THE JOURNAL OF BIOLOGICAL CHEMISTRY Vol. 242, No. 5, Issue of March IO, PP. 784-792, 1967

Printed in U.S.A.

The Effect of Temperature on the Oxygen-linked

Ionizations of Hemoglobin*

(Received for publication, April 25, 1966)

L. ROSSI-BERNARDIS AND F. J. W. ROUGHTON

From the Faculty of Agriculture, Istituto di Chimica Organica, University of Milan, Milan, Italy, and the Department of Colloid Xcience, University of Cambridge, Cambridge, En,gland

SUMMARY cal, but this figure is subject to a wide margin of uncertainty,

On the assumption that only two of the acid groups per owing to the difficulty in obtaining accurate estimates of

heme are affected by oxygenation, the difference in electrical pK’o and PK’~ from data in the acid pH range, wherein

charge, A8, between oxygenated and deoxygenated hemo- hemoglobin is unstable. Preliminary experiments have

globin (OzHb and Hb) at the same pH (as determined from shown that at pH below 6.2 “rapid” titration figures (i.e.

the difference in their titration curves) is given by the equa- within 10 msec) differ significantly from the results obtained

tion by the customary slow titration procedure, which takes several minutes.

A8 = Ko Kb KR Kk -++---- The results of this paper are discussed in light of current

Ko + h Ko + h KR + h KR + h views on the chemical and x-ray structure of 0,Hb and Hb.

where h = hydrogen ion concentration and K,, Klo, KR, and K', are the ionization constants of these “Bohr groups” in OzHb and Hb, respectively.

The above equation has been found to fit (within the limits of experimental error) the data on the “difference” titration During the past 3 years we have been in part engaged in a curves for bovine, human, and horse O,Hb and Hb over the study of the titration curves of oxyhemoglobin (OJIb) and pH range 5.0 to 9.3 at 25-37 ‘* “best” (i.e. least mean square) , deoxyhemoglobin (Hb) in the presence of various constant pres- values of the ionization constants have been estimated sures of carbon dioxide (1, 2). Most of our work has been done statistically by means of an automatic computer program, on human and bovine hemoglobin, since it is only in the case of written in Fortran language. Thus, for human hemoglobin

7.84 (ztO.O06), pKo = 6.84 (&0.009), these two species that data exist as to the direct combination of

at 25’, pKR = reduced hemoglobin and oxyhemoglobin with COZ in the car- pK’a = 5.13 (f0.04), and pK’, = 5.60 (~0.03). These bamino form (3-5). In the course of our recent work it was figures differ by up to 0.7 pK unit from those obtained by necessary to compare the titration curves of oxyhemoglobin and other recent workers, who did not, however, analyze their deoxyhemoglobin at physiological pressures of COZ (40 to 60 data statistically.

Values for the corresponding heats of ionization, Qo, Qo, mm of Hg) with their titration curves at zero CO2 pressure, at

QR, and QIE, have been calculated from the effect of tem- temperatures ranging from 15” to 37”. A detailed study of the results on human and bovine hemoglobin (6), at zero CO2 pres-

perature on the respective ionization constants. The most accurate results have been obtained in the case of human

sure, showed significant discrepancies from the earlier work (and

hemoglobin, wherein it is found that (QE - Qo) is 5,000 ideas) of Wyman and his colleagues on the effect of temperature on the titration curves of oxyhemoglobin and deoxyhemoglobin

(&300) cal. The actual value of QR is of the order of 11,000 and on the heats of ionization of their oxygen-linked acid groups. cal and thus lies outside the usual range for the heat of ionization of imidazole and its derivatives. These conclu-

On turning, however, to horse hemoglobin, which was the species

sions are based upon the experimental data not only of the used by Wyman in his pioneer studies over 25 years ago (for

present paper but also of the recent paper (11) of Antonini, summary see Reference 7), it was noticed that the discrepancies were distinctly smaller.

Wyman, Brunori, Fronticelli, Bucci, and Rossi-Fanelli, the concordance between these two independent sets of results, when statistically analyzed, being very satisfactory.

(Q’. - Q’R) has also been found to be of the order of 5000

NOTATION

* This research has been supported by the United States Air Force under Grant AF 61(052)-771, European Office of Aerospace Research.

$ North Atlantic Treaty Organization Research Fellow, 1961 to 1964.

As in the adjoining paper (8), we denote by H’.Hb.H the reduced hemoglobin species in which both oxygen-linked acid groups are un-ionized. Hb .H is the species in which the more acid of the oxygen-linked groups is ionized but the more alkaline oxygen-linked group is un-ionized, and vice versa for H’.Hb (which, however, can only be present in relatively minute

784

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Issue of March 10, 1967 Rossi-Bernardi and Roughton 785

amounts). Finally, Hb is the species in which both oxygen- linked groups are ionized. H’.OsHb.H, OzHb.H, H’.O?Rb, and OzHb are the symbols for the corresponding species in the case of oxyhemoglobin. KrR, Klo, Ko, and KR are the ioniza- tion constants of the respective species H’oHb, H’.OzHb, OzHb .H, and Hb .H; &In, Q’o, Qo, and QR are the corresponding heats of ionization. The symbols K. and KR were used by Henderson (9) and other earlier writers who were aware of only the more alkaline oxygen-linked acid group in hemoglobin. It has seemed to us simpler to retain this notation, and to introduce the symbols K’o and KIR for the more acid oxygen-linked group subsequently discovered by Wyman, rather than to adopt his symbols, viz. pKi(nb) (for our PK’~), pK1(nbo2) (for our pK’o), pKz(nb) (for our pKR), and pK2(nbo2) (for our pKo). The symbols Qo, etc., are used in place of the conventional symbols AHe, etc., in order to avoid confusion with changes in hydrogen ion concentration.

