fig. 4, a and b and Fig. 4, c and d) and by the energetics of the dimer-tetramer reaction of these species (22). The structural basis for the inter-subunit communication remains to be discovered. The data in Fig. 9d suggest a mechanism by which ligation of an ␣ subunit brings about a change in the tertiary structure of a neighboring ␣ subunit involving the perturbation of a Bohr group. Such a tertiary structural change may also bring about an increase in the ligand affinity of the ␣ subunit. However, this mechanism does not appear to be the general case, as shown in Fig. 9, a-c.
The rupture of a salt bridge, as it occurs in the chemically modified hemoglobins, perturbs the tertiary structure of the subunit, causing a destabilization of the T structure that is not signaled to the other subunits via a T to R transition. This is demonstrated by the finding that two different functional effects of hemoglobin chemically modified by NEM, i.e. the loss of Bohr hydrogen ions (Fig. 8) and the change in energy for the dimer-tetramer assembly reaction (31,32), have the additivity property. Our observations are also consistent with the observation reported by Bettati and Mozzarelli (33) that silica gel-entrapped Hb retains a T structure while binding oxygen with an apparently normal BE.  The experimental data are compared with the theoretical curves calculated by adding to the BE of the monoliganded intermediates (data in Fig. 4, c-d) the Bohr hydrogen ions lost because of the single chemical modification (data in Fig. 8 without error indication). a, experimental data for species (␣␤ ϩCNϪ )(␣ C ␤) and calculated curve for species (␣␤ ϩCNϪ )(␣␤) plus (␣ C ␤)(␣␤); b, experimental data for species (␣ ␤ ϩCNϪ )(␣␤ NEM ) and calculated curve for species (␣␤ ϩCNϪ )(␣␤) plus (␣␤)(␣␤ NEM ). c, experimental data for species (␣ ϩCNϪ ␤)(␣␤ NEM ) and calculated curve for species (␣ ϩCNϪ ␤)(␣␤) plus (␣␤)(␣␤ NEM ). d, experimental data for species (␣ ϩCNϪ ␤)(␣ C ␤) and calculated curve for species (␣ ϩCNϪ ␤)(␣␤) plus (␣ C ␤)(␣␤).