Modelling the Relationships between Haemoglobin Oxygen Affinity and the Oxygen Cascade in Humans

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). Observed P₅₀ values for high, normal and low oxygen-affinity haemoglobin variants (13, 26, 39 mmHg) and corresponding haemoglobin concentrations (19.5, 15.5, 11.4 g dL⁻¹ respectively) are here used to model oxygen consumption as a fraction of delivery at rest ($\dot{\text{V}}$O₂ = 0.25 l min⁻¹, cardiac output = 5.70 l min⁻¹) and during exercise ($\dot{\text{V}}$O₂ = 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.

Introduction

During whole-body exercise, the metabolic demands of the exercising muscles engage all elements of the oxygen transport cascade. Under normal conditions with haemoglobin (Hb) of ~15 g dL⁻¹ and an oxygen capacity of 1.34 mL g⁻¹, ~20 mL of oxygen per 100 mL of whole blood is carried by Hb (Joyner & Casey, 2015). The curvilinear relationship between oxygen partial pressure (PO₂) and saturation (SO₂) is essential to ensure both optimal pulmonary oxygen uptake from the environment and unloading at tissues especially in exercising muscles. The relationship between the oxygen tension (PO₂) and percent of the Hb that is binding oxygen is termed the oxyhaemoglobin dissociation curve (ODC) (Barcroft & Uyeno, 1923; Samaja et al., 2003). The common metric that describes Hb affinity is the P₅₀, which is defined as the PO₂ corresponding to 50% saturation. In humans at rest, the P₅₀ is ~26 mmHg at sea level (Severinghaus, 1958). While the ODC is relatively stable, conformational changes of the Hb chains can alter the affinity for oxygen. For example, acute dynamic exercise often results in temporary decreases in the affinity (increasing P₅₀) due to lowered blood pH, increased temperature or carbon dioxide tension, and greater concentrations of 2,3-biphosphoglycerate (2,3-BPG) (Severinghaus, 1958). Upon cessation of exercise and restoration of blood conditions to resting values, the P₅₀ returns to baseline.

Interestingly, there are numerous reported cases worldwide of rare human Hb variants with permanently altered Hb binding affinity (Fairbanks et al., 1971; Jones & Shih, 1980; Hoyer et al., 1998; Oliveira et al., 2010; Hoyer et al., 2011; Inoue et al., 2012; Szuberski et al., 2012; Taliercio et al., 2013; Collier et al., 2016; Oliveira et al., 2018). Specifically, genetic mutations in the variants’ amino acid sequence of the alpha or beta Hb chains can phenotypically manifest as Hb with altered ODCs (P₅₀ ranging from Hb-Syracuse at 11 mmHg to Hb-Kansas at 48 mmHg). Individuals with these Hb variants frequently have the clinical presentation of polycythaemia (increased affinity) or anaemia (decreased affinity) (Jones & Shih, 1980; Szuberski et al., 2012). Previous studies in various theoretical, (Wagner, 1996, 1997) animal models (Hogan et al., 1991) and humans (Hebbel et al., 1978) have utilized altered P₅₀ in order to investigate the effects of Hb affinity on oxygen transport at rest and during exercise. The conclusions from these investigations remain mixed about the physiological implications of altered Hb affinity for oxygen during exercise. Some studies indicate that decreases in Hb affinity promote oxygen unloading at the tissues to potentially augment $\dot{\text{V}}$O₂ max. Others argue that preserving oxygen uptake at the lung via increases in Hb affinity might be advantageous especially during hypoxia. Finally, there are also studies suggesting that any shifts in Hb affinity will have minimal effects. In this context, individuals with rare Hb variants represent “experiments of nature” to explore how altered Hb oxygen affinity influences the balance between oxygen delivery, extraction and uptake.

With this information as a background, the purpose of this study is threefold. First, we sought to determine the relationship between blood Hb concentrations and P₅₀ using the Mayo Clinic Laboratories rare human Hb variants database. Second, we used the Fick equation to model the relationships between P₅₀, arterial and mixed venous PO₂, Hb concentration and cardiac output at rest and during exercise. Third, using our modelling data we generated key questions related to oxygen transport and utilization that might be addressed in patients with rare Hb variants.

Methods

Rare Haemoglobin Variant Patients:

The database of rare human Hb variants from the Mayo Clinic Laboratories dating from ~1960 to 2018 was reviewed. Evaluation of the venous blood samples for the Hb variants was done under standard conditions including protein analysis or DNA sequencing methods. Haemoglobin and haematocrit laboratory values were determined by standard techniques. Samples that did not have both a Mayo measured P₅₀ and associated laboratory values for Hb were excluded from the analysis.

