Limits for Oxygen and Substrate Transport in Mammals

The idea of a single step of the oxygen cascade limiting oxygen flow through the respiratory system has been a very attractive concept and has dominated physiological thinking until recently. Implicitly or explicitly, most physiologists assumed the heart to be the most important step in aerobic energy transfer. In the 1970s, data on the remarkable variability of skeletal muscle oxidative capacity and capillary supply with endurance exercise training became available (Hoppeler et al. 1973; Holloszy and Booth, 1976), which brought the importance of the periphery for into focus. The year-long debate on the relative importance of central versus peripheral limitations of was finally resolved in a paper entitled ‘Metabolic and circulatory limitation to at the whole animal level’ by diPrampero (1985). Using a deceptively simple algebraic model, he calculated the contribution of the individual steps of the respiratory cascade viewed as resistors in series. He could demonstrate that, for humans exercising in normoxia, approximately 75% of is set by central O₂ transport and the remaining 25% by the periphery. Additionally, he pointed out that the relative importance of the individual transfer steps was greatly affected by external conditions such as hypoxia, work with small muscle groups, etc. Since then, it has become generally accepted that it is the integrated, interactive effects of all steps in the respiratory cascade that help set (Wagner et al. 1997): ‘No single step is the limiting one, a change in the capacity of anyone step will alter ’.

This review explores how is set by structural capacities and functional regulation at each point in the pathway for oxygen from lungs to skeletal muscle mitochondria. For the periphery, we additionally analyze how the pathways for oxygen and substrates converge at the mitochondria and how substrate fluxes intervene in setting ⁠. To study a complex integrated physiological system such as the respiratory cascade, we need to develop an intellectual framework within which we can perform a systems analysis.

If an animal exercises intensely, its muscles elevate its metabolic rate at least tenfold above resting values. A well-trained human or animal athlete doing the same may elevate the rate of O₂ consumption by up to 20-fold above resting values (Fig. 1). In either case, this is accompanied by an increase in cardiac output and heart rate as well as by an increase in minute ventilation and respiratory frequency: O₂ uptake in the lung and O₂ transport by the circulation of blood must be matched to O₂ consumption in the mitochondria of the working muscle cells. At the same time, substrate supply must also be matched to oxidation rate. The basic features of this system are as follows.

1. Respiration is an integral function involving the coordinated action of all the structures that make up the pathway for O₂ from the lung to the respiratory chain enzymes in tissue mitochondria. Under steady-state conditions, the O₂ flow rate is the same at all levels.

2. Respiration is a regulated process matched to the instantaneous demands of aerobic metabolism: as muscle ATP consumption increases, O₂ demand is increased proportionally, requiring regulation of the various O₂ and substrate transport functions.

3. Respiration at the whole-animal level is a limited function. Therate of O₂ consumption can rise to a definable limit, called ⁠, beyond which any additional energy must be covered by anaerobic processes. This limit is a characteristic of the individual and is higher in athletes than in untrained subjects; to a certain extent, it is malleable in that it can be elevated by training.

To approach the question of what sets the limit for aerobic metabolism, we must consider the entire pathway for O₂ from the site of uptake in the lung to the sink in the mitochondria (Fig. 2) as well as the pathways for substrates that fuel oxidation from uptake in the gut to oxidation in the mitochondria. The O₂ pathway is simple: O₂ follows a single path without branches.

The substrate pathways are more complex. Both carbohydrate and lipid pathways branch to form four parallel pathways that converge on the mitochondria (Fig. 3). Proteins can be ignored for the purpose of the current analysis because in well-fed subjects their contribution to aerobic metabolism is minimal. During exercise, when rates of substrate oxidation are highest, blood is shunted away from the gut and rates of substrate uptake are lowest. At this point, stores supply most of the fuel for oxidation. Organismic substrate stores outside muscle are in the liver and in the adipose tissue. Inside the muscle cells, carbohydrates are stored as glycogen granules and fatty acids are stored as lipid droplets (Fig. 4). We will have to delineate the importance of the parallel substrate pathways as a function of exercise intensity and duration. We would like to know whether there is a single step in the oxygen or substrate pathway that sets the upper limit to aerobic metabolic rate, or whether the capacities in each of the steps are approximately matched to each other. We would also like to know whether limiting factors are primarily structural or functional.

