thermodynamic studies on oxygen binding by human red blood cells

Comparative Biochemistry and Physiology Part A 123 (1999) 329–336

Thermodynamic studies on oxygen binding by human red bloodcells

Pierre Vorger *Ser6ice de Physiologie Respiratoire, Pa6illon Beauchant, Hopital Jean Bernard, B.P. 577, F-86021 Poitiers Cedex, France

Received 27 December 1998; received in revised form 16 April 1999; accepted 25 April 1999

Abstract

Oxygen equilibrium curves have been measured on human normal red blood cells, at the temperatures of 20, 25, 30, 37 and41°C, and at pHs ranging from 6.8 to 8.2. The thermodynamical parameters have been determined for the four successive stepsof oxygenation and for overall oxygenation, according to the Adair and MWC models [Monod J, Wyman J, Changeux JP. Onthe nature of allosteric transitions: a plausible model. J Mol Biol 1965;12:88–118]. The heat release appears to be nearly equal forthe four steps. At the first three steps, the DH change is counterbalanced by a nearly equivalent change of DS, resulting in a rathersmall DG value. DG is greater at the fourth step, because of diminution of this enthalpy–entropy compensation phenomenon. Thefour steps are both enthalpy and entropy driven. According to the MWC model, the T to R transition is endothermic, andallosteric quaternary transition occurs at binding of the third oxygen. The average heat release increases by 2.8 kcal/mol when pHraises from 7.4 to 8.2, but flattens below pH 7.4. After correction for the heat of solution of oxygen and for the heat of protonrelease (referred to intracellular pH), an intrinsic heat for oxygenation of the heme of approximately −13 kcal/mol is obtainedfor the successive steps of oxygenation (at pH 7.4, 37°C). These results are compared with those previously obtained for pigeonand trout red blood cells. © 1999 Elsevier Science Inc. All rights reserved.

Keywords: Bohr effect; Human hemoglobin; Human red blood cell; Oxygen affinity; Pigeon red blood cell; Temperature; Trout red blood cell;Vertebrate hemoglobin

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1. Introduction

Cooperative oxygen binding to hemoglobin (Hb) re-lies on transition from a deoxy structure (T) to an oxyone (R) [14]. The T-state is stabilized by ionic bonds,implying non-heme ligands such as protons and anionswhich are stepwise released upon oxygenation. The O2

affinity of the T structure is lower than that of the Rone by the equivalent of the free energy of cooperativ-ity, of 3.6 kcal/mol under nearly physiological condi-tions for human HbA [15,16].

The thermodynamic characteristics of oxygenationfor human HbA solutions, based on the stepwiseAdair’s scheme, have been examined [7,9,10,12,13]. Theintrinsic reactivity of the heme for oxygen is exothermicand constant, and the release of heterotropic ligands,namely H+, Cl− and 2,3 diphosphoglycerate (DPG)modulates the thermodynamics of the system. Measure-

ments of the oxygen equilibria at different temperaturesallow to estimate the enthalpy and entropy contribu-tions to the free energy of binding for each step ofoxygenation, and usefully complete equilibrium dataobtained at a single temperature.

Rather few data in the literature have examined theeffect of temperature on oxygen binding by humanblood, biochemically different and more complex thanthat of dilute Hb solutions, and essentially rely on thetemperature dependence of P50 [2,6,19,20]. Previousstudies have shown that the oxygen equilibria of nor-mal human red blood cells can be satisfactorily de-scribed by the Adair and MWC models [21,23]. In thepresent one, oxygen equilibria of human red blood cellshave been measured at five different temperatures from20 to 41°C, and at eight pH levels from 6.8 to 8.2 inorder to vary the pH-induced constraints on the Hbmolecule. Results have been analysed according to theAdair and MWC models. They provide a description ofthe apparent thermodynamic properties of this system,* Tel.: +33-05-4944-4385; fax: +33-05-4944-4387.

1095-6433/99/$ - see front matter © 1999 Elsevier Science Inc. All rights reserved.PII: S 1 0 9 5 -6433 (99 )00068 -9

P. Vorger / Comparati6e Biochemistry and Physiology, Part A 123 (1999) 329–336330

and may also constitute a basis of comparison forstudies on other Hb systems, since the temperaturedependence of oxygen binding by vertebrate Hbs isknown to exhibit large differences among species [3].

