Abstract
Abnormal hemoglobins can have major consequences for tissue delivery of oxygen. Correct diagnosis of hemoglobinopathies with altered oxygen affinity requires a determination of hemoglobin oxygen dissociation curve (ODC), which relates the hemoglobin oxygen saturation to the partial pressure of oxygen in the blood. Determination of the ODC of human hemoglobin is typically carried out under conditions in which hemoglobin is in equilibrium with O2 at each partial pressure. However, in the human body due to the fast transit of RBCs through tissues hemoglobin oxygen exchanges occur under non-equilibrium conditions. We describe the determination of non-equilibrium ODC, and show that under these conditions Hb cooperativity has two apparent components in the Adair, Perutz, and MWC models of Hb. The first component, which we call sequential cooperativity, accounts for ∼70% of Hb cooperativity, and emerges from the constraint of sequential binding that is shared by the three models. The second component, which we call conformational cooperativity, accounts for ∼30% of Hb cooperativity, and is due either to a conformational equilibrium between low affinity and high affinity tetramers (as in the MWC model), or to a conformational change from low to high affinity once two of the tetramer sites are occupied (Perutz model).
1. Introduction
Hemoglobin (Hb) oxygen dissociation curve (ODC), which relates oxygen saturation (SO2) and partial pressure of oxygen in the blood (PO2), is an important tool for understanding how blood carries and releases oxygen 1.
Classically, factors recognized to influence the ODC include the local CO2 partial pressure (PCO2), pH, temperature, as well as allosteric metabolites like 2,3 diphosphoglycerate (2,3-DPG). The curve is shifted to the right (i.e. lower saturation for a given PO2) by higher PCO2, greater acidity (lower pH), higher temperature, and higher concentration of 2,3-DPG 1-7. The factors that shift the ODC to the right are directly relevant to the conditions which prevail in metabolizing tissues, as they facilitate the unloading of oxygen from hemoglobin. The converse occurs during passage through the pulmonary capillaries, with the greater affinity accompanying a shift of the ODC to the left aiding the uptake of oxygen 8.
The partial pressure of oxygen in the blood at which the hemoglobin is 50% saturated is known as the P50. The P50 of normal hemoglobin is approximately 26 mmHg at a partial CO2 pressure of 40 mmHg 7. In the presence of disease or other conditions that change hemoglobin oxygen affinity and, consequently, shift the curve to the right or left, the P50 changes accordingly 9. Low affinity hemoglobins are characterized by higher P50 and high-affinity hemoglobins by a lower P50.
Hemoglobin ODC was originally determined by manual methods in which the oxygen saturation of hemoglobin was measured by spectrophotometry at every stepwise change of PO2 by the addition of aliquots of air to the pre-deoxygenated sample in a tonometer, after equilibrium between Hb and O2 at each PO2 was reached. Although very accurate, this static method was very laborious and time consuming. To overcome its limitations, dynamic methods were developed in which PO2 was progressively changed in a close vessel, allowing for equilibration in between changes 1,10-14. In the most current implementation of these methods, a Clark oxygen electrode detects the change in oxygen tension, while the resulting increase in oxyhemoglobin fraction is simultaneously monitored by dual-wavelength spectrophotometry at 560 nm and 576 nm 15.
However, equilibrium ODC does not reflect exactly physiological gas exchanges by Hb in the lungs (oxygenation) and in peripheral tissues (deoxygenation) as, due to the fast transit of RBCs through microcirculation 16, hemoglobin O2 exchanges occur under non-equilibrium conditions. We describe the determination and features of non-equilibrium ODC and the contribution of different components of Hb cooperativity to its shape.
2. Material and Method
Rat liver mitochondria were purified by differential centrifugation of tissue homogenate as described in 17, portioned in aliquots of 30-40 mg protein/ml in 0.25 mM sucrose, and stored at - 80 °C till used. Stripped Hb devoid of allosteric heterotropic factors was prepared from whole human blood of healthy donors as in 18 and its concentration, as HbO2, was estimated spectrophotometrically from its heme content, with an εmM at 577 nm of 15.4 19. Alternatively, Vacutainer (Becton, Dickinson and company) collected whole blood was used; in this case the HbO2 concentration was estimated, after dilution of the sample in double distilled water, from the air-equilibrated minus Na2S2O4-supplemented differential spectra, using a ΔεmM at 577-568 nm of 4.8 according to 20; the Hb content (as heme centers) was typically 9-11 nmol/(ml blood).