Structural parameters intervene at all levels of the pathways. For example, the model in Fig. 2 predicts (a) that the pulmonary diffusing capacity depends on the surface area available for gas exchange between air and blood, (b) that the stroke volume (Vs) is determined by the size of the heart ventricles, (c) that the O₂ transport capacity of the blood is determined by the erythrocyte volume density, Vv(ec), and (d) that the capacity of cells for oxidative phosphorylation is related to the volume of mitochondria, V(mt).

Structural parameters cannot be regulated or changed on a short time scale because this requires morphogenetic processes. Structure can be modified in response to chronically altered demand. This regulation involves transcriptional activation of structure genes (Puntschart et al. 1995). It is well known that, during exercise, cardiac output is immediately regulated by increasing heart frequency (fH) up to a maximum, with stroke volume essentially unchanged; in contrast, as a consequence of exercise training, heart size increases and maximal cardiac output becomes elevated by a larger stroke volume at the same maximal heart rate. From this, we conclude that structural parameters set the boundaries within which functional parameters regulate oxygen and substrate fluxes according to the instantaneous demands of the organism. Note that in the example the actual functional limitation is heart rate, which has a fixed maximum because stroke volume can be increased by training. So it is both functional and structural parameters that set the limit.

The question, therefore, is whether the structural designof the respiratory system is such that it allows the limits to of the sequential steps to be matched to each other and to the overall limit. Common sense dictates that this should be the case, because it does not make sense for the body to build and maintain structures of a fundamental and vital functional system that it will never use. To approach this problem, we have proposed a principle of regulated morphogenesis and of economic design, the hypothesis of ‘symmorphosis’ (Taylor and Weibel, 1981). Symmorphosis postulates that the design of all components comprising a system is matched quantitatively to functional demand, ‘enough but not too much’. The principle of symmorphosis is somewhat akin to the concept of ‘homeostasis’. While homeostasis operates in real time on functional variables, symmorphosis operates on structural variables and on different time scales. Symmorphosis is either the consequence of genetic selection or it can be brought about by epigenetic structural malleability.

In a pragmatic approach, we can test the hypothesis of symmorphosis by taking advantage of the fact that varies among individuals and species. We can study the variation of struc tural and functional parameters in relation to the variation in ⁠. By comparing the differences in structural and functional variables with the variation in ⁠, we attem pt to identify parameters that vary directly in proportion to and whose ratio to is, accordingly, invariant.

Ideally, one would like to change in a single individual, e.g. by exercise training or by cold exposure. We call these changes, which reflect the malleability of the respiratory system, induced variation. The problem with induced variation is that only relatively small differences in can be induced experimentally (typically of the order of 15%, approaching the limits of the resolution of the structural measurements). This type of experiment is thereforenot well suited for a systems analysis. Larger variations in are observed among mammalian species as a consequence of two types of selection pressure during evolution.

Metabolic requirements are related to body mass (M_b) in such a way that small animals have higher resting and maximal oxygen consumption rates than large ones. These differences are usually expressed as power functions that describe the change of any functional or structural parameter as body mass changes, is found to be proportional to M_b^0.8; accordingly, (Fig. 5). Allometric variation accounts for enormous differences in ⁠: a mouse consumes approximately six times more O₂ than a cow per unit body mass (Weibel et al. 1981b).

In several size classes, nature has selected species for athletic performance (Fig. 5). Thus, we find that nature’s athletes such as horses and dogs have a that is more than twice that of sedentary species of similar size such as cattle and goats (see Table 1) (Taylor et al. 1987; Jones et al. 1989), and super-athletes such as the pronghorn antelope achieve even higher values.

Comparative studies using allometric and adaptive variations in have proved invaluable for a fundamental understanding of the design of the mammalian respiratory system and its functional limits. Not only do they provide us with large differences in ⁠, and hence with an excellent signal-to-noise ratio for our experiments, but they also offer the advantage that it is possible to sample tissue from all steps of the respiratory cascade. This enables us to sample tissue for morphometric quantification of the functionally relevant structural parameters on all levels. We will exploit the comparative data to generate a perspective of the fundamental design principle of the respiratory system in mammals.

