The position of oxygen equilibrium curve (OEC) for human adult Hb at rest is optimized with respect to the effectiveness of the Bohr shift which is measured by the change in O2 saturation at a venous O2 pressure of 40 torr per unit change in partial pressure of O2 at half saturation (dS(40)/dP50). The effectiveness of the Bohr shift at the physiological P50 of 27 torr depends on the cooperativity of O2 binding calculated by the Hill coefficient n, being maximized at n = 4.
The effectiveness of the Bohr shift during exercise, which was expressed as dS(PvO2)/dP50, was the highest at the PvO2 (venous O2 pressure) of 28 torr. The effectiveness of the Bohr shift at PvO2 of 28 torr increased with increases n value (n value ranged from 2.65 to 3.27), while below PvO2 of 15 torr the opposite was true.
As a whole, the position of the OEC of human adult Hb at rest is optimized with respect to the effectiveness of the Bohr shift while the efficiency of O2 delivery is moderately maintained. On the other hand, during exercise the position of the OEC is adjusted to make the efficiency of O2 delivery at high levels while the effectiveness of the Bohr shift is maintained at the same level as that at rest.
INTRODUCTION
The effect of carbon dioxide (CO2) on the O2 affinity of Hb was first described by Bohr et al. (1904). An increase in the partial pressure of CO2 or a decrease in pH lowers the O2 affinity of Hb, shifting the O2 equilibrium curve (OEC) to the right. This effect caused by PCO2 change and concomitant pH change is called the “classic Bohr effect” while the shift of OEC by pH change only is called the “Bohr effect”. The magnitude of the Bohr effect is given by the change in log P50 (P50 is the O2 pressure at which Hb is 50% saturated with O2) per unit change in pH and is expressed as Δlog P50/ΔpH (the Bohr coefficient). Under the physiological conditions, the Bohr coefficient for human adult Hb is -0.48. A moderate rightward shift of the OEC gives rise to additional O2 unloading from Hb without any change in the ambient PO2. The amount of O2 released from Hb to the tissues upon a rightward shift of the OEC depends not only on the Bohr coefficient, but also on the position and the shape of the OEC (Kobayashi et al., 1996). In the previous paper, we calculated the O2 saturation difference between PO2 of 100 and 40 torr (ΔS(100–40)) and plotted it against P50 for human adult Hb, and its differentiation, which was considered to indicate the effectiveness of the Bohr shift, was maximized when P50 was 28 torr. This P50 is close to the physiological P50 of the Hb (27 torr). However, the dΔS(100–40)/dP50 vs. P50 plot intersected the abscissa at P50 = 62 torr. These phenomena can be explained by the large decreases in O2 saturation of the arterial blood (PO2 of 100 torr) caused by increase in P50. This seems to imply that it is not adequate to use the slope of ΔS(100–40) vs. P50 plot for accurate estimation of the effectiveness of the Bohr shift.
For this reason, in the present study the O2 saturation of the venous blood (S(PvO2)) was plotted against P50, and additional O2 released from Hb to the tissues caused by the Bohr shift was estimated from the slope of this plot (dS(PvO2)/dP50) at rest and during exercise. Based on the results obtained, we propose a new look on the physiological significances of the position and shape of the OEC for human adult Hb that had never been noticed by others. The present analysis which is concerned with the effect of pH change can be equally applied to the effect of PCO2 change. Therefore the term “Bohr shift” used in this study includes both the effect of pH and that of PCO2 which vary concomitantly in whole blood.
