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

Mathematical model for the contribution of individual organs to non-zero y-intercepts in single and multi-compartment linear models of whole-body energy expenditure

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit ‘local linearity.’ Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying ‘latent’ allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses.

The natural science underlying big history

Nature's many varied complex systems—including galaxies, stars, planets, life, and society—are islands of order within the increasingly disordered Universe. All organized systems are subject to physical, biological, or cultural evolution, which together comprise the grander interdisciplinary subject of cosmic evolution. A wealth of observational data supports the hypothesis that increasingly complex systems evolve unceasingly, uncaringly, and unpredictably from big bang to humankind. These are global history greatly extended, big history with a scientific basis, and natural history broadly portrayed across ∼14 billion years of time. Human beings and our cultural inventions are not special, unique, or apart from Nature; rather, we are an integral part of a universal evolutionary process connecting all such complex systems throughout space and time. Such evolution writ large has significant potential to unify the natural sciences into a holistic understanding of who we are and whence we came. No new science (beyond frontier, nonequilibrium thermodynamics) is needed to describe cosmic evolution's major milestones at a deep and empirical level. Quantitative models and experimental tests imply that a remarkable simplicity underlies the emergence and growth of complexity for a wide spectrum of known and diverse systems. Energy is a principal facilitator of the rising complexity of ordered systems within the expanding Universe; energy flows are as central to life and society as they are to stars and galaxies. In particular, energy rate density—contrasting with information content or entropy production—is an objective metric suitable to gauge relative degrees of complexity among a hierarchy of widely assorted systems observed throughout the material Universe. Operationally, those systems capable of utilizing optimum amounts of energy tend to survive, and those that cannot are nonrandomly eliminated.

The influence of increased body fat or lean body mass on aerobic performance

PURPOSE

The purpose of this study was to determine aerobic performance in men with an increased body mass due to (a) high body fat (>21.5%) but with a average (59.0-64.3 kg) lean body mass (HBF group) and (b) high lean body mass (>66.3 kg), but with average body fat (14.0-18.5%) (HLBM group).

METHODS

The men in the HBF and HLBM had similar absolute body mass and body mass index (BMI). The aerobic performance was also determined in control group. Methods: Study participants comprised 39 men aged 21.3 ± 1.9 years who did not participate in competitive sports but were recreationally physically active. Participants were divided into three groups. Each group comprised 13 persons. The study involved anthropometric measurements, assessing aerobic performance (VO2max) using an incremental test on a mechanical treadmill. VO2max was expressed in absolute values, relative to body mass (VO2max ⋅ BM(-1)), relative to lean body mass (VO2max ⋅ LBM(-1)), and relative to BM raised by the exponents of 0.75 and 0.67. Body composition was measured using bioelectrical impedance analysis.

RESULTS

No statistically significant differences in relative values of VO2max were found between the HBF and HLBM groups, in VO2max ⋅ BM(-1) (50.24 ± 4.56 vs. 53.11 ± 5.45 mL ⋅ kg(-1)), VO2max ⋅ LBM(-1) (65.33 ± 5.63 vs. 63.86 ± 7.13 mL ⋅ kgLBM(-1)), and VO2max ⋅ BM(-0.75) (150.29 ± 13.5 vs. 160.39 ± 16.15 mL ⋅ kg(-0.75)). Values of VO2max ⋅ BM(-1) were significantly lower in the HBF and HLBM groups than in the control group (58.23 ± 5.84 mL ⋅ kg(-1)).

CONCLUSION

High body mass, regardless of the cause decreases VO2max ⋅ BM(-1).

Thermodynamics constrains allometric scaling of optimal development time in insects

Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The remaining unexplained variation in development time likely reflects additional ecological and evolutionary differences among insect species.

Intraspecific scaling of the resting and maximum metabolic rates of the crucian carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M (0.776) and MMR = 0.753M (0.785). The scaling exponents for RMR (b r) and MMR (b m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.

