Thermodynamics of inositol hexakisphosphate interaction with human oxyhemoglobin.

The interaction of inositol hexakisphosphate (IHP) with oxygenated human adult hemoglobin (Hb) was investigated at 25 degreesC. The affinity of IHP for oxygenated Hb is strongly pH-dependent, and potentiometric measurements of proton uptake and release upon IHP addition have shown that over the range between pH 8.0 and pH 6.0 in oxygenated Hb there are three groups of residues that change their pKa values after IHP addition, likely because of their interaction with negative charges of the heterotropic effector. On the basis of previous calculations on the electrostatic properties of human Hb (Matthew, J. B., Hanania, G. I. H., and Gurd, F. R. N. (1979) Biochemistry 18, 1919-1928; Lee, A. W.-m., Karplus, M., Poyart, C., and Bursaux, E. (1988) Biochemistry 27, 1285-1301), two of these groups might be Val1beta and His143beta, which are located in the beta1beta2 dyad axis, where they have been also proposed to interact with 2,3-diphosphoglycerate, whereas the third group does not appear easily identifiable. Calorimetric measurements of the heat associated with IHP binding at different pH values over the same range indicate that IHP binding is mostly enthalpy-driven at pH < 7 and mostly entropy-driven at pH > 7.

The interaction of inositol hexakisphosphate (IHP) with oxygenated human adult hemoglobin (Hb) was investigated at 25°C. The affinity of IHP for oxygenated Hb is strongly pH-dependent, and potentiometric measurements of proton uptake and release upon IHP addition have shown that over the range between pH 8.0 and pH 6 27, 1285-1301), two of these groups might be Val 1␤ and His 143␤ , which are located in the ␤ 1 ␤ 2 dyad axis, where they have been also proposed to interact with 2,3diphosphoglycerate, whereas the third group does not appear easily identifiable. Calorimetric measurements of the heat associated with IHP binding at different pH values over the same range indicate that IHP binding is mostly enthalpy-driven at pH < 7 and mostly entropydriven at pH > 7.
In more recent years, another organic phosphate, namely IHP (closely related to the inositol pentaphosphate, which is the physiological effector in avian erythrocytes; see Ref. 7), has often been employed to study the modulation of functional properties of human Hb (8,9). It possesses additional negative charges with respect to 2,3-DPG, and it displays a much larger effect, which suggests the occurrence of additional electrostatic interactions with respect to 2,3-DPG, as from early model building studies on deoxy Hb (10). Therefore, the enhanced functional effect of IHP on the O 2 binding properties of human Hb with respect to 2,3-DPG could be related to a more widespread interaction surface, with the possibility of modulating ligand-linked conformational changes taking place over a larger portion of the whole tetramer.
However, a comprehension of the origin for this enhanced effect starts from the characterization of the IHP interaction energy with deoxyHb and with oxyHb. Previous studies have shown that IHP binds HbO 2 , and its binding properties are pH-dependent (11,12). In this study, we have carried out a detailed analysis of the interaction of IHP with human HbO 2 , measuring the effect on (a) proton titration, (b) O 2 dissociation kinetics from fully liganded tetramer, and (c) heat associated to the reaction in order to give a quantitative description of the system and of the interplay between IHP and proton interaction with human HbO 2 .

EXPERIMENTAL PROCEDURES
Human HbO 2 was obtained from the blood of healthy volunteers and stripped of anions according to the procedure reported by Riggs (13). Cells were washed three times with iso-osmotic NaCl solutions by centrifugation at 1000 ϫ g, and packed cells were lysed by adding 2 volumes of cold bidistilled water. Stroma were removed by centrifugation at 12,000 ϫ g for 30 min. Hemolysate was first filtered through a Sephadex G-25 column, equilibrated with 0.01 M Tris/HCl buffer, pH 8.0, and EDTA 10 Ϫ5 M, and afterward it was passed through a column of mixed bed ion-exchange resin (Bio-Rad AG501-X8). For proton titration experiments, Hb solution was concentrated on Amicon YM10 (Bio-Rad) membranes. For all other experiments, the sample was then extensively dialyzed versus the desired buffer. All experiments were performed at 25°C in the presence of 0.1 M NaCl.