DIFFERENTIAL TITRATION OF OXYHEMOGLOBIN AND REDUCED

HEMOGLOBIN

On the assumption (7) that only two of the acid groups per heme are affected by oxygenation but that all the other acid groups in reduced hemoglobin and oxyhemoglobin are “oxy- stable,” the difference in negative charge per heme, Ax, between oxyhemoglobin and reduced hemoglobin at the same pH, as determined from the difference in their titration curves, is given

by

Ko K:, I

Ax = ~ KR KR

Ko + h +Kb+h----

KR + h KR + h (1)

where h is the hydrogen ion activity. Equation 1 also assumes implicitly that there is no significant

difference between Hb and OsHb in their binding of ions, other than protons, e.g. K+ or Cl-. This may be true only at pH values above the isoionic point, where, indeed, both proteins appear to bind little if any K+ or Cl-.

Values for Ko, K’o, KR, and K’R have been calculated from the experimental values of Ax over the pH range 5.0 to 9.5, on the basis of Equation 1. Table I gives the corresponding values of PK’~, etc., for human and horse hemoglobin at ZO”, (a) as postulated by Wyman and Antonini et al. prior to 1964 (7, 10) and (b) as modified by Antonini et al. (11) in the light of their recent titration curve data over the range 10-40”, the securing of which was stimulated by the discrepancies, especially in regard to human and bovine hemoglobin, to which attention had been drawn a year earlier by Rossi, Chipperfield, and Roughton (6).

Comparison of the horse (a) and (6) figures shows relatively small changes in the pK values, the largest-that in pKR-being only 0.14 unit. Instead, however, of the heats of ionization being all the same at 6500 Cal, i.e. a value characteristic of imidazole, the heats of ionization of the more alkaline oxygen-linked group, Q. and QR, have been raised to 7600 cal (which is still well within the imidazole range) but the heats of ionization of the more acid oxygen-linked group, Q’o, and &‘a, have been drastically dropped to 1500 Cal, i.e. to a value characteristic not of imidazole but of -COOH groups, which Antonini et al. (11) suggested are re- sponsible for the “reversed Bohr effect” in the more acid pH range.

Study of the human (a) and (b) figures in Table I shows that

TABLE I Oxygen-linked ionization constants and heats of ionization of human

and horse OrHb at 20” and ionic strength 0.2 M according to (a) Antonini et al. (IO), before 1964, and (b) Antonini et al. (11)

Species PK’R Q’R PK’O Q’o PKO Qo PKR QR ~~-~ -__--

cd cd Cd cd

Horse (a).. 5.25+6500 5.75 +6500 6.68 +6500 7.93 $6500 Horse (b).. 5.27 +1500 5.87 +1500 6.77 +7600 8.07 +7600

Human (a). 5.30+6500 5.90 $6500 6.95 +6500 8.25 +6500 Human(b).. 5.46 -1500 6.26 -1500 6.45 +9000 7.85 f9000

much larger modifications have been made both in the pK and the Q values. The biggest change, as regards the former, is in pKo, which has been lowered by 0.5 unit from 6.95 to 6.45, cor- responding to a more than a-fold change in the value of the actual ionization constant, Ko. The raising of QR to 9000 cal brings this figure near to the upper limit of that found in simple imida- zole derivatives.

In these recent recalculations of the values of pKo, Qo, etc., Antonini et al. (11) have imposed the restraints that Qo = QR and Q’o = &‘a. A basis for such restraints is their finding that QA, the heat of oxygenation of hemoglobin in the acid range (approximately pH 5), wherein they believe that “Bohr effects” have practically disappeared, tends to the same value (to within 500 to 1000 cal) as QB, the heat of oxygenation of hemoglobin in the alkaline range (above pH 9) wherein “Bohr effects” have also disappeared. As is pointed out in the adjoining paper, however,

QB - &A = C&R - Qo) - (Q'o - Q’R) (2)

Equality of &A and QB thus does not necessarily imply that QR = Qo and Q’R = Q’o, but only that (QR - Qo) = (Q’o - Q’R). For this reason it has seemed to us preferable not to impose any thermochemical restraints on the calculation of Ko, K’,, KR, and K’R at the various temperatures, but, rather, first to find, by an appropriate statistical procedure, the best values of Ko,

K’,, KR, and K’R which will fit the experimental differential titration data at different temperatures (in accord with Equation 1) and then later to examine how far the results so obtained conform with the requirements of Equation 2. To this end we have secured, and report later in this paper, new titration data of our own on human, horse, and bovine hemoglobin at various temperatures. The results of statistical analysis of these results have already been briefly reported (12) and confirm the suggestion made in the preliminary communication of Rossi et al. (6) that QR exceeds Q. by about 5000 cal in the cases of both human and bovine hemoglobin. Some details of the nature of the statistical procedure are also given later in the present paper. Application of this procedure to the recently published data of Antonini et aZ. (11) leads to just the same conclusion in the case of their human hemoglobin data, but in the case of their horse hemoglobin data (QII - Qo) turns out to be appreciably less, thus confirming once more that horse hemoglobin shows a smaller departure from Wyman’s original concepts than does human or bovine hemo- globin. The results of the statistical treatment are also in harmony so far with the requirements of Equation 2, but here the ground is less sure, owing to the relatively large size of the standard errors of Q’. and Q’R, which are due to the present

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E$ect of Temperature on Hemoglobin Ionizations Vol. 242, No. 5

TABLE II

Titration curves of human hemoglobin at 25” and 37" Hemoglobin concentration was 3.08 meq of iron per liter.