Energy and metabolism

Although firmly grounded in metabolic biochemistry, the study of energy metabolism has gone well beyond this discipline and become integrative and comparative as well as ecological and evolutionary in scope. At the cellular level, ATP is hydrolyzed by energy-expending processes and resynthesized by pathways in bioenergetics. A significant development in the study of bioenergetics is the realization that fluxes through pathways as well as metabolic rates in cells, tissues, organs, and whole organisms are "system properties." Therefore, studies of energy metabolism have become, increasingly, experiments in systems biology. A significant challenge continues to be the integration of phenomena over multiple levels of organization. Body mass and temperature are said to account for most of the variation in metabolic rates found in nature. A mechanistic foundation for the understanding of these patterns is outlined. It is emphasized that evolution, leading to adaptation to diverse lifestyles and environments, has resulted in a tremendous amount of deviation from popularly accepted scaling "rules." This is especially so in the deep sea which constitutes most of the biosphere.

Mechanical work and long-distance performance prediction: the influence of allometric scaling

The purpose of this study was to examine the effect of allometric scaling on the relationship between mechanical work and long-distance running performance in recreational runners. Fourteen recreational long-distance runners (male, mean ± SD - age: 29 ± 7 years; body mass: 70.0 ± 10.2 kg; body height: 1.71 ± 0.07 m; maximal oxygen uptake: VO2max 52.0 ± 4.9 ml·kg(-1)·min(-1)) performed two tests: a continuous incremental test to volitional exhaustion in order to determine VO2max, and a 6-minute running submaximal test at 3.1 m·s(-1), during which segments in the sagittal plane were recorded using a digital camera and the internal (Wint), external (Wext) and total (Wtot) mechanic work, in J·kg(-1)·m(-1), was subsequently calculated. The results indicated a significant correlation between mechanical work and performance, however, the strongest correlations were observed when allometric exponents were used (respectively for Wint, Wext and Wtot; non allometric vs. allometric scaling defined by literature (0.75) or determined mathematically (0.49): r = 0.38 vs. r = 0.44 and r = 0.50; r = 0.80 vs. r = 0.83 and r = 0.82; r = 0.70 vs. r = 0.77 and r = 0.78). These results indicate that mechanical work could be used as a predictor of recreational long-distance performance and an allometric model may improve this prediction.

Scale model on performance prediction in recreational and elite endurance runners

PURPOSE

To identify the effect of allometric scaling on the relationship between running efficiency (R(Eff)) and middle-distance-running performance according to performance level.

METHODS

Thirteen male recreational middle-distance runners (mean ± SD age 33.3 ± 8.4 y, body mass 76.4 ± 8.6 kg, maximal oxygen uptake [VO(2max)] 52.8 ± 4.6 mL · kg(-1) · min(-1); G1) and 13 male high-level middle-distance runners (age 25.5 ± 4.2 y, body mass 62.8 ± 2.7 kg, VO(2max) 70.4 ± 1.9 mL · kg(-1) · min(-1); G2) performed a continuous incremental test to volitional exhaustion to determine VO(2max) and a 6-min submaximal running test at 70% of VO(2max) to assess R(Eff).

RESULTS

Significant correlation between R(Eff) and performance were found for both groups; however, the strongest correlations were observed in recreational runners, especially when using the allometric exponent (respectively for G1, nonallometric vs allometric scaling: r = .80 vs r = .86; and for G2, nonallometric vs allometric scaling: r = .55 vs r = .50).

CONCLUSION

These results indicate that an allometric normalization may improve endurance-performance prediction from R(Eff) values in recreational, but not in elite, runners.

On the analytical solution for the Pütter-Bertalanffy growth equation

This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter-Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently solved it. The analytical solution of the PBE was defined by an incomplete beta function and can take a wide range of shapes in its growth curve. The mathematical behavior of PBE due to the change in parameter values was briefly discussed. Most forms of solution consistently hold the implicit functional type with respect to the variable of body size.