Determination of oxygen consumption was carried out by respirometry using Oxygraph-2k (O2k, OROBOROS Instruments, Innsbruck, Austria). The instrument has two measuring chambers (2 ml each) both equipped with a Clark-type electrode; calibration of the instrument was performed according to the manufacturer instructions and all the measurements were carried out at 37 °C. The assay medium constituted by 250 mM sucrose, 1 mg/ml bovine serum albumin, 10 mM KH2(PO4), 27 mM KCl, 1 mM MgCl2, 40 mM Hepes, 0.5 mM EGTA (pH 7.4) was supplemented with 20-50 μg/ml mitochondrial proteins in the absence or presence of either purified Hb or whole blood samples. Oxygen consumption was initiated by the addition of 10 mM succinate as respiratory substrate in the presence of 2 μM rotenone, an inhibitor of the respiratory chain NADH-ubiquinone oxidoreductase/Complex I. Alternatively the measurements were carried out with a single-chamber (0.5-1 ml) oxymeter equipped with a Clark type electrode disc (Hansatech Instruments Ltd, King’s Lynn, UK).
Fitting of the deoxygenation/reoxygenation curves of Hb using either a graphic (see Supplementary Information) or kinetic method (Results section) was carried out using in-house code written for Matlab® (deposited at https://github.com/dgattiwsu/HB_ODC). Kinetic models of Hb (Adair, MWC, Perutz) were built using functions of Matlab basic functionalities and of the Optimization Toolbox. Using these models, a single set of rate constants was derived by global analysis of both the deoxygenation and reoxygenation traces.
3. Results
3.1. Non-equilibrium ODC of human hemoglobin
In the following we describe a typical experimental determination of human hemoglobin non-equilibrium ODC.
2 ml of the assay buffer solution (pH 7.4) were placed inside each of the two glass chambers of the Oroboros oxymeter and supplemented with a small amount of purified rat liver mitochondria to a final concentration of 30 μg prot/ml. With the cell open to the environment, the solutions were allowed to equilibrate under stirring with atmospheric O2 until the observed O2 concentration (based on an earlier calibration of the electrode 21-23) remained stable (∼183 μM) for a few minutes.
Upon insulating the glass cells from air with glass stoppers (containing a small port for microsyringe additions) progressive reduction of the PO2 in the cell was achieved by adding 10 mM succinate according to the reaction catalyzed by the succinate oxidase segment of the respiratory chain (complexes II+III+IV: succinate dehydrogenase, ubiquinol:cytochrome c reductase, cytochrome c oxidase, respectively):
The final concentration of cytochrome c oxidase (the mitochondrial enzyme that uses up O2 reducing it to water) in the cell was estimated to be ∼0.05 μM by visible spectroscopy of the mitochondrial suspension in the 500-650 nanometer range. Upon starting respiration, O2 concentration decreased linearly until anaerobiosis was reached (Fig. 1a).
The linear respiratory activity is due to the affinity of cytochrome c oxidase for O2 whose KM is estimated in the submicromolar range 24,25. Considering that the instrumental limit of detection of O2 concentration is also in the submicromolar range 26, the O2 concentration is practically never limiting the respiratory flux under the prevailing conditions reported here. After adding 5 μM Antimycin A, an inhibitor of respiration at the level of ubiquinol:cytochrome c reductase, the glass stopper was removed, and the cell content was allowed to equilibrate again with air. During this phase oxygen diffuses back in the cell in a non-linear fashion.
When the cycle of deoxygenation/reoxygenation is repeated in the presence of 50 μM (as heme centers) human hemoglobin isolated from blood hydrolysate (Fig. 1b) the final part of the deoxygenation curve is no longer linear due to the release of oxygen from Hb (green arrow). The initial part of the reoxygenation curve is also slower due to the uptake of oxygen by Hb (yellow arrow).
