An electrolytic method for determining oxygen dissociation curves using small blood samples: the effect of temperature on trout and human blood.

1. A detailed account is given of an electrolytic method for determining the oxygen dissociation curve of fish blood using a single sample of 50-100 mul for the whole curve. The accuracy and some of the problems arising from its uses are discussed. 2. Oxygen dissociation curves have been determined for trout blood and human blood at temperatures of 15 and 37 degrees C. The relationship between P50 and temperature is similar to that obtained using other methods. Absolute values of P50 are generally lower than those obtained by other methods, especially in the case of fish blood. 3. The effect of PCO2 and pH on the oxygen dissociation curve of trout blood is tested and it is shown that PCO2 has a more marked effect than pH when the other factor is maintained at a constant level. The Bohr factor (delta log P50/delta pH) appears to be approximately the same and independent of the PCO2. 4.The P50 of ray blood determined from fish during and after an operation showed an increased Bohr factor.     

Effect of hyperoxia on the oxyhemoglobin dissociation curve in various periods of aging

Gas composition of the arterial and venous blood and the oxyhemoglobin dissociation curve were determined before and after 20 minutes of oxygen inhalation in 9 apparently healthy subjects aged 60 to 74 years and in 9 young subjects aged 19 to 32 years. In hyperoxia of younger subjects, there was a shift to the left of both the oxyhemoglobin dissociation curve of the native blood and standard dissociation curve (pH 7.4). In old age, the shift to the left of the standard dissociation curve due to hypoxia was quite negligible and statistically insignificant, whereas in the native blood it was entirely absent because of the increased blood PCO2 and associated Bohr effect.     

Algorithm for computing oxygen dissociation curve with pH,PCO2, and CO in sheep blood

By extending the study of Samaja and Gattinoni¹, an algorithm is described for computing the oxygen dissociation curve with variations in pH, PCO₂, and CO in homozygous HbB sheep blood. The difference in the values of O₂ pressure at 50% saturation in presence of CO computed from the present algorithm and Hill's equation does not exceed 0.5%. It is shown that O₂ affinity increases as the concentration of CO or pH increases or PCO₂ decreases. The algorithm is convenient for representing the oxygen dissociation curve with variation in pH, PCO₂ and the concentration of CO in modelling oxygen transport in sheep blood even under hypoxic conditions.     

Influence of carbon monoxide on hemoglobin-oxygen binding.

The oxygen dissociation curve and Bohr effect were measured in normal whole blood as a function of carboxyhemoglobin concentration [HbCO]. pH was changed by varying CO2 concentration (CO2 Bohr effect) or by addition of isotonic NaOH or HCl at constant PCO2 (fixed acid Bohr effect). As [HbCO] varied through the range of 2, 25, 50, and 75%, P50 was 26.3, 18.0, 11.6, and 6.5 mmHg, respectively. CO2 Bohr effect was highest at low oxygen saturations. This effect did not change as [HbCO] was increased. However, as [HbCO] was increased from 2 to 75%, the fixed acid Bohr factor increased in magnitude from -0.20 to -0.80 at very low oxygen saturations. The effect of molecular CO2 binding (carbamino) on oxygen affinity was eliminated at high [HbCO]. These results are consistent with the initial binding of O2 or CO to the alpha-chain of hemoglobin. The results also suggest that heme-heme interaction is different for oxygen than for carbon monoxide.     