Phylogenetic analyses: comparing species to infer adaptations and physiological mechanisms

Comparisons among species have been a standard tool in animal physiology to understand how organisms function and adapt to their surrounding environment. During the last two decades, conceptual and methodological advances from different fields, including evolutionary biology and systematics, have revolutionized the way comparative analyses are performed, resulting in the advent of modern phylogenetic statistical methods. This development stems from the realization that conventional analytical methods assume that observations are statistically independent, which is not the case for comparative data because species often resemble each other due to shared ancestry. By taking evolutionary history explicitly into consideration, phylogenetic statistical methods can account for the confounding effects of shared ancestry in interspecific comparisons, improving the reliability of standard approaches such as regressions or correlations in comparative analyses. Importantly, these methods have also enabled researchers to address entirely new evolutionary questions, such as the historical sequence of events that resulted in current patterns of form and function, which can only be studied with a phylogenetic perspective. Here, we provide an overview of phylogenetic approaches and their importance for studying the evolution of physiological processes and mechanisms. We discuss the conceptual framework underlying these methods, and explain when and how phylogenetic information should be employed. We then outline the difficulties and limitations inherent to comparative approaches and discuss potential problems researchers may encounter when designing a comparative study. These issues are illustrated with examples from the literature in which the incorporation of phylogenetic information has been useful, or even crucial, for inferences on how species evolve and adapt to their surrounding environment.

Relationship between fish size and metabolic rate in the oxyconforming inanga Galaxias maculatus reveals size-dependent strategies to withstand hypoxia

The relationship between metabolic rate and body size in animals is unlikely to be a constant but is instead shaped by a variety of intrinsic (i.e., physiological) and extrinsic (i.e., environmental) factors. This study examined the effect of environmental oxygen tension on oxygen consumption as a function of body mass in the galaxiid fish, inanga (Galaxias maculatus). As an oxyconformer, this fish lacks overt intrinsic regulation of oxygen consumption, eliminating this as a factor affecting the scaling relationship at different oxygen tensions. The relationship between oxygen consumption rate and body size was best described by a power function, with an exponent of 0.82, higher than the theoretical values of 0.66 or 0.75. The value of this exponent was significantly altered by environmental P(O2), first increasing as P(O2) decreased and then declining at the lowest P(O2) tested. These data suggest that the scaling exponent is species specific and regulated by extrinsic factors. Furthermore, the external P(O2) at which fish lost equilibrium was related to fish size, an effect explained by the scaling of anaerobic capacity with fish mass. Therefore, although bigger fish were forced to depress aerobic metabolism more rapidly than small fish when exposed to progressive hypoxia, they were better able to enact anaerobic metabolism, potentially extending their survival in hypoxia.

The relationship between body mass and field metabolic rate among individual birds and mammals

Summary

The authors provide the first comprehensive empirical analysis of the scaling relationship between field metabolic rate and body mass in individual birds and mammals. The analysis reveals the importance of heterogeneity in the scaling exponent, with consequences for biomass and nutrient flow through communities, and the structure and functioning of whole ecosystems.

Phylogenetic analysis of mammalian maximal oxygen consumption during exercise

We compiled published values of mammalian maximum oxygen consumption during exercise (VO2max) and supplemented these data with new measurements of VO2max for the largest rodent (capybara), 20 species of smaller-bodied rodents, two species of weasels, and one small marsupial. Many of the new data were obtained with running-wheel respirometers instead of the treadmill systems used in most previous measurements of mammalian VO2max. We used both conventional and phylogenetically informed allometric regression models to analyze VO2max of 77 ‘species’ (including subspecies or separate populations within species) in relation to body size, phylogeny, diet, and measurement method. Both body mass and allometrically mass-corrected VO2max showed highly significant phylogenetic signal (i.e., related species tended to resemble each other). The Akaike Information Criterion corrected for sample size was used to compare 27 candidate models predicting VO2max (all of which included body mass). In addition to mass, the two best-fitting models (cumulative Akaike weight = 0.93) included dummy variables coding for three species previously shown to have high VO2max (pronghorn, horse, and a bat), and incorporated a transformation of the phylogenetic branch lengths under an Ornstein-Uhlenbeck model of residual variation (thus indicating phylogenetic signal in the residuals). We found no statistical difference between wheel- and treadmill-elicited values, and diet had no predictive ability for VO2max. Averaged across all models, the allometric scaling exponent was 0.839, with 95% confidence limits of 0.795 and 0.883, which does not provide support for a scaling exponent of 0.67, 0.75 or unity.

