Modelling the relationships between haemoglobin oxygen affinity and the oxygen cascade in humans

Abstract

Key points: Haemoglobin affinity is an integral concept in exercise physiology that impacts oxygen uptake, delivery and consumption. How chronic alterations in haemoglobin affinity impact physiology is unknown. Using human haemoglobin variants, we demonstrate that the affinity of haemoglobin for oxygen is highly correlated with haemoglobin concentration. Using the Fick equation, we model how altered haemoglobin affinity and the associated haemoglobin concentration influences oxygen consumption at rest and during exercise via alterations in cardiac output and mixed-venous $P_{O_2}$ . The combination of low oxygen affinity haemoglobin and reduced haemoglobin concentration seen in vivo may be unable to support oxygen uptake during moderate or heavy exercise.

Abstract: The physiological implications, with regard to exercise, of altered haemoglobin affinity for oxygen are not fully understood. Data from the Mayo Clinic Laboratories database of rare human haemoglobin variants reveal a strong inverse correlation (r = -0.82) between blood haemoglobin concentration and P₅₀ , an index of oxygen affinity [Hb = -0.3135(P₅₀ ) + 23.636]. In the present study, observed P₅₀ values for high, normal and low oxygen-affinity haemoglobin variants (13, 26 and 39 mmHg) and corresponding haemoglobin concentrations (19.5, 15.5 and 11.4 g dL^-1 respectively) are used to model oxygen consumption as a fraction of delivery at rest ( ${\dot{V}}_{O_2}$ = 0.25 L min^-1 , cardiac output = 5.70 L min^-1 ) and during exercise ( ${\dot{V}}_{O_2}$ = 2.75 L min^-1 , cardiac output = 18.9 l min^-1 ). With high-affinity haemoglobin, the model shows that normal levels of oxygen consumption can be achieved at rest and during exercise at the assumed cardiac output levels, with reduced oxygen extraction both at rest (16.8% high affinity vs. 21.7% normal) and during exercise (55.8% high affinity vs. 72.2% normal). With low-affinity haemoglobin, which predicts low haemoglobin concentration, oxygen consumption at rest can be sustained with the assumed cardiac output, with increased oxygen extraction (31.1% low affinity vs. 21.7% normal). However, exercise at 2.75 l min^-1 cannot be achieved with the assumed cardiac output, even with 100% oxygen extraction. In conclusion, the model indicates chronic alterations in P₅₀ associate directly with Hb concentration, highlighting that human Hb variants can serve as 'experiments of nature' to address fundamental hypotheses on oxygen transport and exercise.

Keywords: Cardiac output; Exercise; Fick equation; Haematocrit; Oxygen dissociation curve.

Figure 1:

Oxygen dissociation curves for humans, showing dependence of percent of haemoglobin saturated with oxygen on partial pressure of oxygen in the blood. Control haemoglobin (seen in >99% of humans) is shown in the solid line, low affinity haemoglobin in the dashed line, and high affinity haemoglobin in the dotted line. The P50 is noted for each haemoglobin affinity variant.

Figure 2:

P₅₀ values and haemoglobin for each haemoglobin variant. Blood haemoglobin concentration is plotted against corresponding laboratory P₅₀ values. Data include 50 high affinity haemoglobin variants, 11 low affinity haemoglobin variants, and 6 control subjects. Panel A shows the strong inverse correlation (r = −0.82) between P₅₀ and haemoglobin concentration. Panel B depicts the patient distribution by sex and haemoglobin affinity. Because females have haemoglobin values of 1–2 g dL⁻¹ lower than men, haemoglobin concentrations were increased by 10% in women to obtain comparable data. (Equations: All men and adjusted women combined: Hb= −0.3135(P₅₀) + 23.636, Unadjusted women: Hb = −0.2459(P₅₀) + 18.925, Adjusted women: Hb = −0.2732(P₅₀) + 21.028, Men: Hb = −0.3286(P₅₀) + 24.151).

Figure 3:

Panel A: Mixed venous partial pressure of oxygen in blood vs. haemoglobin concentration at rest during normoxia ($\dot{\text{V}}$O₂ = 0.25 l min⁻¹). HA = High affinity (dotted line, P₅₀ = 13 mmHg), LA = Low affinity (dashed line, P₅₀ = 39 mmHg), C = Control affinity (solid line, P₅₀ = 26 mmHg). Shaded areas represent effects of ±20% variation of normal cardiac output (5.70 l min⁻¹). The open circles represent reference values of haemoglobin for each affinity (HA: 19.5, C: 15.5, LA: 11.4 g dL⁻¹). The dash-dot line indicates predicted mixed venous PO₂ under resting conditions for haemoglobin concentrations associated with P₅₀ values between 13 and 39. Panel B: Oxygen content vs. partial pressure of oxygen in the blood. Vertical lines on plot indicate declines in oxygen content associated with the assumed resting oxygen consumption rate (a: arterial value; v: venous value) for each assumed level of oxygen affinity.

Figure 4:

Panel A: Mixed venous partial pressure of oxygen in the blood vs. corresponding haemoglobin values in an exercising human during normoxia ($\dot{\text{V}}$O₂ = 2.75 l min⁻¹). Panel B: Oxygen content vs. against the partial pressure of oxygen in the blood. Vertical lines on plot indicate declines in oxygen content associated with the assumed exercising oxygen consumption rate for each assumed level of oxygen affinity, with the exception of the case of decreased affinity where this consumption rate cannot be achieved. Symbols and labels are as in Figure 3.