Similarly sized bipeds and quadrupeds use nearly the same amount of metabolic energy to run, despite dramatic differences in morphology and running mechanics. It has been shown that the rate of metabolic energy use in quadrupedal runners and bipedal hoppers can be predicted from just body weight and the time available to generate force as indicated by the duration of foot-ground contact. We tested whether this link between running mechanics and energetics also applies to running bipeds. We measured rates of energy consumption and times of foot contact for humans (mean body mass 78.88 kg) and five species of birds (mean body mass range 0.13-40.1 kg). We find that most (70-90%) of the increase in metabolic rate with speed in running bipeds can be explained by changes in the time available to generate force. The rate of force generation also explains differences in metabolic rate over the size range of birds measured. However, for a given rate of force generation, birds use on average 1.7 times more metabolic energy than quadrupeds. The rate of energy consumption for a given rate of force generation for humans is intermediate between that of birds and quadrupeds. These results support the idea that the cost of muscular force production determines the energy cost of running and suggest that bipedal runners use more energy for a given rate of force production because they require a greater volume of muscle to support their body weight.

Compared with quadrupeds, bipedal runners of the same weight have longer legs, take longer steps and can presumably use slower, more economical muscle fibers. One might predict that bipedal running is less expensive, but it is not. We hypothesized that bipeds recruit a larger volume of muscle to support their weight, eliminating the potential economy of longer legs and slower steps. To test our hypothesis, we calculated the relative volume of muscle needed to support body weight over a stride in small dogs (Canis familiaris) and wild turkeys (Meleagris gallopavo) of the same weight. First, we confirmed that turkeys and dogs use approximately the same amount of energy to run at the same speed, and found that turkeys take 1. 8-fold longer steps. Higher muscle forces and/or longer muscle fibers would require a greater volume of active muscle, since muscle volume is proportional to the product of force and fascicle length. We measured both mean fascicle length and mean mechanical advantage for limb extensor muscles. Turkeys generated approximately the same total muscle force to support their weight during running and used muscle fascicles that are on average 2.1 times as long as in dogs, thus requiring a 2.5-fold greater active muscle volume. The greater volume appears to offset the economy of slower rates of force generation, supporting our hypothesis and providing a simple explanation for why it costs the same to run on two and four legs.

This paper quantifies the fluxes of fatty acids through the pathways supplying muscle mitochondria with oxidative fuel in exercising dogs and goats. We used continuous infusions of 1-[14C]palmitate and indirect calorimetry to measure fatty acid supply from two sources: the circulation and the triglyceride stores within the muscle cells. Our goal was to determine maximal flux through these two branches of the lipid pathway as key functional parameters for testing the principle of symmorphosis, i.e. that structural capacity is quantitatively matched to functional demand in the oxidative substrate pathways. It is under these rate-limiting conditions that we predict that all of the structural capacity will be used. Maximal rates of fatty acid oxidation were reached at low exercise intensities of 40% Mo2max. Fatty acids from the circulation supplied only a small fraction (15-25%) of the total fat oxidized under these conditions. Although dogs were able to oxidize circulatory fatty acids faster than goats, maximal rates were not in proportion to the 2.2-fold difference in aerobic capacity between the two species. Dogs compensated for their relatively lower use of circulatory fatty acids by oxidizing more triglycerides from lipid droplets in their muscle cells. We conclude that fatty acids from intramuscular triglyceride stores are a major source of fuel during maximal rates of lipid oxidation. Furthermore, it is this branch of the fatty acid pathway that is adapted to the large difference in aerobic capacity between dogs and goats.

This paper quantifies maximal flows of carbohydrates and lipids through the pathways supplying the mitochondria. Maximal flow rates are the main functional parameter used in testing the principle of symmorphosis, which states that structural capacities are quantitatively matched to functional demand. Only under rate-limiting conditions will all of the structural capacity be used. Dogs and goats were compared to obtain large differences in absolute rates. We exercised the animals for long enough to reach steady-state O2 and CO2 exchange rates at intensities eliciting 40%, 60% and 85% of the maximal rate of oxygen consumption (MO2max). We then calculated rates of fat and carbohydrate oxidation from the ratio of CO2 produced to O2 consumed (the respiratory exchange ratio). The dog's Mo2max was more than twice that of the goat (6517 versus 3026 mumol O2 kg-1 min-1). We found the same pattern of fuel selection as a function of exercise intensity in both species, and it appears to be general to mammals. Maximal rates of fat oxidation were reached at 40% exercise intensity, where 77% of the energy was supplied by fat. As exercise intensity increased, all additional energy was supplied by carbohydrates. We conclude that the partitioning of fuel supply to the fat and carbohydrate pathways follows the same pattern in both dogs and goats.