2. Materials and methods

All the experimental techniques used in this studyhave been previously described in detail [23,24]. Com-plete sets of oxygen equilibrium curves have beenmeasured on human red blood cells from normalhealthy adult donors, with automatic data acquisition.Blood was diluted in isotonic 0.05 M Tris or bis–Trisbuffer+0.125 M NaCl. The pH of the buffer wasadjusted at the exact temperature of that of measure-ments of the oxygen equilibria.

The Adair constants, ki (i=1–4), MWC parame-ters (KT, the O2 association constant for the T-state,KR that for the R-state, c (=KT/KR) and L (=T0/R0), the allosteric constant) and overall O2 affinity,expressed as P50, were calculated by the method ofImai [8]. The enthalpy and entropy change for thesuccessive steps of oxygenation, i, were calculated bythe van’t Hoff equations:

DHi=RT2 d ln ki/dT

and

DSi=R dT ln ki/dT,

where R and T are the gas constant and the absolutetemperature, respectively.

The average enthalpy and entropy change for over-all oxygenation, DHav and DSav, were obtained fromthe temperature dependence of − ln P50.

The free energy change of ligand binding at thestep i is given by

DGi=DHi−TDSi.

The thermodynamic values for the MWC parame-ters were calculated from the temperature dependenceof ln L, ln KT, and ln KR.

3. Results and discussion

Examples of oxygen equilibria for human normalred blood cells, expressed as Hill plots, are presentedin Fig. 1, for the pH of 7.4 (unless specified, pHvalues are extracellular ones). Measurements wereperformed at the temperatures of 20, 25, 30, 37 and41°C. The experimental data were fitted according tothe Adair equation. The binding curves are roughlyparallel to each other, indicating that the effect oftemperature is nearly independent of the level of oxy-genation, which rejoins early observations [25]. Thesame behavior applies to the other pHs examined(not shown). For the temperatures of 37 or 25°C, thevalues of the Adair (or MWC) constants are similar,within the limits of experimental error, to those ob-tained in previous studies [21,23], and detailed valuesare not given here.

The van’t Hoff plots for the temperature depen-dence of the Adair constants and P50, at pH 7.4, areshown in Fig. 2. The log ki and − log P50 values havebeen plotted against 1/T. Assuming linearity for allthe parameters, the DH and DS values have beencalculated by linear regression.

Table 1 resumes the values of DH, DS, −TDS andDG, obtained for the pHs of 6.8, 7.4, 7.8 and 8.0,and covering the pH range examined. At all pH lev-els, the enthalpies for the four steps of oxygenationappear to be nearly equal, with DH1�DH2�DH3�DH4�DHav. The standard errors are usually largerfor the two intermediate steps, as can be expectedfrom the plot of Fig. 2, due to the less good preci-sion for steps 2 and 3, which was also noted in otherstudies [9,12]. These heats include the heat of solutionof oxygen (−3 kcal/mol), the intrinsic heat of oxygenbinding by the hemes, and all the heats associated tothe release of ions with oxygen binding with a majorrole of protons [5,13]. At each step, the reaction ismarkedly exothermic.

Fig. 1. Example of Hill plots for oxygen equilibria of human redblood cells diluted in 0.05 M Tris+0.125 M NaCl buffer, at pH 7.4.Y, fractional oxygen saturation; P, partial oxygen pressure in mmHg.Temperatures are, from left to right: 20, 25, 30, 37 and 41°C. Linescorrespond to experimental fit by the Adair equation.

P. Vorger / Comparati6e Biochemistry and Physiology, Part A 123 (1999) 329–336 331

Fig. 2. Example of van’t Hoff plots of the temperature dependence oflog ki (i=1–4), and − log P50 for human red blood cells at pH 7.4.T, absolute temperature. �, k1; �, k2; , k3; �, k4; , P50. Linesare obtained by linear least-squares method.

thalpy–entropy compensation process, as pointed outfor oxygen binding by human HbA solutions [7,10]. Asa result, the DG values are much smaller than the DHones. Furthermore, the uniformity observed for theDHs disappears, and the DGs exhibit the typical rela-tion: DG1�DG2�DG3BDG4.

