I. INTRODUCTION

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One of the major requirements of the body is to eliminate CO₂. The large, but highly variable, amount of CO₂ that is produced within muscle cells has to leave the body finally via ventilation of the alveolar space. To get there, diffusion of CO₂ has to occur from the intracellular space of muscles into the convective transport medium blood, and diffusion out of the blood has to take place into the lung gas space across the alveolocapillary barrier.

Carbon dioxide in the body is present in three different forms: dissolved, bound as bicarbonate, or bound as carbamate. The relative contribution of these different forms to overall CO₂ transport changes markedly along this elimination pathway, because for diffusion across membrane barriers, another form is more appropriate than for transport within intra- or extracellular compartments. Thus the kinetics of the interchange between forms become critically important. In addition, the products of one such interchange, the hydration reaction of CO₂, HCO₃, and H⁺, are required for a great variety of other cellular functions such as secretion of acid or base and some reactions of intermediary metabolism. In exercising skeletal muscle, the other "end product" of metabolism, lactic acid, contributes huge amounts of H⁺ and by these affects the predominance of the three forms of CO₂, because HCO₃ as well as carbamate are critically dependent on the concentration of H⁺. Discussion of the overall transport of CO₂ in skeletal muscle has to take into account this contribution of lactic acid and its involvement in kinetics and equilibria of CO₂ reactions. This interdependence of CO₂ and lactic acid elimination is one major aspect of this review, which as far as we know has not before been reviewed in detail.

	II. CARBON DIOXIDE TRANSPORT IN BLOOD

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Carbon dioxide transport forms in blood have been thoroughly reviewed by Klocke (105). We only briefly summarize their respective contribution to overall CO₂ exchange. Table 1 sums up the contribution of the various forms in the two compartments plasma and erythrocytes: in whole arterial and venous blood during rest and during heavy exercise.

Only a small portion, ~5% of total arterial content, is present in the form of dissolved CO₂. Using a solubility coefficient SCO₂ of 3.21 × 10⁵ M/Torr (35) for plasma at 37°C, this gives 1.28 mM dissolved CO₂, or, using SCO₂ of 3.08 × 10⁵ M/Torr (7), 1.23 mM dissolved CO₂ at a PCO₂ of 5.32 kPa (40 Torr). At rest, the contribution of dissolved CO₂ to the total arteriovenous CO₂ concentration difference is only ~10%. However, during heavy exercise, the contribution of dissolved CO₂ can increase sevenfold and then makes up almost one-third of the total CO₂ exchange.

The majority of CO₂ in all compartments is bound as HCO₃. The ratio of HCO₃ over dissolved CO₂ is given by the Henderson-Hasselbalch equation
The pK_a^' has a normal value of 6.10 in human plasma at 37°C and varies with temperature and ionic strength (142). It appears to be slightly different in serum and red blood cells: serum, 6.11; oxygenated erythrocytes, 6.10; deoxygenated erythrocytes, 6.12 (8). During a heavy work load of the muscle, high levels of lactic acid are present in addition to CO₂, aggravating the decrease in pH. With this low pH, the fraction of HCO₃ in total CO₂ is diminished. Although at pH 7.4 HCO₃ is 20-fold compared with dissolved CO₂, it is only 13-fold at the normal intraerythrocytic pH of 7.2, and the ratio may fall to much lower values at plasma pH values of considerably below 7 during maximal exercise. Therefore, although the absolute arteriovenous difference is higher during exercise than during rest, the relative contribution of HCO₃ to overall exchange is less. For the example of heavy exercise given in Table 1, HCO₃ contributes only two-thirds of total CO₂ exchange, whereas at rest this figure is ~85%.

The amount of CO₂ bound as carbamate to hemoglobin in erythrocytes or to plasma proteins depends on O₂ saturation of hemoglobin and 2,3-diphosphoglycerate (2,3-DPG) concentration in the case of erythrocytes, and on H⁺ concentration in the case of both red blood cells and plasma (61, 68, 134, 135). During passage of blood through muscle, O₂ saturation and H⁺ concentration change considerably, in particular during exercise. However, the increase in hemoglobin desaturation and the increase in H⁺ concentration experienced by red blood cells in the capillary during exercise affect the amount of CO₂ bound to hemoglobin in opposite directions. Whereas deoxygenation of hemoglobin increases the amount of CO₂ bound to hemoglobin, acidification decreases the amount of carbamate formed by hemoglobin.

To calculate carbamate concentrations within erythrocytes, we use a single set of constants for the - and -chains in the oxy state of hemoglobin and separate constants for the - and -chains in the deoxy state. Because the calculation of carbamate is dependent on the values of the carbamate equilibrium constant (pK_c) and the ionization equilibrium constant of the amino group (pK_z) employed, errors in the determination of these constants in different studies can lead to changes in the calculation of the carbamate. Therefore, we use two different sets of constants to give an estimate of the variability of the calculated carbamate concentrations.

For oxyhemoglobin, we use the binding constants of Gros et al. (68) (number of CO₂ binding sites per hemoglobin tetramer n = 2, pK_c = 4.73, pK_z = 7.16), and for deoxyhemoglobin, their constants for the -chain -amino groups of n = 2, pK_c = 5.19, pK_z = 7.05. However, because their measurements were done in the absence of 2,3-DPG, their carbamate equilibrium constant (K_c) for the -amino groups of the -chains of deoxyhemoglobin was not used. On the other hand, intraerythrocytic concentration of 2,3-DPG has effectively no influence on the binding of CO₂ to oxyhemoglobin and to the -chain -amino groups of deoxyhemoglobin (132). For the -chain -amino group of deoxyhemoglobin, the ionization constant (K_z; pK_z = 6.13) estimated by Gros et al. (68) was used in conjunction with the CO₂ binding constant  for this same amino group given by Perella et al. (135) for the presence of 2,3-DPG. Perella et al. (135) determined this figure by measuring CO₂ binding of hemoglobin whose -amino groups were differentially blocked by cyanate. Using their value of , one obtains together with the above value of pK_z a carbamate equilibrium constant pK_c = 5.06 for these groups. Thus we describe CO₂ binding by the -amino groups of the -chains of deoxyhemoglobin in the presence of 2,3-DPG with n = 2, pK_z = 6.13, and pK_c = 5.06. With these constants we estimate a contribution of only ~5% (0.09 mM) of carbamate to overall CO₂ exchange during rest (Table 1). When the pK_z and pK_c values reported by Perella et al. (134) and the data of Perella et al. (135) are combined in an analogous fashion to estimate binding constants in the presence of 2,3-DPG, a contribution of 9% (0.16 mM) of carbamate to CO₂ exchange during rest is calculated. The former estimate of 0.09 mM or 5% agrees nicely with measurements of Böning et al. (13). From their data, an arteriovenous difference for carbamate of 0.09 mM is calculated for the blood gas values of Table 1. It should be noted that all these estimates of the contribution of carbamate to overall CO₂ exchange are lower than the value of 12.6% calculated by Klocke (105). However, Klocke's use of the data of Perella et al. (135), which are valid for pH 7.4 rather than the normal intraerythrocytic pH 7.2, may have led to a substantial overestimate of the role of carbamate because carbamate formation increases drastically with increasing pH. Thus it appears that a contribution of 5% by carbamate is a reasonable estimate although markedly lower than previously believed.