When mammals exercise at their maximal rate of oxygen consumption, the mitochondria located in their skeletal muscles consume more than 90% of the available oxygen and substrates (Fig. 2; Mitchell and Blomqvist, 1971). We are therefore justified in concentrating on these particular mitochondria in our search for invariant design parameters in the respiratory system. What is the relevant structural parameter of skeletal muscle mitochondria to relate to the large variation in in allometric and adaptive variation? It has been shown that the volume of mitochondria in skeletal muscle is a good measure of the quantity of matrix enzymes as well as of the quantity of respiratory chain enzymes present and, there fore, it is also an appropriate structural parameter to relate to ⁠. This is the case when comparing mammals; in hummingbirds, reptiles and insects, we may have to use other structural variables with which to relate the rate of oxygen consumption (Suarez, 1992).

How do these parameters change as is varied by allometric, adaptive or induced variation? Because time is the fundamental variable in allometric variation (Lindstedt and Calder, 1981; Schmidt-Nielsen, 1984), we would anticipate a priori that would vary directly with ⁠, being six times greater in a mouse than a cow, whereas V(mt)/M_b should be invariant. This would seem to be an eminently reasonable design principle because the relative volume of muscle fibres occupied by mitochondria would not increase with demand. This is because relative muscle volume, V(musc)/M_b, follows the general allometric rule of organ size and is invariant with body size. On average, skeletal muscles make up some 40–45% of the total body mass (Schmidt-Nielsen, 1984). If V(mt)/M_b changed with ⁠, the contractile machinery would become progressively more diluted as demand increased; this might pose a serious problem for small animals in which mitochondria could occupy a significant fraction of the cell volume.

Contrary to our expectations, small animals have more mitochondria in each gram of muscle than do large animals. Quantitative measurements of mitochondrial volume in animals spanning a range of body masses from less than 20 g (woodmice; Hoppeler et al. 1984) to over 500 kg (steers and horses; Hoppeler et al. 1987a) reveal that the mitocho ndrial volume of skeletal muscles varies almost directly with ⁠,. whereas of the unit mitochondrial volume does not change with size. Compared with the cow, the mouse has six times the volume of mitochondria in its skeletal muscles so that, at ⁠, each millilitre of mitochondria in both cow and mouse would consume, on average, 4–5 ml O2 ml⁻¹ min⁻¹ (Fig. 6). Thus, the five-to tenfold difference in is matched by corresponding differences in the amount of mitochondria that animals make, whereas the functional parameter, the rate at which each unit of structure consumes oxygen, is the same, irrespective of size.

Why is the widespread fundamental design principle that time constants vary with body size violated with respect to mitochondria? A possible explanation may lie in their origin and their genetics. The enzyme systems of mitochondria and their spatial organization within membranes are very similar to those found in bacteria. So similar, in fact, that it has been suggested that mitochondria evolved from bacteria that were incorporated into the first eukaryotes in an endosymbiotic relationship (Margulis, 1981). This is supported by the finding that mitochondria contain their own DNA and ribosomes, which are both similar to those of bacteria. If we consider mitochondria as endosymbiotic bacteria that respond to increased energy demand by reproducing, then their individual size and composition should not change, and there is no reason to expect that the activities of their enzymes will change with the O₂ demand of the host cell.

If we now consider adaptive variation, we find that mitochondria have adapted to the 2.5-fold differences in aerobic capacity among animals of the same size in the same way that mitochondria adapted to differences with allometry (Hoppeler et al. 1987b; Mathieu et al. 1981). The higher demand is met simply by building more of the same structure. The 2.5-fold greater of dogs, ponies and horses compared with that of goats, calves and steers is matched by a 2.5-fold larger total volume of mitochondria in their muscles, whereas the average rate at which each millilitre of mitochondria consumes oxygen is again the same, namely, 4–5 ml O2 ml⁻¹ min⁻¹ (Table 1).

Overall, the comparative approach has revealed that the maximal rate of O₂ consumption by skeletal muscle mitochondria is invariant at ml O₂ ml ¹ min⁻¹ and, accordingly, that O₂ ml⁻¹ min⁻¹ and is invariant under all circumstances.

In this context, humans are different. Because of bipedal locomotion, they normally reach while performing exercises that do not involve all of their muscles, as is the case for quadrupedal animals. As a consequence, apparent is only half of what we find in animals (Fig. 7). Alternatively, this has been interpreted as humans having ‘excess’ muscle oxidative capacity (Gollnick and Saltin, 1982).