Fig. 3 shows the compensation plot, where the valuesof DHi are plotted against those of −DSi, for thevarious pHs examined. All the points corresponding toi=1, 2 and 3 rather well lie on a straight line, calcu-lated by linear regression of these points, while thosefor i=4 are clearly apart from that line. The compen-sation temperature, Tc, given by the reciprocal slope ofthe line, is 324 K, a value close to that of 300 Kobtained for human HbA solutions [7]. For the steps 1,2 and 3, the DH change is nearly counterbalanced bythat of DS, explaining the low value of DG. The in-crease of DG at the fourth step is the consequence of adiminution of the compensation process. This result isfully consistent with that obtained for HbA solutionsunder physiological conditions of pH and [DPG] [7]. Itcorresponds to the typical relation k15k2�k3�k4,also observed for human normal red blood cells [21].According to Perutz [15], the larger value of k4 is due tothe fact that the ionic bonds stabilizing the T-state havebeen broken during earlier steps of oxygenation.The changes of DSi are approximately parallel to

those of DHi. This can be expected from the van’t Hoffequations, and corresponds to the well-known en-

Table 1Thermodynamic parameters for the oxygenation of human red bloodcells, at various pH levelsa

pH 8.0pH 7.8pH 7.4pH 6.8

−11.291.7 −10.291.0DH1 −10.790.9−10.192.0−10.593.1DH2 −6.192.7 −11.095.7 −11.096.3

−8.893.2 −8.494.4 −9.792.7DH3 −5.292.7−12.390.8DH4 −13.990.8−11.692.5 −11.890.6

DHav −11.491.4−10.791.5−9.390.8−9.490.7

−30.195.7DS1 −32.794.5 −28.593.0 −29.792.4−29.6910.3 −13.698.3DS2 −28.5918.5 −28.5918.5

DS3 −24.5910.6−14.798.6 −25.198.7−25.395.2DS4 −29.392.5−22.692.0−22.097.9−25.093.0

−24.792.0 −22.892.5DSav −26.594.7 −28.394.8

9.991.4 8.790.9 9.090.7−TDS1 9.191.79.093.1 4.192.5−TDS2 8.795.6 8.795.6

−TDS3 4.592.6 7.493.2 7.795.6 7.692.6−TDS4 7.690.9 6.792.4 6.990.6 8.990.8

−1.090.4DG1 −1.390.2 −1.590.3 −1.790.3−1.590.8 −2.092.0DG2 −2.391.6−2.392.5−0.790.7 −1.491.1DG3 −0.790.8 −2.191.3

DG4 −4.790.8 −4.992.8 −4.990.7 −5.090.7

a The values of DH, −TDS and DG are in kcal/mol of oxygen, andthe DS values in cal/mol per deg. The standard state for DS is 1 atmof gaseous oxygen. DHav and DSav are averages of enthalpy andentropy changes for steps 1–4. Experimental conditions are as de-scribed in the text.

Fig. 3. Compensation plots of four-steps oxygen binding by humanred blood cells, for pHs 6.8, 7.0, 7.2, 7.4, 7.6, 7.8, 8.0 and 8.2. DSi

values are plotted against DHi values. For each given pH, the fouroxygenation steps are indicated by the same types. The line is drawnby linear least-squares method, through the points corresponding tosteps 1, 2 and 3. All the points clearly apart from that line correspondto step 4. Temperature compensation, Tc, as calculated from thereciprocal slope of the line, is 324 K.


Table 2Thermodynamic contributions to the free energy of cooperativity for human red blood cells oxygenation, at 37°C and various pH levelsa

pH 7.4 pH 7.8 pH 8.0pH 6.8

−3.2 (50%)−T(DS4−DS1) (kcal/mol) −1.8 (19%)−1.5 (31%) −0.1 (16%)DH4−DH1 (kcal/mol) −2.2 (27%) −0.4 (36%) −1.6 (15%) −3.2 (14%)

−3.6 (86%) −3.4 (34%)DG4−DG1 (kcal/mol) −3.3 (30%)−3.7 (58%)

a All values are in kcal/mol of oxygen. The standard errors are indicated in parentheses.