Statistical models for jointly analyzing multiple allometries

As the reciprocal of simple allometry equation, power allometry equation can also be used to define allometry scaling but the scaling exponent has an opposite meaning to that of simple allometry equation. Based on this observation, a joint static allometry scaling model of entire body size on multiple partial body size is established, which can not only simultaneously evaluate allometry scaling of multiple partial body sizes, but also take into account the correlations among multiple partial body sizes, facilitating subsequent statistical inference and practice. Since ontogenetic allometry may be time-dependent, ontogenetic allometry is estimated by jointly analyzing changes of entire and multiple partial body sizes as growth time using multivariate stepwise analysis. Joint analysis of allometry scaling is suitable for multiple biological traits and functions with same property or comparability, which is illustrated by two examples.

Idiosyncratic species effects confound size-based predictions of responses to climate change

Understanding and predicting the consequences of warming for complex ecosystems and indeed individual species remains a major ecological challenge. Here, we investigated the effect of increased seawater temperatures on the metabolic and consumption rates of five distinct marine species. The experimental species reflected different trophic positions within a typical benthic East Atlantic food web, and included a herbivorous gastropod, a scavenging decapod, a predatory echinoderm, a decapod and a benthic-feeding fish. We examined the metabolism-body mass and consumption-body mass scaling for each species, and assessed changes in their consumption efficiencies. Our results indicate that body mass and temperature effects on metabolism were inconsistent across species and that some species were unable to meet metabolic demand at higher temperatures, thus highlighting the vulnerability of individual species to warming. While body size explains a large proportion of the variation in species' physiological responses to warming, it is clear that idiosyncratic species responses, irrespective of body size, complicate predictions of population and ecosystem level response to future scenarios of climate change.

Organ-Tissue Level Model of Resting Energy Expenditure Across Mammals: New Insights into Kleiber's Law

Background. Kleiber’s law describes the quantitative association between whole-body resting energy expenditure (REE, in kcal/d) and body mass (M, in kg) across mature mammals as REE =70.0×M0.75. The basis of this empirical function is uncertain. Objectives. The study objective was to establish an organ-tissue level REE model across mammals and to explore the body composition and physiologic basis of Kleiber’s law. Design. We evaluated the hypothesis that REE in mature mammals can be predicted by a combination of two variables: the mass of individual organs/tissues and their corresponding specific resting metabolic rates. Data on the mass of organs with high metabolic rate (i.e., liver, brain, heart, and kidneys) for 111 species ranging in body mass from 0.0075 (shrew) to 6650 kg (elephant) were obtained from a literature review. Results. REEp predicted by the organ-tissue level model was correlated with body mass (correlation r=0.9975) and resulted in the function REEp=66.33×M0.754, with a coefficient and scaling exponent, respectively, close to 70.0 and 0.75 (P>0.05) as observed by Kleiber. There were no differences between REEp and REEk calculated by Kleiber’s law; REEp was correlated (r=0.9994) with REEk. The mass-specific REEp, that is, (REE/M)p, was correlated with body mass (r=0.9779) with a scaling exponent −0.246, close to −0.25 as observed with Kleiber’s law. Conclusion. Our findings provide new insights into the organ/tissue energetic components of Kleiber’s law. The observed large rise in REE and lowering of REE/M from shrew to elephant can be explained by corresponding changes in organ/tissue mass and associated specific metabolic rate.

Conservation physiology of marine fishes: advancing the predictive capacity of models

At the end of May, 17 scientists involved in an EU COST Action on Conservation Physiology of Marine Fishes met in Oristano, Sardinia, to discuss how physiology can be better used in modelling tools to aid in management of marine ecosystems. Current modelling approaches incorporate physiology to different extents, ranging from no explicit consideration to detailed physiological mechanisms, and across scales from a single fish to global fishery resources. Biologists from different sub-disciplines are collaborating to rise to the challenge of projecting future changes in distribution and productivity, assessing risks for local populations, or predicting and mitigating the spread of invasive species.

Metabolism in the age of ‘omes’

Much research in comparative physiology is now performed using ‘omics’ tools and many results are interpreted in terms of the effects of changes in gene expression on energy metabolism. However, ‘metabolism’ is a complex phenomenon that spans multiple levels of biological organization. In addition rates and directions of flux change dynamically under various physiological circumstances. Within cells, message level cannot be equated with protein level because multiple mechanisms are at play in the ‘regulatory hierarchy’ from gene to mRNA to enzyme protein. This results in many documented instances wherein change in mRNA levels and change in enzyme levels are unrelated. It is also known from metabolic control analysis that the influence of single steps in pathways on flux is often small. Flux is a system property and its control tends to be distributed among multiple steps. Consequently, change in enzyme levels cannot be equated with change in flux. Approaches developed by Hans Westerhoff and colleagues, called ‘hierarchical regulation analysis’, allow quantitative determination of the extent to which ‘hierarchical regulation’, involving change in enzyme level, and ‘metabolic regulation’, involving the modulation of the activity of preexisting enzyme, regulate flux. We outline these approaches and provide examples to show their applicability to problems of interest to comparative physiologists.