In summary, we can conclude that there is a good match between structure and function in the design of the mammalian respiratory system at the level of the mitochondria with allometric and adaptive variations in ⁠. In both cases, the differences in maximal rates of oxygen consumption are matched by corresponding differences in the amount of mitochondrial structure for both oxygen and substrates, whereas the average rate at which each unit of structure consumes oxygen is invariant.

When exercising at , substrates must be transported into the mitochondria at a rate sufficient to fuel oxidative phosphorylation. The oxidation of 1 mol of glucose consumes 6 mol of oxygen, and 1 mol of fat consumes 23 mol of O₂. It has been clearly established in dogs and goats that circulating carbohydrates and lipids can supply only a fraction of the total substrate demand of mitochondria in working muscles (Weber et al. 1996a,b). Both carbohydrate and lipid transport from capillaries into muscle cells appear to be maximal at quite low exercise intensities corresponding to approximately 40% of and cannot be upregulated at higher work intensities. Instead, the mitochondria depend on obtaining their fuels from intracellular substrate stores so that, at , over 80% of the fuel is supplied from glycogen granules. These results were obtained in a comparative setting of adaptive variation, but they are very similar to the situation observed in exercising humans, where a heavy reliance on intracellular substrate stores at higher work intensities has also been demonstrated (Romijn et al. 1993). From this, it follows that substrates for mitochondrial oxidation at work intensities of approximately 80% of must primarily be supplied from glycogen granules and lipid droplets inside the muscle cells, with no more than 20–30% of the fuel coming from the capillaries. There is strong evidence that this is due to a limitation of fuel supply from the capillary, with the sarcolemma acting as the main barrier (Vock et al. 1996a,b).

It is currently not clear what throttles triacylglycerol oxidation in exercising muscle. Is it the transfer of fatty acids to the mitochondrial matrix or is it β-oxidation? In contrast, the rate at which glycogen stores can supply pyruvate to the Krebs cycle is not limited: they can supply it up to the limit of oxidation rate by the mitochondria and can then achieve a further several-fold increase in order to fuel anaerobic glycolysis. Clearly, therefore, oxidation in the mitochondria is not limited by the supply of fuel but rather by the supply of oxygen from the capillaries – or by the quantity of mitochondria that can perform oxidative phosphorylation.

In general terms, the maximal conductance must be related to the volume of capillaries in skeletal muscles, V(c), a structural parameter that has been measured. V(c) is directly proportional to the capillary surface area available for diffusion of oxygen out of the blood, since the diameter of capillaries does not change with either size or adaptation. V(c) also plays an important role in determining the time available for diffusion as blood transits the capillary network.

With allometric variation, small animals have more capillaries in each gram of their muscles than do large animals. When quantitative measurements of capillary volume are made on the same individuals for which mitochondrial volume measurements were made, one finds that average mass-specific capillary volume, like mitochondrial volume, decreases in direct proportion to over the size range from 20 g (mice) to 500 kg (horses), whereas the rate of oxygen delivery per millilitre of capillary, ⁠, is nearly the same over the entire size range of animals (Taylor et al. 1989). Thus, we can conclude that is invariant with size and has a value of 15 ml O₂ ml⁻¹ min⁻¹.

This constant value for ⁠, like that for ⁠, is a minimal value which assumes that, at , all of the capillaries are utilized and that oxygen diffuses out of all of them at the same rate. Irrespective of whether this is the case, it clearly indicates that the capillary surface area available for diffusion increases directly with the rate of diffusion of oxygen out of the capillaries over the five-to tenfold variation in with size. We can see that the ratio V(c)/V(mt) must also be invariant (i.e. approximately 0.3 ml of capillaries for each ml of mitochondria), since both and are invariant with size (Hoppeler et al. 1981).

