Allometric cascade as a unifying principle of body mass effects on metabolism

Moving towards acceleration for estimates of activity-specific metabolic rate in free-living animals: the case of the cormorant

1. Time and energy are key currencies in animal ecology, and judicious management of these is a primary focus for natural selection. At present, however, there are only two main methods for estimation of rate of energy expenditure in the field, heart rate and doubly labelled water, both of which have been used with success; but both also have their limitations. 2. The deployment of data loggers that measure acceleration is emerging as a powerful tool for quantifying the behaviour of free-living animals. Given that animal movement requires the use of energy, the accelerometry technique potentially has application in the quantification of rate of energy expenditure during activity. 3. In the present study, we test the hypothesis that acceleration can serve as a proxy for rate of energy expenditure in free-living animals. We measured rate of energy expenditure as rates of O2 consumption (VO2) and CO2 production (VCO2) in great cormorants (Phalacrocorax carbo) at rest and during pedestrian exercise. VO2 and VCO2 were then related to overall dynamic body acceleration (ODBA) measured with an externally attached three-axis accelerometer. 4. Both VO2 and VCO2 were significantly positively associated with ODBA in great cormorants. This suggests that accelerometric measurements of ODBA can be used to estimate VO2 and VCO2 and, with some additional assumptions regarding metabolic substrate use and the energy equivalence of O2 and CO2, that ODBA can be used to estimate the activity specific rate of energy expenditure of free-living cormorants. 5. To verify that the approach identifies expected trends in from situations with variable power requirements, we measured ODBA in free-living imperial cormorants (Phalacrocorax atriceps) during foraging trips. We compared ODBA during return and outward foraging flights, when birds are expected to be laden and not laden with captured fish, respectively. We also examined changes in ODBA during the descent phase of diving, when power requirements are predicted to decrease with depth due to changes in buoyancy associated with compression of plumage and respiratory air. 6. In free-living imperial cormorants, ODBA, and hence estimated VO2, was higher during the return flight of a foraging bout, and decreased with depth during the descent phase of a dive, supporting the use of accelerometry for the determination of activity-specific rate of energy expenditure.

Allometric scaling in centrarchid fish: origins of intra- and inter-specific variation in oxidative and glycolytic enzyme levels in muscle

The influence of body size on metabolic rate, muscle enzyme activities and the underlying patterns of mRNA for these enzymes were explored in an effort to explain the genetic basis of allometric variation in metabolic enzymes. We studied two pairs of sister species of centrarchid fish: black bass (largemouth bass Micropterus salmoides and smallmouth bass Micropterus dolomieui) and sunfish (pumpkinseed Lepomis gibbosus and bluegill Lepomis macrochirus). Our goal was to assess the regulatory basis of both intraspecific and interspecific variation relative to body size, as well as to gain insights into the evolutionary constraints within lineages. Whole animal routine metabolic rate showed scaling coefficients not significantly different from 1, ranging from (+0.87 to +0.96). However, there were significant effects of body size on the specific activities of oxidative and glycolytic enzymes. Mass-specific activity of the oxidative enzyme citrate synthase (CS) scaled negatively with body size in each species, with scaling coefficients ranging from -0.15 to -0.19, whereas the glycolytic enzyme pyruvate kinase (PK) showed positive scaling, with scaling coefficients ranging from +0.08 to +0.23. The ratio of mass-specific enzyme activity in PK to CS increased with body size, whereas the ratio of mRNA transcripts of PK to CS was unaffected, suggesting the enzyme relationships were not due simply to transcriptional regulation of both genes. The mass-dependent differences in PK activities were best explained by transcriptional regulation of the muscle PK gene; PK mRNA was a good predictor of PK specific enzyme activity within species and between species. Conversely, CS mRNA did not correlate with CS specific enzyme activities, suggesting post-transcriptional mechanisms may explain the observed inter-specific and intraspecific differences in oxidative enzymes.

[Why 37 degrees C? Evolutionary fundamentals of thermoregulation]

Homeothermy is the result of an evolutionary process during which every increase in oxygen supply led to a consecutive increase in metabolic rate and, thus, to a new dependence on favorable ambient conditions. In response to the food scarcity of winter months, some inhabitants of temperate zones developed an ability to hibernate which is characterized by a fully thermocontrolled reduction in body temperature down to near zero values. Hibernation thus illustrates that in homeotherms, not only the body shell is poikilothermic, but also the core temperature is more variable than often assumed. However, in contrast to clinical hypothermia, natural torpidity does not consist of a cold-induced reduction in metabolic rate, but of an endogenous metabolic reduction with subsequent lowering of body temperature. As a factor of metabolic suppression, the pH has been suspected which, in hibernators, is kept constant at 7.4 by relative hypoventilation (pH-stat) which differs from its passive shift in the poikilothermic body shell (alpha-stat). In clinical hypothermia, temperature governs the metabolic rate in that, depending on the state of thermoregulation, either a cold defense reaction with an increased metabolic rate (accidental hypothermia) or a cold-induced reduction in metabolic rate (induced hypothermia) occurs. However, as can be learned from hibernators, the lower limit of hypothermia tolerance seems to be due to a uniform minimal metabolic rate rather than to the species-specific body temperature at which this metabolic limit is reached, depending on body size and basal metabolic rate. Accordingly, in judging the sequelae of hypothermia, the degree of cooling should be given less emphasis than the resulting effects on metabolic rate.

Ontogenetic scaling of fish metabolism in the mouse-to-elephant mass magnitude range

Intraspecific or ontogenetic analyses of mass-metabolism relationships do not often conform to the same allometric correlations as those seen in interspecific analyses. A commonly cited reason for this discrepancy is that ontogenetic studies examine smaller mass ranges than interspecific studies, and are therefore not statistically comparable. In this study the metabolic rate of yellowtail kingfish was measured from 0.6 mg-2.2 kg, a mass range comparable to that between a mouse and an elephant. Linear regression of the log transformed data resulted in a scaling exponent of 0.90 and high correlation coefficient. Statistical and information theory comparisons of three other models showed that a segmented linear regression and curvilinear quadratic function were an improvement over a simple linear regression. This confirmed previous observations that the metabolic scaling exponent of fish changes during ontogeny. Ammonia excretion rates were also measured and scaled linearly with an exponent of 0.87. The data showed that the metabolism of yellowtail kingfish during ontogeny did not scale with the commonly cited 2/3 or 3/4 mass exponent. This demonstrates that differences between interspecific and ontogenetic allometries are not necessarily statistical artefacts.