This paper quantifies the structures involved in the transport and oxidation of carbohydrates and fatty acids within the muscle cell. The structural capacity is measured on whole-body random samples of the musculature of dogs and pygmy goats and compared with maximal rates of oxygen consumption and substrate oxidation. Comparing dogs and goats of the same body size provided a 1.55-fold difference in the maximal rate of oxidation when related to muscle mass. As in previous studies, we found that the volume of mitochondria was approximately proportional to aerobic capacity. The maximal glucose flux from intracellular stores to mitochondria is 1.6 times greater in the dog than in the goat; we find that the amount of glycogen stored in the muscle cells is 4.2 times as great in the dog, but part of the intracellular glycogen pool is used for anaerobic rather than for oxidative metabolism. The maximal fatty acid flux from intracellular stores to mitochondria is 1.5 times larger in the dog, and the amount of lipid stored is 2.3 times as great in the dog. Every lipid droplet is in direct contact with the outer membrane of a mitochondrion and the contact surface area is 3.6 times greater in the dog than in the goat. Additional measurements are needed to investigate the role of structural limitation at this step. The amount of substrates stored intracellularly in the muscle cells of the dog is about twice as much as would match the differences in the maximal rates of utilization. This allows the endurance-specialized dogs to run for longer periods at higher rates of oxidation.

This paper quantifies the structural capacity of the transport steps for oxygen, glucose and fatty acids from the blood in capillaries to the cytosol of muscle cells and compares it with maximal rates of oxygen and substrate transport measured in the same animals and reported in the preceding papers of this series. Dogs have relatively more muscle per unit body mass than goats (37 versus 26%), but the maximal rate of oxidation per gram of muscle is still larger in the dog by a factor of 1.55. The maximal rates of substrate supply from the circulation are similar in both species. We predict that these differences in physiological parameters should be matched by proportional differences in structural capacity. We find that capillary volume and surface area are matched to maximal oxygen demand. The rate of vascular substrate supply is proportional neither to the capillary surface area nor to the length of intercellular junctions. The sarcolemmal surface area per gram of muscle is the same in both species. Using the physiological data presented in the companion papers of this series, we have calculated the maximal flux densities of circulatory glucose and fatty acids across the capillary wall and the sarcolemma. We find, for both substrates, that the flux densities across the sarcolemma reach a maximum at nearly the same level and at low exercise intensities in both species. In contrast, the flux densities across the capillary surface and the endothelial junctions are higher in goats than in dogs. We conclude that the capillaries are designed for O2 supply up to maximal rates of oxidation but not for the supply of the substrates (glucose and fatty acids) at the rates required at high exercise intensities. These are limited by the transport capacities of the sarcolemma.

This paper quantifies maximal fluxes through the pathway supplying carbohydrates to the mitochondria of muscle cells. Continuous infusions of D-[3-(3)H]glucose together with indirect calorimetry were used to investigate the partitioning of the supply of carbohydrates through the two branches of the pathway: from circulating glucose and from glycogen stores within the muscle cells to the mitochondria. The relative contribution of circulating glucose to total carbohydrate oxidation was small, accounting for only 13% and 23% of the carbohydrate oxidized at exercise intensities approaching MO2max in dogs and goats, respectively. Unexpectedly, maximal rates of circulating glucose oxidation were nearly the same in the two species (when expressed in absolute terms; dog:goat ratio = 1.2), despite the 2.2-fold difference in aerobic capacity. We conclude that the glycogen stores in the muscle cells are the major source of substrates at maximal rates of oxidation, supplying 60-70% of the total energy. Furthermore, it is this branch of the carbohydrate pathway that is adapted to the large difference in aerobic capacity between dogs and goats.