B/hen+ PH (Hb) ?H (OzHb) 1 -

B/hem@ PH (Hb)

3.246 9.043 9.006 3.246 8.736

2.850 8.751 8.655 2.850 8.433 2.634 8.563 8.439 2.634 8.306 2.432 8.416 8.266 2.432 8.170

2.027 8.173 8.010 2.027 7.947

1.621 7.985 7.806 1.621 7.764

1.247 7.813 7.626 1.218 7.589 0.911 7.692 7.506 0.911 7.475

0.607 7.560 7.384 0.607 7.363 0 7.353 7.190 0 7.155

-0.607 7.142 6.992 -0.607 6.954 -0.911 7.041 6.896 -0.911 6.843 -1.216 6.934 6.803 -1.216 6.746

-1.621 6.779 6.668 -1.621 6.601 -2.027 6.610 6.534 -2.027 6.431 -2.432 6.436 6.388 -2.432 6.276

-2.736 6.292 6.274 -2.740 6.149 -3.139 6.085 6.113 -3.150 5.978 -3.550 5.877 5.944 -3.540 5.784

-4.051 5.629 5.732 -4.051 5.556 -4.379 5.515 5.619 -4.379 5.452

-4.865 5.305 5.433 -4.865 5.264 -5.514 5.050 5.142 -5.350 5.113

a B/heme is given heme.

in

- milliequivr

- tlents of added base per meq of

370

>H (OzHb)

8.696

8.380 8.203 8.061 7.806 7.617 7.447 7.327 7.207 7.013 6.829 6.728 6.628 6.503 6.363 6.233 6.125 5.988 5.839 5.636 5.545 5.353 5.233

difficulty in obtaining sufficiently extended experimental titra- tion curve data in the acid pH range.

METHODS

Hemoglobin solutions were prepared by the following proce- dure. Immediately after the drawing of the blood from a single donor, the red cells were separated, washed three times with 0.9% NaCl solution, and hemolyzed by addition of distilled water (1 :I). The stromata were removed by centrifugation at 20,000 rpm for 30 min.

The solution of hemoglobin so obtained was then dialyzed in a cold room (2-3”) for about 48 to 72 hours against distilled water. All the experiments were performed within 5 days from the drawing of the blood, and the hemoglobin stock solutions were never allowed to warm up to room temperature. After dialysis the solution was placed in a large container (i.e. 2 liters) and deoxygenated by several shakings with pure nitrogen. (Determinations, by the standard Van Slyke gasometric meth- ods, showed that the residual 02, CO, or CO2 was usually negligi- ble (less than 0.5 volume %), and the methemoglobin con- centration was only around 2 to 3% of the total hemoglobin.

The Hb concentration was obtained by the CO capacity method.

The pH was measured at the required temperature (con- trolled to within less than O.l”) by the use of the microelectrode unit, type E 5021 (Radiometer), connected to a Vibron Re- search pH meter, models C 33 B and 33 B. The calibrating buffers (phthalate, phosphate, and borate) were made up ac-

cording to Bates (13). Stable readings of the pH of the solution were obtained only after washing the capillary electrode several times with the Hb solution until successive pH readings checked to within &0.002 unit.

The range of pH investigated was from about 5.0 to 9.0. No checks for reversibility were carried out in view of the con- trols on this point already reported by Antonini et al. (14) for human Hb.

The titration curves of Hb and OzHb were obtained by the “discontinuous” method so as to maintain constant Hb con- centration and ionic strength (usually 0.2 M) for the whole range of pH analyzed.

The ionic strength, cations, and Hb concentration were ad- justed by the use of the following solutions: Hb in 0.2 M KCl, 0.2 M KCl, KOH in 0.2 M KCl, and HCl in 0.2 M KCl.

Blood from a single individual was used as the source of the hemoglobin in each experiment, since mixed blood was found on several occasions to give unsatisfactory results. The human blood was obtained either from the Istituto Sieroterapico It.aliano, Milan, or from the Blood Transfusion Centre at Cam- bridge. Our best thanks are due to the kindness of these two organizations.

EXPERIMENTAL RESULTS

Four separate samples of human, two of horse, and three of bovine hemoglobin were used for the titration measurements. Table II gives the results in the case of our last human sample at 25” and 37”, and Fig. 1 shows the variation of Ax with pH at the two temperatures. Table III gives corresponding results for horse hemoglobin at the same two temperatures.

The actual values of Aa in this paper and in previous papers (e.g. Wyman (7) and Antonini et al. (11)) were obtained from smoothed curves drawn by hand. Recently Dr. E. C. De Land has developed for the purpose an objective polynomial fitting curve method, which has been adapted to a Fortran program. It, is reassuring to find that the results by this method tally very closely with those derived from the “smoothed curve” method.

1 I I I 6.0 7.0 8.0

PH

FIG. 1. Variation of Ax with pH for human hemoglobin at 25” and 37”.