Mitochondrial oxygen consumption and reactive oxygen species production are independently modulated: implications for aging studies

Various recent investigations relevant to the study of aging mechanisms have recently found that increases in longevity during dietary restriction can occur together with lack of decreases or even increases in O2 consumption. This is frequently interpreted as contradictory with the mitochondrial free radical theory of aging. But this is based on the erroneous assumption that increasing O2 consumption must increase the rate of mitochondrial oxygen radical generation. Here it is shown that the opposite occurs in many important situations. Strong decreases in absolute and relative (per unit of O2 consumed) mitochondrial oxygen radical production occur during aerobic exercise bouts, chronic exercise training, and hyperthyroidism, and notably, during dietary restriction. Mitochondrial oxygen radical generation is also lower in long-lived birds than in short-lived mammals of similar body size and metabolic rate. Total rates of reactive oxygen species generation can also vary between tissues in a way not linked to their differences in oxygen consumption. All this indicates that mitochondrial reactive oxygen species (ROS) production is not a simple byproduct of mitochondrial respiration. Instead, it is regulated independently of O2 consumption in many different physiologic situations, tissues, and animal species. Thus, the apparently paradoxical increases in O2 consumption observed in some models of dietary restriction do not discredit the mitochondrial free radical theory of aging, and they can further strengthen it.

Scaling behaviour of VO2 in athletes and untrained individuals

OBJECTIVE

The present study analysed the allometric relationship (MR = a . M(b)) between human metabolic rate (MR), ranging from resting to maximal metabolic conditions, and body mass (M ), both in athletes of different specialization and untrained individuals.

SUBJECTS AND METHODS

Two hundred and seventy male athletes and 43 untrained men performed a continuous incremental test to volitional exhaustion on a motorized treadmill. Metabolic rate (i.e. VO2) was measured during resting (VO2REST), sub-maximal (walking at 5 km h(-1) VO2WALK; running at 7.5 km h(-1) VO2RUN; ventilatory anaerobic threshold VO2VT) and maximal exercise conditions (maximum oxygen uptake VO2MAX).

RESULTS

A significant difference (p < 0.001) in the MR-body mass relationships between athletes and controls was found. For the control group, the mass exponent b exhibited a non-significant (p = 0.37) increase with increasing metabolic demand (b = 0.69, 0.76, 0.76, 0.84, and 0.89, for VO2REST, VO2WALK, VO2RUN, VO2VT, and VO2MAX, respectively). In contrast, the corresponding mass exponent for the athletic group significantly (p < 0.01) decreased when moving from resting to maximal metabolic conditions (b = 0.98, 0.88, 0.80, 0.69, and 0.67).

CONCLUSION

These results indicate that the recently proposed allometric cascade model may be valid in describing the scaling behaviour of MR in untrained individuals, but not in athletes of different specialization.

The linear allometric relationship between total metabolic energy per life span and body mass of mammals

The aim of this study is to establish and calculate the exact allometric relationship between the total metabolic energy per life span and the body mass in a wide range of mammals with about six orders of magnitude variation of the body mass of animals. The study shows that it exists a linear relationship between the total metabolic energy per life span PT(ls) (kJ) and the body mass M (kg) of 95 mammals (3 monotremes, Subclass Prototheria, 16 marsupialis (Subclass Theria, Infraclass Metatheria) and 76 placentals (Subclass Theria, Infraclass Eutheria)) from type: PT(ls)=A(ls)(+)M(1.0511), where P (kJ/day) is the basal rate of metabolism and T(ls) (days) is the mean life span of animals. The linear coefficient A(ls)(+)=7.158x10(5) kJ/kg is the total metabolic energy, exhausted during the life span per 1 kg body mass of the animals. The mean values of the total metabolic energy per life span, per unit body mass (A(ls)) for orders from Subclass Prototheria and Theria (Infraclass Metatheria) and orders Xenarthra, Pholidota, Soricomorpha, Rodentia (Infraclass Eutheria) varied negligible in interval (4.656-5.80)x10(5) kJ/kg. The coefficient A(ls) grows from (7.68-8.36)x10(5) kJ/kg in Lagomorpha and Artiodactyla (Eutheria) to (10.58-12.64)x10(5) kJ/kg in orders Carnivora, Pinnipeda and Chiroptera (Eutheria). A(ls) grows maximum to 18.5x10(5) kJ/kg in Primates. Thus, the values of coefficient A(ls) differ maximum four-fold in all orders. Across the all species the values of A(ls) are changes about one order of magnitude. Consequently, our survey shows that the changes of the body mass, basal metabolic rate and the life span of animals are three mutually related parameters, so that the product A(ls)=(PT(ls))/M remains relatively constant in comparison to 1 million fold difference in body mass and total metabolic energy per life span between mammals.

Scaling metabolic rate fluctuations

Complex ecological and economic systems show fluctuations in macroscopic quantities such as exchange rates, size of companies or populations that follow non-Gaussian tent-shaped probability distributions of growth rates with power-law decay, which suggests that fluctuations in complex systems may be governed by universal mechanisms, independent of particular details and idiosyncrasies. We propose here that metabolic rate within individual organisms may be considered as an example of an emergent property of a complex system and test the hypothesis that the probability distribution of fluctuations in the metabolic rate of individuals has a "universal" form regardless of body size or taxonomic affiliation. We examined data from 71 individuals belonging to 25 vertebrate species (birds, mammals, and lizards). We report three main results. First, for all these individuals and species, the distribution of metabolic rate fluctuations follows a tent-shaped distribution with power-law decay. Second, the standard deviation of metabolic rate fluctuations decays as a power-law function of both average metabolic rate and body mass, with exponents -0.352 and -1/4 respectively. Finally, we find that the distributions of metabolic rate fluctuations for different organisms can all be rescaled to a single parent distribution, supporting the existence of general principles underlying the structure and functioning of individual organisms.

Allometric exponents do not support a universal metabolic allometry

The debate about the value of the allometric scaling exponent (b) relating metabolic rate to body mass (metabolic rate = a x mass(b)) is ongoing, with published evidence both for and against a 3/4-power scaling law continuing to accumulate. However, this debate often revolves around a dichotomous distinction between the 3/4-power exponent predicted by recent models of nutrient distribution networks and a 2/3 exponent predicted by Euclidean surface-area-to-volume considerations. Such an approach does not allow for the possibility that there is no single "true" exponent. In the present study, we conduct a meta-analysis of 127 interspecific allometric exponents to determine whether there is a universal metabolic allometry or if there are systematic differences between taxa or between metabolic states. This analysis shows that the effect size of mass on metabolic rate is significantly heterogeneous and that, on average, the effect of mass on metabolic rate is stronger for endotherms than for ectotherms. Significant differences between scaling exponents were also identified between ectotherms and endotherms, as well as between metabolic states (e.g., rest, field, and exercise), a result that applies to b values estimated by ordinary least squares, reduced major axis, and phylogenetically correct regression models. The lack of support for a single exponent model suggests that there is no universal metabolic allometry and represents a significant challenge to any model that predicts only a single value of b.