Since the alterations of the deox-/reoxygenation curves are due to the release/uptake of O2 by Hb, it is possible to recover the non-equilibrium ODC using a kinetic model of the cell ensemble as a set of reversible reactions involving the species of Hb in different oxygenation state, cytochrome c oxidase as the terminal O2 acceptor, O2 in the cell, and external air in diffusive equilibrium with the O2 in the cell, when the latter is open. We have evaluated three different kinetic models (Fig. 2): a. a sequential Adair style model with 4 refined parameters (one O2 koff for each Hb(O2)n), b. a two state sequential Perutz style model with 2 refined parameters (one O2 koff for Hb(O2)1,2 and one O2 koff for Hb(O2)3,4), and c. a two state concerted Monod-Wyman-Changeux (MWC) style model (with one Kequil between a tense (T) and a relaxed (R) state of Hb, one O2 koff for all T states and one O2 koff for all R states) (reviewed in 27,28).
The three models fit equally well the oxymetric trace with essentially identical sum of square errors (∼150 μM2) and R-square values (>.99). Each model provides the contribution of all Hb species (Fig. 3a,d,g) at all time points (O2 concentrations). Non-equilibrium ODC’s are derived for each PO2 value as the ratio between the sum of all the oxygenated species and the total amount of Hb (Fig. 3b,e,h). The corresponding Hill plots are shown in Fig. 3c,f,i.
The observed variations in the ODC and Hill plots are due to the fact that for each time point the contributions of individual Hb species are different in the three models. Details of these contributions are shown in a blow-up of the terminal part of Hb deoxygenation phase (Fig. 4a,c,e), and of the initial part of Hb reoxygenation phase (Fig. 4b,d,f). Regardless of the model used, concentration peaks are reached in the order Hb(O2)4 → Hb(O2)3 → Hb(O2)2 → Hb(O2)1 → Hb during deoxygenation, and Hb → Hb(O2)1 → Hb(O2)2 → Hb(O2)3 → Hb(O2)4 during reoxygenation.
In the Perutz and MWC models, intercepts with the X axis of the extrapolated lines from the asymptotic ends of the Hill plot are usually interpreted as the concentration of O2 at which the concentrations of the unliganded and liganded forms of the T and R states are equal (KD). Better values for these magnitudes are calculated directly from the cross-over points (Fig. 4) of the T and R forms derived from the kinetic simulations (Table 1). Non-linear least-squares fit of Adair equation 30, to the combined experimental points from the deoxygenation and reoxygenation non-equilibrium ODC’s can be used to derive values for the equilibrium Adair constants in the three models (Table 1).
4. Sources of cooperativity in the models
A common feature of Adair, Perutz, and MWC models is the presence of sequential reactions. A minimalist model containing four sequential binding reactions, Hb ↔ Hb(O2)1 ↔ Hb(O2)2 ↔ Hb(O2)3 ↔ Hb(O2)4, with a single O2 affinity for all states, and no conformational changes (Fig. 5a), fits experimental observations surprisingly well (sse = 515.5, R2 = 0.998) (Fig. 5b,c,d), giving origin to a sigmoidal ODC (Fig. 5e) and a Hill plot with asymptotic components that suggest the presence of both low and high affinity sites (Fig. 5c), despite none such exist in the model. Accordingly, a fit of Adair equation to the sigmoidal ODC shows that all four Adair constants collapse into a single one corresponding to the refined kon/koff ratio (Table 1). This observation suggests that a first source of cooperativity in the Adair, Perutz, and MWC models might reside in the fact that all three models feature sequential binding reaction of O2 to the four sites of Hb. A single additional conformational change between a low and high affinity state, whether it occurs upon occupancy of the first two sites (Perutz), or at every level of O2 occupancy, provides the remaining character of cooperativity to O2 binding.
We define as the cooperativity gain (cgain) of a model the rms (root mean square) deviation between the model derived ODC and the ODC with the same P50 derived from a model containing 4 independent identical O2 sites. The cooperative gain of the minimalist, Perutz and NWC models is shown in Fig. 5e,g,h.
