pH Dependence of the Adair Constants of Human Hemoglobin NONUNIFORM CONTRIBUTION OF SUCCESSIVE OXYGEN BINDINGS TO THE ALKALINE BOHR EFFECT*

In order to solve the problem of an apparent discrepancy between the pH variance of oxygen equilibrium curve and the linear relation between the number of released Bohr protons and the degree of ligation, precise oxygen equilibrium curves of human hemoglobin were determined at a number of pH values from 6.5 to 8.8. From the equilibrium data individual steps (Adair constants), ki (i equals 1, 2, 3, 4), were obtained and the number of Bohr protons (deltaHi+) released on the ith stage of oxygenation was estimated. The pH dependence of k4 was very small, while the other ks strongly depended on pH over the pH range examined. As a consequence, the contribution of each step of oxygen binding to the alkaline Bohr effect nonuniform: deltaH4 was very small compared with deltaH1+, deltaH2+, and deltaH3+. In spite of this, calcuation has shown that the fractional number of released protons is essentially proportional to fractional oxygen saturation because of cooperative effects in hemoglobin. Thus, the present study indicates that the linear relationship between the fractional number of released protons and the degree of ligation, as obtained from titration experiments, is not necessarily incompatible with the pH variance of the shape of the oxygen equilibrium curve. The nonuniform pH depencence of the Adair constants implies that the two-state allosteric model of Monod, J., Wyman, J., and Changeus, J.P. (1965) J. Mol. Biol. 12, 88-118 is not adequate to describe the heterotropic effect caused by protons.

of partial oxygen pressure, does not change over a wide pH variation (l-5).
The pH invariance of the shape of the oxygen equilibrium curve implied that (a) the four oxygen binding sites of hemoglobin were all equivalent, i.e. the linkages of the four sites to the globin were all the same, (b) the number of released protons was the same for each successive oxygen binding, and (c) the amount of released proton was proportional to oxygen saturation.
Results from titration experiments on horse hemoglobin (6) and human hemoglobin (7) were consistent with the three features above.
Recently Tyuma et al. (8) observed that the shape of the oxygen equilibrium curve for human hemoglobin evidently depends upon pH; the maximal slope of the Hill plot significantly decreases for a change from pH 7.4 to 9.1. These results appear to bc contradictory to the above features since their data suggest that the amount of released proton is not proportional to oxygen saturation.
Therefore, the problem is: to what extent the pH variance of the shape of the oxygen equilibrium curve can be reconciled with the results of the titration experiments.
However, these data cannot be compared directly with the titration data since the change from pH 7.4 to 9.1 is too large to calculate the number of released protons.
In the present study, precise oxygen equilibrium curves of human hemoglobin were determined at values from pH 6.5 to 8.8, the Adair constants were obtained as a function of pH, and the number of released protons was estimated for each stage of oxygen binding.
The analysis indicates that the pH variance of the shape of the equilibrium curve is not necessarily incompatible with the previous titration data. EXPERIMESTAL  Experiments-Oxygen equilibrium curves were determined by the automatic recording method of Imai et al. (9). The spectrophotometer, X-Y recorder, and oxygen electrode employed were a Gary model 118C, a Hewlett-Packard model 7000 AMR, and a Beckman Polarographic Oxygen Sensor (No. 39065), respectively. Experimental conditions were: heme concentration, 60 pM; in 0.1 M potassium phosphate buffer; 20" f 0.1". Oxygen saturation was calculated from the absorbance change at 560 nm. Methemoglobin contents of all the samples used were determined from the ratio of absorbance at 577 nm to that at 500 nm and were less than 4% after oxygen equilibrium experiments.
To obtain equilibrium curves of high precision, previously detailed precautions were used (10). Since hemoglobin was not fully saturated with oxygen even after flushing with pure oxygen, the saturation point was obtained by extrapolation of the AA versus l/p plot, where AA and p were absorbance change and oxygen pressure, respectively (see Fig. 1). This procedure was useful to obtain accurate data at the top of curves since calculated oxygen saturation at the top strongly depends on the position of the saturation point.
Analysis-In this study, we assume that the 01 and @ chains of hemoglobin are equivalent in function, i.e. oxygen randomly combines with these chains at any stage of oxygenation.