This paper integrates the results of a series of studies on the supply of O2 and substrates for oxidative muscle metabolism and draws conclusions on the role of structural design in partitioning and limiting substrate supply. The studies compared dogs and goats exercising at different intensities and combined physiological, biochemical and morphometric investigations. In both species, the rate of fatty acid oxidation reached an upper limit at low exercise intensities, and only glucose consumption was increased at higher exercise intensities. The supply of both glucose and fatty acids from the capillaries reached maximal rates at low exercise intensities; this limitation is related to the design of the sarcolemma as calculations suggest that the endothelium introduces only a small resistance to substrate flux. From these findings, it appears that the capillaries are designed to satisfy O2 supply up to maximal O2 demand. The increase in substrate supply to the mitochondria at higher exercise intensities is achieved by drawing on intracellular stores of glycogen and lipids. The size of these stores is larger in dogs than in goats, providing the athletic species with twice the fuel reserves. These findings are interpreted on the basis of a network model with fluxes partitioned between direct and indirect pathways and with some structures shared by more than one function. Whereas O2 is supplied through a direct pathway, the supply of both substrates is split temporally to allow, during exercise, immediate fuel supply to the mitochondria from intracellular stores; these are replaced from the vasculature, during periods of rest, to a size commensurate with high rates of combustion. Considering this complexity, we conclude that the results are compatible with the principle of symmorphosis applied to a network structure and that the adjustment of design to functional demand involves different structures for O2 and for substrates.

This first paper in a series develops a model of structure-function relationships for the oxygen and substrate pathways of oxidative metabolism in working muscle. This will be used in the subsequent experimental papers in asking how biological structures are designed if they serve more than one function and whether one function can be served by more than one structural pathway. We have used the concept of symmorphosis to address this question; in its original form, it postulates that no more structure is built and maintained at each step in a pathway than is required to meet functional demands. The concept of symmorphosis was developed to deal with the problem of modelling the pathway for oxygen from the environment to mitochondria, essentially a single series of interconnected transfer steps. In the present context, the application of this concept is more complex. Both oxygen and substrates are transported directly from the blood to the mitochondria in what appear to be shared steps. The flows along this direct pathway are adjusted during muscular work. However, substrates have an additional option. They can be stored intracellularly as lipid droplets or glycogen, and thus their supply to mitochondria can occur in two steps separated in time: from capillaries to stores during rest, and from stores to mitochondria during work. The integrated pathways have a network structure and the functional flows are partitioned to different branches of the network, and we must ask whether the partitioning of fluxes is related to design constraints. The principle of symmorphosis predicts that the best use is made of the available options and that the design of each step is matched to the specific functional demand in view of a balance to be achieved over the entire network. This will be tested in subsequent papers by determining maximal flows for oxygen, carbohydrates and lipids through each of the transport steps and their respective structural capacities, comparing dogs and goats, animals of the same size whose maximal oxidative capacities differ by more than twofold. Finally, we will ask whether the principle of symmorphosis can be extended to apply to network systems.

Large animals have a much better fuel economy than small ones, both when they rest and when they run. At rest, each gram of tissue of the largest land animal, the African elephant, consumes metabolic energy at 1/20 the rate of a mouse; using existing allometric relationships, we calculate that it should be able to carry 1 g of its tissue (or a load) for 1 km at 1/40 the cost for a mouse. These relationships between energetics and size are so consistent that they have been characterized as biological laws. The elephant has massive legs and lumbers along awkwardly, suggesting that it might expend more energy to move about than other animals. We find, however, that its energetic cost of locomotion is predicted remarkably well by the allometric relationships and is the lowest recorded for any living land animal.

The mean minimal transit time for blood in muscle capillaries (tc) was estimated in six species, spanning two orders of magnitude in body mass and aerobic capacity: horse, steer, dog, goat, fox and agouti. Arterial (CaO2) and mixed venous (CvO2) blood O2 concentrations, blood hemoglobin concentrations ([Hb]) and oxygen uptake rates were measured while the animals ran on a treadmill at a speed that elicited the maximal oxygen consumption rate (VO2max) from each animal. Blood flow to the muscles (Qm) was assumed to be 85% of cardiac output, which was calculated using the Fick relationship. Total muscle capillary blood volume (Vc) and total muscle mitochondrial volume were estimated by morphometry, using a whole-body muscle sampling scheme. The tc was computed as Vc/Qm. The tc was 0.3-0.5 s in the 4 kg foxes and agoutis, 0.7-0.8 s in the 25 kg dogs and goats, and 0.8-1.0 s in the 400 kg horses and steers. The tc was positively correlated with body mass and negatively correlated with transcapillary O2 release rate per unit capillary length. Mitochondrial content was positively correlated with VO2max and with the product of Qm and [Hb]. These data suggested that Qm, Vc, maximal hemoglobin flux, and consequently tc, are co-adjusted to result in muscle O2 supply conditions that are matched to the O2 demands of the muscles at VO2max.