Table 2 shows the enthalpy and entropy contribu-tions to cooperativity for oxygenation of human nor-mal red blood cells, expressed as the free energy change,DG4–DG1, between the fourth and the first steps ofoxygenation. Results are rather homogeneous for allthe pHs examined, with DG4–DG1 values ranging be-tween −3.7 and −3.3 kcal/mol. Although the esti-mates of DG4–DG1 are affected by rather large errors, itappears that cooperative oxygenation of human redblood cells is not purely enthalpic in origin, but theconsequence of both enthalpic and entropicphenomena.

The present data have been also examined on thebasis of the MWC model. The temperature dependenceof log L at pH 7.4 is shown in Fig. 4 (the temperaturedependence of KT and KR is identical to that of k1 andk4 (Fig. 2), respectively). Calculations were done asdescribed by Imai [7], and results at pH 7.4 and 37°Care shown in Table 3. At each step of oxygenation, theT�R transition is endothermic. The allosteric quater-nary transition occurs at the third step, when DGi

trans

becomes negative, the entropic contribution exceedingthe enthalpic one. Roughly similar results were ob-tained for the other pHs (not shown). The allostericswitch can also be expressed by is (= − log L/log c),the allosteric switchover [8]. At pH 7.4, is is equal to2.8. Similar values of 2.8, 3.0 and 2.6, i.e. close to 3,were obtained at pHs 6.8, 7.8 and 8.0, respectively.These results qualitatively agree with those for HbAsolutions [7]. They are consistent with the proposal byPerutz [16] that a fundamental event in the Hb

molecule occurs at the binding of the third oxygen.In Fig. 5, the DHav values have been plotted against

the pH. From pH 7.4 to 8.2, DHav augments by 2.8kcal, which can be attributed to a lower release of Bohrprotons at high pH, with diminution of their endother-mic contribution [1]. Below pH�7.4, the DHav valueflattens. Although more difficult to explain, this resultrejoins the observation of larger heats at pH 6.5 than atpH 7.4, for HbA solutions [7]. At pH 7.4, the value of−9.3 kcal/mol is in agreement with that of −8.2kcal/mol for human whole blood [19]. In the case ofintact red blood cells, as in the present study, it isassumed that the change of temperature has no effecton the pH difference between the extra and intracellularmilieus [18].

The values of the temperature coefficient, expressedas log P50/DT, are reported in Table 4. As DHav, thisparameter exhibits a slight pH-dependence, rangingfrom 0.022 at low pH to 0.028 at pH 8.2. At pH 7.4,the present value of 0.022 agrees with those of theliterature: 0.023 [19], 0.0226 [6] or 0.0229 [20].

A close relation is known to exist between the releaseof heat and the release of ions at the successive steps ofoxygenation [7,13]. It has been proposed [5] that therelease of Bohr protons would entirely account for theenthalpy change differences at the successive steps,according to the relation: DHi

obs=DH int−DnDHH+,

Table 3Thermodynamic parameters for allosteric T�R transition of humanred blood cells, according to the MWC model, at 37°C and pH 7.4,at successive oxgenation stepsa

Lci (Ti/Ri) −TDSitrans DGi

transDHitrans

(kcal/mol)(kcal/mol)(kcal/mol)

T0�R0 16×106 8.7 1.3 10T1�R1 38.4×103 8.3 −1.9 6.4

2.6−5.37.9T2�R2 0.9×102

T3�R3 7.52.2×10−1 −8.6 −1.1T4�R4 −4.8−11.95×10−4 7.1

a DHitrans=DH0

trans−i(DHT−DHR), and DSitrans=DS0

trans−i(DST−DSR). DH0

trans and DS0trans are calculated from the tempera-

ture dependence of ln L. DHT, DHR, DST and DSR are identical toDH1, DH4, DS1 and DS4, respectively, at pH 7.4 (Table 1). Parametersobtained according to the MWC model at 37°C and pH 7.4, are:KT=0.0071 mmHg−1, KR=2.9 mmHg−1, c=0.0024, L=16.9×106, is=2.8.

Fig. 4. Temperature dependence of log L, for normal human redblood cells, at pH 7.4.


Fig. 5. pH dependence of the average heat, DHav, for oxygenation ofhuman red blood cells. Heat values are in kcal/mol. Line is fitted byeye.