Acid-base and respiratory properties of a buffered bovine erythrocyte perfusion medium

Current research in organ physiology often utilizes in situ or isolated perfused tissues. We have characterized a perfusion medium associated with excellent performance characteristics in perfused mammalian skeletal muscle. The perfusion medium consisting of Krebs-Henseleit buffer, bovine serum albumin, and fresh bovine erythrocytes was studied with respect to its gas-carrying relationships and its response to manipulation of acid-base state. Equilibration of the perfusion medium at base excess of -10, -5, 0, 5, and 10 mmol X L-1 to humidified gas mixtures varying in their CO2 and O2 content was followed by measurements of perfusate hematocrit, hemoglobin concentration, pH, Pco2, Cco2, Po2, and percent oxygen saturation. The oxygen dissociation curve was similar to that of mammalian bloods, having a P50 of 32 Torr (1 Torr = 133.3 Pa), Hill's constant n of 2.87 +/- 0.15, and a Bohr factor of -0.47, showing the typical Bohr shifts with respect to CO2 and pH. The oxygen capacity was calculated to be 190 mL X L-1 blood. The carbon dioxide dissociation curve was also similar to that of mammalian blood. The in vitro nonbicarbonate buffer capacity (delta [HCO3-] X delta pH-1) at zero base excess was -24.6 and -29.9 mmol X L-1 X pH-1 for the perfusate and buffer, respectively. The effects of reduced oxygen saturation on base excess and pH of the medium were quantified. The data were used to construct an acid-base alignment diagram for the medium, which may be used to quantify the flux of nonvolatile acid or base added to the venous effluent during tissue perfusions.     

A model of oxygen exchange between an arteriole or venule and the surrounding tissue

A mathematical model is developed to study the effect of capillary convection on oxygen transport around segments of arterioles and venules that are surrounded by capillaries. These capillaries carry unidirectional flow perpendicular to the vessel. The discrete capillary structure is distributed in a manner determined by the capillary blood flow and capillary density. A nonlinear oxyhemoglobin dissociation curve described by the Hill equation is used in the analysis. Oxygen flux from the vessel is expressed as a relationship between Sherwood and Peclet numbers, as well as other dimensionless combinations involving parameters of the capillary bed. A numerical solution is obtained with a finite difference method. The numerical results obtained within the physiological range of parameters allow the prediction of longitudinal gradients of hemoglobin-oxygen saturation along the arterioles and venules.     

Blood osmolality in vitro: dependence on PCO2, lactic acid concentration, and O2 saturation

Changes of osmolality (Osm) were measured by freezing-point determination in true plasma of 10 healthy subjects. This was done after equilibration with CO2 (0.5-10.0%), after the addition of lactic acid (10 and 20 mmol/l), and after deoxygenation. The graph for the dependence of Osm on CO2 partial pressure (PCO2) in oxygenated blood resembles the classical CO2 absorption curve. The increase of Osm with PCO2 (approximately 0.2 mosmol . kg H2O-1 . Torr-1) is almost as great as the increase in dissolved CO2 plus bicarbonate (HCO-3). Addition of lactic acid shifts the curve upward by only 0.6 mosmol/mmol because of displacement of HCO-3. Deoxygenation has no significant effect at constant PCO2 despite an increase in [HCO-3]. This is probably due to the binding of 2,3-diphosphoglycerate to hemoglobin. It can be seen in the Osm-pH diagram that differences between CO2 and lactic acid titration largely disappear. For each lactic acid concentration there is a linear dependence corresponding to the linear [HCO-3]-pH relation in plasma. At constant pH, Osm increases after deoxygenation. The observed in vitro relation might explain part of the osmolality increase during physical exercise.     

Heart rate changes caused by varying the oxygen supply to isolated hind legs of rats