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Issue of March 10, 1967 Rossi-Bernardi and Roughton 787

Statistical Evaluation of “Best” Values of

Ko, K,, K’o, and KIR

Principle of Statistical Method--For fitting the constants of Equation 1 by the method of least squares, use was made of the procedure outlined by Daniels for the determination of the four intermediate constants for the equilibrium between oxygen and hemoglobin (see appendix to the paper of Roughton, Otis, and Lyster (15)). The first step is to obtain reasonable trial values of Ko, KR, K’o, and K’,. As a starting point we have used the constants recently reported by Antonini et al. (11) at 25” for human hemoglobin. Use of preliminary values of the constants differing even 200 to 300% from the correctly fitted ones did not alter the final values obtained.

Denoting the required adjustments, 6Ki = Ki - Kit, where Ki = correctly fitted parameter and Kit = initial trial value, the correctly fitted equation is expanded to the first order of small quantities, giving

where the subscript t indicates that the trial values have been inserted, AX, being the value of AX obtained at any pH by the use of the trial values.

The 6K,, 6Ko, etc., are now determined by the method of least squares. 6AXJ is the deviation of the Jth observed value of AX from the correctly fitted curve; the 6K,, etc., are chosen to minimize

where sAXJ1 is the observed deviation from the trial curve, WJ (the weight) being taken as 1 for all the observations, and

aAXi ---A- hi IKE . (KR~ + hd2

(4.1)

aaxi ---.-A hi aKo . (Kot + hJ2

(4.2)

dAXi hi aKkY

’ - (Kkt+hi)2 (4.3)

CiA& . hi

aKb’ (Kht + hd2 (4.4) where

The procedure from this point on is the same as described by Daniels (see Reference 15).

(5)

Because of the heavy computations involved, it was found best to program the whole problem in Fortran language and solve it by the use of a 7040 IBM computer.’

The solutions of the four normal equations which are obtained by minimization of Equation 3 gives the required adjustments and hence the fitted constants Ko, KR, K’o, and K’R. The fitting process has then to be repeated starting from the new values of Kn, Ko, etc. Usually two or three iterations were

Results by Statistical Method-Table IV gives the statistically determined values of Eo, KR, K’o, and K’,, together with their standard errors, for human and horse hemoglobin solutions, the titration data of which were reported in Tables II and III, respectively. Values of Qo, QR, &lo, and &IR, with their standard errors, are also included in Table IV.

1 The authors wish to express their gratitude for the help re- ceived in this respect from Dr. G. Kacin, of the Centro di Calcolo, Politecnico di Milano, and to Professor G. Maccacaro and Dr. V. Pietra of the Centro di Biometria, University of Milan.

It will be noted that the values of Ko, etc., and Qo, etc., for the human hemoglobin solution, as calculated statistically, differ substantially from those given by Antonini et al. (11) and, in particular, that the difference of approximately 5000 cal between QR and Q. for human Hb, which was originally suggested by Rossi et al. (6), is confirmed. In order to check

TABLE III Titration curves of horse hemoglobin at 15” and 37’

Hemoglobin concentration was 3.35 meq of iron per liter.

B/hem’” PH (Hb) pH (OnHb)

3.790 9.134 9.092 3.432 8.890 8.815 3.044 8.650 8.514 2.850 8.536 8.360 2.447 8.334 8.147 2.044 8.164 7.962 1.647 8.004 7.792 1.189 7.816 7.529 0.443 7.568 7.340 0.000 7.410 7.200

-0.746 7.157 6.973 -1.364 6.944 6.786 -1.976 6.696 6.584 -2.546 6.436 6.385 -3.110 6.175 6.185 -3.731 5.812 5.900 -4.298 5.525 5.656 -4.925 5.240 5.385 -6.029 4.876 4.984

250

B/hen@ PH (Hb) pH (OzHb)

3.910 8.830 8.820 3.432 8.580 8.514 2.985 8.336 8.212 2.388 8.054 7.875 1.758 7.795 7.602 1.194 7.570 7.380 0.597 7.378 7.180 0.000 7.194 7.000

-0.749 6.936 6.767 -1.343 6.740 6.593 -1.940 6.500 6.400 -2.537 6.276 6.210 -3.134 5.977 5.975

-3.731 5.700 5.758 -4.328 5.402 5.512 -4.925 5.180 5.295

370 -

D B/heme is given in milliequivalents of added base per meq of heme.

enough to fix the constants to the third decimal point. Any further improvement would be physicochemically meaningless for this problem. The program automatically provides the standard errors of the fitted constants.

The heats of ionization are obtained from the fitted values of K,, KR, K’o, K’,, and their standard errors at different temperatures by the use of the usual van’t Hoff formula,

RT,A Q=--- TP - TI

The standard error of Q can be obtained from the standard errors of the K values by use of the formula given by Livingstone

W,

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788 Effect of Temperature on Hemoglobin Ionizations

TABLE IV

Vol. 242, No. 5

Values of ionization constants and heats of ionization of oxygen-linked acid groups in hemoglobin and oxyhemoglobin of man and horse as computed statistically from data of Tables II and III

Temperature K’R K’o Ko KR

Man 25"

37"

Horse 25"

37"

9.61 (f0.93) x 10-e PK’~ = 5.02

7.41 (zkl.16) X 1O-6 pK’fi = 5.13

Q’R = -3,870 (f2,729)

1.05 (ctO.12) x 10-s ~K’R = 4.979

6.54 (zt1.32) X lo+ ~K’B = 5.184

Q’R = -7,200 (zt3,520)