Fig. 6. Oxygen equilibria for normal human red blood cells sus-pended in 0.05 M bis–Tris or Tris buffer+0.125 M NaCl, at 37°Cand several pH values. P, partial oxygen pressure in mmHg; Y,fractional saturation. pHs are from left to right: 6.8, 7.0, 7.2, 7.4, 7.6,7.8, 8.0, 8.2 (extracellular pHs). Lines correspond to experimental fitby the Adair equation.

where DHiobs is the observed enthalpy change at the

step i, corrected for heat of solution of oxygen, DH int isthe intrinsic heat of heme oxygenation, Dn the numberof Bohr protons released at the corresponding step, andDHH+ the heat of proton released. This relation hasbeen examined for the present data. The oxygen equi-libria of human red blood cells at pHs ranging from 6.8to 8.2, at the temperature of 37°C, are shown in Fig. 6.Fig. 7 illustrates the pH-dependence of the Adair con-stants and P50. Here, the values of log ki and − log P50

have been plotted against the intracellular pH (pHi). Itis pHi which must be considered instead of extracellularpH (pHe), since it corresponds to the true pH of theinterior of the red blood cell. The pHi values werecalculated according to the relation: pHi=0.774 pHe+1.504 [23]. All the values of the Bohr effect werecalculated by linear regression, in the 6.77–7.7 pHi

range (corresponding to the 6.8–8.0 pHe range). Theassumption of linearity seems to be valid for k1 and k4.It may be accepted as a first approximation for k2, k3

and P50, since acceptable smoothing of the points,reproducible for other temperature levels, was notfound possible (excepting P50). The estimates of Dn aregiven by d log ki/dpH for the ith step, and by −d log P50/dpH for overall oxygenation. Results are pre-sented in Table 5. Values for the two intermediate steps

[2,3] have been combined [5]. It is clear that the releaseof protons, Dn, is not identical for the successive stepsof oxygenation, especially it is smaller at the fourthstep, as was observed for HbA solutions [11,12]. Avalue of 11 kcal/mol for DHH+ [5] was used. Theaverage DH int value (−12.8 kcal/mol) is in correctagreement with those given for HbA solutions, of ap-proximately −14 kcal/mol [5,7]. For the successivesteps of oxygenation, the DH int values do not signifi-cantly diverge from the average one. The standarderrors are large, e.g. 75% for step 4, accounting forerrors in the estimates of both DHi

obs and Dn. Neverthe-less, the present data appear to be consistent with theproposal of Chu et al. [5], i.e. a nearly constant heat foroxygen binding to the heme is observed after correctionof the observed heat for the heat release of Bohrprotons, for the normal human Hb system.

This approach can be extended to other Hbs. In aprevious study [23], the heats of oxygenation of pigeonred blood cells had been measured, together with the

Table 4Temperature coefficient, Dlog P50/DT for human red blood cells, at various pH values

7.4 7.6 7.8 8.0pH 6.8 8.27.0 7.2

Dlog P50/DT 0.022 0.022 0.215 0.022 0.023 0.025 0.027 0.028


Fig. 7. pH dependence of the Adair constants and P50 for humannormal red blood cells, at 37°C. pHi, intracellular pH. �, k1; �, k2; , k3; �, k4; , P50. Lines are calculated by linear least-squaresmethod. The derived stepwise Bohr effect values (Dn) are presented inTable 5.

above described, DH int values comprised between ap-proximately −12 and −13 kcal/mol are obtained, i.e.rather similar to those of human red blood cells. So, itappears that the low enthalpy values of pigeon redblood cells are probably essentially due to a larger(intracellular) Bohr effect, and not to a difference be-tween the intrinsic heats of heme oxygenation of pigeonand human Hb. This near equality of DH int for the twoHbs is not necessarily a rule. It has been reported forinstance that the DH int value of bovine Hb would behalf that of human HbA [17].