MATERIALS AND METHODS
The experimental data used for the present analysis were taken from the published standard OEC for human adult whole blood (Hohammed Mawjood and Imai, 1999), as well as the OECs for human adult Hb solutions that were measured under various experimental conditions (Imai, 1982; Imai and Yonetani, 1975; Imaizumi et al., 1982; Tyuma et al., 1973). All these OECs were described by the Adair equation (Adair, 1925). According to the equation, the O2 saturation (S) is expressed as a function of the partial pressure of O2 (P) as follows:
where, ki (i = 1 to 4) is the intrinsic association constant at the ith oxygenation step (the stepwise Adair constant). The Adair constant values for the standard OEC are k1 = 0.0037 torr−1, k2 = 0.047 torr −1, k3 = 0.012 torr −1, and k4 = 1.1 torr −1 (P50 = 26.7 torr, n = 2.65 at 37°C, pH 7.4 and PCO2 of 40 torr; Hohammed Mawjood and Imai, 1999; Imai personal communication). The hypothetical OECs with different P50 values were constructed from the published set of four Adair constants, which were varied by multiplication with a common factor, i.e., ki · constant (i = 1 to 4). On this multiplication, the position of the hypothetical OEC, that was expressed by S vs. log P plot, was shifted along the abscissa without any change in shape.
The effect of change in cooperativity (n) on the effectiveness of the Bohr shift were investigated in a wide range of n value, using Hill's empirical equation (Hill, 1910),
where n is a quantitative expression of the cooperativity of O2 binding (the degree of sigmoidicity of OEC).
RESULTS AND DISCUSSION
Calculation of O2 transported by Hb and the effectiveness of the Bohr shift
The total amount of O2 available for the tissues is determined by the quantity of O2 delivered by unit volume of the blood and the rate of blood flow. In this paper, the rate of blood flow was not considered, because it is a separate subject concerning the regulatory system of circulation. Fig. 1 illustrates the standard OEC for the arterial whole blood (37°C, pH 7.4 and PCO2 of 40 torr) of human adult. The quantity of O2 transported by Hb is defined by the O2 saturation difference between at PO2 of 100 torr and of 40 torr (ΔS(100–40)). The rightward shifted OEC (broken line) stands for the venous blood. The amount of additional O2 released from Hb caused by the Bohr shift is defined by the O2 saturation difference between arterial and venous blood at PO2 of 40 torr, and designated as (S(40)a–S(40)v). Total quantity of O2 delivered by Hb is given by ΔS(100–40) plus (S(40)a–S(40)v).
Fig. 1
The O2 equilibrium curves of human adult Hb, showing the relationship of blood O2 transport. The full curve (solid line, ⓐ) applies to arterial blood, while the broken line applies to venous blood (vⓥ). S(40)a and S(40)v represent the O2 saturation of arterial and venous blood at PO2 = 40 torr, respectively. ΔS(100–40) represents the O2 transported by blood without the Bohr shift. (S(40)a–S(40)v) is the additional O2 released from Hb caused by the Bohr shift. ΔS(100–40) plus (S(40)a–S(40)v) are the total quantity O2 delivered by blood from the lungs to the tissues. The standard OEC data set of human adult whole blood, which was measured under physiological conditions, 37°C, pH 7.4 and a PCO2 of 40 torr, taken from Hohammed Mawjood and Imai (1999), was used for arterial blood while the curve for venous blood was calculated from the Adair constant values of the standard OEC.
Fig. 2 shows the relation between ΔS(100–40) and P50, and between S(40) and P50. As shown by the broken line, the O2 transported by Hb increased gradually with increases in P50, reaching its maximal value at P50 of 62 torr. The P50 value that gives the maximal O2 transport may be called the “optimal P50 for O2 transport” (Sold, 1982; Willford et al., 1982). At the physiological P50 value for adult whole blood (P50 = 27 torr), the O2 transported by Hb was relatively low (ΔS(100–40) = 0.22). This value was about two-fifths that of the theoretical maximal value (ΔS(100–40) = 0.54). As shown by the solid line, the S(40) value decreased with increases in P50, and the S(40) vs. P50 plot was sigmoid.