Titrations were performed at 25°C using a thermostatted autotitrator (Radiometer, Copenhagen, Denmark) equipped with a SAM90 sample station, ABU93 triburette unity, and VIT90 titration controller, adding automated 100-l aliquots of 2 mM NaOH (prepared from 0.01 M Normex and checked by acid titration). For each experiment, three solutions (between 0.75 and 2.00 ml) were titrated, namely (a) HbO 2 ranging between 1.0 and 1.5 mM tetramer, (b) IHP ranging between 20 and 25 mM, and (c) IHP plus HbO 2 at the same concentrations employed in a and b. We also carried out experiments at 0.2 mM heme concentration (i.e. the concentration at which kinetic experiments were performed; see below), but no appreciable difference was noticed, indicating that the dimer-tetramer equilibrium does not affect these results to a detectable extent. From titration curves, composed of more than 150 experimental points and elaborated by our own programs in order to express constant pH increments, the proton buffering capacities (␦ mol/␦ pH) were obtained. Buffering capacities of IHP-bound HbO 2 were computed by subtracting the contribution of IHP from the overall buffering capacities measured on IHP plus HbO 2 solution. The integration of this differential buffering capacity gave the corrected titration curve of IHP-bound HbO 2 , the position of which relative to IHP-free HbO 2 should be independently determined. Therefore, proton uptake for the formation of the IHP-HbO 2 (i.e. ⌬Z) was obtained at several fixed pH values by measuring the moles of HCl per mole of HbO 2 needed to recover the starting pH value after the addition to oxyHb of a saturating amount of concentrated IHP (IHP/HbO 2 molar ratio 20:1 with [HbO 2 ] ϭ 1.5 mM tetramer) and the correction for IHP dilution effects (obtained by IHP blank titration). These values allowed us to establish the relative position of the titration curves and thus to obtain experimental ⌬Z values over the whole pH range investigated (i.e. between 6.0 and 8.0). Outside this pH range, the reproducibility of data decreased dramatically, and thus the errors were too large to allow any meaningful analysis of experimental curves. The value of ⌬Z as a function of pH (see Fig. 1A) is related to the pH dependence of the IHP binding equilibrium constant K according to the following equation (14).
Upon integration, this relation becomes the following equation. log The value of K at a given pH value (in our case, pH ϭ 7.1) was determined by subsequent additions of subsaturating amounts of IHP to HbO 2 and measuring after each addition the moles of HCl needed to maintain a constant pH value. The knowledge of the moles of HCl, of ⌬Z at that pH, of the moles of HbO 2 , and of the moles of IHP added allows one to determine the moles of free IHP after each addition and the saturation degree of the IHP-HbO 2 complex (Y). If one assumes a single binding site for IHP to the tetrameric HbO 2 (under these experimental conditions; see Ref. 12), it is then possible to fit values of Y as a function of x moles of free IHP (see Fig. 1B), according to the following equation.
where x is given by the equation, where C IHP is the IHP concentration of the stock solution employed and V IHP and V tot are the volume added of IHP stock solution and the total volume of the sample solution, respectively. The extent of IHP binding Y is given by the following equation.
Y ϭ mol of HCl/⌬Z/mol of HbO 2 (Eq. 5) Thus, using Equation 2, the value of K at pH 7.1 (by Equation 3), and ⌬Z dependence on pH, we were able to calculate K over the pH range between 6.0 and 8.0 (see Fig. 2). Kinetics of O 2 dissociation in fully liganded Hb was undertaken employing a Hi-Tech SF-51 stopped-flow apparatus with a 2-cm path length observation cell that was interfaced with a desktop computer for fast data acquisition. Oxygen dissociation was followed by mixing HbO 2 (0.2 mM heme after mixing) with a CO-saturated buffer containing sodium dithionite and following the conversion of HbO 2 to HbCO at ϭ 563 nm (15). No CO concentration dependence was observed for these kinetics, down to a concentration of 50 M, a value 10 times lower than that employed for all observations reported in this study (i.e. 0.5 mM after mixing). The amount of free IHP was calculated, implying that the IHP-dependent effect on the O 2 dissociation rate constant is linearly dependent on the percentage of IHP-HbO 2 complex with respect to the total concentration of tetrameric HbO 2 .
The Hb solution was kept inside the sample cell (total cell volume, 184 l), and the injection syringe was filled with the concentrated IHP solution. In order to reduce the heat of dilution, small volumes of IHP solution (i.e. 2 l) were added each time, and corrections were made for the heat effects due to stirring and dilution (16). Calibration experiments were carried out, employing HCl/NaOH titrations and electrical calibrations (16).