Exceptional longevity in songbirds is associated with high rates of evolution of cytochrome b, suggesting selection for reduced generation of free radicals

In animals, longevity (maximal lifespan) is inversely related to mass-specific basal metabolic rates. However, contrary to expectation, in several mammalian taxa, exceptional longevity is associated with high basal metabolic rate, and also fast evolution of mtDNA-coded proteins. The association of these traits was suggested to result from adaptive selection of mutations in mtDNA-coded proteins, which accelerates basal respiration, thus inhibiting the generation of reactive oxygen species that constrain longevity. In birds, all the genera with high rate of cytochrome b evolution are songbirds (oscines). Within the songbirds group, both longevity residuals and lifetime expenditure of energy are positively correlated with the rate of cytochrome b evolution. Moreover, within the large songbirds family Fringillidae (true finches) mass-specific basal metabolic rates, longevity,longevity residuals and lifetime expenditure of energy are all positively correlated with the rate of evolution of cytochrome b. In Serinus, a genus of finches (canaries) that exhibits the highest rate of cytochrome b evolution, and the highest values of exceptional longevity and lifetime expenditure of energy in all birds, many of the substitutions in cytochrome b are clustered around Qi, a ubiquinone binding site adjacent to the mitochondrial matrix, apparently selected to increase the rate of ubiquinone reduction. We therefore suggest that, in songbirds, the accelerated evolution of cytochrome binvolved selection of mutations that reduce the generation of reactive oxygen species, thus contributing to the evolution of exceptional longevity, and possibly also exceptional long-term memory, which is necessary for learning songs.

Changes in body temperature influence the scaling of VO2max and aerobic scope in mammals

Debate on the mechanism(s) responsible for the scaling of metabolic rate with body size in mammals has focused on why the maximum metabolic rate (VO2max ) appears to scale more steeply with body size than the basal metabolic rate (BMR). Consequently, metabolic scope, defined as VO2max/BMR, systematically increases with body size. These observations have led some to suggest that VO2max, and BMR are controlled by fundamentally different processes, and to discount the generality of models that predict a single power-law scaling exponent for the size dependence of the metabolic rate. We present a model that predicts a steeper size dependence for VO2max than BMR based on the observation that changes in muscle temperature from rest to maximal activity are greater in larger mammals. Empirical data support the model's prediction. This model thus provides a potential theoretical and mechanistic link between BMR and VO2 max.

Ontogeny of energetics in leatherback (Dermochelys coriacea) and olive ridley (Lepidochelys olivacea) sea turtle hatchlings

Changes in activity related oxygen consumption were measured in leatherback and olive ridley sea turtle hatchlings over their first month after emergence from the nest. Leatherbacks emerged with 75-90 KJ of energy in the residual yolk for growth and activity whereas olive ridleys emerged with 45 KJ. In leatherbacks (n=8), resting mass-specific oxygen consumption rates decreased by 53% over the first post-hatching month (0.34+0.03 mL O(2) h(-1) g(-1) to 0.16+0.01 mL O(2) h(-1) g(-1), respectively), while for ridleys (n=8) the fall was 35% (0.20+0.03 mL O(2) h(-1) g(-1) to 0.13+0.01 mL O(2) h(-1) g(-1), respectively). Olive ridley factorial aerobic scope doubled (1.93+0.30 to 3.97+0.51) over the first month but there was no significant increase in leatherback factorial aerobic scope (1.39+0.21 to 1.60+0.13). Leatherback hatchlings gained on average 20% initial body mass (7.68+1.66 g) over the first week, with 70 to 80% of this increase due to water accumulation. Olive ridleys gained 14% (1.83+0.16 g) in initial mass over the first week of age. We propose that the differences in aerobic scope and energy reserves are related to differences in early life ecological stratagems of these species.

Perinatal adaptation in mammals: the impact of metabolic rate

Mammalian birth is accompanied by profound changes in metabolic rate that can be described in terms of body size relationship (Kleiber's rule). Whereas the fetus, probably as an adaptation to the low intrauterine pO2, exhibits an "inappropriately" low, adult-like specific metabolic rate, the term neonate undergoes a rapid metabolic increase up to the level to be expected from body size. A similar, albeit slowed, "switching-on" of metabolic size allometry is found in human preterm neonates whereas animals that are normally born in a very immature state are able to retard or even suppress the postnatal metabolic increase in favor of weight gain and O2 supply. Moreover, small immature mammalian neonates exhibit a temporary oxyconforming behavior which enhances their hypoxia tolerance, yet is lost to the extent by which the size-adjusted metabolic rate is "locked" by increasing mitochondrial density. Beyond the perinatal period, there are no other deviations from metabolic size allometry among mammals except in hibernation where the temporary "switching-off" of Kleiber's rule is accompanied by a deep reduction in tissue pO2. This gives support to the hypothesis that the postnatal metabolic increase represents an "escape from oxygen" similar to the evolutionary roots of mitochondrial respiration, and that the overall increase in specific metabolic rate with decreasing size might contribute to prevent tissues from O2 toxicity.

Global and regional brain metabolic scaling and its functional consequences

BACKGROUND

Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous, reflecting the complex activity patterns in the mammalian brain.

RESULTS

In this study, it was found, based on empirical data, that despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent: around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent of -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical, at 0.86 +/- 0.03, which is significantly larger than the exponents 3/4 and 2/3 that have been suggested for whole body basal metabolism on body mass.

CONCLUSION

These findings show explicitly that in mammals: (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.

Robustness to Failure of Assumptions of Tests for a Common Slope Amongst Several Allometric Lines – A Simulation Study

In allometry, researchers are commonly interested in estimating the slope of the major axis or standardized major axis (methods of bivariate line fitting related to principal components analysis). This study considers the robustness of two tests for a common slope amongst several axes. It is of particular interest to measure the robustness of these tests to slight violations of assumptions that may not be readily detected in sample datasets. Type I error is estimated in simulations of data generated with varying levels of nonnormality, heteroscedasticity and nonlinearity. The assumption failures introduced in simulations were difficult to detect in a moderately sized dataset, with an expert panel only able to correct detect assumption violations 34-45% of the time. While the common slope tests were robust to nonnormal and heteroscedastic errors from the line, Type I error was inflated if the two variables were related in a slightly nonlinear fashion. Similar results were also observed for the linear regression case. The common slope tests were more liberal when the simulated data had greater nonlinearity, and this effect was more evident when the underlying distribution had longer tails than the normal. This result raises concerns for common slopes testing, as slight nonlinearities such as those in simulations are often undetectable in moderately sized datasets. Consequently, practitioners should take care in checking for nonlinearity and interpreting the results of a test for common slope. This work has implications for the robustness of inference in linear models in general.