Running downhill causes structural damage in deep slow-twitch extensor muscles of the limbs. Both mechanical and metabolic hypotheses have been proposed to explain the damage. The purpose of this study was to use measurements of glycogen loss in the muscles and metabolic rates of rats running on the level and up and down 16 degrees inclines at 26 m min-1 to try to distinguish between these hypotheses. Glycogen loss in the soleus and medial head to the triceps brachii muscles during running on the three inclines was proportional to whole-animal oxygen consumption, indicating that there were no unusual metabolic demands on these muscles during the downhill exercise. The minimum area of these muscles showing glycogen loss was smaller during downhill than during uphill running. Average forces in the muscles are similar during locomotion on different inclines at the same speed, suggesting that stresses in the active motor units were greater during downhill running. Thus, the results are more consistent with a mechanical than with a metabolic etiology for the muscle injury resulting from downhill running.

In this study we investigate how speed and stride frequency change with body size. We use this information to define ‘equivalent speeds’ for animals of different size and to explore the factors underlying the six-fold difference in mass-specific energy cost of locomotion between mouse- and horse-sized animals at these speeds. Speeds and stride frequencies within a trot and a gallop were measured on a treadmill in 16 species of wild and domestic quadrupeds, ranging in body size from 30 g mice to 200 kg horses. We found that the minimum, preferred and maximum sustained speeds within a trot and a gallop all change in the same rather dramatic manner with body size, differing by nine-fold between mice and horses (i.e. all three speeds scale with about the 0.2 power of body mass). Although the absolute speeds differ greatly, the maximum sustainable speed was about 2.6-fold greater than the minimum within a trot, and 2.1-fold greater within a gallop. The frequencies used to sustain the equivalent speeds (with the exception of the minimum trotting speed) scale with about the same factor, the −0.15 power of body mass. Combining this speed and frequency data with previously published data on the energetic cost of locomotion, we find that the mass-specific energetic cost of locomotion is almost directly proportional to the stride frequency used to sustain a constant speed at all the equivalent speeds within a trot and a gallop, except for the minimum trotting speed (where it changes by a factor of two over the size range of animals studied). Thus the energy cost per kilogram per stride at five of the six equivalent speeds is about the same for all animals, independent of body size, but increases with speed: 5.0 J kg-1 stride-1 at the preferred trotting speed; 5.3 J kg-1 stride-1 at the trot-gallop transition speed; 7.5 J kg-1 stride-1 at the preferred galloping speed; and 9.4 J kg-1 stride-1 at the maximum sustained galloping speed. The cost of locomotion is determined primarily by the cost of activating muscles and of generating a unit of force for a unit of time. Our data show that both these costs increase directly with the stride frequency used at equivalent speeds by different-sized animals. The increase in cost per stride with muscles (necessitating higher muscle forces for the same ground reaction force) as stride length increases both in the trot and in the gallop.