5. Discussion
We have presented a typical experiment showing the determination of hemoglobin non-equilibrium ODC. The experimental component of the method requires the acquisition of a deoxygenation curve of Hb, and optionally, also of a reoxygenation curve. The computational component is based on the minimization of the sum of square errors (sse) between an experimentally observed O2 polarographic trace and a simulated O2 trace based on a kinetic model of choice (Figs. 2-4). Since it does not require an optical determination of the Hb saturation, this method can be directly used with a red cell suspension or whole blood without the added complications of the dual-wavelength or full sphere spectrometry that are necessary to eliminate light scattering noise 10.
It has not escaped our notice that the equilibrium constants calculated with our method for each Hb oxygenation step are significantly different from those reported by other authors (i.e. 1, Table 1). It is important to recognize that while traditional ODC’s are derived under conditions of full equilibrium between Hb and O2 at different values of PO2, our method, based on a continuous change of the O2 concentration due to mitochondrial respiration or O2 diffusion from the air, derives a non-equilibrium ODC, that possibly reflects more closely the physiological condition of red blood cells moving rapidly in the blood stream across regions of different PO2.
Three kinetic models (Adair sequential, Perutz two state sequential, MWC two state concerted) were all equally effective in fitting the experimental polarographic traces. Thus, as such, the methodology presented here does not offer any new ways to discriminate between these models. However, the predictions made by the three models with respect to the concentrations of oxygenation and conformational intermediates are quite different, and may offer inspiration for future experiments.
The origin of cooperativity in Hb has been a point of intense debate for over a century (reviewed in 27,28,31). Our experiments were carried out with stripped Hb devoid of allosteric heterotropic factors, and thus under these conditions we observed the intrinsic cooperative behavior of tetrameric Hb. A minimalist model, containing no induced (by O2 binding) or intrinsic conformational equilibria between a low and a high affinity state, is sufficient to provide, by virtue of the constraint of sequential binding reactions of identical affinity, a large fraction (∼69% in cgain scale) of the cooperative behavior of Hb, as judged by the magnitude of its cooperative gain (= 0.1052) with respect to a model containing 4 independent identical O2 binding sites. We call this component the sequential cooperativity of Hb. A smaller component (∼31% in cgain scale) of cooperativity is provided by inclusion in the model of a single conformational equilibrium between a low and a high affinity state, as shown by the values of the cooperative gain in the Perutz (cgain = 0.1505) and MWC models (cgain = 0.1526). We call this component the conformational cooperativity of Hb. Together, sequential and conformational cooperativity account for the entire cooperativity gain of Hb under non-equilibrium conditions.
Declarations of interest
None.
Data repository
Test data and Matlab scripts to carry out the graphic and/or kinetic method for ODC determination are freely available at https://github.com/dgattiwsu/HB_ODC.
Funding
This work was supported by a Wayne State University Research Enhancement Program in Computational Biology grant to DLG, and by grants from the University of Foggia to RS, and NC.
Supplementary Information
Since the reoxygenation of Hb occurs more rapidly (∼65 seconds, panel B) than its deoxygenation (∼560 seconds, panel A), the reoxygenation ODC (dashed blue line, panel C) is based on fewer experimental points, and is thus inherently less accurate than the deoxygenation ODC (continuous red line, panel C). Accordingly, the amount of Hb estimated from the reoxygenation phase is less accurate than that estimated from the deoxygenation phase. These shortcomings of the graphic fit are completely avoided with the global fit of both deoxygenation and reoxygenation phases with a single Hb concentration and a single set of rate constants, using kinetic models of O2 binding to Hb as described in the Results section.
As the experiment was conducted at the atmospheric PCO2 of 0.3 mmHg, the estimated P50 of 20.2 mmHg using the graphic method is left shifted with respect to the standard values of 26 mmHg at a PCO2 of 40 mmHg 1. A correction for the difference in PCO2 at pH of 7.4 based on the equation 2: would yield a P50 value of 24.3 mmHg. Since Hb devoid of allosteric heterotropic factors was used in this experiment, based on the equation 2: the loss of 2,3DPG binding (estimated in a difference in erythrocyte concentration of ∼3.2 mM 3) would justify an additional correction of the P50 value, with a right shift of ∼2.3 mmHg.
Footnotes
Literature cited
Supplementary Information References
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