Relationships between pulmonary oxygen uptake kinetics and other measures of aerobic fitness in middle- and long-distance runners

The purpose of this study was to assess the relationships between on- and off-transient pulmonary oxygen uptake kinetics and other measures of aerobic fitness in middle-distance (MD) and long-distance (LD) runners. 16 MD and 16 LD runners participated and each completed a series of tests to determine their maximal oxygen uptake (VO2max) gas-exchange threshold (GET), running economy (RE) and the primary time-constant for VO2 at the onset (tau(on)) and offset (tau(off)) of moderate-intensity treadmill exercise. Relationships between measures were established using Pearson product moment correlations (r). The relationships between VO2 kinetic parameter and other aerobic measures varied depending on classification of runner (MD or LD runner). There was a significant relationship between (VO2max) and tau(on) and tau(off) in LD runners (tau(on): r = -0.70, P = 0.003; tau(off): r = -0.55, P = 0.029), but not for MD (tau(on): r = 0.24, P = 0.366; tau(off): r = -0.09, P = 0.739). Similar relationships also existed between GET, RE and kinetic parameters for LD but not MD runners. The inconsistent relationships between VO2 kinetic parameters and other measures of aerobic fitness in MD and LD runners is intriguing. Further work is now required to identify how the volume and intensity of training influence peripheral adaptations in Type I and Type II fibres and how these may, or may not influence VO2 kinetic responses in the moderate- and heavy-intensity domain.

Do insect metabolic rates at rest and during flight scale with body mass?

Energetically costly behaviours, such as flight, push physiological systems to their limits requiring metabolic rates (MR) that are highly elevated above the resting MR (RMR). Both RMR and MR during exercise (e.g. flight or running) in birds and mammals scale allometrically, although there is little consensus about the underlying mechanisms or the scaling relationships themselves. Even less is known about the allometric scaling of RMR and MR during exercise in insects. We analysed data on the resting and flight MR (FMR) of over 50 insect species that fly to determine whether RMR and FMR scale allometrically. RMR scaled with body mass to the power of 0.66 (M0.66), whereas FMR scaled with M1.10. Further analysis suggested that FMR scaled with two separate relationships; insects weighing less than 10mg had fourfold lower FMR than predicted from the scaling of FMR in insects weighing more than 10mg, although both groups scaled with M0.86. The scaling exponents of RMR and FMR in insects were not significantly different from those of birds and mammals, suggesting that they might be determined by similar factors. We argue that low FMR in small insects suggests these insects may be making considerable energy savings during flight, which could be extremely important for the physiology and evolution of insect flight.

The scaling and temperature dependence of vertebrate metabolism

Body size and temperature are primary determinants of metabolic rate, and the standard metabolic rate (SMR) of animals ranging in size from unicells to mammals has been thought to be proportional to body mass (M) raised to the power of three-quarters for over 40 years. However, recent evidence from rigorously selected datasets suggests that this is not the case for birds and mammals. To determine whether the influence of body mass on the metabolic rate of vertebrates is indeed universal, we compiled SMR measurements for 938 species spanning six orders of magnitude variation in mass. When normalized to a common temperature of 38 degrees C, the SMR scaling exponents of fish, amphibians, reptiles, birds and mammals are significantly heterogeneous. This suggests both that there is no universal metabolic allometry and that models that attempt to explain only quarter-power scaling of metabolic rate are unlikely to succeed.

On the depth and scale of metabolic rate variation: scaling of oxygen consumption rates and enzymatic activity in the Class Cephalopoda(Mollusca)

Recent ecological theory depends, for predictive power, on the apparent similarity of metabolic rates within broad taxonomic or functional groups of organisms (e.g. invertebrates or ectotherms). Such metabolic commonality is challenged here, as I demonstrate more than 200-fold variation in metabolic rates independent of body mass and temperature in a single class of animals,the Cephalopoda, over seven orders of magnitude size range. I further demonstrate wide variation in the slopes of metabolic scaling curves. The observed variation in metabolism reflects differential selection among species for locomotory capacity rather than mass or temperature constraints. Such selection is highest among epipelagic squids (Lolignidae and Ommastrephidae)that, as adults, have temperature-corrected metabolic rates higher than mammals of similar size.

Energy use and animal abundance in litter and soil communities

Tools from metabolic scaling and food web theory were used to construct a general model of carbon flux by litter and soil invertebrates. The flux model was used to explore the energetic basis of invertebrate abundance and predicted that abundance should (1) scale linearly with net primary production; (2) be related to the body mass of animals as a power function, with an exponent between -0.65 and -0.85; (3) be related to the average body temperature of animals according to the Boltzmann factor, with an activation energy between 0.27 and 0.79 eV; and (4) decrease by a factor of 0.05 to 0.15 across trophic levels due to gross production efficiency of prey. Model predictions were generally supported by a global data set on invertebrate abundance that was amassed during the International Biological Programme, indicating that fundamental energetic principles explain a large degree of variation in invertebrate abundance across the globe.

Abnormal cortical development after premature birth shown by altered allometric scaling of brain growth

BACKGROUND

We postulated that during ontogenesis cortical surface area and cerebral volume are related by a scaling law whose exponent gives a quantitative measure of cortical development. We used this approach to investigate the hypothesis that premature termination of the intrauterine environment by preterm birth reduces cortical development in a dose-dependent manner, providing a neural substrate for functional impairment.

METHODS AND FINDINGS

We analyzed 274 magnetic resonance images that recorded brain growth from 23 to 48 wk of gestation in 113 extremely preterm infants born at 22 to 29 wk of gestation, 63 of whom underwent neurodevelopmental assessment at a median age of 2 y. Cortical surface area was related to cerebral volume by a scaling law with an exponent of 1.29 (95% confidence interval, 1.25-1.33), which was proportional to later neurodevelopmental impairment. Increasing prematurity and male gender were associated with a lower scaling exponent (p < 0.0001) independent of intrauterine or postnatal somatic growth.

CONCLUSIONS

Human brain growth obeys an allometric scaling relation that is disrupted by preterm birth in a dose-dependent, sexually dimorphic fashion that directly parallels the incidence of neurodevelopmental impairments in preterm infants. This result focuses attention on brain growth and cortical development during the weeks following preterm delivery as a neural substrate for neurodevelopmental impairment after premature delivery.

Modeling physiological and anthropometric variables known to vary with body size and other confounding variables

This review explores the most appropriate methods of identifying population differences in physiological and anthropometric variables known to differ with body size and other confounding variables. We shall provide an overview of such problems from a historical point of view. We shall then give some guidelines as to the choice of body-size covariates as well as other confounding variables, and show how these might be incorporated into the model, depending on the physiological dependent variable and the nature of the population being studied. We shall also recommend appropriate goodness-of-fit statistics that will enable researchers to confirm the most appropriate choice of model, including, for example, how to compare proportional allometric models with the equivalent linear or additive polynomial models. We shall also discuss alternative body-size scaling variables (height, fat-free mass, body surface area, and projected area of skeletal bone), and whether empirical vs. theoretical scaling methodologies should be reported. We shall offer some cautionary advice (limitations) when interpreting the parameters obtained when fitting proportional power function or allometric models, due to the fact that human physiques are not geometrically similar to each other. In conclusion, a variety of different models will be identified to describe physiological and anthropometric variables known to vary with body size and other confounding variables. These include simple ratio standards (e.g., per body mass ratios), linear and additive polynomial models, and proportional allometric or power function models. Proportional allometric models are shown to be superior to either simple ratio standards or linear and additive polynomial models for a variety of different reasons. These include: 1) providing biologically interpretable models that yield sensible estimates within and beyond the range of data; and 2) providing a superior fit based on the Akaike information criterion (AIC), Bayes information criterion (BIC), or maximum log-likelihood criteria (resulting in a smaller error variance). As such, these models will also: 3) naturally lead to a more powerful analysis-of-covariance test of significance, which will 4) subsequently lead to more correct conclusions when investigating population (epidemiological) or experimental differences in physiological and anthropometric variables known to vary with body size.