Mathematical modelling:

We developed a model on the basis of fundamental physiological principles to explain the observed Hb values in subjects with altered values of P₅₀. Calculations were performed for conditions of rest (V.O₂ = 250 mL min⁻¹) and exercise (V.O₂ = 2750 mL min⁻¹), with approximate workloads of 0 W and 220 W respectively. This exercise value is near typical V.O_2max for young untrained male subjects and represents moderate exercise for trained male athletes (Bacon et al., 2013; Joyner & Casey, 2015). Depending on the fitness of the subjects, significant changes in blood pH and other variables that affect the O₂-haemoglobin dissociation curve may occur in exercise. However, the effects of such changes on O₂-haemoglobin dissociation characteristics appear qualitatively similar in the variant and normal haemoglobins.

Cardiac output was estimated using the average of two correlations developed from data obtained by two different methods in trained subjects (Calbet et al., 2005; Calbet et al., 2015a). The Hill equation with n = 2.6 was used to calculate saturation assuming a value of P₅₀ = 26 mmHg in the normal controls. The Fick principle was used to calculate the mixed venous oxygen content based on the arterial content, oxygen consumption, and cardiac output as follows:

$$1.34\cdot Hb\cdot Sv{O}_2=1.34\cdot Hb\cdot Sa{O}_2-0.1\cdot \dot{V}{O}_2/Q$$

where Hb is haemoglobin (g dl⁻¹), SvO₂ is oxyhaemoglobin saturation of venous blood (%), SaO₂ is oxyhaemoglobin saturation of arterial blood (%), V.O₂ is oxygen uptake mL min⁻¹), Q is cardiac output (L min⁻¹) and 1.34 (mL O₂ g⁻¹) is the oxygen carrying capacity for Hb. The arterial oxygen saturation was based on an assumed arterial PO₂ of 100 mmHg. The minimal amount of dissolved oxygen was not considered. The reference Hb was assumed to be 15.5 g dL⁻¹ on the basis of the control cases used in our correlational analysis described above. The target venous PO₂ corresponding to the calculated SvO₂ was considered to be the mixed venous PO₂ in the case of a normal P₅₀. It is assumed that any right shift in the O₂-haemoglobin dissociation curve due to acidosis and hyperthermia in the exercising muscles is similar in subjects with variant and with normal Hb (Thomson et al., 1974; Dempsey et al., 1975; Dempsey et al., 1984; Dempsey & Wagner, 1999).

Calculations were performed at rest and exercise for normal (control) affinity Hb (P₅₀ = 26 mmHg), increased affinity (P₅₀ = 13 mmHg) and decreased affinity (P₅₀ = 39 mmHg) Hb variants. While the range of known variant P₅₀ values are 11 to 48 mmHg, the P₅₀ values of 13 and 39 mmHg were selected for our calculations as they represented a 13 mmHg change in either direction from the control (26 mmHg) value (Figure 1). Additionally, many patients with variants in this P₅₀ range have limited or no medical complaints and are identified based on incidental findings during blood testing for other reasons.

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.

In order to assess the effect of Hb affinity at the lungs, an oxygen uptake model based on a single compartment model and Fick’s law of diffusion (Wagner, 1996; Kavanagh et al., 2002) was used to estimate arterial PO₂. The value used for the effective lung diffusing capacity was predicted based on a theoretical model (Roy & Secomb, 2014) designed to incorporate the effects of heterogeneous blood flow through the lung (Roy & Secomb, 2019). The lung model was used to calculate the arterial oxygen tension in conjunction with a tissue model to predict venous values based on the Fick principle; the corresponding input and output PO₂ values from each compartment were iterated to convergence on arterial and venous oxygen tensions. The same value of P₅₀ was assumed for the lung and tissue compartments, and intracompartment variations of P₅₀ were not considered.

Results

Subjects:

The Mayo Clinic Metabolic Haematology Laboratory clinical files were searched for Hb variants reported as having altered oxygen affinity by the Human Haemoglobin Variants database (HbVar) (Patrinos et al., 2004). Of these, 186 unique rare variants were identified and a total of 62 patients (individual variants) met inclusion criteria for a complete record, including each patient having a verified P₅₀, blood laboratory analysis, and Hb variant with DNA confirmation. Controls were obtained from healthy volunteers from other studies (n=5). Given that females typically have Hb values of 1–2 g dL⁻¹ lower than males (Murphy, 2014), haemoglobin concentrations of the females (n=31) were increased by 10% to account for any sex differences.