The Adair constants, kl, k~, kl, and ka, were obtained by a least squares curve-fitting procedure on 20 experimental points of the oxygen equilibrium curve, as previously described (10). The median oxygen pressure (ll), P,, and maximal slope of the Hill plot, G,,~, were calculated from the Adair constants (10). From the pH dependence of the Adair constants, the number of released Bohr protons was obtained for several pH conditions by using the following relation (6), where AH;+ (i = 1,2,3,4) is the number of Bohr protons released at the ith stage of oxygenation. The total number of Bohr protons released on full oxygenation of hemoglobin is AHt+ = AHI+ + AHz+ + AHz+ + AHd+ (2) or AH*+ = 4 d log (l/P,,,)/d pH (3) since l/P, = i/klklkaka (10). The fractional number of Bohr protons released during oxygenation from Y = 0 to Y = Y, where Y is fractional saturation, was obtained by two methods. In one method, the fractional number, AH t+ was calculated using the following equation where p is the partial oxygen pressure, X is a quantity which infhences the oxygen equilibrium, ai = ktkn . . . ki, and a's = d ai/d X. Letting X be -ln(H+), where a'{ = 0.434 d a,/d pH. Since (a log p/a pH)rdY expresses the number of Bohr protons bound to hemoglobin during oxygenation from Y to Y + d Y (ll), AHt+ is given by where 2 is the right-hand side of Equation 6 and The least squares estimation of & Adair constants and other computations were made using aPDP-10 digital computer and a Calcomp plotter at the Medical School Computer Center, University of Pennsylvania. Fig. 2 presents the Hill plots of oxygen binding by hemoglobin at various pH values. It is evident that the shape of the oxygen equilibrium curve depends on the pH value. It is hardly possible to distinguish the pH variance of the shape in the middle range ' of saturation from 5 to 95y0, 2.e. -1.3 to + 1.3 in the ordinate of the Hill plot, because the pH variance appears at the extreme ends of the oxygen equilibrium curve. Fig. 2 also shows that the lower asymptotes diverge while the upper asymptotes converge, indicating that /cl depends on pH more markedly than kq.

RESULTS
Estimated values of the Adair constants are listed in Table I, which also includes values of P, and nmax. Coefficients of variation for the Adair constants, which were simultaneously estimated during the least squares curve fitting, were about 10, 20, 20, and 10% for kl, kz, kS, and kq, respectively.
The parameters listed in Table I are plotted against pH in Fig. 3. As predicted from Fig. 2, the pH dependence of kq is much smaller than that of kl. The pH dependences of kz and k3 are greater than the pH dependence of kl. Thus, the present study has shown that the Adair constants depend on pH in a nonuniform manner. This is another expression of the pH variance of the shape of oxygen equilibrium curve. The present result is in qualitative agreement with the earlier observation by Tyuma et al. (8) that in the presence of 2,3-diphosphoglycerate, k4 is insensitive to a pH change from 7.4 to 9.1, whereas kl, kz, and ICI are markedly increased on the pH change. As seen in Fig. 3, nmax is also pH-dependent; it becomes smaller as the pH becomes higher than 7.4. This change of nmax is significant, since experience with our automatic oxygenation instrument indicates that the S.E. for nmnx is smaller than 0.1. We are, however, not confident whether or not the nmax significantly depends on pH below 7.4.  Table I. Some of the data are not presented in this figure in order to avoid overcrowding. From the pH-dependence plots for log ki and log (l/P,), the numbers of released l3ohr protons were calculated using Equations I to 3, and the result is shown in Fig. 4. Small deviations between AHt+ calculated from Equation 2 and AZ-It+ calculated from Equation 3 result from errors in smoothing the pH-dependence plots of log ki and log (l/P,) and in reading slopes of the smoothed curves in Fig. 3, and this deviation is regarded as insignificant.
The pH dependence of AH,+ is in accordance with the earlier result of Antonini et al. which was obtained from oxygen equilibrium data under similar conditions. (See Fig. 7, curve 2 in Ref. 4. iSote that AHtf is given per heme in that reference.) Fig. 4 clearly shows that the number of released protons is not uniform for each stage of oxygenation. At pH 7.4, for example, contributions of the first, second, and third oxygen bindings to the total proton release are approximately 18, 29, and 50'%, respectively.
This situation changes at other pH values. Over  the pH range covered by the present experiments, the contribution of the fourth oxygen binding is very small, being only 3% of total proton release at pH 7.4. This means that almost all of the Bohr protons are released before the fourth stage of oxygenation.
In Fig. 5, the fractional number of released protons, AHe+, which was calculated using Equation 7, is plotted as a function are fairly good straight lines, indicating that AH t+ is essent,ially proportional to Y. Maximal deviation of the plots from the diagonal line was 0.8% at pH 7.0 and 2.4% at pH 7.9 in terms of the ordinate scale. Since no data on the linearity of AHt+ versus oxygen saturation have been obtained from direct titration experiments, the present results were compared with the linearity data obtained from titration experiments using carboxyhemoglobin (7). This comparison would be meaningful since the Bohr effect is the same, or very nearly so, for oxygen and carbon monoxide (7). Fig. 5 includes experimental points which were obtained by Antonini et al. (7) under similar conditions. Although their experimental points slightly deviate from the present calculated lines, agreement between both of the plots is good if we take into account the difference of experimental conditions such as medium and heme concentration and the possible difference between oxyhemoglobin and carboxyhemoglobin.

DISCUSSION
The present study has shown that the shape of the oxygen equilibrium curve of hemoglobin depends on pH over a wide range of pH values. This finding is due to the improvement of accuracy for determination of oxygen equilibrium curves particularly at the top and bottom of the curve.
