Carbon dioxide is moderately soluble in water. According to Henry’s law of solubility:

(1)

The solubility coefficient of carbon dioxide (α) is expressed in units of mmol.l⁻¹ kPa⁻¹ (or mmol.l⁻¹.mmHg⁻¹). The value depends on temperature, and examples are listed in Table 10.1. The contribution of dissolved carbon dioxide to the total carriage of the gas in blood is shown in Table 10.2.

Table 10.1 Values for solubility of carbon dioxide in plasma and pK′ at different temperatures

Table 10.2 Normal values for carbon dioxide carriage in blood

In solution, carbon dioxide hydrates to form carbonic acid:

(2)

The equilibrium of this reaction is far to the left under physiological conditions. Published work shows some disagreement on the value of the equilibrium constant, but it seems likely that less than 1% of the molecules of carbon dioxide are in the form of carbonic acid. There is a very misleading medical convention by which both forms of carbon dioxide in equation (2) are sometimes shown as carbonic acid. Thus the term H₂CO₃ may, in some situations, mean the total concentrations of dissolved CO₂ and H₂CO₃; to avoid confusion it is preferable to use αPco₂ as in equation (7) below. This does not apply to equations (4) and (5) below, where H₂CO₃ has its correct meaning.

Carbonic anhydrase.^4,5 The reaction of carbon dioxide with water (equation 2) is non-ionic and slow, requiring a period of minutes for equilibrium to be attained. This would be far too slow for the time available for gas exchange in pulmonary and systemic capillaries if the reaction were not catalysed in both directions by the enzyme carbonic anhydrase (CA). In addition to its role in the respiratory transport of carbon dioxide, CA plays a fundamental role in many body tissues, for example the generation of hydrogen and bicarbonate ions in secretory organs including the stomach and kidney, and the intracellular transfer of carbon dioxide within both skeletal and cardiac muscle. In mammals there are now 16 isozymes of CA identified, of which two are involved in blood carbon dioxide transport.

Red blood cells (RBCs) contain large amounts of CA II, one of the fastest enzymes known, whilst CA IV is a membrane bound isozyme present in pulmonary capillaries. There is no CA activity in plasma. Carbonic anhydrase is a zinc-containing enzyme of low molecular weight, and there is now extensive knowledge of the molecular mechanisms of CA.^5,6 First, the zinc atom hydrolyses water to a reactive Zn–OH⁻ species, whilst a nearby histidine residue acts as a ‘proton shuttle’, removing the H⁺ from the metal-ion centre and transferring it to any buffer molecules near the enzyme. Carbon dioxide then combines with the Zn–OH⁻ species and the formed rapidly dissociates from the zinc atom. The maximal rate of catalysis is determined by the buffering power in the vicinity of the enzyme, as the speed of the enzyme reactions are so fast that its kinetics are determined mostly by the ability of the surrounding buffers to provide/remove H⁺ ions to/from the enzyme.

Carbonic anhydrase is inhibited by a large number of compounds, including some drugs such as thiazide diuretics and various heterocyclic sulphonamides, of which acetazolamide is the most important. Acetazolamide is non-specific for the different CA isozymes and so inhibits CA in all organs at a dose of 5–20 mg.kg⁻¹ and has no other pharmacological effects of importance. Acetazolamide has been used extensively in the study of carbonic anhydrase and has revealed the surprising fact that it is not essential to life. The quantity and efficiency of RBC CA is such that more than 98% of activity must be blocked before there is any discernible change in carbon dioxide transport, though when total inhibition is achieved, Pco₂ gradients between tissues and alveolar gas are increased, pulmonary ventilation is increased and alveolar Pco₂ is decreased.

The largest fraction of carbon dioxide in the blood is in the form of bicarbonate ion, which is formed by ionisation of carbonic acid thus:

(3)

The second dissociation occurs only at high pH (above 9) and is not a factor in the carriage of carbon dioxide by the blood. The first dissociation is, however, of the greatest importance within the physiological range. The pK₁′ is about 6.1 and carbonic acid is about 96% dissociated under physiological conditions.