Calorimetric IHP titration experiments of human HbO 2 were carried over the pH 6.0 -8.0 range, employing an IHP concentration range that was enough to fully saturate the HbO 2 , and this occurrence was deter-mined when no heat was produced upon further addition of IHP. The data analysis is based on a titration in which IHP concentration is increased at each step i from x i Ϫ 1 to x i , and the quantity of heat q i Ϫ 1 is associated with the binding of IHP to HbO 2 in this step. The value of q i Ϫ 1 is then given by the equation, where m T is the moles of HbO 2 employed in each calorimetric experiment. The excess enthalpies (H Ϫ H 00 ) i depend on the ligand concentration x i according to the following equation.
The latter expression is a van't Hoff formulation in terms of the binding polynomial P (17). The heat q i Ϫ 1, i is the experimentally measurable quantity in isothermal titration calorimetry. If one assumes only one site for the FIG. 1. A, observed pH dependence at 25°C of proton uptake or release (⌬Z) upon binding of saturated amounts of IHP to HbO 2 . The error bars refer to the distribution of errors based on five different measurements of the same sample. The data presented are limited to the pH range between 6.0 and 8.0 because outside this range, data become very unreliable. The continuous line corresponds to the behavior expected for Equation 10, employing the parameters reported in Table I. Dashed line corresponds to the fit of data employing only two protonating groups. For further details, see text. B, saturation function (Y) of HbO 2 as a function of IHP addition at pH 7.1 and 25°C. The continuous line was obtained by nonlinear least-squares fitting of experimental data according to Equation 3. The fitted limiting values for Y ϭ 1.0 (i.e. under saturating amounts of IHP) have been employed to calculate ⌬Z at the given pH. For further details, see text.
interaction of IHP with HbO 2 , the van't Hoff expression reduces to the following equation.
The value of the observed enthalpy change ⌬H obs , as calculated from the van't Hoff expression, can be dissected into two main contributions, one related to the IHP binding phenomenon itself and the other one ascribable to the ligand-linked proton equilibria in the buffer. Therefore, because there is a linkage between IHP binding to HbO 2 and proton release or uptake, the observed ⌬H obs is represented by the equation, where ⌬H bc is the buffer-corrected enthalpy change for IHP interaction with HbO 2 , which still contains the contribution arising from the ionization enthalpy of HbO 2 (18). The second term in Equation 9 refers to the apparent enthalpy change obtained when ⌬ moles of protons are released or taken up to a buffer with a ⌬H ion ionization enthalpy change. The value of ⌬H bc was determined at every pH investigated, carrying out the same calorimetric experiment in buffers with different ionization enthalpy, such as MES, HEPES, PIPES, Bis-Tris, and MOPS, and extrapolating to ⌬H ion ϭ 0 (see Equation 9 and Ref.  1A shows that the total proton uptake of human HbO 2 at 25°C in the presence of 30 mM IHP, a concentration sufficiently high to guarantee the full saturation of the higher affinity site for IHP in the liganded hemoglobin (11,12), is pH-dependent, approaching 0 at pH Ն 8.0, attaining a maximum value of ⌬Z Х 2.8 at pH Ϸ 7, and then decreasing upon pH lowering. It is important to note that over the same pH range, the buffering capacity (and thus the amount of protons exchanged with bulk solvent) of a 30 mM solution of IHP alone was much less than that observed for a solution of 1.5 mM tetrameric HbO 2 alone, clearly indicating that the phenomenon reported in Fig. 1A is mostly related to the proton exchange involving the Hb molecule and not the IHP molecule. Because ⌬Z is the derivative of the proton-linked effect on the IHP binding constant to HbO 2 (see Equation 1), a quantitative analysis of ⌬Z data as a function of pH (Fig. 1A) allows the determination of the linkage between IHP binding and shifts of pK a values for groups affected by IHP interaction with HbO 2 . The analysis of these data requires the involvement of (at least) three classes of residues, according to the following relationship.