Optimal power-to-mass ratios when predicting flat and hill-climbing time-trial cycling

The purpose of this article was to establish whether previously reported oxygen-to-mass ratios, used to predict flat and hill-climbing cycling performance, extend to similar power-to-mass ratios incorporating other, often quick and convenient measures of power output recorded in the laboratory [maximum aerobic power (W(MAP)), power output at ventilatory threshold (W(VT)) and average power output (W(AVG)) maintained during a 1 h performance test]. A proportional allometric model was used to predict the optimal power-to-mass ratios associated with cycling speeds during flat and hill-climbing cycling. The optimal models predicting flat time-trial cycling speeds were found to be (W(MAP)m(-0.48))(0.54), (W(VT)m(-0.48))(0.46) and (W(AVG)m(-0.34))(0.58) that explained 69.3, 59.1 and 96.3% of the variance in cycling speeds, respectively. Cross-validation results suggest that, in conjunction with body mass, W(MAP) can provide an accurate and independent prediction of time-trial cycling, explaining 94.6% of the variance in cycling speeds with the standard deviation about the regression line, s=0.686 km h(-1). Based on these models, there is evidence to support that previously reported VO2-to-mass ratios associated with flat cycling speed extend to other laboratory-recorded measures of power output (i.e. Wm(-0.32)). However, the power-function exponents (0.54, 0.46 and 0.58) would appear to conflict with the assumption that the cyclists' speeds should be proportional to the cube root (0.33) of power demand/expended, a finding that could be explained by other confounding variables such as bicycle geometry, tractional resistance and/or the presence of a tailwind. The models predicting 6 and 12% hill-climbing cycling speeds were found to be proportional to (W(MAP)m(-0.91))(0.66), revealing a mass exponent, 0.91, that also supports previous research.

Phenotypic plasticity in the scaling of avian basal metabolic rate

Many birds exhibit short-term, reversible adjustments in basal metabolic rate (BMR), but the overall contribution of phenotypic plasticity to avian metabolic diversity remains unclear. The available BMR data include estimates from birds living in natural environments and captive-raised birds in more homogenous, artificial environments. All previous analyses of interspecific variation in BMR have pooled these data. We hypothesized that phenotypic plasticity is an important contributor to interspecific variation in avian BMR, and that captive-raised populations exhibit general differences in BMR compared to wild-caught populations. We tested this hypothesis by fitting general linear models to BMR data for 231 bird species, using the generalized least-squares approach to correct for phylogenetic relatedness when necessary. The scaling exponent relating BMR to body mass in captive-raised birds (0.670) was significantly shallower than in wild-caught birds (0.744). The differences in metabolic scaling between captive-raised and wild-caught birds persisted when migratory tendency and habitat aridity were controlled for. Our results reveal that phenotypic plasticity is a major contributor to avian interspecific metabolic variation. The finding that metabolic scaling in birds is partly determined by environmental factors provides further support for models that predict variation in scaling exponents, such as the allometric cascade model.

Metabolic scaling associated with unusual size changes during larval development of the frog, Pseudis paradoxus

The early larvae of P. paradoxus grow large but metamorphose into relatively small frogs, the diminished post-metamorphic growth producing a marked contrast between maximum larval size and adult. Thus, O(2) uptake does not appear to limit the energy expenditure on growth processes, and unlike in other anuran larvae, may not be a surface area-related function in P. paradoxus larvae. The resting rates of metabolism (M(O(2))) and partitioning between aquatic (Mw(O(2))) and aerial O(2) uptake (Ma(O(2))) were measured on tadpoles and froglets by closed system respirometry, using water of P(O(2)) ranging from 145 to 40 mmHg. Correlative changes in body glycogen and lactate were examined by standard enzyme assays. Scaling patterns in the growth and degrowth stages were analysed on whole-body, log-transformed data using linear regressions. In normoxia, M(O(2)) was 2.1-2.5 mumol g(-1) h(-1) in the early larvae, increasing more than twofold on forelimb emergence and decreasing sharply in the froglets; M(O(2)) varies in strict proportion to body mass (M(b)), both in the growth (b=1.02) and degrowth (b=0.97) phases, according to the equation M(O(2))=aM(b)(b), where b is the scaling coefficient. Mw(O(2)) constitutes >90% of total uptake in the growth stages, increasing with b=1.02 while Ma(O(2)) increases with b=1.13; during degrowth there is a change in the pattern related to intensification of metamorphosis. Hypoxic water did not affect M(O(2)); however, in all larval stages Mw(O(2)) and Ma(O(2)) changed with a decrease in P(O(2)). At 60 mmHg, rates are more severely affected in the largest tadpoles, causing the b values for Mw(O(2)) and Ma(O(2)) to change to 0.11 and 1.44, respectively, in the growth phase. Glycogen and lactate levels increase out of proportion with body mass increase (b=2.05 and 1.47, respectively) in the growth stages, and increase anaerobic capacity in late metamorphosis. In hypoxic water, glycogen levels decrease in the growth stages and the largest tadpoles accumulate surplus lactate, possibly related to surfacing activity. Our results may reveal the consequences of size on energy demand at the tissue level in P. paradoxus larvae, indicating that air breathing must subsidise energy expenditure during larval development.

Maximal oxygen consumption in relation to subordinate traits in lines of house mice selectively bred for high voluntary wheel running

We studied relations between maximal O2 consumption (VO2 max) during forced exercise and subordinate traits associated with blood O2 transport and cellular respiration in four lines of mice selectively bred for high voluntary wheel running (S lines) and their four nonselected control (C) lines. Previously, we reported VO2 max of 59 females at three Po2 (hypoxia = 14% O2, normoxia = 21%, hyperoxia = 30%). Here, we test the hypothesis that variation in VO2 max can be explained, in part, by hemoglobin concentration and Po2 necessary to obtain 50% O2 saturation of Hb (an estimate of Hb affinity for O2) of the blood as well as citrate synthase activity and myoglobin concentration of ventricles and gastrocnemius muscle. Statistical analyses controlled for body mass, compared S and C lines, and also considered effects of the mini-muscle phenotype (present only in S lines and resulting from a Mendelian recessive allele), which reduces hindlimb muscle mass while increasing muscle mass-specific aerobic capacity. Although S lines had higher VO2 max than C, subordinate traits showed no statistical differences when the presence of the mini-muscle phenotype was controlled. However, subordinate traits did account for some of the individual variation in VO2 max. Ventricle size was a positive predictor of VO2 max at all three Po2. Blood Hb concentration was a positive predictor of VO2 max in S lines but a negative predictor in C lines, indicating that the physiological underpinnings of VO2 max have been altered by selective breeding. Mice with the mini-muscle phenotype had enlarged ventricles, with higher mass-specific citrate synthase activity and myoglobin concentration, which may account for their higher VO2 max in hypoxia.