With adaptive variation, we find a different pattern of adjustment of capillaries to oxygen demand (Conley et al. 1987). V(c)/Mb changes by only 1.7-fold with the 2.5-fold difference in between the dog/goat, pony/calf and horse/steer pairs (Table 1). Using equation 3, we can calculate that oxygen diffuses out of each millilitre of capillary (each square centimetre of its surface) 1.5 times faster in the more aerobic species. Part of the explanation for this higher rate of diffusion lies in a 1.6-fold higher oxygen concentration in the arterial blood entering the capillary and a corresponding 1.6-fold greater extraction of oxygen as the blood transits the capillary bed. This results from a 1.5-fold higher haemoglobin concentration in the blood of the athletic species, which is due to a higher haematocrit or erythrocyte concentration, Vv(ec). Multiplying the 1.7-fold greater volume of capillaries by the 1.6-fold greater extraction of oxygen across the capillary gives a 2.7-fold greater oxygen delivery during the transit of the blood through the capillary bed.

We can thus conclude that there is a reasonably good match between structure and the oxygen supply function at the level of the capillaries. In the case of allometric variations in ⁠, the higher rates of oxygen consumption are matched by corresponding differences in the amount of capillary structure, whereas the rate at which O₂ diffuses from each square centimetre of capillary surface is invariant in this case. The design of the capillaries at this level is closely matched to that of the mitochondria that consume the oxygen. In adaptive variation, capillaries are incompletely matched, but this is compensated by a higher haemoglobin or erythrocyte concentration. For both allometric and adaptive variation, it therefore appears that the mass of haemoglobin in capillaries is matched to the mass of mitochondria; this is achieved by varying capillary volume and haemoglobin concentration. The invariant ratio of structural parameters, therefore, is expressed as: V(ec)/V(mt)≈M(Hb)/V(mt) = 4×10⁻² g ml⁻¹, where M(Hb) is mass of hemoglobin and V(ec) is erythrocyte volume. Consequently, we find thatthe invariant ratio to is expressed as: O₂ s⁻¹), where Vv(ec) is the volume density of erythrocytes, and thus involves. two structural variables, i.e. capillary volume V(c) and erythrocyte concentration in the blood.

Reviewing the transfer processes for oxygen and substrates from capillaries to myocytes, we can conclude that the muscle microvasculature is optimally designed for the transfer of oxygen, but not for the transfer of substrates. Because of the lack of substantial oxygen stores, oxygen has to be supplied by the circulation at a rate to match the demand of the contracting muscle cells. In contrast, only a limited quantity of substrates is supplied from the vasculature during exercise. Animals and humans working at intensities above 30% of rely increasingly on intracellular substrate stores, mainly on glycogen, at high work intensities. These stores will eventually be exhausted during exercise, leading to muscle fatigue. The intracellular stores can then be replenished during periods of rest at low transfer rates.

In allometric variation, we would anticipate that time (i.e. fH) would vary with size, while the structural parameters, haemoglobin concentration and Vs/M_b, would be invariant. What information we have supports this idea. On average, the heart makes up the same fraction of body mass over the size range of mammals from mice to cows, approximately 0.58% (Prothero, 1979); likewise, haemoglobin concentration and the oxygen-carrying capacity of the blood do not vary systematically with body size. Mammals spanning a range of body size from bats to horses have, on average, approximately 13 g of haemoglobin per 100 ml of blood, which can carry 17.5 ml of oxygen (Schmidt-Nielsen, 1984). The invariant heart size and O₂-carrying capacity of the blood suggest that body-size-dependent differences in circulatory transport are brought about entirely by increases in heart frequency.

The structural and functional variations in circulatory transport of oxygen with adaptive variation are very clear-cut. Here, the animals follow the general principles of design: fH is determined by size, and structures vary with O₂ demand. Maximal heart frequencies of goats and dogs, ponies and calves, and horses and steers are nearly identical pairwise for animals of the same size, despite 1.4- to 2.5-fold difference in (Jones et al. 1989; Karas et al. 1987b). The structural parameters Vs/M_b and haemoglobin concentration account for all of the 2.5-fold difference in oxygen delivery at this step. These studies indicate that these animals are operating at or close to the upper limit of their structural capacity for convective transport of oxygen in the circulatory system at (Taylor et al. 1987). The available structures (stroke volume and haemoglobin concentration) for both Q̇_max and appear to be fully exploited by the time an animal has increased its rate of oxygen consumption from resting to maximal levels. Thus, at this step of O₂ transport in the respiratory system, there appears to be a match between maximal rates of O₂ delivery and the structures involved, a finding that is in accord with the predictions of symmorphosis.

The limited information we have therefore suggests that the structural parameters Vs/M_b and Vv(ec) are invariant in allometric variation, but variant in adaptive variation, whereas the functional parameter fH is invariant in adaptive variation, but variant in allometric variation.