Terrestrial animals have ‘preferred speeds’ within each gait, that are used much more frequently than others for moving along the ground. Energy costs reach minimal values at these speeds within each gait. In this study we asked whether these speeds are mechanically equivalent among different animals (i.e. speeds where the same levels of peak muscle stress occur). If so, this would help in establishing a link between the energetics and the mechanics of the active muscles at these speeds, providing a first step in understanding why energy costs are minimal. We also asked whether peak muscle stress reaches a similar fraction of the maximal isometric stress at these speeds. If so, this would suggest that muscles are structured so that a similar reserve capacity remains, with a similar safety factor for avoidance of injury in response to prolonged repetitive loading. We compared two species that use quite different locomotory methods at their preferred speeds: white rats that gallop and kangaroo rats that hop. We measured peak stress in the ankle extensor muscles of these two species, as they moved at their preferred speeds, using a force platform/cine analysis technique. We also measured the maximum isometric force that this muscle group could develop in situ in the same individuals. We found the ankle extensors of white rats and kangaroo rats developed virtually identical levels of peak stress at their preferred speeds (70 +/− 6 kPa and 69 +/− 6 kPa, respectively, mean +/− S.E.), despite a fourfold difference in peak ground reaction force per unit body mass exerted on each limb. The values of peak isometric stress in situ were also virtually identical (206 +/− 17 kPa and 200 +/− 9 kPa, respectively). Our finding that the peak muscle stress is about one-third of maximum isometric stress at the preferred speeds is consistent with the idea that these are mechanically equivalent speeds, where the same fraction of available muscle fibres is recruited. Finding nearly identical values in two species that move in such different ways (galloping vs hopping), and have such large differences in ground reaction force exerted by each limb, suggests this may be true more generally for terrestrial vertebrates.

The muscle forces and stresses occurring during normal locomotor activity in kangaroo rats are compared with the peak isometric force developed by the same muscles in situ. Two methods were used simultaneously to determine the stresses (force/cross-sectional area) acting in the ankle extensors during steady-speed hopping and during jumps when animals were startled: a direct measurement using a force buckle surgically implanted around a tendon; and an indirect measurement using a force platform/cine analysis technique. We obtained essentially the same values with the two techniques. We found that at slow speeds (0.7 m s-1) the ankle extensor muscles of kangaroo rats exerted 20% of the maximum isometric force developed when the muscles were stimulated via the tibial nerve. This increased to 53% at higher speeds (1.9 m s-1). At the animals's preferred hopping speed (1.5 m s-1), peak force was approximately 40% of maximum isometric force. In jumps when animals were startled, peak forces as high as 175% of the maximal elicited isometric force were recorded. These high forces always occurred when the muscles were being stretched. It appears that kangaroo rats utilize nearly the entire range of muscle force possible during normal locomotor events (i.e. up to 175% of maximum isometric force when muscles are stretched).

Principal strains were recorded in vivo from the radial and tibial midshafts of three goats as they increased speed and changed gait. These data were compared with strain data measured for the radius and tibia of the dog (Rubin & Lanyon, 1982) and the horse (Biewener, Thomason & Lanyon, 1983b) in order to test the hypothesis that similar peak bone strains (stresses) occur at functionally equivalent points in the gaits of different species. Multiple recordings of in vivo strain along the caudal diaphyses of the radius and tibia of one goat were made to test the validity of this technique for measuring peak locomotor stress. Measured strains were extremely consistent over the animal's full range of speed (coefficient of variation for the radius 0.05-0.08, and for the tibia 0.06-0.11). The data from the three gauges, which were spaced 15 mm apart, demonstrated that maximal strains act at the midshaft, substantiating the use of this technique to measure peak locomotor bone strains. Strain levels recorded at the trot-gallop transition and top galloping speeds of the goat were similar to the values reported for the dog and horse, despite large differences in absolute speed (goat, 4.3 ms-1; dog, 6.9 ms-1; horse, 7.5 ms-1 at maximum gallop). The second moments of area of the tibia and radius (+ ulna) of the dog are 29% and 113% greater than for goats of equal size, explaining how similar strains are achieved in the dog at higher speeds than the goat. Furthermore, peak bone strains recorded at the fastest trotting speed were similar to those recorded at the fastest galloping speed for each species. Peak strains recorded for the goat at a maximum gallop correspond to stresses of +37.9 MPa (cranial) and −47.7 MPa (caudal) in the radius and +36.3 MPa (cranial) and −50.3 MPa (caudal) in the tibia, representing a safety factor to yield failure of three.

This paper develops three simple ideas about force development during sustained locomotion which provide some insights into the mechanisms that determine why animals change gait, how fast they can run, and how much metabolic energy they consume. The first idea is that the alternate stretch-shorten pattern of activity of the muscles involved in locomotion allows muscle-tendon units to function as springs, affecting the amount of force a given cross-sectional area of muscle develops, and the metabolic requirements of the muscles for force development. Animals select speeds and stride frequencies which optimize the performance of these springs. The second idea is that muscle stress (force/cross-sectional area) determines when animals change gait, how fast they run and their peak accelerations and decelerations. It is proposed that terrestrial birds and mammals develop similar muscle stresses under equivalent conditions (i.e. preferred speed within a gait) and that animals change gaits in order to reduce peak stresses as they increase speed. Finally, evidence is presented to support the idea that it is the time course of force development during locomotion, rather than the mechanical work that the muscles perform, that determines the metabolic cost of locomotion.