In a rat with an isolated hind leg circulation perfused with varying tyrode solutions, heart rate (HR) changes were studied in dependence of VO2 in the isolated hind leg and of PCO2, [K+], pH and lactic acid concentration ([Lac]) measured in the venous outflow of the isolated hind leg. In experimental series I the inflow PO2 (PiO2) was kept constantly high (either about 65 or 72 kPa). The perfusion pressure alternated between 16 and 24 kPa leading to flow rates in isolated hind legs (Qa) from 30 to 50 ml . 100 g-1 . min-1. The VO2 depended on the momentary Qa (flow-limited oxygen uptake). The [K+] and [Lac], the pH and the AVDO2 remained nearly constant while the PCO2 was lower at small flow rates. The HR decreases some 4 min after initial enhancement of Qa and VO2. Series II comprised experiments with low flow rates and a medium oxygen supply (Qa = 2.5-17.4 ml . 100 g-1 . min-1), PiO2 = 17.5-62.7 kPa). The VO2 ranged between 0.02 and 0.2 ml . 100 g-1 . min-1. The [K+] and [Lac], the PCO2 and the HR increased while the pH decreased. The [Lac] in the outflow showed a strong dependence on oxygen uptake and--at a weak oxygen supply--on the time. Cross-correlation analyses between the parameters confirmed that the HR was best temporally correlated to the [Lac] in the outflow.(ABSTRACT TRUNCATED AT 250 WORDS)     

Configuration of the hemoglobin oxygen dissociation curve demystified: a basic mathematical proof for medical and biological sciences undergraduates

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and 2,3-diphosphoglycerate concentrations that enable their applications in various clinical situations. The modeling techniques employed in many existing models are notably borrowed from advanced and highly sophisticated mathematics that are likely to surpass the comprehensibility of many medical and bioscience students due to the high level of "mathematical maturity" required. It is, however, a worthy teaching point in physiology lectures to illustrate in simple mathematics the fundamental reason for the crucial sigmoidal configuration of the ODC such that the medical and bioscience undergraduates can readily appreciate it, which is the objective of this basic dissertation.     

Hemoglobins of the tadpole of the bullfrog, Rana catesbeiana. Temperature dependence of oxygen binding and pH dependence of subunit dissociation.

The temperature dependence of the oxygen equilibrium of tadpole hemoglobin has been determined between 0 degrees and 32 degrees for the unfractionated but phosphate-free lysate and between 12 degrees and 32 degrees for each of the four isolated components between pH 6 and 10 in 0.05 M cacodylate, Tris, or glycine buffers containing 0.1 M NaCl and 1 mM EDTA. Under these conditions the Bohr effect (defined as deltalog p50/deltapH) of the unfractionated lysate is positive at low temperatures between pH 6 and 8.5 and is negative above pH 8.5 to 8.8 at any temperature. As the temperature rises the Bohr effect below pH 8.5 changes greatly. In the interval pH 7.0 to 7.5, the magnitude of the Bohr effect decreases from + 0.28 at 0 degrees to zero at about 24 degrees and becomes negative, as in mammalian hemoglobins, above this temperature. Measurements with the isolated components show that the temperature dependence of oxygen binding for Components I and II and for Components III and IV is very similar. For both sets of components the apparent overall enthalpy of oxygenation at pH 7.5 is about -16.4 kcal/mol and -12.6 kcal/mol at pH 9.5. The measured enthalpies include contributions from the active Bohr groups, the buffer ions themselves, the hemoglobin groups contributing buffering, and any pH-dependent, oxygenation-dependent binding of ions such as chloride by the hemoglobin. The apportioning of the total enthalpy among these various processes remains to be determined. Between pH 8 and 10.5 tadpole oxyhemoglobin undergoes a pH-dependent dissociation from tetramer to dimer. The pH dependence of the apparent tetramer-dimer dissociation constant indicates that at pH 9.5 the dissociation of each tetramer is accompanied by the release of approximately 2 protons. In this pH range the oxygen equilibrium measurements indicate that about 0.5 proton is released for each oxygen molecule bound. The results are consistent with the conclusion that one acid group per alphabeta dimer changes its pK from about 10 to 8 or below upon dissociation of the tetramer.     

Saturation dependency of the Bohr effect: interactions among H-+, CO2, and DPG.