2.29 (ztO.15) x 10-e pK’o = 5.64

2.51 (50.27) X 1OF PK’~ = 5.60

Q’o = 1,400 (%1,910)

2.05 (rt0.21) X 1O-6 pK’o = 5.688

1.88 (f0.35) x 10-e pK’o = 5.726

Q’o = -1,330 (&3,200)

TABLE V

1.46 (AO.03) x 10-T pKn = 6.84

2.11 (f0.06) X 10-T pKo = 6.68

Qo = 5,600 (5457)

1.76 (ztO.11) x 10-T pKo = 6.754

3.0 (zk0.23) X lo+ pKo = 6.523

Qo = 7,730 (ztl,430)

1.45 (&to.02 x 10-s pKz = 7.84

2.92 (zkO.04) x 10-s pKz = 7.53

QR = 10,700 (f352) --

8.44 (f0.38) x 10-9 ~KR = 8.074

1.8 (zkO.06) X 10-a pKo = 7.745

QR = 11,400 (~850)

Comparison of values of ionization constants (a) chosen by Antonini et al. (ii) with (b) those computed statistically from their data on human hemoglobin

Temperature

10" (a)

10 (b)

20 (a)

20 @I

30 (a) 30 @I

40 (a) 40 (b)

8.2 -

8.0 - PKR

7.8 -

7.6 -

K’R K’o

3.80 X 1O-6 5.84 (zk0.16) X lo+

6 X 1OW’ 1.66 (fO.32) X 1O-6

3.47 x 10-e 5.5 x 10-7 1.49 (f0.37) x 10-5 2.85 (f0.45) x 10-e

3.20 X lo+' 5.07 x 10-T 9.82 (51.17) X 1O-6 2.80 (rtO.27) X lo+

0.288 X 1O-5 2.65 (f1.51) X 1O-5

4.57 x 10-7 6.78 (zkl.71) x lo-”

PKO 6.8

6.6

6.41 7 3.2X 10." 3.4 3.6 3.2 3.4 3.6 3.2 3.4 3.6

l/T l/T l/l

FIG. 2. The relationship between pKo and pKll (ordinates) and the reciprocal of the absolute temperathre. A, human hemo- globin; B, horse hemoglobin; C, bovine hemoglobin. Estimated values from the data of Antonini et al. (11) are plotted as triangles, and those from the data of the present paper as circles.

Ko

2.09 x 10-7 8.32 X 1O-9 0.828 (~0.05) x 10-T 5.54 (zt0.25) X lo-+

3.55 x 10-T 1.41 x 10-8 1.30 (f0.09) x 10-Y 0.895 (f0.052) X lo-8

5.89 x 10-1 2.34 X 10-s 1.96 (ztO.08) x 10-T 1.78 (zkO.05) x lo-8

9.55 x 10-T 3.80 X lo-8 2.37 (h0.09) x lo-' 3.32 (f0.09) x lo-8

-

KR

whether the discrepancy from the conclusions of Antonini et al. might have been due to a difference in the individual human hemoglobin samples used, we have applied the same statistical procedure to the estimation of “best” values of Ko, KR, K’,,

and Klt2 from their data. Table V gives a comparison of the values so derived with those chosen by Antonini et al. (11). In the case of KR the discrepancies are relatively small; far otherwise is it with K’,, wherein discrepancies ranging up tc lo-fold or higher are seen.

Fig. 2A shows a plot of the statistically fitted values of pKo and PKR against the reciprocal of the absolute temperature for the data of Antonini et al. (A, human OzHb; A, human Hb) and for our data ( l , OzHb; 0, Hb). The agreement between the data from the two laboratories is obviously satisfactory. The values of Q. and QR are proportional to the slope of the lines relating pK to l/T, which in the case of deoxygenated human hemoglobin (& = 10,700 f 352 Cal) is nearly double that in the case of oxyhemoglobin (Q. = 5,600 + 457 Cal). The value of QR tallies satisfactorily with that deduced in the adjoining paper from direct calorimetric experiments, i.e. 11,100 f ~1,000 Cal, on other samples of human hemoglobin.

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For, horse hcnio~lol~in (Fig. Z?), tlro tlatn of .\ntonini et nl., \~h~n analyzed statistically, gave satisfactory results only at 20” and 30”. The coml)arison with our results in this ra<c is thus 1~s complett, although lair. Thaw seems some indication that (Qn - Qo) from the data of .intorrini et nl. ma\- only be about a half as great as our figure (vix. 3TO0 cal; see l’ablt~ IV), but the margin 01’ (‘rwr is, unfortunat,rly, twice or so as great as in the case of human hrmoglobin. A lower valllc~, i.e. of about 2000 cal, for (CJ,? - Qo) for horw hemoglobin would bc mow nearly in lirw \yith \Vyman’s or,iginal concepts (7) Hazel on his early pork with horw hemoglobin.

‘I’htx still mow limited data for hovim, hemoglobin I)‘ccntrd in Fig. 2C indicate> a value of 9800 cal for QH and of 5900 cal for Qo, The figuws for this species thus wscmblc rathw closely thos;r COI, human hemoglobin. I-nfortunatrly, for wasons which 3x not rlcar, the coc~fficients of variation (i.e. standard crwr f wtimatrtl cwor of constant) for K, and R, are found to br i to 8 times greater in the case of bovine Hb than in human Hb, while l’or K’, and K’, the cotfficientjs of varint,ion for borinc Hh arc so large as make the csl~imated valws of these constants mcan- inglcss.