Energetics of the smallest: Do bacteria breathe at the same rate as whales?

Power laws describing the dependence of metabolic rate on body mass have been established for many taxa, but not for prokaryotes, despite the ecological dominance of the smallest living beings. Our analysis of 80 prokaryote species with cell volumes ranging more than 1,000,000-fold revealed no significant relationship between mass-specific metabolic rate q and cell mass. By absolute values, mean endogenous mass-specific metabolic rates of non-growing bacteria are similar to basal rates of eukaryote unicells, terrestrial arthropods and mammals. Maximum mass-specific metabolic rates displayed by growing bacteria are close to the record tissue-specific metabolic rates of insects, amphibia, birds and mammals. Minimum mass-specific metabolic rates of prokaryotes coincide with those of larger organisms in various energy-saving regimes: sit-and-wait strategists in arthropods, poikilotherms surviving anoxia, hibernating mammals. These observations suggest a size-independent value around which the mass-specific metabolic rates vary bounded by universal upper and lower limits in all body size intervals.

The Power of Fitness in Mammals: Perceptions from the African Slipstream

Evolutionary physiology is the emerging physiological discipline. Unlike environmental physiology or ecophysiology, whose definitions have long been made quite clear, evolutionary physiology has a broader scope of objectives, and its definition lacks a concise treatise. This paper presents the argument that the lack of a common definition of evolutionary physiology is retarding the unification of the mechanistic and amechanistic physiological sciences, a multidisciplinary obligation crucial for a holistic understanding of a physiological basis of fitness. The divide between mechanistic "how" questions, devoted primarily to homeostasis, and evolutionary "why" questions, concerned with understanding phenotypic and genotypic physiological variation, remains broad and is currently not conducive to synergy in the physiological disciplines. Unification may be facilitated, however, by embracing a common currency of measurement and analysis. A likely candidate is the cascade of energy from the environment to offspring and the evolution of physiological form and function, including homeostasis, associated with power management. This currency approach seeks to identify an energetic basis of fitness, namely, whether or how the evolution of life-history traits is influenced by energetic constraints and/or trade-offs.

Energetics during Hatchling Dispersal of the Olive Ridley TurtleLepidochelys olivaceaUsing Doubly Labeled Water

Studies of metabolism are central to the understanding of the ecology, behavior, and evolution of reptiles. This study focuses on one phase of the sea turtle life cycle, hatchling dispersal, and gives insight into energetic constraints that dispersal imposes on hatchlings. Hatchling dispersal is an energetically expensive phase in the life cycle of the olive ridley turtle Lepidochelys olivacea. Field metabolic rates (FMRs), determined using the doubly labeled water (DLW) method, for L. olivacea hatchlings digging out of their nest chamber, crawling at the sand surface, and swimming were five, four, and seven times, respectively, the resting metabolic rate (RMR). The cost of swimming was 1.5 and 1.8 times the cost of the digging and crawling phases, respectively, and we estimated that if L. olivacea hatchlings swim at frenzy levels, they can rely on yolk reserves to supply energy for only 3-6 d once they reach the ocean. We compared our RMR and FMR values by establishing an interspecific RMR mass-scaling relationship for a wide range of species in the order Testudines and found a scaling exponent of 1.06. This study demonstrates the feasibility of using the DLW method to estimate energetic costs of free-living sea turtle hatchlings and emphasizes the need for metabolic studies in various life-history stages.

Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.

Plant allometry, leaf nitrogen and phosphorus stoichiometry, and interspecific trends in annual growth rates

BACKGROUND

Life forms as diverse as unicellular algae, zooplankton, vascular plants, and mammals appear to obey quarter-power scaling rules. Among the most famous of these rules is Kleiber's (i.e. basal metabolic rates scale as the three-quarters power of body mass), which has a botanical analogue (i.e. annual plant growth rates scale as the three-quarters power of total body mass). Numerous theories have tried to explain why these rules exist, but each has been heavily criticized either on conceptual or empirical grounds. N,P-STOICHIOMETRY: Recent models predicting growth rates on the basis of how total cell, tissue, or organism nitrogen and phosphorus are allocated, respectively, to protein and rRNA contents may provide the answer, particularly in light of the observation that annual plant growth rates scale linearly with respect to standing leaf mass and that total leaf mass scales isometrically with respect to nitrogen but as the three-quarters power of leaf phosphorus. For example, when these relationships are juxtaposed with other allometric trends, a simple N,P-stoichiometric model successfully predicts the relative growth rates of 131 diverse C3 and C4 species.

CONCLUSIONS

The melding of allometric and N,P-stoichiometric theoretical insights provides a robust modelling approach that conceptually links the subcellular 'machinery' of protein/ribosomal metabolism to observed growth rates of uni- and multicellular organisms. Because the operation of this 'machinery' is basic to the biology of all life forms, its allometry may provide a mechanistic explanation for the apparent ubiquity of quarter-power scaling rules.

Maximum aerobic performance in lines ofMusselected for high wheel-running activity: effects of selection, oxygen availability and the mini-muscle phenotype

We compared maximum aerobic capacity during forced exercise(V̇O2max) in hypoxia (PO2=14% O2), normoxia (21%) and hyperoxia (30%) of lines of house mice selectively bred for high voluntary wheel running (S lines) with their four unselected control (C) lines. We also tested for pleiotropic effects of the `mighty mini-muscle' allele, a Mendelian recessive that causes a 50% reduction in hind limb muscle but a doubling of mass-specific aerobic enzyme activity, among other pleiotropic effects. V̇O2max of female mice was measured during forced exercise on a motorized treadmill enclosed in a metabolic chamber that allowed altered PO2. Individual variation in V̇O2max was highly repeatable within each PO2, and values were also significantly correlated across PO2. Analysis of covariance showed that S mice had higher body-mass-adjusted V̇O2max than C at all PO2, ranging from +10.7% in hypoxia to +20.8% in hyperoxia. V̇O2maxof S lines increased practically linearly with PO2,whereas that of C lines plateaued from normoxia to hyperoxia, and respiratory exchange ratio (=CO2production/V̇O2max)was lower for S lines. These results suggest that the physiological underpinnings of V̇O2max differ between the S and C lines. Apparently, at least in S lines, peripheral tissues may sustain higher rates of oxidative metabolism if central organs provide more O2. Although the existence of central limitations in S lines cannot be excluded based solely on the present data, we have previously reported that both S and C lines can attain considerably higher V̇O2max during cold exposure in a He-O2 atmosphere, suggesting that limitations on V̇O2max depend on interactions between the central and peripheral organs involved. In addition,mini-muscle individuals had higher V̇O2max than did those with normal muscles, suggesting that the former might have higher hypoxia tolerance. This would imply that the mini-muscle phenotype could be a good model to test how exercise performance and hypoxia tolerance could evolve in a correlated fashion, as previous researchers have suggested.