The Bohr effect was measured in normal whole blood and in blood with low DPG concentration as a function of oxygen saturation. pH was changed by varying CO2 concentration (CO2 Bohr effect) or by addition of isotonic NaOH or HC1 at constant PCO2 (fixed acid Bohr effect). At nornal DPG concentration CO2 Bohr effect was -0.52 at 50% blood oxygen saturation, increasing in magnitude at lower saturation and decreasing in magnitude at higher saturation. In DPG depleted blood with base excess (BE) similar to 0 meq/1, there was similar dependence of CO2 Bohr effect on oxygen saturation. At BE similar to -10 meq/1, influence of saturation was comparable, but the magnitude of the Bohr effect was markedly increased at all saturations. Fixed acid Bohr effect at normal DPG concentration was -0.45 at saturations of 50-90% but decreased at lower saturations. In DPG-depleted blood fixed acid Bohr effect averaged about -0.33 with minimal variation with saturation. Influence of DPG on oxygen affinity was greater at intermediate saturations and less at saturations below 20% and above 80%. Effect of CO2, independent of pH, was many fold greater at lower oxygen saturations than at higher saturations. These results support the suggestion that the alpha chain of hemoglobin is the site of the initial oxygenation reaction. Physiologically they indicate that the relative contribution of CO2 and fixed acid, as well as the level of oxygen saturation and DPG concentration, may be important in determining PO2 of capillary blood and resulting oxygen delivery.     

Temperature dependence of the decay of the UV absorption difference spectrum of heavy meromyosin induced by adenosine triphosphate and inosine triphosphate.

The UV absorption difference spectrum of heavy meromyosin induced by ATP was measured at various temperatures. At higher temperatures, the difference spectrum formed rapidly after adding ATP and continued steadily during the steady state which we have called the ATP-form of difference spectrum. At lower temperatures, the ATP-form of difference spectrum decayed into the other form before the steady state was attained. This was identical to the difference spectrum obtained by adding ADP and has been called the ADP-form of difference spectrum. At intermediate temperatures, biphasic decay was observed. The results indicate that the dominant intermediate at the steady state is altered from the one showing the ATP-form of difference spectrum at higher temperatures to that showing the ADP-form at lower temperatures. The population of the two intermediates depends on the temperature between the two extremes. This temperature-induced transition was observed in the presence of any divalent cation such as Mg2+, Mn2+, or Ca2+. A similar transition was observed with the difference spectrum induced by ITP in the presence of MgCl2. The pH dependence of the single early decay of the ATP-induced difference spectrum was measured in the presence of MnCl2 at 1 degree. The apparent rate constant of the decay showed a biphasic pH dependence, having the same shape as the pH activity curve of ATPase [EC 3.6.1.3] observed at higher temperatures. The rate determining step for the steady state ATPase at higher temperatures is thought to be the step of changing from the intermediate complex showing the ATP-form of difference spectrum to that showing the ADP-form. This is inconsistent with our previous mechanism (Yazawa, M. et al. (1973) J. Biochem. 74, 1107-1117). The rate determining step at lower temperatures was assigned as a step of ADP dissociation.     

Transient kinetics of oxygen dissociation from ferrous subunits of iron-cobalt hybrid hemoglobins. The principal reaction controlling the co-operativity

The oxygen dissociation constants from Fe subunits in the half-ligated intermediate states of Fe-Co hybrid hemoglobins, alpha(Fe-O2)2 beta(Co)2 and alpha(Co)2 beta(Fe-O2)2, have been determined as functions of pH, temperature and inositol hexaphosphate. The oxygen dissociation rates from alpha(Fe-O2)2 beta(Co)2 are estimated to be more than 1300 s-1 for the deoxy quaternary state (T-state) and less than 3 s-1 for the oxy quaternary state (R-state) at 15 degrees C in 50 mM-Tris or Bis-Tris buffer containing 0.1 M-Cl-, while those of alpha(Co)2 beta(Fe-O2)2 are more than 180 s-1 and less than 5 s-1 for the T and R-states, respectively. The pH dependence of the oxygen dissociation rate from Fe subunits is large enough to be accounted for by the R-T transition, and implies that those half-ligated intermediate hybrids mainly exist in the R-state at pH 8.8, and in the T-state at pH 6.6, while other studies indicated that the half-ligated hybrids are essentially in the R-state at pH 7. Large activation energies of the oxygen dissociation process of 19 to 31 kcal/mol determined from the temperature dependence suggest that the process is entropy-driven.     