During heavy exercise as defined in Table 1, ~6% (10.8% with the data of Perella and co-workers, Refs. 134, 135) of the arteriovenous concentration difference of total CO₂ is calculated to be due to a change in carbamate. Böning et al. (13) have measured an ~10% contribution to overall exchange during aerobic exercise, but during heavy exercise with considerable anaerobic metabolism they found that carbamate does not contribute to CO₂ exchange at all; arterial blood contained a carbamate concentration that was higher by 0.06-0.13 mol/mol hemoglobin than that of venous blood in the presence of lactic acid. The data of Table 1 thus represent an intermediate position between these extreme types of exercise.

Carbamate concentration in plasma does not contribute to overall CO₂ exchange according to Table 1, which is in agreement with Klocke's conclusion (105). During heavy exercise, arterial plasma contains an even higher concentration of carbamate than venous plasma. The physicochemical reason for this is that, in the absence of an oxylabile carbamate fraction as exhibited by hemoglobin, the increase in carbamate by the elevated PCO₂ in venous plasma is counteracted or overruled by a decrease in carbamate caused by the fall in pH.

Figure 1 shows that overall CO₂ transport is the sum of the diffusion of 1) dissolved CO₂ and 2) CO₂ bound as HCO₃. The contribution of HCO₃ to CO₂ transport is called "facilitated CO₂ diffusion" and was first described by Longmuir et al. (111). Gros and Moll (66) and Gros et al. (67) have shown that facilitated CO₂ diffusion involves a flux of H⁺ equivalent to that of HCO₃, a fact which matches the other fact that hydration of CO₂ produces equal amounts of H⁺ and HCO₃. Facilitated CO₂ diffusion by HCO₃ diffusion under steady-state conditions then requires 1) rapid conversion of CO₂ into HCO₃ and H⁺, which at the short diffusion distances as they occur in cells (<1 mm) implies that the presence of carbonic anhydrase (CA) catalyzing CO₂ hydration is essential for facilitation to occur, and 2) equal fluxes of H⁺ and HCO₃, where 3) significant fluxes of H⁺ can only be achieved when they occur by facilitated H⁺ diffusion, i.e., by the diffusion of mobile buffers carrying H⁺ and present at concentrations comparable to that of HCO₃. This leads to the following scheme of facilitated CO₂ diffusion shown in Figure 1.

View larger version (45K): [in this window] [in a new window]   Fig. 1. Mechanism of facilitated diffusion of CO2. White background area indicates free diffusion (physically dissolved) CO2, and the shaded background indicates the process of facilitated CO2 diffusion. "Buffer" is any mobile buffer with an appropriate pK value, such as phosphate at pH ~7.

Diffusion coefficients (=diffusion constant/SCO₂) have been measured under conditions where only little facilitated diffusion is present. In a 33g% hemoglobin solution, the hemoglobin concentration that prevails inside the red blood cell, the CO₂ diffusion coefficient, is reduced to less than one-half of its value in water (Table 2). It is not clear why the figure of Uchida et al. (173) is three times lower than the figure of Gros and Moll (64) for this condition. Compared with diffusion in water, diffusion is hindered by the presence of hemoglobin as it is by the presence of other intracellular proteins. It appears that proteins are virtually impermeable to CO₂ and represent the major obstacles to CO₂ diffusion within cells (64). Accordingly, CO₂ diffusion constants decrease in a defined manner with increasing hemoglobin concentration (curve in Fig. 2) that can be explained quantitatively on the basis of the geometry of the water space in a hemoglobin solution (64). Similarly, the CO₂ diffusion constant in various tissues varies systematically with the protein concentration of these tissues (points in Fig. 2). It is obvious that, for a given protein concentration, the CO₂ diffusion constants in these different cells or tissues agree very nicely.

View larger version (17K): [in this window] [in a new window]   Fig. 2. Diffusion constants of CO2 (in cm2·min1·atm1) at 22°C in different tissues as a function of the protein concentration (points) and in hemoglobin solutions of different hemoglobin concentrations (solid line). [Redrawn from Gros and Moll (64).]

The diffusion coefficients for HCO₃ are about one-half as great as those for CO₂, and in the presence of proteins, its diffusion can be expected to be hindered to an extent comparable to that observed for CO₂ diffusion. The HCO₃ diffusion coefficient is calculated from the equivalent conductivity of HCO₃ (67, 108), 11.7 × 10⁶ cm²/s in pure water at 25°C, and is reduced to 8.7 × 10⁶ cm²/s at physiological ionic strength and 25°C (67). Again, Uchida et al. (173) report a surprisingly low value of 1.4 × 10⁶ cm²/s for HCO₃ diffusion in "100% hemolysate" at 37°C. The relative contribution of HCO₃ to total CO₂ diffusion (=facilitated diffusion) can be evaluated on the basis of these diffusion coefficients. The contribution of HCO₃ diffusion, and thus of facilitated diffusion, to total CO₂ diffusion depends greatly on the partial pressure range of CO₂ in which the transport process takes place. This can be predicted from the general shape of CO₂ binding curves, which are steep at low PCO₂ values and become flatter with increasing PCO₂. Therefore, the HCO₃ concentration gradient per CO₂ concentration gradient is higher at low PCO₂, and vice versa. This implies that the relative contribution of facilitated diffusion is highest at lowest PCO₂ values and decreases consistently with increasing PCO₂ (66, 67).