Scaling of resting and maximum hopping metabolic rate throughout the life cycle of the locust Locusta migratoria

The hemimetabolous migratory locust Locusta migratoria progresses through five instars to the adult, increasing in size from 0.02 to 0.95 g, a 45-fold change. Hopping locomotion occurs at all life stages and is supported by aerobic metabolism and provision of oxygen through the tracheal system. This allometric study investigates the effect of body mass (Mb) on oxygen consumption rate (MO2, μmol h(-1)) to establish resting metabolic rate (MRO2), maximum metabolic rate during hopping (MMO2) and maximum metabolic rate of the hopping muscles (MMO2,hop) in first instar, third instar, fifth instar and adult locusts. Oxygen consumption rates increased throughout development according to the allometric equations MRO2=30.1Mb(0.83±0.02), MMO2=155Mb(1.01±0.02), MMO2,hop=120Mb(1.07±0.02) and, if adults are excluded, MMO2,juv=136Mb(0.97±0.02) and MMO2,juv,hop=103Mb(1.02±0.02). Increasing body mass by 20-45% with attached weights did not increase mass-specific MMO2 significantly at any life stage, although mean mass-specific hopping MO2 was slightly higher (ca. 8%) when juvenile data were pooled. The allometric exponents for all measures of metabolic rate are much greater than 0.75, and therefore do not support West, Brown and Enquist’s optimised fractal network model, which predicts that metabolism scales with a 3⁄4-power exponent owing to limitations in the rate at which resources can be transported within the body.

Scaling of brain metabolism and blood flow in relation to capillary and neural scaling

Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume as , brain capillary diameter increases as , and density of capillary length decreases as . It is predicted that velocity of capillary blood is almost invariant (), capillary transit time scales as , capillary length increases as , and capillary number as , where is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.

Enzymatic correlates of energy status in wild yellow perch inhabiting clean and contaminated environments

Enzymes representing a variety of metabolic pathways were examined in yellow perch (Perca flavescens) collected from a metal-contaminated region (Rouyn-Noranda, Québec, Canada) to determine which were most closely related to fish condition factor, pyloric caeca weight, and visceral lipid accumulation, as well to seek a better understanding of the influence of metal contamination on the physiology and biometrics of perch. Compared to laboratory fish, wild perch were under important energy restrictions. The condition factor of wild fish was correlated with indicators of aerobic metabolism (citrate synthase, cytochrome C oxidase), protein anabolism (nucleoside diphosphokinase), and indicators of lipid accumulation (glucose-6-phosphate dehydrogenase, visceral lipid index). Pyloric caeca weights were well correlated with indicators of protein anabolism, but only when both seasons were examined together, possibly indicating a lag in the response of enzymes to changes in diet. The addition of contaminant stress to existing energy restrictions led to changes in the relationships between enzymes and biometrics, reducing the predictive power of the models for perch in contaminated lakes. The present study broadens our knowledge of the impact of metal contamination on energy accumulation and tissue metabolic capacities in wild perch.