This is the second paper in a series examining the link between energetics and mechanics of terrestrial locomotion. In this paper, the changes in the kinetic energy of the limbs and body relative to the centre of mass of an animal (EKE, tot) are measured as functions of speed and body size. High-speed films (light or X-ray) of four species of quadrupeds and four species of bipeds running on a treadmill were analysed to determine EKE, tot. A mass-specific power term, EKE, tot/Mb was calculated by adding all of the increments in EKE during an integral number of strides and dividing by the time interval for the strides and body mass. The equations relating EKE, tot/Mb and speed were similar for all bipeds and quadrupeds regardless of size. One general equation for the rate at which muscle and tendons must supply energy to accelerate the limbs and body relative to the centre of mass seems to apply for all of the animals: E'KE, tot/Mb = 0.478 vg1.53 where E'KE, tot/Mb has the units W kg-1 and vg is ground speed in m s-1. Therefore, E'KE, tot/Mb does not change in parallel with the mass-specific rate at which animals consume energy (Emetab/Mb), either as a function of speed or as a function of body size.

This series of four papers investigates the link between the energetics and the mechanics of terrestrial locomotion. Two experimental variables are used throughout the study: speed and body size. Mass-specific metabolic rates of running animals can be varied by about tenfold using either variable. This first paper considers metabolic energy consumed during terrestrial locomotion. New data relating rate of oxygen consumption and speed are reported for: eight species of wild and domestic artiodactyls; seven species of carnivores; four species of primates; and one species of rodent. These are combined with previously published data to formulate a new allometric equation relating mass-specific rates of oxygen consumed (VO2/Mb) during locomotion at a constant speed to speed and body mass (based on data from 62 avian and mammalian species): VO2/Mb = 0.533 Mb-0.316.vg + 0.300 Mb-0.303 where VO2/Mb has the units ml O2 s-1 kg-1; Mb is in kg; and vg is in m s-1. This equation can be expressed in terms of mass-specific rates of energy consumption (Emetab/Mb) using the energetic equivalent of 1 ml O2 = 20.1 J because the contribution of anaerobic glycolysis was negligible: Emetab/Mb = 10.7 Mb-0.316.vg + 6.03 Mb-0.303 where Emetab/Mb has the units watts/kg. This new relationship applies equally well to bipeds and quadrupeds and differs little from the allometric equation reported 12 years ago by Taylor, Schmid-Nielsen & Raab (1970). Ninety per cent of the values calculated from this genera equation for the diverse assortment of avian and mammalian species included in this regression fall within 25% of the observed values at the middle of the speed range where measurements were made. This agreement is impressive when one considers that mass-specific rates of oxygen consumption differed by more than 1400% over this size range of animals.

This is the third in a series of four papers examining the link between the energetics and mechanics of terrestrial locomotion. It reports measurements of the mechanical work required (ECM, tot) to lift and reaccelerate an animal's centre of mass within each step as a function of speed and body size during level, constant average speed locomotion. A force platform was used in this study to measure ECM, tot for small bipeds, quadrupeds and hoppers. We have already published similar data from large animals. The total power required to lift and reaccelerate the centre of mass (ECM, tot) increased nearly linearly with speed for all the animals. Expressed in mass-specific terms, it was independent of body size and could be expressed by a simple equation: ECM, tot/Mb = 0.685 vg + 0.072 where ECM, tot/Mb has the units of W kg-1 and vg is speed in m s-1. Walking involves the same pendulum-like mechanism in small animals as has been described in humans and large animals. Also, running, trotting and hopping produce similar curves of ECM, tot as a function of time during a stride for both the small and large animals. Galloping, however, appears to be different in small and large animals. In small animals the front legs are used mainly for braking, while the back legs are used to reaccelerate the centre of mass within a stride. In large animals the front and hind legs serve to both brake and reaccelerate the animal; this difference in mechanics is significant in that it does not allow the utilization of elastic energy in the legs of small animals, but does in the legs of large animals.