The diffusion coefficient of free H⁺ in aqueous solutions at 25°C is 9.3 × 10⁵ cm²/s (123), i.e., H⁺ possess a more than five times greater diffusivity in water than CO₂. Nevertheless, free diffusion of H⁺ is a rather ineffective mechanism of H⁺ transport, because at physiological values of pH, the H⁺ concentration gradients within cells cannot exceed the order of 10⁷ to 10⁸ M. In the presence of buffering substances at physiological concentrations of 10³ to 10² M, such differences of free H⁺ concentrations are accompanied by concentration differences of buffered H⁺ of at least of 10³ to 10² M or more. This very much higher concentration difference of the bound H⁺ compensates for the lower diffusion coefficients of mobile buffers. The diffusion coefficient for a mobile buffer such as phosphate is of the same order of magnitude as that of HCO₃, 7.0 × 10⁶ cm²/s (67). Consider as an example an intracellular pH difference of 0.1 between absolute pH values of 7.1 and 7.2; then, the expected flux of H⁺ by free H⁺ diffusion, estimated as diffusion coefficient (D) × concentration difference (c), gives 9.3 × 10⁵ × 1.62 × 10⁸ mmol·cm¹·s¹ = 1.5 × 10¹² mmol·cm¹·s¹. Estimating facilitated H⁺ flux by diffusion of buffered H⁺ with the assumption of a buffer capacity of 40 mM/pH and the above value of D for phosphate in an analogous fashion yields 7.0 × 10⁶ × 0.1 × 40 × 10³ mmol·cm¹·s¹ = 2.8 × 10⁸ mmol·cm¹·s¹. Thus facilitated H⁺ diffusion by buffer diffusion in this example is more than 10,000 times more effective than free diffusion of H⁺. It has been shown that not only the diffusion of low-molecular-weight buffers such as phosphate (67) but also the diffusion of protein buffers (66) is a highly effective means of H⁺ transport. In the case of very large protein molecules, it has even been shown that facilitated H⁺ transport occurs very efficiently not only by translational but in addition by rotational protein diffusion (62, 63). Thus facilitated CO₂ diffusion essentially occurs by diffusion of HCO₃ and simultaneous buffer-facilitated H⁺ diffusion. That buffer mobility is indispensable for this process to take place has been shown by Gros et al. (67) by demonstrating that immobilized phosphate buffer cannot entertain facilitated CO₂ diffusion.

Al-Baldawi and Abercrombie (3) have reported measurements of H⁺ diffusion in cytoplasm extracted from giant neurons of a marine invertebrate. An apparent diffusion coefficient for H⁺ of only 1.4 × 10⁶ cm²/s was determined, which was 5 times lower than the estimated diffusion coefficient of the mobile buffers and 70 times lower than the diffusion coefficient of free H⁺. This appears to be in contradiction to the above considerations. However, because the authors performed their measurements under non-steady-state conditions by observing the relaxation of pH after a sudden pH change at one surface of the cytoplasm sample, it appears likely that this value represents a substantial underestimate of the apparent H⁺ diffusivity that one would observe under steady-state conditions. A pH transient will be greatly slowed down by the presence of buffers whose buffering capacity is so overwhelming compared with free H⁺ concentration. This problem was aggravated in the experiments of Al-Baldawi and Abercrombie (3) by the presence in the cytoplasm of a substantial fraction of immobile buffers.

The contribution of facilitated diffusion to overall diffusion depends on the actual concentration differences for HCO₃ and for buffered H⁺. These in turn are dependent on the actual pH gradient and the pK value(s) of the mobile buffer(s) present. As an example, calculated CO₂ fluxes are shown in Figure 3 as a function of the average pH with boundary PCO₂ values of 5.32 and 6.65 kPa (40 and 50 mmHg) in a 66 mM phosphate solution (pK 6.84, 25°C). Total CO₂ diffusion is more than twice as high as free diffusion of dissolved CO₂ in a pH range of ~6.9-7.8. Thus more than one-half of the CO₂ transport in this model system occurs by facilitated diffusion, which means that at a physiological pH of the intracellular or extracellular spaces more HCO₃ than CO₂ molecules contribute to total CO₂ flux within the compartment. Facilitated diffusion does not reach its maximum exactly at the pK value of the phosphate, i.e., at the maximal buffer capacity of the solution. The reason for this is that whereas above pH 6.84 the buffer capacity decreases, the pH difference across the layer increases markedly. The sum of these two effects leads to an increase with increasing pH in the concentration differences of HCO₃ and of the H⁺-carrying H₂PO₄ beyond the pK of the phosphate buffer. Under physiological conditions, the course of this curve may be different, since buffering is accomplished by different sets of buffers with more than one pK value. Although proteins, which are important buffers in intact cells, possess a lower diffusivity than inorganic phosphate, their large buffer capacity for H⁺ results in a facilitation of CO₂ diffusion in intact cells that is of a similar order of magnitude as shown in Figure 3 for phosphate. For the condition within red blood cells, in a hemoglobin solution of 30 g% Hb at 38°C and at roughly physiological pH and PCO₂, Gros and Moll (65) have measured a contribution of facilitated CO₂ diffusion of ~85% to total intraerythrocytic CO₂ transport.

View larger version (11K): [in this window] [in a new window]   Fig. 3. Calculated CO2 fluxes across a layer of buffer solution as a function of the average pH value in this layer. The boundary CO2 partial pressures are constant with 6.65 and 5.32 kPa (50 and 40 mmHg), respectively. The solution is 66 mM phosphate with varying contents of base. Thickness of the layer is 180 µm. Carbonic anhydrase is assumed to be present in excess. Solid curve represents the total flux of CO2, and dashed curve represents the flux by free diffusion only. [Redrawn from Gros et al. (67).]