Figure 2 Panel A shows the linear inverse relationship between Hb and P₅₀. The strong correlation (r = −0.82) indicates that when Hb affinity is increased (lower P₅₀) or decreased (greater P₅₀) there are increases or decreases in Hb concentrations respectively (Hb = −0.3135(P₅₀) + 23.636). Figure 2 Panel B identifies the sex and type of affinity change (increase or decrease) for each 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 depicts model predictions for the three affinity variants under conditions of rest with a V.O₂ of 250 ml min⁻¹. The target mixed venous PO₂ in this case is 40 mmHg. For each variant, Panel A shows the predicted dependence of mixed venous PO₂ on Hb concentration and Panel B shows the relationship between oxygen content and PO₂. For normal affinity (C, solid line), the Hb concentration estimated from the regression equation in Figure 2 is 15.5 g dL⁻¹ and arterial and mixed venous oxygen content are then 20.1 and 15.8 mL dL⁻¹ respectively. Because cardiac output is held fixed for these curves, mixed venous PO₂ drops as Hb concentration decreases (Panel A). To demonstrate the effects of altered cardiac output, the shaded areas around the curves represent ranges of cardiac output ± 20% of normal. Results are also shown for increased (HA, dotted lines) and decreased (LA, dashed lines) affinity Hb variants, with Hb concentrations estimated from the regression in Figure 2. Oxygen extraction is 21.7% for normal affinity, 16.8% for increased affinity and 31.1% for decreased affinity. Of note, the mixed venous PO₂ with decreased affinity Hb is similar to the target (40 mmHg), despite the lower Hb concentration. Conversely, the mixed venous PO₂ for increased affinity Hb is much lower than the target value, even though the Hb concentration is higher.

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 shows corresponding results for exercise (V.O₂ = 2750 ml min⁻¹) with a target mixed venous PO₂ of 15.8 mmHg and content of 20.1 mL dL⁻¹. Oxygen extraction is 72.2% for normal affinity and 55.8% for increased affinity. With increased affinity, mixed venous PO₂ is maintained. With decreased affinity, oxygen consumption of 2750 ml min⁻¹ cannot be achieved even with 100% oxygen extraction, as a result of the reduced blood Hb concentration.

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.

Discussion

Major findings:

The major findings from this paper are two-fold. First, we found a significant inverse correlation (r = −0.82) between Hb oxygen affinity variants as indexed by P₅₀ and Hb concentration in the blood. Second, we used the Fick equation to model the influence of altered Hb affinities and concentrations on the oxygen transport cascade at rest and during exercise. The inclusion in the model of effects of both the changes in P₅₀ and the associated changes in Hb is a novel aspect of this approach. The model demonstrates that, at a resting level of oxygen consumption, increased affinity Hb results in lower mixed venous PO₂ (22 vs 40 mmHg). By contrast, during exercise with increased affinity Hb, the mixed venous PO₂ required to support an oxygen consumption of 2750 mL min⁻¹ is similar to control when cardiac output is within ±20% of the typically observed value. These trends are reversed for decreased affinity Hb. Under resting conditions, the mixed venous PO₂ is then similar to that for normal Hb, whereas in exercise the available convective oxygen supply is insufficient and is supply limited to support the assumed oxygen consumption rate. Based on the assumed parameter values, all combinations of haemoglobin and cardiac output considered resulted in essentially complete equilibration of oxygen uptake across the lung, implying that for the cases considered, the role of P₅₀ in pulmonary oxygen uptake was minimal.

The kidney as a critometer:

The observed relationship between P₅₀ and Hb concentration is consistent with the idea that the kidney acts as an oxygen sensor or “critometer” (Donnelly, 2001). Because increased affinity Hb can hinder oxygen unloading and thus tissue oxygenation, a compensatory increase in Hb is postulated to occur on the basis of low renal tissue PO₂ and stimulation of the erythropoietin pathway. This series of events would increase Hb concentration and arterial oxygen content, thus permitting normal renal tissue oxygenation when Hb affinity is increased. By contrast, decreased affinity haemoglobin augments tissue oxygen unloading and a compensatory decrease in Hb occurs. In this scheme, intrarenal oxygen tension is subject to long-term regulation. In this context, the kidney is an ideal long-term oxygen sensor and critometer given the relationships among oxygen consumption, sodium reabsorption and oxygen delivery to the proximal tubule (Donnelly, 2001). Consistent with this interpretation, a reduction of haematocrit in patients with increased affinity Hb by phlebotomy to 45% from a baseline of 53%, produces an increase in erythropoietin secretion similar to that observed when haematocrit is reduced to 33% in subjects with normal affinity haemoglobin (Adamson, 1968).