where x ϭ 10 ϪpH and K i ϭ 10 ϪpKi (i ϭ 1-3) are the proton binding association constants of the three groups, and the superscript b and f refer to IHP-bound and IHP-free HbO 2 , respectively. P b and P f are the binding polynomials for proton binding to IHP-bound and IHP-free HbO 2 , respectively. and It is important to note that Equations 10 -12 imply that the three groups are protonating in a concerted way; that is, the protonation of the first group alters the protonation of the second group, and the protonation of both the first and the second group affects the protonation of the third group. In other words, groups 2 and 3, which would not protonate in the range investigated, change their proton affinity upon protonation of group 1. Therefore, by virtue of the cooperative behavior, the values of K i may be indeed treated as intrinsic binding constants, and they can be immediately referred to the pK a values of the various residues involved. The pK a values of groups involved in the IHP binding to HbO 2 resulting from the fit of data in Fig. 1A according to Equation 10 are reported in Table  I, and they correspond to the continuous line in Fig. 1A. It is important to note that in Table I the pK 3 for IHP-free HbO 2 is reported only as being Ͻ4.5, because any value below 4.5 gives an equally good fit of data, and we can consider its value as partially undetermined. Fig. 1B displays the fitting of pH-stat data on the equilibrium titration of human HbO 2 with IHP at pH 7.1 according to Equation 3, which allows one to calculate the affinity of IHP for HbO 2 at this pH. Combination of the information obtained from the experiments reported in the two panels of Fig. 1, namely (a) ⌬Z as a function of pH (Fig. 1A), and (b) the equilibrium IHP binding constant at a given pH value (Fig. 1B), allows one to calculate, according to Equation 2 (14), the logK for IHP binding to human HbO 2 over the pH range covered by the proton titration reported in Fig. 1A. In Fig. 2, the pH dependence of the equilibrium IHP binding constant to human HbO 2 is reported at 25°C. The continuous line reported in Fig. 2 was obtained employing the following equation.
where K obs is the observed IHP equilibrium binding constant, K 0 is the IHP equilibrium binding constant to unprotonated HbO 2 , and P b and P f are the proton binding polynomials to IHP-bound and IHP-free human HbO 2 , respectively, (see Equations 11 and 12), employing the values of K i reported in Table  I. Therefore, the interrelationship between IHP and proton linkage can be represented by the following Scheme.
P ϩ H ϩ L | ; Scheme I and the pK a values reported in Table I deserve some further comment. As a matter of fact, the behavior observed in Table I underlies a cooperative proton-linked process, such that protonation of one residue facilitates the protonation of another residue. This concerted process may envisage the occurrence of a pH-dependent conformational transition in liganded human Hb, as also suggested by previous observations (15). Furthermore, Scheme I indicates that IHP and protons act synergistically to facilitate the conformational transition, raising the pK a of interacting groups upon binding of the negatively charged IHP. Obviously, with our experimental approach, we cannot absolutely rule out a contribution arising, in addition, from a change in the protonation state between Hb-free and Hb-bound IHP, even though the small amount of proton exchanged by IHP alone (see above) indicates that this contribution is not relevant. This conclusion is further supported by a previous observation on deoxy Hb and on HbCO by 31 P NMR, where a change in the protonation state of IHP upon binding Hb indeed was detected, but it turned out to be pH-independent between pH 5.2 and 8.5 (20). Therefore, the observed pH dependence for IHP binding to HbO 2 (see Fig. 2) can be almost completely attributed to a pH-dependent difference in protons bound by IHP-free and IHP-bound oxyHb. This proton-linked behavior is calculated on the basis of the proton titration carried out on IHP-free and IHP-bound human HbO 2 , but a confirmation of its validity may come from an independent measurement of IHP binding to fully liganded HbO 2 . This can be carried out by investigating the effect of IHP on the displacement kinetics of oxygen by CO. Thus, in this experimental approach, the rate of CO binding is rendered much faster than the O 2 dissociation process, and the observation concerns a fully liganded protein, allowing a direct determination of IHP binding to HbO 2 . In Fig. 3, the values of rate constants for O 2 dissociation from fully liganded Hb are reported as a function of free IHP concentration at different pH values. It is important to note that the continuous lines in Fig.  3 are not fit to experimental points; instead, they simply show the correlation between the predicted pH dependence of K (see Fig. 2) and the observed pH dependence of the IHP effect on the O 2 dissociation rate constant from fully liganded Hb. Therefore, they are constrained to the expected IHP dependence on the basis of the IHP binding equilibrium constant at the same pH according to the parameters reported in Table I, employed to fit the data reported in Fig. 1A, and used to obtain the continuous line in Fig. 2. The agreement is quite impressive and allows a very strong degree of confidence in the correctness of the prediction based on data in Fig. 1A and on Equation 2, and thus in the accuracy of parameters in Table I, as well as in the pH dependence described in Fig. 2, to quantitatively describe the linkage between proton and IHP binding to human HbO 2 .
