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 O_{2} saturation at a venous O_{2} pressure of 40 torr per unit change in partial pressure of O_{2} at half saturation (dS_{(40)}/dP_{50}). The effectiveness of the Bohr shift at the physiological P_{50} of 27 torr depends on the cooperativity of O_{2} 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)/dP_{50}, was the highest at the PvO_{2} (venous O_{2} pressure) of 28 torr. The effectiveness of the Bohr shift at PvO_{2} of 28 torr increased with increases n value (n value ranged from 2.65 to 3.27), while below PvO_{2} 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 O_{2} delivery is moderately maintained. On the other hand, during exercise the position of the OEC is adjusted to make the efficiency of O_{2} 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 (CO_{2}) on the O_{2} affinity of Hb was first described by Bohr *et al.* (1904). An increase in the partial pressure of CO_{2} or a decrease in pH lowers the O_{2} affinity of Hb, shifting the O_{2} equilibrium curve (OEC) to the right. This effect caused by PCO_{2} 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 P_{50} (P_{50} is the O_{2} pressure at which Hb is 50% saturated with O_{2}) per unit change in pH and is expressed as Δlog P_{50}/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 O_{2} unloading from Hb without any change in the ambient PO_{2}. The amount of O_{2} 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 O_{2} saturation difference between PO_{2} of 100 and 40 torr (ΔS_{(100–40)}) and plotted it against P_{50} for human adult Hb, and its differentiation, which was considered to indicate the effectiveness of the Bohr shift, was maximized when P_{50} was 28 torr. This P_{50} is close to the physiological P_{50} of the Hb (27 torr). However, the dΔS(100–40)/dP_{50} vs. P_{50} plot intersected the abscissa at P_{50} = 62 torr. These phenomena can be explained by the large decreases in O_{2} saturation of the arterial blood (PO_{2} of 100 torr) caused by increase in P_{50}. This seems to imply that it is not adequate to use the slope of ΔS_{(100–40}) vs. P_{50} plot for accurate estimation of the effectiveness of the Bohr shift.

For this reason, in the present study the O_{2} saturation of the venous blood (S_{(PvO2)}) was plotted against P_{50}, and additional O_{2} released from Hb to the tissues caused by the Bohr shift was estimated from the slope of this plot (dS(PvO2)/dP_{50}) 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 PCO_{2} change. Therefore the term “Bohr shift” used in this study includes both the effect of pH and that of PCO_{2} 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 O_{2} saturation (S) is expressed as a function of the partial pressure of O_{2} (P) as follows:

_{1}= 0.0037 torr

^{−1}, k

_{2}= 0.047 torr

^{−1}, k

_{3}= 0.012 torr

^{−1}, and k

_{4}= 1.1 torr

^{−1}(P

_{50}= 26.7 torr, n = 2.65 at 37°C, pH 7.4 and PCO

_{2}of 40 torr; Hohammed Mawjood and Imai, 1999; Imai personal communication). The hypothetical OECs with different P

_{50}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 O_{2}binding (the degree of sigmoidicity of OEC).

## RESULTS AND DISCUSSION

### Calculation of O_{2} transported by Hb and the effectiveness of the Bohr shift

The total amount of O_{2} available for the tissues is determined by the quantity of O_{2} 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 PCO_{2} of 40 torr) of human adult. The quantity of O_{2} transported by Hb is defined by the O_{2} saturation difference between at PO_{2} 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 O_{2} released from Hb caused by the Bohr shift is defined by the O_{2} saturation difference between arterial and venous blood at PO_{2} of 40 torr, and designated as (S(40)a–S(40)v). Total quantity of O_{2} delivered by Hb is given by ΔS_{(100–40)} plus (S_{(40)a}–S_{(40)v}).

Fig. 2 shows the relation between ΔS_{(100–40)} and P_{50}, and between S_{(40)} and P_{50}. As shown by the broken line, the O_{2} transported by Hb increased gradually with increases in P_{50}, reaching its maximal value at P_{50} of 62 torr. The P_{50} value that gives the maximal O_{2} transport may be called the “optimal P_{50} for O_{2} transport” (Sold, 1982; Willford *et al.*, 1982). At the physiological P_{50} value for adult whole blood (P_{50} = 27 torr), the O_{2} 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 P_{50}, and the S_{(40)} vs. P_{50} plot was sigmoid.