Cell membranes are generally considered to be highly permeable to gases such as CO₂ or O₂, with one of the few exceptions being the apical membrane of parietal and chief cells of gastric glands, which have been described to possess "no detectable permeability to NH₃, NH₄⁺, CO₂, and HCO₃" and whose surface area times permeability product was found to be about three orders of magnitude lower than that of the basolateral membranes of the same cells (15, 176). Erythrocyte membranes, though, are highly permeable to CO₂, the absolute permeability values cited being in the range of 0.35-3 cm/s (Table 3), as has been thoroughly discussed by Klocke (105). More recently, Forster et al. (47) measured the rate of depletion of C¹⁶O¹⁸O in erythrocyte suspensions by mass spectroscopy. They evaluated their measurements to give the CO₂ permeability of the human red cell membrane and obtained a value of ~1 cm/s. If we simplistically equate physiological CO₂ concentration with CO₂ concentration difference across the membrane (cCO₂), we can estimate the possible order of magnitude of physiologically occurring CO₂ fluxes from PCO₂ × cCO₂ = 1 cm/s × 1 mM = 1 × 10³ mmol·cm²·s¹.

Permeability for HCO₃ of artificial phospholipid vesicles, which are devoid of any anion exchanger, is six orders of magnitude lower (Table 3; Ref. 127) than it is for dissolved CO₂. However, erythrocyte membranes of all vertebrates with the exception of agnathans (hagfishes and lampreys; see reviews, Refs. 80, 126, 136) do have a rapid anion (HCO₃/Cl) exchange protein, capnophorin or band 3 (see review by Jennings, Ref. 90), which exchanges HCO₃ for Cl at a ratio of 1:1. An overview of the distribution of this transporter in red blood cells is given in Table 4. Thus the permeability of the erythrocyte membrane to HCO₃ is considerably increased over that of lipid bilayers but still about three to four orders of magnitude lower than the permeability for dissolved CO₂ (Table 3). Net driving force for HCO₃/Cl exchange is proportional to the difference in the electrochemical potential for both ions. The turnover number of this transporter is 4-5 × 10⁴ Cl·s¹·transporter molecule¹ at 37°C (16, 56). With this figure and the number of 1.0-1.2 × 10⁶ copies of capnophorin per red blood cell (90), a maximal flux across the membrane of ~6 × 10⁵ mmol Cl·cm²·s¹ can be calculated using an erythrocytic volume of 80 × 10¹² cm³ and a red cell surface of 1.6 × 10⁶ cm². Maximal HCO₃ flux is expected to be in the same range as that of Cl. Flux measurements at 0°C have shown a maximal value for HCO₃ flux of 1% of this theoretical value, ~5 × 10⁷ mmol HCO₃·cm²·s¹ (48). When the large temperature dependence of the anion transporter with a turnover number at 0°C of only ~200 Cl·s¹·molecule¹ (56) is taken into account, this agrees well with the value calculated above for maximal flux at 37°C. Values of HCO₃ permeability of erythrocyte membranes are similar for humans and birds (as well as in several other species). In red blood cells of adult humans and of chicken HCO₃ permeability (P_HCO3) was measured to be 5.6 × 10⁴ and 7 × 10⁴ cm/s, respectively (160). These latter authors showed that a functionally active band 3 protein is present in the erythrocyte membrane of the chicken at very early stages of development. In the dogfish (Mustelus canis), flux of HCO₃ across red cell membrane was reported to equal flux across human red cell membranes (128). It should be mentioned that a very large number of measurements have been reported for the HCO₃ permeability of the human red blood cell (e.g., Refs. 19, 30, 88, 103), most of which yielded numbers very similar to that of Sieger et al. (160), as cited in Table 3. Estimating the physiologically possible HCO₃ flux across the red cell membrane in a fashion analogous to that used above for CO₂, one obtains the following: P_HCO3 × c_HCO3 = 5 × 10⁴ cm/s × 10 mM = 5 × 10⁶ mmol·cm²·s¹, which is ~10 times less than the maximal flux of 6 × 10⁵ mmol·cm²·s¹ estimated above from turnover number and number of copies of capnophorin per red blood cell but more than two orders of magnitude smaller than the above CO₂ flux.

View this table: [in this window] [in a new window]   Table 4. Carbonic anhydrase activity and HCO3/Cl exchanger in blood of different species

Proton permeability of phospholipid vesicles is five times higher than HCO₃ permeability, 1.8 × 10⁵ cm/s (127). However, because the H⁺ concentration gradient across the cell membrane is very small (intracellular pH 7.2, extracellular pH 7.4, pH 0.2), the product permeability × concentration gradient, is also very small: P_H⁺ × c_H⁺ = 1.8 × 10⁵ cm/s × 2.3 × 10⁸ M = 4 × 10¹³ mmol H⁺·cm²·s¹. Thus diffusion of free H⁺ across the membrane is so small that it cannot support any facilitated CO₂ diffusion. However, in addition to free H⁺ diffusion, there are several other more efficient mechanisms of H⁺ transport across the red cell membrane. The significance of these pathways for overall H⁺ flux across the erythrocytic membrane depends on the specific conditions. Proton fluxes (or reverse OH⁺ fluxes) in erythrocyte membranes can be achieved via 1) the Jacobs-Stewart cycle, which includes HCO₃/Cl exchange via capnophorin; 2) H⁺ flux via HCl cotransport (or OH⁺-Cl countertransport); and 3) H⁺ flux via H⁺-lactate cotransport and nonionic lactic acid diffusion.