How far this thermodynamic scheme, in favor of aclose link between the release of heat and that of Bohrprotons, might it be generalized? Thermodynamic stud-ies on fish Hbs reveal more complex Hb systems,different from a both quantitative and qualitative view-point, with characteristics highly dependent on the pHlevel. Oxygen binding curves for trout red cells hadbeen measured in this laboratory at pH 7.8 and 8.4, at15, 20 and 25°C [22]. The thermodynamic parametersobtained at physiological pH (7.8) for trout normal redcells are resumed in Table 7, and those at pH 8.4 inTable 8. The values for the two intermediate steps havebeen included. At both pHs, the DGs are about halfthose for human red blood cells, meaning that the troutHb system is less cooperative. At pH 7.8, the enthalpyvalues are small and negative throughout all the oxy-genation. DHav is only −4.6 kcal/mol. DH1 is near zero(−0.2 kcal/mol), so that, after correction for the heatof solution of oxygen, the first reaction with oxygen is

Bohr effect, and rather low enthalpy values had beenobserved. In Table 6, the values of DHi

obs, Dn (referredto intracellular pH) and DH int have been reported foroxygen binding of pigeon red blood cells at pHe 7.4,37°C. After correction for the heat of Bohr protons, as

Table 5Proton release and intrinsic heat of heme oxygenation upon stepwise oxygenation for human red blood cells at pH 7.4 and 37°Ca

Steps 2+3Step 1 AverageStep 4

0.4590.13Dn (mol/heme) 1.7090.26 0.1690.11 0.5990.12−14.9911.9 −11.692.5 −9.390.8DHi

obs (kcal/mol) −11.291.7−27.699.7 −10.497.8DH int (kcal/mol) −12.894.1−13.194.8

a Dn, number of protons released at the considered step of oxygenation. Values are obtained from the data presented in Fig. 7, for the 6.77–7.7intracellular pH (pHi) interval, i.e. 6.8–8.0 extracellular pH (pHe) interval. The pHi values were obtained according to the relation: pHi=0.774 pHe+1.504 [23]. All Dn values were calculated by linear regression in the considered pH range. Dn is given by d log ki/dpH at the step i,and −d log P50/dpH for overall oxygenation. DH int, intrinsic heat of heme oxygenation for the considered step. DH int=DHi

obs−DH sol−DnDHH+, where DHi

obs, DH sol and DHH+ are observed heat of oxygenation at the step i, heat of solution of oxygen (−3 kcal/mol) and heat ofproton release, respectively. A value of 11 kcal [5] was used for DHH+.

Table 6Proton release and intrinsic heat of heme oxygenation upon stepwise oxygenation for pigeon red blood cells at pH 7.4 and 37°Ca

AverageStep 4Steps 2+3Step 1

Dn (mol/heme) 0.7390.03 1.4790.27 0.6690.17 0.7190.02−8.690.4 −11.795.2DHi

obs (kcal/mol) −8.591.6 −7.290.7−12.893.3−21.898.4−13.690.7DH int (kcal/mol) −12.091.6

a Abbreviations are as in the footnote to Table 5. The original data are taken from [23]. Pigeon red cells are diluted in 0.05 M Tris or bis–Trisbuffer+0.125 M NaCl. Dn values were measured in the 6.83–7.53 pHi interval (i.e. 7.0–8.2 pHe interval). The pHi values were obtained accordingto the relation: pHi=0.58 pHe+2.775. The original oxygenation parameters were recalculated according to the Adair analysis in order to obtainvalues for the two intermediate steps 2 and 3. Calculations were performed as described in the footnote to Table 5.


Table 7Thermodynamic parameters for the oxygenation of trout normal red blood cells at pH 7.8, 20°Ca

Step 2 Step 3 Step 4Step 1 Average

0.036 0.072k (mmHg−1) 0.0980.0064−2.6 −12.4−0.2 −3.1DH (kcal/mol) −4.6−2.3 −35.5DS (e.u.) −1.72.5 −9.2

0.7 10.4−0.7 0.5−TDS (kcal/mol) 2.7−0.9DG (kcal/mol) −1.9 −2.0 −2.6 −1.9

a Data are taken from Ref. [22]. k, Adair constants in mmHg−1. Other abbreviations are as in the footnote to Table 1. Trout red blood cellsare diluted in 0.05 M Tris or bis–Tris+0.125 M NaCl buffer. Temperature measurements are 15, 20 and 25°C. Standard errors, correspondingto the least squares method, are lower than 50%, except for step 1.