Parameters in Table I clearly indicate that the pH-dependence of IHP binding constant depends on the pK a shift of three classes of residues that increase their pK a values by Х0.96, 0.92, and Ͼ3.7, respectively, upon interaction with negative charges of IHP. It is important to note that in free HbO 2 the pK a values of at least two of these residues turn out to be low enough to rule out the relevant role in the "alkaline" Bohr effect, whereas a third residue displays a pK a of 6.72 (see Table  I) in the IHP-free HbO 2 , which makes it a good candidate for a contribution to the alkaline Bohr effect (21)(22)(23). On the other hand, such pK a values for IHP-free HbO 2 are within the pH range of a conformational transition, which has been detected in human HbO 2 in the absence of anions (15) and which is characterized by an enhancement of the O 2 dissociation rate constant in the fully liganded form. A similar behavior was observed in the presence of 0.1 M Cl Ϫ (Fig. 4), and it can be accounted for by employing the three pK a values reported in Table I for IHP-free HbO 2 , as from the continuous line reported in Fig. 4. The same consideration can be applied to the pH dependence of the O 2 dissociation rate constant for fully liganded Hb in the presence of saturating amounts of IHP (i.e. 30 mM), which also is fully described employing the pK a values reported in Table I for IHP-bound human HbO 2 (see Fig. 4).
Altogether, these data strengthen our confidence in the possibility of giving a quantitative description of the thermodynamics of IHP interaction with human HbO 2 . Therefore, we can claim that (a) the protonation of three residues, the pK a of which values range in IHP-free HbO 2 between Ϸ4.0 and 6.7 (see Table I), brings about a conformational transition in fully liganded human Hb, (b) this event is closely related to the pH-dependent enhancement of the IHP equilibrium binding constant to HbO 2 (Fig. 2), and (c) IHP binding is accompanied by a more or less marked raising of pK a values of these three classes of residues.
The identification of the three residues involved in the proton-linked IHP binding to HbO 2 is not easy, but previous observations indicated that some potentially important residues  Table I  display low pK a values in oxyHb in the absence of organic phosphates (24). In particular, a fairly low pK a value (i.e. pK a Ͻ 4.5) has been reported by several authors for His 143␤ in HbO 2 (25), a residue that has been already proposed to be involved in the binding of organic phosphate (6,10). A second residue might be Val 1␤ , which has been proposed to display a pK a Ϸ 6.8 in IHP-free HbO 2 (25) and which might be tentatively recognized in the residue characterized by a pK a ϭ 6.72 (see Table I). The third residue (characterized by a pK a ϭ 5.96 in IHP-free HbO 2 ; see Table I) is very difficult to identify, even with some uncertainty, and we cannot rule out at this stage that the effect attributed to this IHP-linked group is instead attributable to a widespread small effect on several residues, such as His 72␣ and His 77␤ , which have been reported to have in HbO 2 pK a values below 6.5 (25). However, it must be pointed out that a fairly low pK a Ͻ 6.5 has been also proposed for His 2␤ (24,25), another residue in the ␤-dyad axis cavity where organic phosphates bind (6,10). The possibility of a role by His 2␤ in the interaction of IHP with HbO 2 is not in contradiction with the observation on a mutant, namely Hb Deer Lodge (where His2␤ is substituted by Arg; see Ref. 26), in which the IHP effect on oxygenation appears unmodified. Thus, (a) Arg may substitute reasonably well for His in the interaction, such that the effect of the substitution is substantially reduced, and (b) in the oxygenation, an effect is observed only if there is a difference in the IHP binding mode between deoxy-and oxyHb, and this seems to be not true for His 2␤ (24,25). The role of Lys 82␤ has not been taken into account in our analysis of the pH dependence simply because its pK a is much too high to come into play over the pH range investigated (25,27), but its contribution to the free energy of IHP binding is probably a major one in determining the affinity for pH Ͼ 8.0.