Measurement of pH in blood vessels and interstitium of 4 and 6 days-old chick embryos

The pH in intra- and extraembryonic blood vessels and in the embryonic interstitium has been measured in 4 and 6 days-old chick embryos using pH microelectrodes. The mean pH of the lateral vitelline vein was 8.0 at day 4 and 7.89 at day 6 and that of the vitelline artery 7.8 and 7.66, respectively. The pH of the blood in the embryonic heart was the same at day 4 and 6 (7.68 and 7.67). The lowest blood pH was recorded in the jugular vein (7.42 at day 6). The pH values measured in the interstitium show less variability. However a clear cranio-caudal gradient was apparent at day 4 where pH fell from 7.68 to 7.47. At day 6 the pH values of the interstitium ranged between 7.61 and 7.52 showing no preferential distribution. Using previously determined values for blood PO2 and the oxygen haemoglobin equilibrium curves, we calculated the oxygen saturation of the blood at the measured pH. In the vitelline vein the O2 saturation is 89% at day 4 and more than 95% at day 6, whereas that of the vitelline artery is 37% and 25%, respectively. When ambient PCO2 is raised to about 8 torr the pH falls to 7.81 (7.68) in the vitelline vein at day 4 (6) and the oxygen saturation decreases to 64% and 79%, respectively. Thus the high pH values found in the vitelline vein seem to be necessary for adequate oxygen uptake of the embryo.     

Blood osmolality during in vivo changes of CO2 pressure

In 16 experiments male subjects, age 22.4 +/- 0.5 (SE) yr, inspired CO2 for 15 min (8% end-tidal CO2) or hyperventilated for 30 min (2.5% end-tidal CO2). Osmolality (Osm) and acid-base status of arterialized venous blood were determined at short intervals until 30 min after hypo- and hypercapnia, respectively. During hypocapnia [CO2 partial pressure (PCO2) -2.31 +/- 0.32 kPa (-17.4 Torr), pH + 0.19 units], Osm decreased by 3.9 +/- 0.3 mosmol/kg H2O; during hypercapnia [PCO2 + 2.10 +/- 0.28 kPa (+15.8 Torr), pH -0.12 units], Osm increased by 5.8 +/- 0.7 mosmol/kg H2O. Presentation of the data in Osm-PCO2 or Osm-pH diagrams yields hysteresis loops probably caused by exchange between blood and tissues. The dependence of Osm on PCO2 must result mainly from CO2 buffering and therefore from the formation of bicarbonate. In spite of the different buffer capacities in various body compartments, water exchange allows rapid restoration of osmotic equilibrium throughout the organism. Thus delta Osm/delta pH during a PCO2 jump largely depends on the mean buffer capacity of the whole body. The high estimated buffer value during hypercapnia (38 mmol/kg H2O) compared with hypocapnia (19 mmol/kg H2O) seems to result from very strong muscle buffering during moderate acidosis.     

Effect of water alkalinity on gill CO2 exchange and internal PCO2 in aquatic animals

In addition to metabolic CO2 production and gill ventilatory flow rate, expired water PCO2 is very dependent on water acid-base balance in a complex way. This is particularly true in carbonated waters at low ambient PCO2 and high pH, where CO2 excreted in the gill water may be buffered by carbonate ions, leading to an increased CO2 capacitance coefficient. The higher the carbonate alkalinity (CA) and the lower the inspired PCO2 (i.e., the higher the inspired water pH), the stronger the carbonate buffering and the smaller the increase of PCO2 in the gill water during respiratory CO2 exchanges. As a consequence, as shown by a number of reported data, increasing the CA leads to blood hypocapnia and respiratory alkalosis at constant low, but not at high, inspired PCO2. In the low range of inspired PCO2, internal PCO2 becomes very sensitive to even small changes of water PCO2, which may explain at least in part the large variability of reported blood PCO2 values in gill breathers. Water CA also influences the amplitude of respiratory acid-base disturbances caused by changes of the gill ventilatory flow rate. Carbonate buffering of excreted CO2 and thus dependence of blood PCO2 on water alkalinity requires catalysis of CO2 hydration by carbonic anhydrase, that must be available from the water side of the gill epithelium.     