In most of the conventional oxygen equilibrium experiments using tonometers and manometers, the range of oxygen saturation covered by experiments has been limited to the middle ranges, in which the Hill plot is approximated by a straight line. It is hardly possible to recognize the pH variance of the shape of the equilibrium curve from those experiments, since the pH variance appears at the extremes of the equilibrium curve. Use of the Hill plot rather than Y versus log p plot is advantageous to distinguish the change of shape of the equilibrium curves since the top and bottom of the curves are expanded in the Hill plot.
The present study rules out the earlier idea of Wyman (2) and Rossi-Fanelli et al. (5) that the four hemes have the same oxygenlinked groups and oxygenation has the same effect on all of them. There is a profound difference among contributions.of successive oxygen bindings to the release of the Bohr protons.
The point is that even a linear relationship between proton release and ligand saturation, unless strictly linear, necessarily implies neither the pH invariance of the shape of the ligand binding curve nor the equivalence of proton binding sites. In fact, the present study has shown that even a virtually linear AHt+ versus Y plot can be reconciled with oxygen equilibrium data which shows the pH variance of the shape of the equilibrium curve and the nonequivalence of oxygen-linked groups. Thus, the present oxygen equilibrium data are not necessarily incompatible with the previous titration data of Antonini et al. (7). Why is it possible, then, that oxygen equilibrium data showing pH dependence of the shape of the equilibrium curve provide virtually linear relationships between proton release and oxygen saturation? This can be attributed reasonably to the cooperative oxygen binding by hemoglobin, i.e. to instability of the intermediate species which appear during oxygenation.
Thus, facilitated successive oxygen bindings make the change of the population of Hb(Oz)4 approximately proportional to oxygen saturation, producing a linear relation between proton release and oxygen saturation.
A major part of the alkaline Bohr effect is contributed by oxygen-linked ionization of the imidazole groups of the COOHterminal histines of the p chains and the a-amino groups of the cy chains (12)(13)(14). This is consistent with the present conclusion that the oxygen-linked groups are nonequivalent for each oxygen binding site. Kilmart,in et al. (15) obtained pK values for these ionizing groups in both the oxy and deoxy forms and estimated contributions of these groups to the alkaline Bohr effect. At this time, it is impossible to assign these groups to particular stages of oxygenation on the basis of the present data, since the present analysis is too simple in the sense that the four oxygen binding sites are treated as equivalent in function.
It is noteworthy, however, that the pH-dependence plots for AHi+, AHz+, and AH3+ in Fig. 4 are similar to calculated pa-dependence plots for valine la, histidine 146p, and unknown alkaline Bohr groups, respectively, which are presented in Fig. 5 of Ref. 15. If we extend the Adair scheme (Equation 1 in Ref. 10) to a generalized case in which the cr and p chains are treated as nonequivalent, ki is equal to (k, + ks)/2, where k, and lea are microscopic oxygen association constants for the (Y chains and p chains, respectively, combining with the first oxygen molecule. If we assume that the first oxygen molecule combines with one of the (Y chains in preference to the p chains (i.e. k, >> ks), as predicted by Perutz (16), kl is approximated by km/2 and then the pHdependence plot for AH I+ will represent the contribution by the valine la, as suggested above. Similar consideration for the other oxygenation stages is not easy since the other ks are related to the microscopic oxygen association constants in more complicated manners.
As a result of the nonuniform pH dependence of the Adair constants, the mechanism of the cooperative oxygen binding seems to be dependent on pH values. Under acidic conditions, there is no substantial enhancement of oxygen affinity during the binding of the first three oxygen molecules, i.e. kl to ka but, this is followed by a large increase in the Adair constant, lea to k4 (see Fig. 3). Under alkaline conditions, the oxygen affinity toward the individual hemes is successively increased.
It may follow that the conformational transition takes place in a concerted manner at lower pH values while in a sequential manner at higher pH values.
The nonuniform pH dependence of the Adair constants throws doubt on the validity of the two-state allosteric model proposed by Monod et al. (17). Parameter estimation by the least squares curve-fitting (10) with the present equilibrium data gave the following values: KR = 8.90 mm Hg-1, Kr = 0.124 mm Kg-', c = 0.0140, and L = 1.5 X lo4 at pH 8.8 and KR = 8.38 mm Hg-l, KT = 0.0145 mm Hg-1, c = 0.00173, and L = 1.2 X IO* at pH 6.5, where KB and KT are oxygen association constants for the R state and 2' state, respectively, c is the ratio KT :KR, and L is the allosteric constant. Evidently, the value of c strongly depends on pH as a result of the nonuniform pH dependence of K&C k4) and KT(e /cl). This is contradictory to the allosteric model since by definition c must remain constant with changes of concentration of the allosteric effector, proton. Thus, the two-state allosteric model is no more adequate to describe the heterotropic effect caused by proton than to describe the heterotropic effect caused by 2,3-diphosphoglycerate (10). As recently pointed out (18), at least three affinity states would be required to consistent,ly describe both the homotropic and heterotropic effects which involve oxygen, proton, and anions.