In summary, while maximal heart rate is important for modulating cardiac output with allometric variation of body mass, in adaptive as well as in induced variation, stroke volume is the main factor determining cardiac output in mammals of a given body size. An important additional component is haematocrit, which is found to be larger in athletic animals.

The morphometric parameters entering the calculation of (see Weibel, 1997) are essentially determined by two variables: the lung volume, V(L), and the size or density of the ‘building blocks’ of the gas-exchange units in the lung parenchyma. The ultimate building block of the gas exchanger is the alveolar septum, with morphometric characteristics being the fraction of septum occupied by capillaries, the capillary volume per septal (alveolar) surface area, V(c)/S(A), the density of erythrocytes or the haematocrit and the harmonic mean thickness of the tissue barrier (Fig. 10). These septa are built into the acinus as alveolar walls in the form of a three-dimensional maze; accordingly, the alveolar surface density, Sv(A), is a measure of the building-block characteristics of lung parenchyma. This hierarchical design provides several options for varying diffusing capacity. Thus, the total alveolar surface area, S(A), is the product of V(L) and the alveolar surface density, Sv(A); furthermore, capillary volume is the product of V(c)/S(A) and S(A). To increase ⁠, the lung would have to increase, for example, the alveolar surface area, and this can be achieved either by increasing lung volume or by increasing the alveolar surface density by packing more alveolar septa into the unit volume of lung parenchyma. Alternatively or additionally, the loading of capillaries onto the septum could be increased or the barrier thickness could be decreased.

The first questions with respect to the design of the gas exchanger are which of these options are used, or whether any of these basic design param eters are invariant with allometric and adaptive variation in .

Let us first consider lung volume. The general idea is that mass-specific lung volume is invariant with body size. At closer inspection, we find, however, that V(L) increases slightly (but significantly) as M_b^1.06 (Gehr et al. 1981), with the result that V(L)/M_b varies from 35 ml kg⁻¹ in shrews and mice to 60 ml kg⁻¹ in dog, man and cow and can even reach 100 ml kg⁻¹ in the horse. This last value indicates that, in adaptive variation, relative lung volume is an important variable, being larger in the athletic species (Weibel et al. 1987; Constantinopol et al. 1989). In a study of the pronghorn antelope, whose is twice that of the dog, we found the increase in lung volume (to nearly 5 l for a heavy 20 kg animal!) to account for most of the adaptive lung change (Lindstedt et al. 1991).

Among the building-block characteristics, the parameters that characterize septum structure are invariant in adaptive variation (Weibel et al. 1987; Constantinopol et al. 1989), but they show a weak allometric variability (Gehr et al. 1981). The packing of alveolar septa into lung parenchyma, measured by Sv(A) (which is inversely proportional to alveolar diameter), appears to be invariant in the size range of animals between 1 and 100 kg (Weibel et al. 1981a), assuming values of 400–500 cm⁻¹ irrespective of whether the animals are athletic or sedentary. However, it increases drastically in small mammals, up to 1500 cm⁻¹ in the shrews, and it falls to 250 cm⁻¹ in large mammals so that, over the entire mammalian size range, we find that Sv(A) decreases as M_b^−0.11.

Quite evidently, all these parameters are subject to a number of constraints. The lung volume is limited by the space available in the chest cavity. The packing of alveolar septa into the air space is limited by the requirements for adequate ventilation, as well as by mechanical constraints related to surface tension. The smaller the alveoli, the greater the surface forces; and the larger the alveoli, the more costly is alveolar ventilation. Mammals may have indeed found an optimum range for the size of these building blocks from which they deviate only in the very small species and perhaps in the largest, but to a lesser extent.

How are these building blocks related to O₂ uptake at ? Specifically, is O₂ uptake by the unit capillary volume invariant? We find that it is not. In allometric variation, varies as M_b^−0.2, ranging from 12 ml O₂ min⁻¹ ml⁻¹ in large animals to 42 ml O₂ ml⁻¹ min⁻¹ in small (500 g) animals, and it may be even higher in mice and shrews (Gehr et al. 1981). In adaptive variation, we find that athletic species load approximately twice as much O₂ into their blood per unit time, a rate that appears to be approximately proportional to their higher haematocrit (Weibel et al. 1987; Constantinopol et al. 1989). The rate of oxygen uptake by the pulmonary capillary unit is therefore clearly not invariant, in partial contrast to the situation in themuscle capillaries where we have found the discharge rate to be invariant with allometric variation, whereas a similar difference was found between the adaptive pairs. It is noteworthy that the discharge rates are similar in lung and muscle capillaries, at least in the non-athletic species; the observed differences can be explained by different transit times.