Interdependence between oxygen affinity, haemoglobin concentration, cardiac output, and mixed venous saturation in oxygen transport during rest and during exercise:

The ability of the Hb variants to achieve normal oxygen transport is dependent on the interplay of numerous factors. Based on our model, for increased affinity Hb variants the increases in Hb concentration can largely compensate for the enhanced binding of oxygen to Hb across a range of oxygen uptake rates. The increased affinity variants result in lower mixed venous PO₂ values relative to normal Hb under resting conditions, but these values are similar to normal values during exercise. Fractional oxygen extraction is reduced in both rest and exercise for given levels of oxygen consumption, because higher Hb concentrations result in increased oxygen supply.

Consistent with this interpretation, Wranne and colleagues (Wranne et al., 1983; Wranne et al., 1991) showed in two subjects with increased affinity haemoglobin (Hb 20 g dL⁻¹, P₅₀ ~13.5 mmHg) that leg blood flow was in the normal range at rest and during heavy cycle exercise. Additionally, while the total volume of oxygen extracted across the leg was similar to values for control subjects, the fraction of the oxygen extracted from the arterial blood was reduced for a given femoral venous PO₂.

For the variants with decreased oxygen affinity, mixed venous PO₂ is maintained under resting conditions because the augmented unloading of oxygen is sufficient to support resting oxygen consumption in spite of their lower Hb concentrations. However, during exercise the decreased affinity variants do not have sufficient oxygen supply to support the metabolic demands of the exercising muscles without increases in cardiac output, and their anaemia becomes the dominant factor limiting oxygen uptake.

Implications for experimental hypotheses concerning Hb affinity and oxygen transport in humans.

In this context, rare Hb variant patients as “experiments of nature” may be a useful model to address fundamental questions in humans. We highlight three:

First, when humans are acutely exposed to altitude, Hb affinity decreases in order to promote oxygen unloading and preserve oxygen uptake (Lenfant et al., 1971). However, this acute response is at odds with the characteristics of animals that are evolutionarily adapted to high altitude. For example, both llamas (residing in Andean Mountains (Banchero & Grover, 1972) and bar-headed geese (migratory flights over Himalaya (Scott et al., 2015) have increased Hb affinity compared to their lowland counterparts. Studying the acute and chronic responses to hypoxia of humans with permanently increased Hb affinity could yield insight into whether the decrease in Hb affinity during hypoxia is beneficial or maladaptive and if so under what circumstances.

Second, the range of haemoglobin concentrations seen in patients with haemoglobin variants may be useful in testing ideas concerning blood viscosity and oxygen delivery both at the systemic and local levels. In this context, there is some evidence that that an ideal viscosity for blood flows and O₂ delivery occurs at a haematocrit of ~55% (Gaehtgens et al., 1979). If this is the case, then phlebotomy might have little or no effect on V.O_2max in increased affinity patients. Such an observation would contrast to the well-known reduction in exercise capacity seen with phlebotomy in subjects with normal Hb (Andersen & Saltin, 1985; Joyner & Casey, 2015). Thus patients with rare Hb variants might allow important questions related to blood viscosity and the local and systemic control of the circulation to be addressed.

Third, the study of oxygen uptake kinetics during exercise seeks to characterize the interactions of the respiratory, cardiovascular, and muscular systems operating in concert to meet the O₂ demands of the exercising muscles (Rossiter, 2011; Poole & Jones, 2012). The relationship between $\dot{\text{V}}$O₂ kinetics and exercise tolerance has been a major area of study (Xu & Rhodes, 1999; Rossiter, 2011; Poole & Jones, 2012). Expanding on this by investigating the kinetics at which oxygen is unloading at the working muscles in variant haemoglobin patients could determine how oxygen flux influences the response to aerobic and anaerobic training along with the role of muscle fibre type. For example, increased affinity Hb variants may have slower unloading of oxygen which may lead to greater anaerobic conditions requiring alterations in muscle physiology or training adaptations. Slow V.O₂ kinetics incurs a high oxygen deficit usually resulting in poor exercise tolerance (Whipp, 1994; Calbet et al., 2005; Lundby et al., 2006; Rossiter, 2011; Calbet et al., 2015a). How this change in muscle milieu influences the response to acute exercise and training would be valuable in advancing the understanding of the oxygen transport and utilization in athletes, with aging, and in patients suffering from pathological disease states. In contrast to a scenario where high affinity Hb slows V.O₂ kinetics, there is evidence in a mouse model genetically modified for a low affinity Hb variant (Presbyterian) of improved exercise capacity and a shift towards more oxidative skeletal muscle fiber type (Izumizaki et al., 2003).