Fig. 2
The effect of P50 on the ΔS(100–40) and the S(40). The broken line represents the dependence of the O2 saturation difference between at PO2 = 100 and PO2 = 40 torr (ΔS(100–40)) on P50. The solid line represents the relationship between S(40) and P50. The open arrow indicates the maximal ΔS(100–40) value, and the closed arrow indicates the ΔS(100–40) at physiological P50 of 27 torr. All the calculated lines were obtained using the four Adair constants of the OEC in fig. 1.
Effectiveness of the Bohr shift at rest
As the venous PO2 of 40 torr, the change in S(40) per unit change in P50 (dS(40)/dP50), was calculated from the slope of the S(40) vs. P50 plot to estimate the effectiveness of the Bohr shift (Fig. 3). The dS(40)/dP50 value depended on P50, and the minimal value (the highest effectiveness of the Bohr shift) occurred at P50 of 30 torr (the solid line, Fig. 3). This indicates that when the P50 value is adjusted to 30 torr, the quantity of additional O2 released from Hb to the tissues caused by the Bohr shift is maximized. When the P50 value is either above or below 30 torr, the dS(40)/dP50 value becomes smaller. Therefore, the P50 value that gives the minimal dS(40)/dP50 value may be called the “optimal P50 for the effectiveness of the Bohr shift”. It should be noted that there is only a slight difference in the dS(40)/dP50 value between at the optimal P50 and at the physiological P50. It is, therefore, concluded that the position of the OEC at rest is optimized to achieve the maximal action of the Bohr effect.
Fig. 3
Change in S(40) per unit change in P50 (dS(40)/dP50) as plotted against P50 (solid line). The open arrow indicates the minimal dS(40)/dP50value, and the closed arrow indicates the dS(40)/dP50 value at the physiological P50 of 27 torr. Note that the dS(40)/dP50 value is negative. The dΔS(100–40)/dP50 vs. P50 plot (broken line) was shown for comparison.
The dS(40)/dP50 vs. P50 plot was compared with the previously reported dΔS(100–40)/dP50 vs. P50 plot (the broken line, Fig. 3). The two optimal P50 values for the effectiveness of the Bohr effect in both of the plots are almost equal. These plots deviated from each other more at high P50 values, and the dΔS(100–40)/dP50 vs. P50 plot intersected the abscissa at P50 = 62 torr. The reason for the zero and negative values of dΔS(100–40)/dP50 above P50 = 62 torr can be ascribed to the substantial decreases in the O2 saturation at 100 torr with increases in P50. A zero value of additional O2 released from Hb indicates that the Bohr shift has no effect. On the other hand, dS(40)/dP50 value tends to zero but never intercepts the abscissa even at high P50 values. From these points of view, the dS(40)/dP50 is more rational for accurate estimation of the effectiveness of the Bohr shift.
The effect of cooperativity (n) on dS(40)/dP50 was investigated using the Adair equation and the Hill equation over a wide range of n value, from 1 to 6 (Fig. 4). The dS(40)/dP50 value calculated with physiological P50 of 27 torr decreased with increases in n, reaching the minimal value at about n = 4 (note that the dS(40)/dP50 value is negative). This phenomenon is interesting because the molecule of human adult Hb has a tetrameric structure.
Fig. 4
The effect of cooperativity (n) on the dS(40)/dP50 at the physiological P50 of 27 torr. The dS(40)/dP50 values (·) were calculated using Adair equation from the human Hb OEC data sets taken from Imai (1982), Imai and Yonetani (1975), Imaizumi et al. (1982) and Tyuma et al. (1973). Data represented by the solid lines was calculated using Hill's equation.
In the lungs, pH increases with lowering of CO2 pressure, the OEC moves to the left and enhances the O2 loading. To estimate the effectiveness of the Bohr shift in arterial blood, the same calculation was applied to the arterial blood (PO2 = 100 torr) to obtain dS(100)/dP50 values. The degree of the effectiveness of the Bohr shift at physiological P50 of 27 torr was very low, about one-seventh that of the venous blood. This implies that the Bohr shift seems to be much less important for O2 loading at the lungs.