The linkage relationship between proton and IHP interaction with human HbO 2 can be described in quantitative energetic terms by calorimetric measurements of the heat that accompanies binding of IHP at different pH values. In this way, information concerning ⌬H of the interaction allowed us to attempt a correlation between (a) protonation of residues in IHP-free and IHP-bound HbO 2 , (b) the free energy involved in the interaction, and (c) the entropic contribution to the binding process. Fig. 5 shows such relationships in the pH range between 6 and 8, from which it was concluded that (a) at pH Ͻ 7.0, the IHP binding is essentially enthalpy-driven (⌬H being strongly exothermic and pH-independent, with a value of ХϪ59 kJ/mol), whereas the pH dependence of ⌬G is completely attributable to the pH dependence of ⌬S, which is always positive for values of pH Յ 7.0; (b) at pH Ͼ 7.0 there is a progressive decrease of ⌬S, which becomes negative at pH Ͼ 7.4, accompanied by a decrease of the exothermicity of the process, which becomes endothermic at pH Ͼ 7.5. Therefore, at pH Ͼ 7.0, the entropy role in determining the affinity of IHP for HbO 2 becomes progressively predominant as pH increases, and a proton-linked enthalpy-entropy compensation comes into play in regulating the pH dependence of the free energy for IHP binding. Therefore, it appears as if two different interaction modes are operative in modulating the IHP binding, one predominating at pH Ͻ 7.0 and the other predominating at pH Ͼ 7.0. We must stress at this point that a previous calorimetric investigation of the interaction of IHP with HbCO at few pH values gave results fully compatible with ours, at least at the corresponding pH values (28).
Altogether, this behavior may be tentatively correlated with the pK a shifts reported above (see Table I). Thus, at very alkaline pH (i.e. Ն8.0), IHP interaction is not accompanied by any proton release or uptake, and it appears to be an endothermic process, displaying a negative ⌬S. As the pH is decreased toward 7.0, the three IHP-linked protonating groups take up protons when IHP interacts with HbO 2 , increasing the ⌬Z (see Fig. 1B). The proton uptake during IHP binding also brings about a progressive decrease of the endothermicity, with a ⌬H Ͻ 0 at pH Ͻ 7.5, mirrored by a parallel increase of ⌬S, which becomes positive at pH Ͻ 7.4. (see Fig. 5). As the pH is  3 , where k obs is the observed O 2 dissociation rate constant from HbO 2 , k 1 , k 2 , k 3 , and k 4 are the O 2 dissociation rate constants from unprotonated, singly protonated, doubly protonated, and triply protonated HbO 2 , respectively (and were the only free-floating parameters), P is the binding polynomial for proton binding to either IHP-free (see Equation 12) or IHP-bound (see Equation 11) HbO 2 . Values of K 1 , K 2 , and K 3 were those reported in Table I for the IHP-free and IHP-bound HbO 2 . For IHP-free HbO 2 , the continuous curve was obtained using k 1 ϭ 15.3 s Ϫ1 , k 2 ϭ 37.3 s Ϫ1 , k 3 ϭ 72.3 s Ϫ1 , and k 4 ϭ 130 s Ϫ1 . For IHP-bound HbO 2 , the continuous curve was obtained using k 1 ϭ 15.3 s Ϫ1 , k 2 ϭ 50 s Ϫ1 , k 3 ϭ 90 s Ϫ1 , and k 4 ϭ 130 s Ϫ1 . However, it must be noticed that in the case of IHP-bound HbO 2 , the values of k 2 and k 3 are very poorly defined, because the curve is scarcely affected by changes of their values. For further details, see text.  Fig. 2, values of ⌬H were obtained from calorimetric measurements (see Equation 9 under "Experimental Procedures"), and values of T⌬S were derived according to the relationship T⌬S ϭ ⌬H Ϫ ⌬G. lowered below 7.0, the three IHP-linked protonating groups begin to take up protons in IHP-free HbO 2 as well, corresponding to a decrease of ⌬Z (Fig. 1B). Such a process seems to affect the ⌬S of IHP interaction, decreasing its positive value and thus increasing the ⌬G of binding, whereas ⌬H appears not to depend on the protonation of these groups in IHP-free HbO 2 (Fig. 5).
Therefore, it seems that the progressively increasing exothermicity of IHP interaction upon pH lowering indeed may be related to the heat released by the groups that take up protons when IHP binds (29). However, the pH-independent value of ⌬H at pH Ͻ 7.0, over a range in which the groups are already protonated in IHP-free HbO 2 and the extent of IHP-linked proton uptake (i.e. ⌬Z) decreases, seems to suggest that additional factors might come into play to determine the observed exothermicity of IHP binding at low pH, such as the electrostatic interaction between the positive charges of HbO 2 and the negative charges of IHP.