Bisognano et al. (12) measured H⁺ fluxes across red cell membranes by a pH stat method. They induced these fluxes by establishing an outward Cl concentration gradient through increasing the osmotic strength of the extracellular solution with sucrose. Without lactate/lactic acid present, two-thirds of the measured apparent H⁺ flux was mediated via the Jacobs-Stewart cycle (89), and one-third was due to a DIDS-sensitive HCl cotransport. The Jacobs-Stewart cycle brings about a H⁺ efflux from the red blood cell by the following sequence of processes: 1) H⁺ in the cell reacts with HCO₃ to give CO₂, 2) CO₂ leaves the cell and 3) is hydrated extracellularly to give H⁺ and HCO₃, where 4) the H⁺ remains outside while the HCO₃ enters the cell in exchange for Cl via the Cl/HCO₃ exchanger. Bisognano et al. (12) base their study on the assumption that the Jacobs-Stewart cycle-mediated H⁺ flux is inhibitable by the CA inhibitor ethoxzolamide, whereas HCl cotransport is not affected by this drug but suppressed by DIDS. Under their conditions, an initial flux via HCl cotransport was observed at 0.5 × 10⁹ mmol H⁺·cm²·s¹, compared with 1 × 10⁹ mmol H⁺·cm²·s¹ mediated by the Jacobs-Stewart cycle, giving a total H⁺ flux by these two mechanisms of 1.5 × 10⁹ mmol·cm²·s¹.

Compared with free H⁺ diffusion, this value is very high; it is considerably lower than the HCO₃ flux estimated above and substantially lower than the estimated CO₂ flux.

A third mechanism of H⁺ transport across the red cell membrane is by the H⁺/lactate carrier and by nonionic diffusion of lactic acid, both of which require the presence of lactate (27, 138). Proton fluxes via this mechanism were calculated from flux measurements of Fishbein et al. (42) and of Poole and Halestrap (138) in human red blood cells to be 2-2.5 × 10⁹ mmol H⁺·cm²·s¹. Thus, in the presence of lactate, the above H⁺ flux estimate would have to be raised to ~4 × 10⁹ mmol·cm²· s¹, which is much lower than the flux estimate for HCO₃. The fluxes of both ions, however, are more than two orders of magnitude smaller than a physiological CO₂ flux. Thus a significant facilitation of CO₂ diffusion across the red cell membrane does not occur. It may be noted that the activity of the H⁺-lactate cotransport can be increased considerably in Plasmodium falciparum-infected human erythrocytes (96).

In conclusion, the permeability of dissolved CO₂ is much greater than the effective permeability of HCO₃ and H⁺. At the same time, more than two-thirds of the CO₂ transported in either red blood cells or plasma is transported in the form of HCO₃. This makes it appear essential that CO₂ and HCO₃ can be converted into each other quite rapidly at the boundary between the two compartments: intraerythrocytic space and plasma. A high velocity of this interconversion is achieved by the enzyme CA.

Although HCO₃ and H⁺ are produced in equal amounts by the hydration of CO₂, the distribution of the two products among the two compartments, intraerythrocytic space and plasma, is quite different at electrochemical equilibrium. Bicarbonate is transported to a larger fraction within plasma than within erythrocytes because the equilibrium pH of the plasma is more alkaline than the intraerythrocytic pH (Table 1). In contrast, H⁺ are transported to a larger fraction within erythrocytes than in plasma because the nonbicarbonate buffer capacity of erythrocytes exceeds that of plasma by a factor of ~10.

The CO₂ entering the blood during capillary passage through the peripheral tissue can encounter two different situations: 1) a situation where CA is present in red blood cells only, or 2) a situation where CA is available in red blood cells and in plasma,

A) RAPID CATALYSIS OCCURS ONLY WITHIN ERYTHROCYTES. Carbon dioxide enters the red blood cells, and there is rapidly converted to HCO₃ and H⁺. When the red blood cell has reached the end of the capillary, electrochemical equilibrium across erythrocyte membrane is not yet established, because H⁺ concentration and even more so HCO₃ concentration are too high within red blood cells compared with plasma concentrations. A significant fraction of the intraerythrocytic HCO₃ has left the cell via HCO₃/Cl exchange already during capillary transit. After blood has left the capillary, part of HCO₃ and H⁺ that has been produced within the red blood cell is dehydrated back to give CO₂; CO₂ then leaves the cell and enters the plasma, where the slow uncatalyzed reaction hydrates CO₂ to establish final equilibrium. During this postcapillary process, the plasma pH shifts slowly in the acidic direction.

B) RAPID CATALYSIS OCCURS IN ERYTHROCYTES AND IN PLASMA. Carbon dioxide enters red blood cells and is rapidly converted there, but also within plasma, to HCO₃ and H⁺. Equilibration between the two compartments is no longer rate limited by the slow CO₂ hydration reaction in plasma. The pH of the blood leaving the capillary can be expected to be constant and in equilibrium. However, as is shown in section IVD2, in the presence of lactic acid production in the tissue, this must not necessarily be so. At the end of capillary transit, it may even be possible that H⁺ concentration in plasma is too high compared with intraerythrocytic concentration for equilibrium to be established across the erythrocytic wall, since equilibration of lactic acid across this wall is a slow process.

For CO₂ excretion, it is essential that there is a rapid chemical reaction of CO₂. However, how and how fast acid-base equilibrium is established in the blood depends on the sites of CA localization and its activity. This and the velocity of other CO₂ reactions will therefore be considered in the following sections.

The interconversion between CO₂ and HCO₃ without a catalyst is rather slow and may require more than 1 min to approach completion, a time much too long compared with the capillary transit time, which is ~1 s. Carbon dioxide hydration/dehydration reactions are accelerated between 13- and 25,000-fold by intraerythrocytic CA activities (46, 47). With such a CA activity, the interconversion between CO₂ and HCO₃ inside erythrocytes requires only 2 ms for 95% completion.

The participants of this reaction, HCO₃ and, in particular, the H⁺ (see sects. IIIC1, IIID, and IV) are involved in other reactions, so the time course of their concentration is also dependent on the kinetics of other reactions. For a complete understanding of the overall time course of CO₂ exchange, these reactions have also to be considered.

Carbonic anhydrase is found in the blood of all vertebrates. With respect to location, isozyme types, and coexpression of the anion exchanger (capnophorin), there are very interesting variations between different species from the lower vertebrates to mammals (Table 4) that may shed light on the increasing efficiency of CO₂ excretion in the course of evolution.