slightly endothermic. Simply increasing the pH by 0.6U results in a different picture. At pH 8.4, DHav islarger (−8.5 kcal/mol), and the release of heat duringoxygenation is markedly discontinuous: DH1 remainsvery low (−1.3 kcal/mol) and the third step of oxy-genation is endothermic (+10.6 kcal/mol), while thesteps 2 and 4 are exothermic (−22.5 and −20.5kcal/mol, respectively). Accordingly, the shape of thebinding curve is nearly temperature-independent at pH7.8, but exhibits a pronounced dependence upon thetemperature at pH 8.4 [22]. This particular thermody-namic behavior is probably not specific of Root effectHbs, since a rather similarly discontinuous release ofheat has been described for bovine Hb at pH 9.0, whenthe release of Bohr protons is finished [17]. For troutred blood cells, the larger value of DHav at pH 8.4, ascompared to pH 7.8, may be explained by a loweroverall Bohr effect [21]. But no clear correlation ap-pears to exist between the values of DHi and the releaseof protons, at the successive oxygenation steps, fortrout. The explanation for the non-uniform heat releasemight rest on conformational changes of the Hbmolecule upon oxygenation, with hydrophobic modifi-cations responsible for endothermic events [4]. The roleof water molecules in the oxygenation process has beenpointed out [8]. These interactions would be ‘intrinsic’features of the Hb molecule, independent of ion release,and may be expected to differ among vertebrate Hbs.The present observations suggest that the relation be-tween DHobs and the stepwise release of protons [5]would not necessarily apply to all the vertebrate Hbs,for all experimental conditions.

It has been shown that the experimental conditions(buffer, ions surrounding the Hb molecule) are of con-siderable importance in functional studies on Hb [16].The biochemical complexity of the intracellular milieumakes it difficult to mimic exactly the ‘true’ physiologi-cal conditions for studies performed on dilute Hb solu-tions. (a) The Hb concentration is very high (20mM-heme), and the true pKs of Hb are uncertain forsuch conditions [16]. (b) Anions and cations can inter-act with each other, so that the heterotropic interac-tions of certain organic phosphates with Hb can bemuch lower than expected [22]. (c) There is a gradientof protons across the membrane of the red blood cell,and the localization of the molecules inside the red cellis unknown. (d) Multiplicity of the Hb components isfrequent in low vertebrate species, such as trout, andHb may also aggregate in the red blood cell [3]. (e) Redcells are different in age and biochemical composition.Nevertheless, when scrutinizing the human Hb system,it appears that the thermodynamic properties of oxy-genation by the red blood cells are similar to thosemeasured for HbA in dilute solution, in other laborato-ries. No discrepancy can be evidenced which wouldexceed the reasonable limits of experimental accuracy,for experimental conditions that remain close to thephysiological ones (absence of strong organic phos-phates such as IHP, especially, which are known tomodify the allosteric equilibrium). The situation may bemore complicated for other Hb systems, such as trout.Unfortunately, these systems of remarkable interest arealso more difficult to examine, partly due to the highinstability of these Hbs in solution [3].

Table 8Thermodynamic parameters for the oxygenation of trout normal red blood cells at pH 8.4, 20°Ca

Step 4 AverageStep 1 Step 2 Step 3

k (mmHg−1) 0.550.0136 0.053 0.051−8.5−20.510.6DH (kcal/mol) −22.5−1.3

DS (e.u.) −58.50.4 −20.6−69.6 43.6−12.820.4−0.1−TDS (kcal/mol) 6.017.1

−1.4 −2.5−3.4−2.2−2.1DG (kcal/mol)

a Data are taken from Ref. [22]. Abbreviations and experimental conditions, except pH, are as in the footnote to Table 7. Standard errors arelower than 30%, except for step 1.


In conclusion, the DHi but not the DGi for oxygena-tion of human red blood cells are rougly independent ofi, for the 6.8–8.2 pH range, and the shape of thebinding curve is nearly independent of temperature.The effect of pH is manifested by an increase of DHav

by 2.8 kcal/mol above pH�7.4, and an intrinsic heatof heme oxygenation of approximately −13 kcal/molis obtained after correction for heat of Bohr protonrelease.

Acknowledgements

I acknowledge Dr K. Imai who provided me with theprograms for calculating the oxygenation parameters.

References

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thermodynamic studies on oxygen binding by human red blood cells

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