According to the law of mass action:

(4)

Rearrangement of equation (4) gives the following:

(5)

The left-hand side is the hydrogen ion concentration, and this equation is the non-logarithmic form of the Henderson–Hasselbalch equation.⁷ The concentration of carbonic acid cannot be measured and the equation may be modified by replacing this term with the total concentration of dissolved CO₂ and H₂CO₃, most conveniently quantified as αPco₂ as described above. The equation now takes the form:

(6)

The new constant K′ is the apparent first dissociation constant of carbonic acid, and includes a factor that allows for the substitution of total dissolved carbon dioxide concentration for carbonic acid.

The equation is now in a useful form and permits the direct relation of plasma hydrogen ion concentration, Pco₂ and bicarbonate concentration, all quantities that can be measured. The value of K′ cannot be derived theoretically and is determined experimentally by simultaneous measurements of the three variables. Under normal physiological conditions, if [H⁺] is in nmol.l⁻¹, Pco₂ in kPa, and [] in mmol.l⁻¹, the value of the combined parameter (αK′) is about 180. If Pco₂ is in mmHg, the value of the parameter is 24.

Most people prefer to use the pH scale and so follow the approach described by Hasselbalch in 1916 and take logarithms of the reciprocal of each term in equation (6) with the following familiar result:⁸

(7)

where pK′ has an experimentally derived value of the order of 6.1, but varies with temperature and pH (see Table 10.1). ‘[CO₂]’ refers to the total concentration of carbon dioxide in all forms (dissolved CO₂, H₂CO₃ and bicarbonate) in plasma and not in whole blood.

Amino and carboxyl groups concerned in peptide linkages have no buffering power. Neither have most side chain groups (e.g. in lysine and glutamic acid) because their pK values are far removed from the physiological range of pH. In contrast is the imidazole group of the amino acid histidine, which is almost the only amino acid to be an effective buffer in the normal range of pH. Imidazole groups constitute the major part of the considerable buffering power of haemoglobin, each tetramer containing 38 histidine residues. The buffering power of plasma proteins is less and is directly proportional to their histidine content.

The four haem groups of a molecule of haemoglobin are attached to the corresponding four amino acid chains at one of the histidine residues on each chain (page 188), and the dissociation constant of the imidazole groups of these four histidine residues is strongly influenced by the state of oxygenation of the haem. Reduction causes the corresponding imidazole group to become more basic. The converse is also true: in the acidic form of the imidazole group of the histidine, the strength of the oxygen bond is weakened. Each reaction is of great physiological interest and both effects were noticed many decades before their mechanisms were elucidated.

Total deoxygenation of the haemoglobin in blood would raise the pH by about 0.03 if the Pco₂ were held constant at 5.3 kPa (40 mmHg), and this would correspond roughly to the addition of 3 mmol of base to 1 litre of blood. The normal degree of desaturation in the course of the change from arterial to venous blood is about 25%, corresponding to a pH increase of about 0.007 if Pco₂ remains constant. In fact, Pco₂ rises by about 0.8 kPa (6 mmHg), which would cause a decrease of pH of 0.040 if the oxygen saturation were to remain the same. The combination of an increase of Pco₂ of 0.8 kPa and a decrease of saturation of 25% thus results in a fall of pH of 0.033 (Table 10.2).

Table 10.2 shows the forms in which carbon dioxide is carried in normal arterial and mixed venous blood. Although the amount carried in solution is small, most of the carbon dioxide enters and leaves the blood as CO₂ itself (Figure 10.3). Within the plasma there is little chemical combination of carbon dioxide, for three reasons. First, there is no carbonic anhydrase in plasma and therefore carbonic acid is formed only very slowly. Secondly, there is little buffering power in plasma to promote the dissociation of carbonic acid. Thirdly, the formation of carbamino compounds by plasma proteins is not great, and must be almost identical for arterial and venous blood.