Dependence of morphometric allometries on the growth kinetics of body parts

As overall size varies, the sizes of body parts of many animals often appear to be related to each other by a power law, commonly called the allometric equation. Orderly scaling relationships among body parts are widespread in the animal world, but there is no general agreement about how these relationships come about. Presumably they depend on the patterns of growth of body parts, and simple analyses have shown that exponential growth can lead to size relationships that are well-described by the allometric equation. Exponential growth kinetics also allow for a simple biological interpretation of the coefficients of the power relationship. Nevertheless, many tissues do not grow with exponential kinetics, nor do they grow for the same period of time, and the consequences of more realistic growth patterns on the resulting allometric relationships of body parts are not well understood. In this paper I derive a set of allometric equations that assume different kinetics of growth: linear, exponential and sigmoidal. In these derivations I also include differences in development times as a variable, in addition to differences in the growth rates and initial sizes of the two structures whose allometric relationship is compared. I show how these equations can be used to deduce the effect of different causes of variation in absolute size on the resulting allometry. Variation in size can be due to variation in the duration of development, variation in growth rate or variation in initial size. I show that the meaning of the coefficients of the allometric equation depends on exactly how size variation comes about. I show that if two structures are assumed to grow with sigmoidal kinetics (logistic and Gompertz) the resulting allometric equations do not have a simple and intuitive structure and produce graphs that, over a sufficiently large range of sizes, can vary from linear, to sigmoidal to hump-shaped. Over a smaller range of absolute sizes, these sigmoid growth kinetics can produce nearly linear allometries in both the arithmetic and logarithmic domains. I will argue that although growth kinetics are likely to be sigmoidal in most cases, natural selection will restrict variation in absolute size and the parameters of growth kinetics to regions where the allometric relations are linear, or nearly so.

Analytic theories of allometric scaling

During the 13 years since it was first advanced, the fractal network theory (FNT), an analytic theory of allometric scaling, has been subjected to a wide range of methodological, mathematical and empirical criticisms, not all of which have been answered satisfactorily. FNT presumes a two-variable power-law relationship between metabolic rate and body mass. This assumption has been widely accepted in the past, but a growing body of evidence during the past quarter century has raised questions about its general validity. There is now a need for alternative theories of metabolic scaling that are consistent with empirical observations over a broad range of biological applications. In this article, we briefly review the limitations of FNT, examine the evidence that the two-variable power-law assumption is invalid, and outline alternative perspectives. In particular, we discuss quantum metabolism (QM), an analytic theory based on molecular-cellular processes. QM predicts the large variations in scaling exponent that are found empirically and also predicts the temperature dependence of the proportionality constant, issues that have eluded models such as FNT that are based on macroscopic and network properties of organisms.

Allometric Prediction of Energy Expenditure in Infants and Children

Predicting energy needs in children is complicated by the wide range of patient sizes, confusing traditional estimation equations, nonobjective stress-activity factors, and so on. These complications promote errors in bedside estimates of nutritional needs by rendering the estimation methods functionally unavailable to bedside clinicians. Here, the authors develop a simple heuristic energy prediction equation that requires only body mass (not height, age, or sex) as input. Expert estimation of energy expenditure suggested a power-law relationship between mass and energy. A similar mass-energy expenditure relationship was derived from published pediatric echocardiographic data using a Monte Carlo model of energy expenditure based on oxygen delivery and consumption. A simplified form of the equation was compared with energy required for normal growth in a cohort of historical patients weighing 2 to 70 kg. All 3 methods demonstrate that variation in energy expenditure in children is dominated by mass and can be estimated by the following equation: Power(kcal/kg/d) = 200 × [Mass(kg)^(−0.4)]. This relationship explains 85% of the variability in energy required to maintain expected growth over a broad range of surgical clinical contexts. A simplified power-law equation predicts real-world energy needs for growth in patients over a wide range of body sizes and clinical contexts, providing a more useful bedside tool than traditional estimators.

Origins of interspecies variation in mammalian muscle metabolic enzymes

Do the transcriptional mechanisms that control an individual's mitochondrial content, PGC1α (peroxisome proliferator-activated receptor γ coactivator-1α) and NRF1 (nuclear respiratory factor-1), also cause differences between species? We explored the determinants of cytochrome c oxidase (COX) activities in muscles from 12 rodents differing 1,000-fold in mass. Hindlimb muscles differed in scaling patterns from isometric (soleus, gastrocnemius) to allometric (tibialis anterior, scaling coefficient = -0.16). Consideration of myonuclear domain reduced the differences within species, but interspecies differences remained. For tibialis anterior, there was no significant scaling relationship in mRNA/g for COX4-1, PGC1α, or NRF1, yet COX4-1 mRNA/g was a good predictor of COX activity (r(2) = 0.55), PGC1α and NRF1 mRNA correlated with each other (r(2) = 0.42), and both could predict COX4-1 mRNA (r(2) = 0.48 and 0.52) and COX activity (r(2) = 0.55 and 0.49). This paradox was resolved by multivariate analysis, which explained 90% of interspecies variation, about equally partitioned between mass effects and PGC1α (or NRF1) mRNA levels, independent of mass. To explore the determinants of PGC1α mRNA, we analyzed 52 mammalian PGC1α proximal promoters and found no size dependence in regulatory element distribution. Likewise, the activity of PGC1α promoter reporter genes from 30 mammals showed no significant relationship with body mass. Collectively, these studies suggest that not all muscles scale equivalently, but for those that show allometric scaling, transcriptional regulation of the master regulators, PGC1α and NRF1, does not account for scaling patterns, though it does contribute to interspecies differences in COX activities independent of mass.