:\s a teat of “gootlnrsa of fit,” Ihc discrepancies bttwwn t,he obscrwd and calculated values of As have been tabulated for lli~ srts of ionization constants chown by *1ntonini et al. (11) and for thr sets of ionization ronstant,s computed from their data by t,he present stat,ist,ical method. Table Vl (for the human results) shows that s = [Z (discrcpancy)2/n]*, where n is thr numbrr of rspcr%~~ents, is about 3 times gwater in the former case than in thr latter.

Tablr VI also shows that 8 for our own human data at 25” ant1 37” is only about half as great as 8 for the human data of -1ntonini et al., when bot,h se& arc calculated statistically.

Table VII gives a comparison of the values of the ionization constants of horse hemoglobin as chosen by Xntonini et al. (11) Cth those dcrivcd statistically from their data. The “goodness of fit,” in the latter casr, is about twiw as good; this establishes, once more, the expected superiority of thr statistical mrthod for, cvaluat,ing the consl,ants.

Sote on _ 1 pprozimaie Independent Estimation 01 Ii, jrom Values o,f Aa in -1 &al&e pH Range

Thcrr is littlr doubt, from tht present and previous investiga- tionb, that the value of K, is only of the order of one-trnth that of the smallest of the other ionization constants of the series Ko, R’,, and k”,. ;Yccordingly, at pH > I>&, Equation 1 may be replaced by the approximate form

&(l-&)+(1-A)-(1-s)

(6.0)

AZ 1 -=-++ h KR + h

10” 20 25 30 37 40

Antonini el al. (11). I

G.BG X 1OP 2.05 X 1O-2l G.87 x 10-2, 2.G4 x IOP

i.5 x 10-J 4.32 x 10-Z; 1.18 x 10-Z

5.32 x 10-i’ 3.11 x 10-2~ 1.30 x 10-Z

Temperature

10” 3.14 X 1OP 2.40 X 10-2: 20 5.84 x 10-Z 1.98 x 10-z 25 l.i5 X 1O-2 30 2.02 x 10-z 1.92 x 10-z 37 2.30 x 10-z 40 3.41 x 1OP -a

Antonini c/ al. (11) I

o For this case convergerrce was rrot obtnincd I,- the least squares method of fitting.

Let As and Aa, be the values of Aa at two hydrogen ion corl- centrations, $ and hn, in this region. Thrn, by Equation 6.1,

AX, 1 --==++

h KR + h

AZ, 1 -=

hn ~ +4 Kn + h2

so that

Ax-2 AX1

= (-

1 1

hz h KR + hy Kn + hl > !R.2)

and there is t,hus a possibility of wtimating Zi, indrpcntlentl\ of the other oxygen-linked ionization constants, I<,, K’,, and

K’R. 12s an esamplc, from the data on human hemo$obin at 25”

in Table IT and Fig. 1, WC have

hl = 10-s, A~I = 0.334; hr = 4 x lOP, 1x2 = 0.101

Ai’% Ai!?, 1 - - - = 1.435 x 10’ = ---.--~ _

1

h h2 Kfi + 4 x 1OF Kn + lo-8

whrnce KH = 1.345 X 1 OP, as compared with the statisticall? fitt,cd value of 1.45 x 1 OV. Similarly, from the data on human hemoglobin at 37”,

hl = X 10-8, ASI = 0.312; h2 = 8 x 10-9, .iLF2 = 0.182

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790 i3fect of Temperature on Hemoglobin Ionizations Vol. 242, n-o. 5

whence Kn = 2.75 X lOF, compared with the statistically fitted value of 2.92 X 1OP. The actual values of Axr, Ax,, hr, and hz in these two examples have been chosen so as to minimize the errors in the estimated value of Kn. Assuming an uncer- tainty in (Ax-, - Aa,) of +O.Ol, the value of K, calculat’ed in t,his way can, in fact, be shown by numerical trials to be subject to an error of about &7% of itself. Actually it will be noted that the values of K, obtained in the two examples are each about 7c/o lower than the statistically fitted values (proba- bly owing to the approximations in deriving Equation 6.0), but that their ratio at the two temperatures (on which the indirectly calculated value of Qn depends) viz. 2.75 X 10~*/1.345 X lo-*, or 2.045, agrees very closely with the ratio of the statistically fitted values at the two temperatures, viz. 2.92 X 10~*/1.45 X lo-*, or 2.015.

pioneer work of Steinhardt et al. (17-19) on the unmasking of protonic groups of hemoglobin in the acid range. This faster method has brought to light new phenomena over and above those reported by Steinhardt et al. A preliminary account of this work is given in the next section.

Rapid and Slow Titration Curves of Hb and OzHb

The experimental setup for the rapid pH measurements will be described in detail by one of us (L. Rossi-Bernardi) elsewhere. The procedure, in brief, is to drive Hb solution and acid (or alkaline) solution into a continuous flow Hartridge-Roughton rapid reaction apparatus, and to record the pH at a lapsed time of about 10 msec after mixture by means of a glass electrode located in the observation tube at an appropriate distance from the mixing chamber.