The effectiveness of the Bohr shift during exercise
As the venous O2 pressure (PvO2) falls to 20 torr during exercise, the effectiveness of the Bohr shift (dS(PvO2)/dP50) was calculated at physiological P50 (27 torr) in the range of PvO2 from 10 to 55 torr (Fig. 5). The dS(PvO2)/dP50 value was a convex function of PvO2, and the minimal value was observed at an intermediate PvO2 of 28 torr: at this PvO2 the Bohr shift is most effective. The dS(PvO2)/dP50 value at PvO2 of 20 torr is approximately equal to that at rest where PvO2 is 40 torr. When PvO2 is about 35 torr, the theoretical minimal dS(PvO2)/dP50 shown by broken line is equal to that of at physiological P50 of 27 torr.
Fig. 5
The dependence of dS(PvO2)/dP50 value on PvO2 value as varied from 10 to 55 torr at P50 of 27 torr. Bold solid line overlaid on the dotted line of n = 2.65 represents the dS(PvO2)/dP50 value under physiological O2 condition (PvO2 ranges from 40 to 20 torr). Dotted line represents the dS(PvO2)/dP50 value at n = 2.39 and 3.27. The broken line represents the minimal dS(PvO2)/dP50 value at the optimal P50 for the effectiveness of the Bohr shift and physiological n value of 2.65. The OEC data set of n = 2.65 was the same as that of fig. 1, and the OEC data set of n of 2.39 and 3.27 were taken from Imai (1982).
The effectiveness of the Bohr shift at the intermediate PvO2 (28 torr) increased with increases in n value. The reverse effect of n was observed below PvO2 of 15 torr. The strong dependence of dS(PvO2)/dP50 on PvO2 at low PvO2 values seem to explain the lower critical point of PvO2 during hard exercise.
Fig. 6 illustrates the relationship between the effectiveness of the Bohr shift (dS(PvO2)/dP50) and the ability of O2 trans-port (ΔS(100–PvO2)) at various P50 values at three different PvO2 levels of 40, 30 and 20 torr (PaO2 was fixed at 100 torr). As seen in the figure, relatively higher O2 affinity is advantageous for the effectiveness of the Bohr shift, while lower O2 affinity tends to be advantageous for O2 transport. The trace of the data point as PvO2 is varied with physiological P50 of 27 torr is shown by the bold broken line. The position of the OEC at rest (P50<PvO2<PaO2) is optimized with respect to the effectiveness of the Bohr shift while the efficiency of O2 transport is moderately maintained (point A). On the other hand, during exercise (PvO2<P50<PaO2), the physiological P50 tends to be advantageous for the ability of O2 transport while the effectiveness of the Bohr shift is remained at the same level as that at rest (point B).
Fig. 6
The relationships between dS(PvO2)/dP50 and ΔS(100–PvO2) at various PvO2 and P50 values. The numbers in the circles represent the PvO2 values; the numbers in the squares represent the p50 values. The OEC data set used for the calculation was the same as that of fig. 1 (n = 2.65). The solid lines represents the relationships when P50 is varied with PvO2 fixed at either 20, 30 or 40 torr. The thin broken lines represent the relationships when PvO2 is varied with P50 fixed at the value indicated. The bold broken line represents the relationship at physiological P50 of 27 torr. Point A represents the PvO2 at rest, and point B represents the PvO2 at hard exercise.
In summary, the quantitative analysis performed in our present study gave several new aspects of physiological importance. The OEC is adjusted to such the position that the Bohr shift is optimized at rest while the O2 transport is made highly efficient during exercise remaining the degree of the effectiveness of the Bohr shift at the same level as that at rest. These situations seem to be the results from the molecular adaptation, involving fine tuning of the allosteric properties, of the tetrameric human Hb to the in vivo O2 environments and the circulation regulatory system.
Acknowledgments
We wish to express our thanks Professor N. Makino, Ibaraki Prefectural University of Health Sciences for valuable comments on manuscript.