Dissociation and oxygen equilibrium properties of the extracellular hemoglobin of Eisenia foetida

The dissociation and oxygen equilibrium properties of whole blood and the purified hemoglobin from Eisenia foetida were compared. Oxygen affinities agreed approximately with each other in the range of pH 6.0 to 9.5. The values of n1/2 were higher in whole blood than in the purified hemoglobin between pH 7.0 and 9.5. The maximum values, obtained near pH 8, were about 6 in whole blood and 3.5 in the purified hemoglobin. In the purified hemoglobin, alkaline dissociation started at pH 7.8, and the approximately 60 S whole molecule dissociated completely into approximately 10 S and 5-6 S components at pH 9.1. In whole blood, however, the dissociation started at pH 8.2 and the complete disappearance of the approximately 60 S molecule occurred at pH 9.6. The values of n1/2 for the dissociation products were lower than those of the purified hemoglobin between pH 7.0 and 9.0. The value of n1/2 decreased with increasing dissociation of the approximately 60 S whole molecule with a pH rise in both whole blood and the purified hemoglobin. Addition of CaCl2 or MgCl2 up to 10 mM to the purified hemoglobin at pH 8.0-8.1 induced increases in oxygen affinity and cooperativity and in the stability of the approximately 60 S whole molecule. The effect on the oxygenation properties was greater with CaCl2 than MgCl2 at the same molar concentration. The stabilizing effect on the approximately 60 S molecule was almost the same with both CaCl2 and MgCl2. These results suggest that the dissociation of property of the hemoglobin in whole blood is controlled by both Ca2+ and Mg2+, and that its oxygenation property is controlled by Ca2+.     

Placental gas exchange in the guinea-pig: fetal blood gas tensions following the reduction of maternal oxygen capacity with carbon monoxide

The effect of CO hypoxia on the placental exchange of respiratory gases was studied in anaesthetized pregnant guinea-pigs near term. Fetal PO2 and PCO2 were measured by mass spectrometry from a blood gas catheter in the right atrium. Administration of 5 ml CO over 65 s reduced maternal oxygen capacity by 26%. There was a rapid fall in fetal arterial PO2 and a more gradual rise in fetal PCO2. It was shown in separate experiments that the carboxyhaemoglobin content of fetal blood did not alter greatly in the first few min. after CO administration, which is the interval within which fetal PO2 was seen to fall. The alteration in fetal gas tensions can therefore be ascribed to the increased oxygen affinity and reduced oxygen capacity occasioned by the presence of carboxyhaemoglobin in the maternal blood. The alteration in placental oxygen transfer was calculated from the experimental findings, using a mathematical model of placental gas exchange in the guinea-pig. The total reduction in the oxygen transfer was 32% of the initial value. It was calculated that the reduction in maternal oxygen capacity was responsible for about two-thirds of this decrease, the remainder being due to the increased oxygen affinity of maternal blood.     

Effect of enzyme and ligand protonation on the binding of folates to recombinant human dihydrofolate reductase: implications for the evolution of eukaryotic enzyme efficiency.