DISCUSSION

The experimental values of A8 between pH 7.0 and 9.0 indi- cate that in this range 0.5 to 0.6 H+ ion per heme is liberated on oxygenation, thus implying that the hemoglobin molecule (HbJ must contain at least three “alkaline Bohr” groups. In the more acid range, 0.3 to 0.4 H+ ion per heme is absorbed on oxygenation, which means in turn a minimum of two “acid Bohr” groups per Hb4 molecule. The classical scheme of Wyman (7) does not go far beyond these minimal requirements, involving as it does one identical “alkaline Bohr” group and one identical “acid Bohr” group for each heme, thus making eight Bohr groups in all per Hb,. Our statistical computations have shown that this scheme can explain, within the limits of experimental error, the differential titration curve data for human and horse hemoglobin, both in the case of the data of Antonini et al. (11) and of our own. The estimated values of K’, and KIo have, however, coefficients of variation several times higher than those of KK and Ko; correspondingly, the calculated heats of ionization, &IX and Q’o, are subject to uncertainties of the order of 1500 to 3000 cal. The difficulty in obtaining better values of KtR and K’,, and thence of QrR and Q’o, stems from the lack, in Tables II and III, of titration curve data below pH 5.0, as a result of the instability of hemoglobin at acid pH. We have sought to obtain reliable data in this labile zone by means of rapid, continuous flow tit’ration techniques, the earliest observa- tions being taken at intervals of approximately 10 msec after mixture, which thus far arc shorter than those studied in the

The esperimental conditions in a typical run (summarized in Table VIII) were as follows. Solution A: deoxygenated bovine hemoglobin solution (Hb concentration, 7.16 meq per liter; ionic strength, 0.2 M KCl). Solution B : HCl + KC1 or NaOH + KC1 in variable proportions, the ionic strength being kept con- stant at 0.2 M while H+ and OH- were varied. Temperature, 25”.

For the “slow” titration points, the mixed liquid emerging from the observation tube of the rapid reaction apparatus was collected anaerobically in a tonomcter of the Barcroft type. The pH of the liquid therefrom was measured after 10 and 20 min in exactly the same way as before. Above pH 4.7 the “slow” readings, at 10 and 20 min, were found to agree to within experi- mental error (&O.Ol pH unit), but were significantly different from the IO-msec readings in the acid range of pH as is shown in Table VIII. Slow drifting between 10 and 20 min was only observed for the points pH 3.96 and 4.67, in accord with the previous finding of Steinhardt and Zaiser (17). A graphical plot of the results in Table VIII reveals a nearly constant differ- ence between the fast and slow titration curves between pH 6.0 and pH 4.0. At pH 5.0 the transition between fast and slow readings is accompanied by the uptake of about 0.5 meq of H+ per heme, i.e. approximately 2 meq of Hf per mole of hemo- globin. Above pH 6.8 there is no difference bctwecn fast and the slow titration curves. In future work it is hoped to follow the kinetics of the transition between 10 msec and 10 min, and also to investigate whether there are any pH changes between 10 msec and the earliest measurable time after mixture, viz. about 2 msec.

TABLE VIII Nature of “Acid Bohr” Groups Rapid and slow titration CUTO~S of bovine Hba

I PH

In due course it is hoped to obtain rapid titration curves of OzHb and Hb down, if possible, to about pH 3 and to analyze the “rapid” differential titration curve by statistical procedures similar to those already applied above in the case of the “slow” differential titration curve. Furthermore, it should be pointed out that no allowance has been made so far for the possible effects of Cl- binding by Hb and OzHb in the acid range. Addi- tional work along both these lines is clearly needed for a more informed understanding of the differences in acid-binding prop- erties of Hb and OzHb below pH 6.7.

Additions to 7.16 meq of Hb

Rapid (10 msec) jlow (lo-20 min)

0.07 M HCl, 0.13 M KCl.. 0.05 M HCl, 0.15 M KU.. . 0.03 M HCl, 0.17 M KCl.. 0.015 M HCl, 0.185 M KCl..

0.015 M NaOH, 0.185 M KC1 0.03 M NaOH, 0.17 M KCl.. 0.06 M NaOH, 0.14 M KCl..

3.72 3.96 4.59 4.67 5.42 5.50 6.6G 6.66

8.32 8.32 ,9.62 9.62 10.48 10.48

- 0 Similar differences were observed between the rapid and slow

titration curves of bovine OsHb.

Nature of “Alkaline Bohr” Groups

Originally it was supposed that the group responsible is the imidazole residue directly attached to the iron atom, and that the corresponding pK is the same for each of the four chains of

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Issue of March 10, 1967 Rossi-Bernadi and Roughton 791

the hemoglobin molecule. This view was, however, abandoned some years ago, partly on account of studies on chemical modifi- cations of hemoglobin (for discussion, see Benesch and Benesch (20)) and partly on account of the fact that myoglobin, although containing an iron-histidine linkage identical with that found in hemoglobin, shows hardly any Bohr effects. Consideration of other possibilities led to the suggestion that the group involved might be a neighboring imidazole residue, other than the one linked to the iron atom.

The demonstration that the amino acid sequences of the a: chains and p chains of the hemoglobin molecule differ from one another has raised the possibility that the Bohr groups in the two chains may not be identical. Lack of identity of the four “alkaline Bohr” groups had also been suggested by the finding that the effect of pH on the 02-Hb equilibrium curve appears to be much less at high saturation of hemoglobin with oxygen (21) than the traditional, uniform effect of pH over the main part of the equilibrium curve.