Limitations of our model:

There are several limitations that warrant discussion. First, our correlation of P₅₀ and Hb was obtained by retrospectively analysing a large database originating from samples sent to a reference lab for analysis. As such these data do not include a detailed clinical history and for many samples we are unable to quantify other variables that are known to influence Hb levels (e.g. smoking, aerobic fitness, history of phlebotomy, age, etc.). Second, when modelling oxygen content, we assume arterial oxygen levels during exercise reflect those at rest. While this is consistent with most individuals, some well-trained men (Dempsey & Wagner, 1999) and some women of all fitness levels (Dominelli et al., 2013) can develop arterial hypoxemia during exercise. However, to date, this phenomenon is difficult to predict in individuals and is more commonly associated with significantly greater oxygen uptakes (>3.5 l min⁻¹) than used in our model. Third, for the exercise aspect, we were not able to account for blood flow redistribution that can occur during exercise (Harms et al., 1997; Calbet et al., 2004) and can alter the mixed venous PO₂. It is also unknown if the altered haematocrit or P₅₀ alters blood flow distribution per se. Fourth, we did not model potential alterations in Hb affinity as blood traverses the exercising muscles, associated with local changes in temperature, pH, or CO₂. There are certainly differences and challenges of in-vivo versus in-vitro measurements of the oxygen dissociation curve dynamics at both the lungs and muscles in response to variables such as temperature, pH, and 2,3 DPG. A few studies (Thomson et al., 1974; Dempsey et al., 1975; Dempsey et al., 1984; Calbet et al., 2015b) show that the additive effects of temperature and pH are responsible for shifting the oxygen dissociation curve affinity, especially with prolonged exercise. However it is still debated and not well understood how significant of contribution this makes to oxygen delivery and exchange. In particular it is not known how the haemoglobin variants compare for heterogeneity in exercising blood flow distribution, efficiency between unloading at one muscle group versus another larger or smaller group, exercise induced hypoxemia, lactate responses, and responses to increased dilution or concentration. Lundby et al., (2006) studied lowlanders and high-altitude natives during maximal exercise at sea level and during acute normobaric hypoxia (F_iO₂ = 0.13). They calculated P₅₀ and found a left-ward shift in oxyhemoglobin dissociation curve in the arterial P₅₀ (sea level P₅₀ = 36 mmHg vs. hypoxia P₅₀ = 32 mmHg) and muscle P₅₀ (sea level P₅₀ = 43 mmHg, vs. hypoxia P₅₀ = 38 mmHg). Interestingly, these values did not decrease further with 8 weeks of acclimatization to 4100 m and were not statistically different compared to high-altitude Bolivian natives’ responses. They concluded that although the muscle diffusing capacity is reduced, the fractional muscle oxygen extraction is not impaired with altitude exposure. While the O₂ delivery and V.O_2max is unaltered, the mismatch between CaO₂ and V.O_2max must be due to other factors (Lundby et al., 2006). We assumed that the Hill coefficient along with red cell morphology was similar for all of the variant haemoglobins and acknowledge that it would be very difficult to determine the exact relationship within each unique variant. Finally, we did not consider the impact of haematocrit and changes in viscosity on tissue blood flow and cardiac output, which as noted above is a key topic for future experimental studies.

Conclusion

In this paper we present a model based on fundamental physiological principles and data from rare Hb variant patients to explore the relationships between P₅₀, PO₂, cardiac output, mixed venous PO₂, and Hb concentrations at rest and during exercise in humans. With high-affinity Hb, the model shows normal levels of oxygen consumption can be achieved at rest and during reference exercise conditions. However with low-affinity Hb variants, the same exercise cannot be achieved with the assumed cardiac output, even with 100% oxygen extraction. With this we highlighted a number of ways that Hb variant patients can serve as “experiments of nature” to help address fundamental hypotheses related to oxygen transport and exercise in humans which may have many clinical and translational applications.

Key points summary:

• 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 modelled 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 PO₂.

• 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.

Abbreviations list:

Q

Cardiac output

Hb

haemoglobin

ODC

oxyhaemoglobin dissociation curve

Pa_O2

arterial oxygen tension

P₅₀

partial pressure at which haemoglobin is 50% saturated with oxygen

SaO2

arterial oxyhaemoglobin saturation

SvO2

venous oxyhaemoglobin saturation

$\dot{\text{V}}$O_2max

maximal oxygen uptake