A) CYTOPLASM OF ERYTHROCYTES. Carbonic anhydrase was first detected by Meldrum and Roughton (118) [for review, see Maren (113) and Klocke (105)]. Briefly, isozyme CA I with a relatively low specific activity occurs in the red blood cells of all vertebrate groups with the exception of the cat family and a few other species; it is absent in the red blood cells of the cat, lion, jaguar, tiger, leopard, ox, chicken, and frog (18, 115). In primitive agnathans (lamprey, hagfish) and elasmobranchs (dogfish), CA I is the only isozyme present (114). It is somewhat less inhibitable by sulfonamides and considerably more susceptible to anions than CA II. Isozyme CA II with a specific activity that is ~10 times higher than that of CA I is probably the most widespread form and occurs in the red blood cells of all vertebrates except agnathans and elasmobranchs.

A mechanism for rapid HCO₃/Cl exchange across the erythrocyte membrane is present in almost all vertebrate red blood cells and is missing only in the most primitive vertebrate group, the agnathans (lamprey, hagfish; Refs. 39, 131, 171, 172). The consequence of this has been discussed by Nikinmaa (126). In these fish this precludes the utilization of plasma HCO₃ in CO₂ excretion on a physiological time scale. Together with the rather flat CO₂ binding curve, CO₂ transport in these animals appears rather inefficient, yet in the lamprey, CO₂ transport potential is as great as in the highly active teleosts despite the missing anion exchanger. In this species, the disadvantage is overcome by a high intraerythrocytic pH, resulting in a high intracellular binding capacity for CO₂ and a marked Haldane effect. However, the intracellular buffering capacity is separated from the plasma compartment in lampreys due to the low membrane permeability to HCO₃. As a consequence, extracellular metabolic acid loads cause marked fluctuations in plasma pH. Thus the major advantage gained by the rapid anion exchanger appears to consist of an improved effective extracellular buffering (with access to the intracellular buffering power) rather than in a major improvement of gas transport (126).

The acceleration of the hydration-dehydration velocity by CA within erythrocytes is considerable. An activity (factor by which the rate of CO₂ hydration is accelerated) of 13-14,000 was reported by Forster and Itada (46), and figures of 23,000 and 25,000 have been obtained by Wistrand (184) and by Forster et al. (47). The cytosolic CA enzymes may be not uniformly distributed within the red blood cells. Some indications have been proposed to suggest that their concentration may be increased near the cellular border. Interactions of CA are reported with the plasmalemmal anion exchanger (capnophorin = band 3; Ref. 98), and it would seem a most efficient place to catalyze CO₂-HCO₃ hydration-dehydration reaction in close neighborhood to HCO₃/Cl exchange. Parkes and Coleman (133) reported an enhancement of CA activity by erythrocytic membranes; CA II and CA I activity were increased 3.5- and 1.6-fold, respectively, by the presence of red cell membranes. Whether in their erythrocytic membrane preparation the effective structure was the band 3 protein can only be speculated. Although these observations have not been confirmed yet by other investigators, there are several studies of the problem whether part of red cell CA is firmly bound to the erythrocyte membrane. Whereas Enns (40) had found CA in red cell ghosts, later studies by Tappan (170), Rosenberg and Guidotti (145), and Randall and Maren (139) came to the conclusion that red cell CA is a truly cytosolic enzyme and not membrane bound.

B) PLASMA. No CA activity aside from that attributable to lysed erythrocytes was ever found in plasma, with the sole exception of dogfish (Scyliorhinus canicula; Ref. 186). Also, there is no CA activity on the outside surface of erythrocytes or available to plasma, as was confirmed by Effros et al. (37).

However, in tissues where especially large amounts of CO₂ leave or enter the blood, there is extracellular catalysis available to the capillary plasma in some species. This is achieved by an extracellular CA bound to membranes, the membrane-bound isozyme CA IV, which provides catalytic activity to the plasma. Such a membrane-bound CA was found in the lung (36, 104, 150) and gill (28). In skeletal muscle, the first evidence for the presence of such a CA in dog, cat, and rabbit was provided by measurements of the distribution space of labeled HCO₃ (37, 50, 51, 189) and by measurements of the postcapillary pH kinetics (128).

With the histochemical method of Hanson, staining of endothelial membranes as well as sarcolemma was observed in skeletal muscle (140, 141). Immunohistochemical studies employing anti-CA IV antibodies at the light microscopic level revealed staining of capillary walls, which would indicate that CA IV is associated with endothelial cell membranes (157). With the use of semithin sections and a more sensitive immunocytochemical technique, however, capillaries and sarcolemma were found to be stained, and in antibody-treated ultrathin sections of skeletal muscle studied by electron microscopy, membrane-bound CA IV was found to be associated with capillary endothelium, sarcolemma, and sarcoplasmic reticulum (SR) (24). That sarcolemmal and SR CA IV were visible in ultrathin sections but not in cryosections was attributed to a poor accessibility of CA IV at these locations in the 7-µm-thick untreated cryosections. Another approach has been used by Geers et al. (51). Measuring the space of distribution of labeled HCO₃ and its reduction by CA inhibitors, Geers et al. (51) observed that the effectiveness of macromolecular CA inhibitors of different molecular size (Prontosil-dextrans of mol wt 5,000 vs. 100,000) indicates the presence of CA in the interstitial space. Indirect although strong evidence for this CA to be associated with the sarcolemma was obtained by intracellular and cell surface pH microelectrode measurements on skeletal muscle fibers by deHemptinne et al. (25). They observed a transient alkaline pH shift on the surface of these fibers upon exposure to propionate, whose magnitude was greatly increased in the presence of the CA inhibitor acetazolamide in the extracellular space. This was interpreted to show that in the presence of extracellular sarcolemmal CA CO₂-HCO₃ acts as a rapid and efficient source of H⁺ that enter the cells together with the propionate ion. Analysis of isolated sarcolemmal vesicles demonstrated the presence of high activities of CA associated with the sarcolemma (179), and it was shown by Western blotting with anti-CA IV antibody that this sarcolemmal CA is isozyme CA IV (175). In conclusion then, the present state of evidence indicates that in skeletal muscle, membrane-bound CA IV is associated with endothelial as well as with sarcolemmal membranes, in addition to a CA bound to the sarcoplasmic reticulum membrane.