Integrative biology of sticky feet in geckos

Geckos have gained ecological access to novel microhabitats by exploiting intermolecular van der Waals forces, which allow them to climb smooth vertical surfaces. They use microscopic surface-based phenomena to thrive in a macroscopic mass- and kinetic energy-based world. Here we detail this as a premier example of integrative biology, spanning seven orders of magnitude and a lot of interesting biology. Emergent properties arising from molecular adhesion include several adaptive radiations that have produced a great diversity of geckos worldwide.

Supply-demand balance in outward-directed networks and Kleiber's law

BACKGROUND

Recent theories have attempted to derive the value of the exponent alpha in the allometric formula for scaling of basal metabolic rate from the properties of distribution network models for arteries and capillaries. It has recently been stated that a basic theorem relating the sum of nutrient currents to the specific nutrient uptake rate, together with a relationship claimed to be required in order to match nutrient supply to nutrient demand in 3-dimensional outward-directed networks, leads to Kleiber's law (b = 3/4).

METHODS

The validity of the supply-demand matching principle and the assumptions required to prove the basic theorem are assessed. The supply-demand principle is evaluated by examining the supply term and the demand term in outward-directed lattice models of nutrient and water distribution systems and by applying the principle to fractal-like models of mammalian arterial systems.

RESULTS

Application of the supply-demand principle to bifurcating fractal-like networks that are outward-directed does not predict 3/4-power scaling, and evaluation of water distribution system models shows that the matching principle does not match supply to demand in such systems. Furthermore, proof of the basic theorem is shown to require that the covariance of nutrient uptake and current path length is 0, an assumption unlikely to be true in mammalian arterial systems.

CONCLUSION

The supply-demand matching principle does not lead to a satisfactory explanation for the approximately 3/4-power scaling of mammalian basal metabolic rate.

Basal Metabolic Rate in Carnivores Is Associated with Diet after Controlling for Phylogeny

Studies of basal metabolic rate (BMR), the minimum metabolic rate of postabsorptive, inactive endotherms while in their rest phase and thermal neutral zone, have contributed significantly to our understanding of animal energetics. Besides body mass, the main determinant of BMR, researchers have invoked diet and phylogenetic history as important factors that influence BMR, although their relative importance has been controversial. For 58 species within the Carnivora, we tested the hypothesis that BMR is correlated with home range size, a proxy for level of activity, and diet, using conventional least squares regression (CLSR) and regression based on phylogenetic independent contrasts (PIC). Results showed that BMR of Carnivora was positively correlated with home range size after controlling for body mass, regardless of the statistical method employed. We also found that diet and mass-adjusted home range size were correlated. When we simultaneously tested the effect of diet and mass-adjusted home range on mass-adjusted BMR, home range size was insignificant because of its colinearity with diet. Then we eliminated home range size from our model, and diet proved to be significant with both CLSR and PIC. We concluded that species that eat meat have larger home ranges and higher BMR than species that eat vegetable matter. To advance our understanding of the potential mechanisms that might explain our results, we propose the "muscle performance hypothesis," which suggests that selection for different muscle fiber types can account for the differences in BMR observed between meat eaters and vegetarian species within the Carnivora.

Population pharmacokinetic studies in pediatrics: issues in design and analysis

The current review addresses the following 3 frequently encountered challenges in the design and analysis of population pharmacokinetic studies in pediatrics: (1) body size adjustments during the development of pharmacostatistical models, (2) design and validation of limited sampling strategies, and (3) the integration of historical priors in data analysis and trial simulation. Size adjustments with empiric approaches based on body weight or body surface area have frequently proven as a pragmatic tool to overcome large size differences in a pediatric study population. Allometric size adjustments, however, provide a more mechanistic, physiologically based approach that, if used a priori, allows delineation of the effect of size from that of other covariates that show a high degree of collinearity. The frequent lack of dense data sets in pediatric clinical pharmacology because of ethical and logistic constraints in study design can be overcome with the application of D-optimality-based limited sampling schemes in combination with Bayesian and nonlinear mixed-effects modeling approaches. Empirically based dose selection and clinical trial designs for pediatric clinical pharmacology studies can be improved by applying clinical trial simulation techniques, especially if they integrate adult and pediatric in vitro and/or in vivo data as historic priors. Although integration of these concepts and techniques in population pharmacokinetic analyses is not only limited to pediatric research, their application allows researchers to overcome some major hurdles frequently encountered in pharmacokinetic studies in pediatrics and, thus, provides the basis for additional clinical pharmacology research in this previously insufficiently studied fraction of the general population.

Data from necropsy studies and in vitro tissue studies lead to a model for allometric scaling of basal metabolic rate

Background

The basal metabolic rate (BMR) of a mammal of mass M is commonly described by the power function αM^β where α and β are constants determined by linear regression of the logarithm of BMR on the logarithm of M (i. e., β is the slope and α is the intercept in regression analysis). Since Kleiber's demonstration that, for 13 measurements of BMR, the logarithm of BMR is closely approximated by a straight line with slope 0.75, it has often been assumed that the value of β is exactly 3/4 (Kleiber's law).

Results

For two large collections of BMR data (n = 391 and n = 619 species), the logarithm of BMR is not a linear function of the logarithm of M but is a function with increasing slope as M increases. The increasing slope is explained by a multi-compartment model incorporating three factors: 1) scaling of brain tissue and the tissues that form the surface epithelium of the skin and gastrointestinal tract, 2) scaling of tissues such as muscle that scale approximately proportionally to body mass, and 3) allometric scaling of the metabolic rate per unit cell mass. The model predicts that the scaling exponent for small mammals (body weight < 0.2 kg) should be less than the exponent for large mammals (> 10 kg). For the simplest multi-compartment model, the two-compartment model, predictions are shown to be consistent with results of analysis using regression models that are first-order and second-order polynomials of log(M). The two-compartment model fits BMR data significantly better than Kleiber's law does.

Conclusion

The F test for reduction of variance shows that the simplest multi-compartment allometric model, the two-compartment model, fits BMR data significantly better than Kleiber's law does and explains the upward curvature observed in the BMR.