### Effectiveness of the Bohr shift at rest

As the venous PO_{2} of 40 torr, the change in S_{(40)} per unit change in P_{50} (dS_{(40)}/dP_{50}), was calculated from the slope of the S_{(40)} vs. P_{50} plot to estimate the effectiveness of the Bohr shift (Fig. 3). The dS_{(40)}/dP_{50} value depended on P_{50}, and the minimal value (the highest effectiveness of the Bohr shift) occurred at P_{50} of 30 torr (the solid line, Fig. 3). This indicates that when the P_{50} value is adjusted to 30 torr, the quantity of additional O_{2} released from Hb to the tissues caused by the Bohr shift is maximized. When the P_{50} value is either above or below 30 torr, the dS_{(40)}/dP_{50} value becomes smaller. Therefore, the P_{50} value that gives the minimal dS_{(40)}/dP_{50} value may be called the “optimal P_{50} for the effectiveness of the Bohr shift”. It should be noted that there is only a slight difference in the dS_{(40)}/dP_{50} value between at the optimal P_{50} and at the physiological P_{50}. It is, therefore, concluded that the position of the OEC at rest is optimized to achieve the maximal action of the Bohr effect.

The dS_{(40)}/dP_{50} vs. P_{50} plot was compared with the previously reported dΔS_{(100–40)}/dP_{50} vs. P_{50} plot (the broken line, Fig. 3). The two optimal P_{50} 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 P_{50} values, and the dΔS_{(100–40)}/dP_{50} vs. P_{50} plot intersected the abscissa at P_{50} = 62 torr. The reason for the zero and negative values of dΔS_{(100–40)}/dP_{50} above P_{50} = 62 torr can be ascribed to the substantial decreases in the O_{2} saturation at 100 torr with increases in P_{50}. A zero value of additional O_{2} released from Hb indicates that the Bohr shift has no effect. On the other hand, dS_{(40)}/dP_{50} value tends to zero but never intercepts the abscissa even at high P_{50} values. From these points of view, the dS_{(40)}/dP_{50} is more rational for accurate estimation of the effectiveness of the Bohr shift.

The effect of cooperativity (n) on dS_{(40)}/dP_{50} 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)}/dP_{50} value calculated with physiological P_{50} of 27 torr decreased with increases in n, reaching the minimal value at about n = 4 (note that the dS_{(40)}/dP_{50} value is negative). This phenomenon is interesting because the molecule of human adult Hb has a tetrameric structure.

In the lungs, pH increases with lowering of CO_{2} pressure, the OEC moves to the left and enhances the O_{2} loading. To estimate the effectiveness of the Bohr shift in arterial blood, the same calculation was applied to the arterial blood (PO_{2} = 100 torr) to obtain dS(100)/dP_{50} values. The degree of the effectiveness of the Bohr shift at physiological P_{50} 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 O_{2} loading at the lungs.

### The effectiveness of the Bohr shift during exercise

As the venous O_{2} pressure (PvO_{2}) falls to 20 torr during exercise, the effectiveness of the Bohr shift (dS_{(PvO2)}/dP_{50}) was calculated at physiological P_{50} (27 torr) in the range of PvO_{2} from 10 to 55 torr (Fig. 5). The dS(PvO2)/dP_{50} value was a convex function of PvO_{2}, and the minimal value was observed at an intermediate PvO_{2} of 28 torr: at this PvO_{2} the Bohr shift is most effective. The dS(PvO2)/dP_{50} value at PvO_{2} of 20 torr is approximately equal to that at rest where PvO_{2} is 40 torr. When PvO_{2} is about 35 torr, the theoretical minimal dS(PvO2)/dP_{50} shown by broken line is equal to that of at physiological P_{50} of 27 torr.

The effectiveness of the Bohr shift at the intermediate PvO_{2} (28 torr) increased with increases in n value. The reverse effect of n was observed below PvO_{2} of 15 torr. The strong dependence of dS(PvO2)/dP_{50} on PvO_{2} at low PvO_{2} values seem to explain the lower critical point of PvO_{2} during hard exercise.

Fig. 6 illustrates the relationship between the effectiveness of the Bohr shift (dS(PvO2)/dP_{50}) and the ability of O_{2} trans-port (ΔS(100–PvO2)) at various P_{50} values at three different PvO_{2} levels of 40, 30 and 20 torr (PaO_{2} was fixed at 100 torr). As seen in the figure, relatively higher O_{2} affinity is advantageous for the effectiveness of the Bohr shift, while lower O_{2} affinity tends to be advantageous for O_{2} transport. The trace of the data point as PvO_{2} is varied with physiological P_{50} of 27 torr is shown by the bold broken line. The position of the OEC at rest (P_{50}<PvO_{2}<PaO_{2}) is optimized with respect to the effectiveness of the Bohr shift while the efficiency of O_{2} transport is moderately maintained (point A). On the other hand, during exercise (PvO_{2}<P_{50}<PaO_{2}), the physiological P_{50} tends to be advantageous for the ability of O_{2} transport while the effectiveness of the Bohr shift is remained at the same level as that at rest (point B).

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 O_{2} 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 O_{2} 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.

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