In the case of lung tissue, it was estimated by Bidani et al. (11) that the CA of rat pulmonary vasculature catalyzes the extracellular hydration-dehydration reaction by a factor of 130-150, a figure that may appear rather small compared with the intraerythrocytic activity of >10,000. However, the calculations described below indicate that an activity of 100 in the plasma within the capillary bed of skeletal muscle should be sufficient physiologically (see sect. IVD2). No estimates of intracapillary CA activity in muscle capillaries are available.

The localization pattern of CA in blood is further complicated by the presence of a CA inhibitor in the plasma of some species, which ensures the absence of any activity of soluble CA in plasma. This was first described for dog and fish (14) and later for pig, sheep, rabbit, and various fish species (74, 75, 77, 83, 109, 137, 149). The molecular size of this endogenous CA inhibitor was determined to be 10-30 kDa for the eel (74) and 79 kDa for the pig (148).

In view of the presence of an extracellular membrane-bound CA activity available to plasma in lung and muscle, the existence of a plasma CA inhibitor seems astonishing. However, some experiments indicate that the plasma inhibitor inhibits erythrocytic cytosolic CA rather well, but CA from lung tissue homogenate (membrane-bound CA; dog) only incompletely (83). Similarly, plasma inhibitor from pigs showed a less than complete inhibition of vascular CA activity in lungs of rats (78), where the vascular activity of CA is known to be CA IV located on the extracellular luminal surface of capillary endothelial cells.

It may be hypothesized that, due to its molecular size, the plasma inhibitor has no access to the interstitial space. Thus a CA associated with the sarcolemma may be left uninhibited by the plasma inhibitor, because a macromolecule of this size may not enter the interstitial space to a great extent. Even the endothelial membrane-bound CA IV in the lung appears to be only partly inhibited, and this should also be true for capillary CA IV of muscle (and, for example, of the brain).

We conclude that the plasma inhibitor will inhibit erythocytic CA released from any hemolyzed red blood cells throughout the blood vessels rather completely, thus reducing the dehydration/hydration reaction in the plasma to the uncatalyzed velocity, whereas in vascular regions with a membrane-bound CA, e.g., muscle, heart, lungs, and others, a marked catalysis of the dehydration/hydration reaction can take place even in the presence of a plasma inhibitor. Thus CA activity available to plasma appears to be confined to precise localizations within the circulation that are equipped with a capillary CA.

The effect of presence of CA in the plasma has been studied by Wood and Munger (186) for the rainbow trout. They found that CA attenuated postexercise increases in PCO₂ and decreases in arterial pH by producing an increase in CO₂ excretion during exercise. However, the normal postexercise hyperventilation was also greatly attenuated when CA was present in the plasma, as was the normal increase in the plasma levels of epinephrine and norepinephrine. They concluded that CO₂ is an important secondary drive to ventilation in fish, and by increasing CO₂ excretion by the presence of CA in the plasma this drive is diminished. The plasma CA inhibitor will ensure that no CA activity of hemolysed erythrocytes is present and thus will contribute to maintain a high level of ventilation in certain situations, which will be favorable for O₂ supply.

The kinetics of oxylabile carbamate was thoroughly reviewed by Klocke (105). We only briefly summarize the relevant facts in these sections.

The kinetics of this interconversion do not seem to be important for overall CO₂ kinetics, since venous and arterial plasma carbamate concentrations are almost identical. The kinetics of plasma carbamate formation were characterized by Gros et al. (61) by a half-time of this reaction of 0.047 s.

The binding of CO₂ to hemoglobin in solution has long been known to be quite rapid, requiring a time to reach completion of 0.1-0.2 s (44), which corresponds to a half-time of ~0.04 s. Gros et al. (68) have studied the kinetics of hemoglobin carbamate formation in a wide range of pH and PCO₂ values using a pH stopped-flow technique. They determined kinetic constants for the forward reaction of amino groups and CO₂, k_a, for the -chain and the -chain -NH₂ groups in addition to the e-NH₂ groups of human oxy- and deoxyhemoglobin. Table 5 shows the complete set of constants reported by Gros et al. (68) with k_a, pK_z, and pK_c, which describe their kinetic measurements. With these constants, overall carbamate kinetics under physiological conditions of pH and PCO₂ were estimated to possess a half-time of 200 ms and to require ~1 s to reach equilibrium by 95%. Their measurements were performed in the absence of 2,3-DPG, and these times may become slightly shorter when 2,3-DPG is present. Nevertheless, their estimate of the half-time of carbamate formation is considerably greater than that of Forster et al. (44) but is similar to Klocke's estimate (102) of the half-time of mobilization of oxylabile carbamate of 0.12 s, which was obtained in the presence of 2,3-DPG.

	III. CARBON DIOXIDE TRANSPORT IN MUSCLE

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Unlike most other tissues, muscle exhibits a vast range of aerobic (and anaerobic) metabolic rates. In humans, O₂ consumption of muscle tissue can rise 15- to 20-fold from resting values of ~10 µmol·min¹·100 g¹, and even higher increases have been reported from 6.3 mmol·min¹·100 g¹ at rest to 200 µmol·min¹·100 g¹ at maximal exercise of a small muscle group (forearm; Ref. 73). Carbon dioxide production rates can be calculated from these O₂ consumption rates using a RQ of ~0.85. The PCO₂ values in the venous blood leaving the skeletal muscle have also been measured and are ~5.32-5.99 kPa (40-45 mmHg) at rest and can rise to as much as ~13.3 kPa (100 mmHg) during exercise (for example, Ref. 95).

Although different muscle types and different mammalian species have vastly different maximal specific O₂ consumption rates, maximal specific mitochondrial O₂ consumption differs considerably less. At maximum O₂ consumption (VO_2max), mitochondria of different species consumed 4.56 ± 0.61 ml O₂·min¹·ml¹ (87). This indicates that it is essentially mitochondrial density in muscle fibers that determines maximal specific O₂ consumption of these fibers.