Fig. 10.3 How carbon dioxide enters the blood in molecular form. Within the plasma, there is only negligible carbamino carriage by plasma proteins and a slow rate of hydration to carbonic acid due to the absence of carbonic anhydrase. The greater part of CO₂ diffuses into the red blood cell where conditions for carbamino carriage (by haemoglobin) are more favourable. In addition, more rapid formation of carbonic acid is facilitated by carbonic anhydrase, the removal of hydrogen ions by haemoglobin buffering and the transfer of bicarbonate out of the red blood cell in exchange for chloride by the Band 3 ion-exchange protein (Hamburger shift).

Carbon dioxide can, however, diffuse freely into the RBC, where two courses are open. First, increasing intracellular Pco₂ will increase carbamino carriage of CO₂ by haemoglobin, an effect greatly enhanced by the fall in oxygen saturation which is likely to be occurring at the same time (Figure 10.1). The second course is hydration and dissociation of CO₂ to produce hydrogen and bicarbonate ions, facilitated by the presence of carbonic anhydrase in the RBC. However, accumulation of intracellular hydrogen and bicarbonate ions will quickly tip the equilibrium of the reaction against further dissociation of carbonic acid, a situation that is avoided in the RBC by two mechanisms:

Hamburger shift. Hydration of CO₂ and buffering of the hydrogen ions results in the formation of considerable quantities of bicarbonate ion within the RBC. These excess bicarbonate ions are actively transported out of the cell into the plasma in exchange for chloride ions to maintain electrical neutrality across the RBC membrane. This ionic exchange was first suggested by Hamburger in 1918,¹¹ and believed to be a passive process. It is now known to be facilitated by a complex membrane bound protein that has been extensively studied and named Band 3 after its position on a gel electrophoresis plate.^12,13,14 Band 3 exchanges bicarbonate and chloride ions by a ‘ping-pong’ mechanism in which one ion first moves out of the RBC before the other ion moves inwards, in contrast to most other ion pumps, which simultaneously exchange the two ions. Band 3 protein is also intimately related to other proteins in the RBC (Figure 10.4):^13,14

RBC cytoskeleton. The cytoplasmic domain of band 3 acts as an anchoring site for many of the proteins involved in the maintenance of cell shape and membrane stability such as ankyrin and spectrin. A genetically engineered deficiency of band 3 in animals results in small, fragile, spherical RBCs,¹² and in humans an inherited defect of band 3 is responsible for hereditary spherocytosis in which RBCs become spheroidal in shape and fragile.^15,16 RBC shape and deformability are now known to be important in oxygen transport in the capillaries (page 148) and it is possible that band 3 is involved in bringing about these shape changes.

Carbonic anhydrase. Band 3 is also closely associated with carbonic anhydrase, and the protein complex formed is believed to act as a metabolon, a term describing the channelling of a substrate directly between proteins that catalyse sequential reactions in a metabolic pathway.¹³ In this case the substrate is bicarbonate, which after its formation by CA is transferred directly to band 3, which rapidly exports it from the cell.

Haemoglobin. Band 3 is also associated with haemoglobin, with which it is believed to form another metabolon system exporting nitric oxide derived nitrosothiols, possibly to regulate capillary blood flow and oxygen release from haemoglobin (page 195).

Glycolytic enzymes. Some of the enzymes involved in glycolysis (page 198), including glyceraldehyde-3-phosphate dehydrogenase, phosphofructokinase and aldolase, are bound to band 3; the functional significance of this is unknown.

Fig. 10.4 Proteins associated with band 3 in the red blood cell membrane. Band 3 has twelve trans-membrane domains forming the bicarbonate/chloride exchange ion channel, and four globular cytoplasmic domains (a–d), each of which is associated with different groups of intra-cellular proteins. (a) Ankyrin and spectrin, to maintain and possibly alter red cell shape; (b) Carbonic anhydrase, with which band 3 acts as a metabolon to directly export bicarbonate ions from the red cell; (c) Haemoglobin, with which band 3 may act as a metabolon to export nitric oxide; (d) Glycolytic enzymes – the functional significance of this association is unknown.

In the pulmonary capillary, where Pco₂ is low, the series of events described above goes into reverse and the CO₂ released from the RBC diffuses into the alveolus and is excreted.