Current thought tends to associate the more alkaline Bohr effects in hemoglobin much more with the p chains than with the o( chains. Striking new ideas have indeed been opened up by the discovery of nluirhead and Perutz (22) and Perutz et al. (23) that the distance between the hemes in the two /3 chains of the oxygenated molecule is 7 A less than in the deoxygenated molecule, because of a moving apart of the /3 chains in the latter case. This phenomenon (see Perutz (24)) suggests several possible stereochemical effects on the pK values of protonic groups of the p chains on oxygenation. (a) The close spatial apposition, in oxyhemoglobin of the terminal -NH2 group of the p chain to the terminal, -COOH group of its partner p chain might promote the formation of two salt bridges, Icading to an increase of pK of the terminal -XHz groups of the p chains (i.e. a negative Bohr effect). Although the pK of the terminal -COOH groups would conversely be expected to be lowered, the pH at which their ionizations occur should be below the range of these studies (pH 4 t,o 10). (b) In addition, a pair of hydrogen bonds may be formed by the y-amino group of asparagine H 17 with the imidazolc rings of H 21 and II 24 of its partner p chain, thus leading to a lowering of the pK values of each of these imidazole rings (i.e. positive Bohr effects). There might thus be formed, between the terminal regions of the two p chains of oxghcmoglobin, a total of two salt bridges and four hydrogen bonds, making in all six hypothetical groups, the ionization constants of which might show “Bohr” behavior, two in one sense and four in the other.

Returning to the cr chains, it should be noted that Hill’s (25) direct estimations of the pK of the terminal -NH% groups of the (Y chains, at 25” and ionic st’rength 0.1 RZ, indicate a value of 7.71 (hO.03) for human hemoglobin and 6.72 (&0.03) for human carbon monoxide hemoglobin, i.e. a positive Bohr effect. Fur- ther work of this kind will be eagerly awaited.

Although it has proved quantitatively possible to interpret the differential titration data, both of Antonini et al. (11) and of the present paper, in terms of no more than two identical Bohr groups per heme, it is clear from the preceding discussion that the real solution of the problem may prove more complicated. Much interesting work has recently been carried out, and is currently in progress, on the individual chemical properties and interrelations of the OL and p chains of the hemoglobin molecule. No doubt a substantial part of this new knowledge will in due course have to be incorporated, as and when the

underlying mechanism of the Bohr effects becomes more and more completely elucidated.

DiJerence between Qn and Q.

The studies in the present paper suggest that QR exceeds Q. by about 5,000 cal in the case of human hemoglobin, and perhaps by somewhat less in bovine and horse hemoglobin. It is, of course, natural to ask whether such a conclusion is reasonable, especially since the free energy changes of the respective ioniza- tions only differ by about 1,400 Cal. Up to the present it must be admitted that no simple explanation of the suggested finding is at hand. Only a minor fraction of the effect could be attrib- uted to differences in hydrogen bond formation, although the latter is known to bc unusually strong in imidazole -NH com- pounds (26). The well known difference of approximately 5,000 cal between the heat of ionization of free phenolic groups and of the phenolic groups in serum albumin is generally now explained by changes in conformation of the serum albumin, in the pH range in which ionization of phenolic groups occurs. Perhaps the change in conformation between Hb and OzHb, as revealed by x-ray crystal structure studies, might, in this case, also be a relevant and important factor. A conceivable, although perhaps far-fetched, su,, vwestion is that an imidazole uroup which is titratable in OJIb (with a heat of ionization a of 6,000 to 9,000 Cal) might become submerged on deoxygenation and be replaced by a titratable -KHz group (with a heat of ionization of about 11,000 Cal).

Electrostatic Interaction Effects between Charged Groups in Proteins

Neither in the paper of Antonini et al. (ll), nor so far in the present paper, has any allowance been made for the electrostatic interaction effects between charged groups in proteins, as in the classical Linderstr@m-Lang treatment. On the simple hy- pothesis that the protein molecule may be treated as a charged sphere, the degree of ionization, ol, of any group of intrinsic ionization constant, li=int, is given by

pH = pKi,t + log [a/(1 - a)] - 0.8ti8 wg (7)

where 2 is the average net charge in proton units2 and w, for a protein of the dimensions of the tetramer hemoglobin molecule, would be of the order of 0.087 (27), assuming as a first approxima- tion that w is the same for OzHb as for Hb. The data in Tables II and III were accordingly adjusted, by adding to each pH value a quantity equal to 0.075 2 (or -0.075 2). The pH value, as so adjusted, may be written pHint and Equation 7 then becomes

pIlint = pKnt + log b/(1 - 41

Values of AXi,, over the range of values of pHi,t in Table II for human hemoglobin were then calculated, and the adjusted data were submitted to the statistical procedure, but the com- putations failed to converge. Several possible suggestions to account for this failure might be advanced. (a) It may bc wrong to assume that w for Hb is the same as for OzHb. (b) It may well be doubted whether the simple electrical sphere model is applicable to the individual oxylabile ionizing groups in Hb and OnHb; it may, rather, be necessary to take account of the de- tailed geometry of the neighboring charges in the protein, if

2 Note that 2 = -8.

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792 ltflect of Temperabe on Hemoylobin Ionizations Vol. 242, ATo. 5

and Ivhen more csact kno\vledge in this field becomes available. (c) There may, as already indicated, be more than trvo osylabilc groups per heme and these may be not identical in the case of

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L. Rossi-Bernardi and F. J. W. RoughtonThe Effect of Temperature on the Oxygen-linked Ionizations of Hemoglobin

1967, 242:784-792.J. Biol. Chem. 

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