When we now consider the total pulmonary diffusing capacity, we must note that it is composed of two main components (a) the membrane diffusing capacity, ⁠, which is exclusively determined by structural variables, and (b) the blood or erythrocyte diffusing capacity, ⁠, which depends on capillary blood volume and haematocrit, two parameters that are also subject to some functional variation.

The hypothesis of symmorpho sis predicts that and should be proportional to . This is not what we find. We note that mass-specific does not change with size, so that the ratio increases as Mb^0.2. This means that a 300 kg cow has six times as much diffusing capacity available as a 30 g mouse to accomplish O₂ uptake at . Therefore, the driving force for O₂ uptake in the lung is smaller in the cow than in the mouse. Why this occurs is unknown. Various possibilities have been suggested, such as (a) appreciable differences in capillary transit time (Lindstedt, 1984) or (b) differences in the pressure head as a result of the fact that the size of acini varies considerably with body size (Rodriguez et al. 1987; Haefeli-Bleuer and Weibel, 1988), and this could influence alveolar ventilation (Karas et al. 1987a; Weibel et al. 1981b).

In adaptive variation, we find that the athletic species have a larger than the non-athletic animals, but this increase is not proportional to the differences in . Here again, athletic species accomplish their higher rate of O₂ uptake by adding to their increased an elevated driving force. In this instance, we were able to show that this is partly due to the fact that the athletic species use a greater fraction, approximately 80%, of their shorter transit time to accomplish equilibration of the capillary blood with alveolar air, whereas the sedentary species use only 50%, with the remainder appearing as a redundancy (Constantinopol et al. 1989; Karas et al. 1987a).

In conclusion, we find that the ratio is not invariant, either in allometric or in adaptive variation. To find an invariant ratio, we must consider all structural and functional variables, because only the following relationship applies: is invariant.

We must therefore conclude that functional variables are usedto a large extent to modulate the rate of O₂ uptake even at . This is possible because the pulmonary gas exchanger maintains an appreciable level of redundancy or excess capacity (Karas et al. 1987a). One is tempted to speculate that maintaining such redundancy in the part of the respiratory system that forms the interface with the environment may well be a survival strategy allowing the organism to cope with adverse environmental factors such as hypoxia. It has indeed been shown that goats can maintain their even in high-altitude conditions (Karas et al. 1987a), presumably because they increase their cardiac output during hypoxia and their gas exchanger is redundant when judged at sea-level conditions.

The limits for the aerobic performance capacity have been assessed in a systematic analysis of the pathway for oxygen from the lung to skeletal muscle mitochondria, taking into account the role played by substrate availability for oxidative metabolism of muscle cells. Current thinking indicates that the ‘limitation’ is distributed over all levels of the respiratory system, with some steps having more ‘resistance’ than others under certain conditions. To unravel the basic design principles, we have taken a comparative approach by studying the structure and function of the respiratory system in animals differing widely in mass-specific . A detailed analysis of each transfer step of oxygen made use of the concept of ‘symmorphosis’, i.e. assuming, for each level of the respiratory cascade, that animals maintain just enough structure to support flux rates at ⁠, but not more. We found all levels of the cascade to conform with the principle of symmorphosis except for the lungs, which seem to be built with significant, though limited, excess structural capacity. However, this redundancy is variable: it is smaller in athletic than in sedentary species, with probably no structural redundancy in the very ‘best’ of animal (and human) endurance athletes. The analysis also shows that this system is built on the constraint of supplying oxygen rather than substrates to active muscle mitochondria under conditions of maximal aerobic work. Carbohydrate and lipid supply rates are probably ‘throttled’ by transport processes at the level of the sarcolemma. To ensure adequate substrate supply at high work loads, both lipids and carbohydrates are stored within muscle cells. These substrate stores are replenished at low flux rates during periods of rest to reach a size adequate for high rates of combustion during exercise.