Roles of hierarchical and metabolic regulation in the allometric scaling of metabolism in Panamanian orchid bees

Assessment of the relative importance of variation in enzyme concentration[E] and metabolic regulation in accounting for interspecific variation in metabolic rates is an unrealized area of research. Towards this end, we used metabolic flux rates during hovering and enzymatic flux capacities(Vmax values, equal to [E]×kcat,where kcat is catalytic efficiency) in flight muscles measured in vitro from 14 orchid bee species ranging in body mass from 47 to 1065 mg. Previous studies revealed that, across orchid bee species,wingbeat frequencies and metabolic rates decline in parallel with increasing body mass. Vmax values at some enzymatic steps in pathways of energy metabolism decline with increasing mass while, at most other steps, Vmax values are mass-independent. We quantified the relative importance of `hierarchical regulation' (alteration in Vmax, indicative of alteration in [E]) and `metabolic regulation' (resulting from variation in substrate, product or modulator concentrations) in accounting for interspecific variation in flux across species. In addition, we applied the method of phylogenetically independent contrasts to remove the potentially confounding effects of phylogenetic relationships among species. In the evolution of orchid bees, hierarchical regulation completely accounts for allometric variation in flux rates at the hexokinase step while, at other reactions, variation in flux is completely accounted for by metabolic regulation. The predominant role played by metabolic regulation is examined at the phosphoglucoisomerase step using the Haldane relationship. We find that extremely small variation in the concentration ratio of [product]/[substrate] is enough to cause the observed interspecific variation in net flux at this reaction in glycolysis.

Metabolism and thermoregulation during fasting in king penguins,Aptenodytes patagonicus,in air and water

We measured oxygen consumption rate (V̇o2) and body temperatures in 10 king penguins in air and water. V̇o2was measured during rest and at submaximal and maximal exercise before (fed) and after (fasted) an average fasting duration of 14.4 ± 2.3 days (mean ± 1 SD, range 10–19 days) in air and water. Concurrently, we measured subcutaneous temperature and temperature of the upper (heart and liver), middle (stomach) and lower (intestine) abdomen. The mean body mass (Mb) was 13.8 ± 1.2 kg in fed and 11.0 ± 0.6 kg in fasted birds. After fasting, resting V̇o2was 93% higher in water than in air (air: 86.9 ± 8.8 ml/min; water: 167.3 ± 36.7 ml/min, P < 0.01), while there was no difference in resting V̇o2between air and water in fed animals (air: 117.1 ± 20.0 ml O2/min; water: 114.8 ± 32.7 ml O2/min, P > 0.6). In air, V̇o2decreased with Mb, while it increased with Mbin water. Body temperature did not change with fasting in air, whereas in water, there were complex changes in the peripheral body temperatures. These latter changes may, therefore, be indicative of a loss in body insulation and of variations in peripheral perfusion. Four animals were given a single meal after fasting and the temperature changes were partly reversed 24 h after refeeding in all body regions except the subcutaneous, indicating a rapid reversal to a prefasting state where body heat loss is minimal. The data emphasize the importance in considering nutritional status when studying king penguins and that the fasting-related physiological changes diverge in air and water.

Allometric scaling of the maximum metabolic rate of mammals: oxygen transport from the lungs to the heart is a limiting step

Background

The maximum metabolic rate (MMR) of mammals is approximately proportional to M^0.9, where M is the mammal's body weight. Therefore, MMR increases with body weight faster than does the basal metabolic rate (BMR), which is approximately proportional to M^0.7. MMR is strongly associated with the capacity of the cardiovascular system to deliver blood to capillaries in the systemic circulation, but properties of this vascular system have not produced an explanation for the scaling of MMR.

Results

Here we focus on the pulmonary circulation where resistance to blood flow (impedance) places a limit on the rate that blood can be pumped through the lungs before pulmonary edema occurs. The maximum pressure gradient that does not produce edema determines the maximum rate that blood can flow through the pulmonary veins without compromising the diffusing capacity of oxygen. We show that modeling the pulmonary venous tree as a fractal-like vascular network leads to a scaling equation for maximum cardiac output that predicts MMR as a function of M as well as the conventional power function aM^b does and that least-squares regression estimates of the equation's slope-determining parameter correspond closely to the value of the parameter calculated directly from Murray's law.

Conclusion

The assumption that cardiac output at the MMR is limited by pulmonary capillary pressures that produce edema leads to a model that is in agreement with experimental measurements of MMR scaling, and the rate of blood flow in pulmonary veins may be rate-limiting for the pathway of oxygen.

Percent relative cumulative frequency analysis in indirect calorimetry: application to studies of transgenic mice

Indirect calorimetry is commonly used in research and clinical settings to assess characteristics of energy expenditure. Respiration chambers in indirect calorimetry allow measurements over long periods of time (e.g., hours to days) and thus the collection of large sets of data. Current methods of data analysis usually involve the extraction of only a selected small proportion of data, most commonly the data that reflects resting metabolic rate. Here, we describe a simple quantitative approach for the analysis of large data sets that is capable of detecting small differences in energy metabolism. We refer to it as the percent relative cumulative frequency (PRCF) approach and have applied it to the study of uncoupling protein-1 (UCP1) deficient and control mice. The approach involves sorting data in ascending order, calculating their cumulative frequency, and expressing the frequencies in the form of percentile curves. Results demonstrate the sensitivity of the PRCF approach for analyses of oxygen consumption (.VO2) as well as respiratory exchange ratio data. Statistical comparisons of PRCF curves are based on the 50th percentile values and curve slopes (H values). The application of the PRCF approach revealed that energy expenditure in UCP1-deficient mice housed and studied at room temperature (24 degrees C) is on average 10% lower (p < 0.0001) than in littermate controls. The gradual acclimation of mice to 12 degrees C caused a near-doubling of .VO2 in both UCP1-deficient and control mice. At this lower environmental temperature, there were no differences in .VO2 between groups. The latter is likely due to augmented shivering thermogenesis in UCP1-deficient mice compared with controls. With the increased availability of murine models of metabolic disease, indirect calorimetry is increasingly used, and the PRCF approach provides a novel and powerful means for data analysis.

Dissecting the variance-covariance structure in insect physiology: the multivariate association between metabolism and morphology in the nymphs of the sand cricket (Gryllus firmus)

Energy metabolism in animals has been largely studied in relation to exogenous sources of variation. However, because they give insight into the relationship between whole metabolism and lower organizational levels such as organs and tissues, examination of endogenous determinants of metabolism other than body mass is itself very important. We studied the multivariate association of body parts and several aspects of energy metabolism in an insect, the nymphs of the sand cricket, Gryllus firmus. By using a variety of both univariate and multivariate techniques, we explored the resultant variance-covariance matrix to build a path diagram with latent variables. After controlling for body mass, we found a significant canonical correlation between metabolism and morphology. According to the factor loadings and path coefficients, the most important contributions of morphology to the correlation were thorax and abdomen size measures, whereas the most important metabolic contribution was resting metabolism. Activity metabolism was mostly explained by body mass rather than body parts, which could be a result of resting rates being chronic consequences of the functioning of the metabolic machinery that the insect must maintain.