There is marked pH dependence of the rate constant (koff) for tetrahydrofolate (H4folate) dissociation from its ternary complex with human dihydrofolate reductase (hDHFR) and NADPH. Similar pH dependence of H4folate dissociation from the ternary complex of a variant of hDHFR with the substitution Phe31----Leu (F31L hDHFR) causes this dissociation to become rate limiting in the enzyme mechanism at pH approximately 5, and this accounts for the marked decrease in kcat for this variant as the pH is decreased from 7 to 5. This decreased kcat at low pH is not seen for most DHFRs. koff for dissociation of folate, dihydrofolate (H2folate), and H4folate from their binary complexes with hDHFR is similarly pH dependent. For all the complexes examined, the pH dependence of koff in the range pH 5-7 is well described by a pKa of about 6.2 and must be due to ionization of a group on the enzyme. In the higher pH range (7-10), koff increases further as the pH is raised, and this relation is governed by a second pKa which is close to the pKa for ionization of the amide group (HN3-C4O) of the respective ligands. Thus, ionization of the ligand amide group also increases koff. Evidence is presented that the dependence of pH on koff for hDHFR accounts for the shape of the kcat versus pH curve for both hDHFR as well as its F31L variant and contributes to the higher efficiency of hDHFR compared with bacterial DHFR.     

Tetramer-dimer dissociation in homoglobin and the Bohr effect.

The pH dependence of the apparent tetramer to dimer dissociation constant has been determined at 20 degrees for both oxy- and deoxyhemoglobins A and Kansas. These measurements were made by three different procedures: gel chromatography, sedimentation velocity, and kinetic methods in either of three buffer systems: 0.05 M cacodylate, Tris, or glycine with 1 mM EDTA and 0.1 M NaCl between pH 6.5 and 11. The tetramer-dimer dissociation constant of human oxyhemoglobin A decreases from about 3.2 X 10(-6) M at pH 6.0 to about 3.2 X 10(-8) M at pH 8.5. The slope of this line indicates that the dissociation of tetramer to dimer is accompanied by the uptake of about 0.6 protons per mol of tetramer in this region. The corresponding dissociation constant for deoxyhemoglobin in the same pH region increases apparently almost linearly from 1.0 x 10(-12) M at pH 6.5 to about 1.0 x 10(-5) M at pH 11. To dimer is associated with the release of about 1.6 protons per mol of tetramer. Comparison of these data with the known proton release accompanying the oxygenation of tetramers confirms that the pH dependence of oxygen binding by dimers must be very small. The present data predict that the overall proton release or uptake per oxygen bound by dimer should be less than 0.1. The tetramer-dimer dissociation equilibria of oxy- and deoxyhemoglobins above pH 8.5 have identical pH dependences. In this range the dissociation constant of deoxy-Hb is about one-tenth that of oxyhemoglobin. Human oxyhemoglobin Kansas is known to have an enhanced tetramer-dimer dissociation compared with that of hemoglobin A. Below pH 8.5 the tetramer-dimer dissociation constant of Hb Kansas is about 400 times greater than that of HbA in the absence of phosphate buffers. In contrast, the tetramer-dimer dissociation constants of deoxyhemoglobins A and Kansas appear to be identical. These findings are consistent with previous structural observations on these hemoglobins. The data on the tetramer-dimer dissociation of human hemoglobin were used to calculate the total free energy of binding of oxygen to the tetramer and the median oxygen pressure on the basis of fundamental linkage relations and a pH-independent estimate of the total free energy of binding oxygen to dimer. Simulated oxygen binding curves were generated with the equations of Ackers and Halvorson (Ackers, G. K., and Halvorson, H. (1974) Proc. Natl. Acad. Sci. U.S.A. 71, 4312-4316) by making two assumptions: (a) that the dimers are noncooperative and pH-independent in O2 binding and (b) that the distribution of cooperative energy in the oxygenation of tetramers is independent of pH. We have compared these simulations with experimental data obtained at low protein concentrations (30 to 124 muM heme) to show that the variation in oxygen affinity with pH can be described in terms of the subunit equilibria. We conclude that an accurate analysis of the contributions of individual oxygen binding steps to the Bohr effect cannot be made without considering the contributions of the dimers to oxygen binding...