Carbon dioxide produced within muscle mitochondria has to diffuse through the intracellular compartment and cross the sarcolemmal membrane and the capillary wall to reach the convective medium blood. Because all the membranes crossed by CO₂ along this diffusion pathway are considered highly permeable to CO₂, their surface area is of no relevance for CO₂ transport, but this area may be important for the permeation of ions associated with gaseous exchange. Among these membrane barriers, the capillary wall has by far the smallest surface area, only ~1/5 of the entire area of the sarcolemma (185) and only ~1/200 of the total area of the inner mitochondrial membranes (87). The following fluxes of respiratory gases occur across the surface of the capillary wall. Maximal flow of O₂ per area of capillary wall is 1.3-1.9 µl O₂·min¹·cm² as calculated from Conley et al. (20), where the higher values have been measured in more athletic species (dog, pony) and the lower values in less athletic ones (goat, calf). Corresponding maximal total CO₂ flux across capillary wall can be expected to be ~15% lower than the respective O₂ fluxes (~60 nmol CO₂·min¹·cm²). The area of inner mitochondrial membranes being larger, CO₂ flux across this membrane is expected to be ~0.3 nmol CO₂·min¹·cm². This may indicate that the capillary wall could be a significant barrier to ion fluxes associated with CO₂ transport.

Several types of CA are present in various parts of skeletal muscle as has been reviewed by Gros and Dogson (60) and recently by Henry (79). Table 6 gives a summary of CA localizations in skeletal muscle.

Carbonic anhydrase associated with this membrane was found with a variety of methods. The first evidence for the presence of an extracellular catalysis of the hydration/dehydration reaction in the capillary bed of skeletal muscle arose from functional studies. From observation of the distribution space of H¹⁴CO₃ and its reduction in the presence of CA inhibitors, it was concluded that an extracellular CA in mammalian skeletal muscle exists (38). Its inhibition properties were different from those of the cytosolic enzymes, and it was concluded that this isozyme is present in the interstitial space and probably bound to the sarcolemma (50, 51). Other functional studies have indicated that an extracellular CA available to plasma is involved in fast pH equilibration of the venous effluent and the interstitial space. With the use of a stop-flow technique, it was shown that an electrolyte perfusate had access to a CA while it passed through the hindlimb capillary bed. By inhibiting this extracellular CA, a pH disequilibrium developed in the venous saline perfusate, and the pH of the effluent slowly became more acidic after the saline had left the capillary bed, i.e., a so-called postcapillary acid pH shift developed (129). It appears likely now that these effects, at least partly, are due to capillary endothelial CA IV.

Transient changes of surface pH, induced by sudden addition and withdrawal of propionic acid, were magnified when CA was inhibited in isolated soleus muscle from mouse and rat and in cardiac muscle from sheep, rabbit, and cat (25). Transient changes of surface pH induced by a sudden increase and decrease of PCO₂ were blocked by CA inhibitors in a nonvertebrate muscle, the crayfish muscle (151). In the former case, surface pH change is due to a net movement of H⁺ across the membrane together with propionate. When sarcolemmal CA is blocked, the efficacy of the CO₂/HCO₃ buffer is diminished, producing an increased pH transient. In the latter experiment, inhibition of the sarcolemmal CA activity leads to a suppression of surface pH transients that are caused by net fluxes of CO₂, which go along with rapid changes in surface PCO₂ that are followed by H⁺ production or consumption when CA is present on the cell surface, but are not (or very slowly) when CA is inhibited. These effects are clearly due to a CA bound to the external surface of muscle fibers.

In sarcolemmal vesicles, a CA was found in preparations from red and from white muscles of the rabbit. The inhibition constants (K_i) of this sarcolemmal CA toward acetazolamide, chlorzolamide, and cyanate were shown to be different from those of CA II or CA III (179). With CA IV antibodies this sarcolemmal CA was identified to be CA IV (175). In semithin and ultrathin sections of rat soleus muscle, CA IV was found immunocytochemically to be associated with the sarcolemma in addition to its association with the capillary endothelium and the SR (24). In mammalian heart, CA IV was also found to be associated with the sarcolemma in addition to the capillaries (156). Thus the present state of information indicates that sarcolemmal CA is the membrane-bound, glycosyl-phosphatidylinositol (GPI)-anchored isoform CA IV.

It is well known that the sulfonamide-resistant isozyme CA III is present in high concentration in the cytoplasm of mammalian skeletal muscle type I (slow-oxidative fibers) (review, Ref. 60). A sulfonamide-sensitive CA, probably CA II, was found in the cytosol of white muscles of the rabbit (161) and in the mouse soleus (21). In the latter case, however, no measurements of the erythrocytic contamination of the muscle homogenates were done; thus CA II of erythrocytes could be present in these experiments. In contrast, in the former case, red cell contamination was carefully controlled. In the cytoplasm of white as well as red hindlimb muscles of the rat, no sulfonamide-sensitive CA was present (54). For other animal groups, studies are scarce; from functional studies, the presence of a CA in the cytosol of crayfish muscle was deduced (151), and there is one report indicating that frog white muscle has a CA II-type isozyme (155).

Mammalian heart muscle appears to contain no cytosolic enzyme but high activities of the membrane-bound form (17, 54).

A membrane-bound CA was detected in preparations of SR vesicles from red as well as white skeletal muscle of the rabbit (17). This finding was confirmed by histochemical results employing the fluorescent CA inhibitor dansylsulfonamide for CA staining (17, 26). Although it has not been possible to visualize SR-CA immunocytochemically at the light microscopic level (157), membrane-bound CA IV was found to be associated with SR by electron microscopy and use of CA IV antibodies (24). This latter finding corresponds with a reaction of SR membranes with anti-CA IV in Western blots (175). Wetzel and Gros (180) have found that nevertheless the inhibitory properties of the CA of SR toward sulfonamides are significantly different from those of the CA of the sarcolemma, which may indicate either that SR-CA is an isoform somewhat different from CA IV or has different properties because of a different membrane environment. In the mammalian heart, immunocytochemical evidence at the electron microscopic level indicates that CA IV is also associated with the SR (156).

Mitochondrial CA, CA V, is present in high activities in liver and kidney mitochondria (see review, Ref. 60). In skeletal muscle, mitochondrial CA was found only in muscles of the guinea pig but was not detectable in skeletal muscles of the rabbit or the rat or the mouse (Table 6). Carbonic anhydrase V has been detected in immunocytochemical studies in the mitochondria of rat skeletal muscle in addition to those in several other rat ^<