Regulation of whole body energy homeostasis with growth hormone replacement therapy and endurance exercise

We hypothesized that network analysis is useful to expose coordination between whole body and myocellular levels of energy metabolism and can identify entities that underlie skeletal muscle's contribution to growth hormone-stimulated lipid handling and metabolic fitness. We assessed 112 metabolic parameters characterizing metabolic rate and substrate handling in tibialis anterior muscle and vascular compartment at rest, after a meal and exercise with growth hormone replacement therapy (GH-RT) of hypopituitary patients (n = 11). The topology of linear relationships (| r | ≥ 0.7, P ≤ 0.01) and mutual dependencies exposed the organization of metabolic relationships in three entities reflecting basal and exercise-induced metabolic rate, triglyceride handling, and substrate utilization in the pre- and postprandial state, respectively. GH-RT improved aerobic performance (+5%), lean-to-fat mass (+19%), and muscle area of tibialis anterior (+2%) but did not alter its mitochondrial and capillary content. Concomitantly, connectivity was established between myocellular parameters of mitochondrial lipid metabolism and meal-induced triglyceride handling in serum. This was mediated via the recruitment of transcripts of muscle lipid mobilization (LIPE, FABP3, and FABP4) and fatty acid-sensitive transcription factors (PPARA, PPARG) to the metabolic network. The interdependence of gene regulatory elements of muscle lipid metabolism reflected the norm in healthy subjects (n = 12) and distinguished the regulation of the mitochondrial respiration factor COX1 by GH and endurance exercise. Our observations validate the use of network analysis for systems medicine and highlight the notion that an improved stochiometry between muscle and whole body lipid metabolism, rather than alterations of single bottlenecks, contributes to GH-driven elevations in metabolic fitness.

Temperature, metabolic power and the evolution of endothermy

Endothermy has evolved at least twice, in the precursors to modern mammals and birds. The most widely accepted explanation for the evolution of endothermy has been selection for enhanced aerobic capacity. We review this hypothesis in the light of advances in our understanding of ATP generation by mitochondria and muscle performance. Together with the development of isotope-based techniques for the measurement of metabolic rate in free-ranging vertebrates these have confirmed the importance of aerobic scope in the evolution of endothermy: absolute aerobic scope, ATP generation by mitochondria and muscle power output are all strongly temperature-dependent, indicating that there would have been significant improvement in whole-organism locomotor ability with a warmer body. New data on mitochondrial ATP generation and proton leak suggest that the thermal physiology of mitochondria may differ between organisms of contrasting ecology and thermal flexibility. Together with recent biophysical modelling, this strengthens the long-held view that endothermy originated in smaller, active eurythermal ectotherms living in a cool but variable thermal environment. We propose that rather than being a secondary consequence of the evolution of an enhanced aerobic scope, a warmer body was the means by which that enhanced aerobic scope was achieved. This modified hypothesis requires that the rise in metabolic rate and the insulation necessary to retain metabolic heat arose early in the lineages leading to birds and mammals. Large dinosaurs were warm, but were not endotherms, and the metabolic status of pterosaurs remains unresolved.

The evolutionary consequences of oxygenic photosynthesis: a body size perspective

The high concentration of molecular oxygen in Earth's atmosphere is arguably the most conspicuous and geologically important signature of life. Earth's early atmosphere lacked oxygen; accumulation began after the evolution of oxygenic photosynthesis in cyanobacteria around 3.0-2.5 billion years ago (Gya). Concentrations of oxygen have since varied, first reaching near-modern values ~600 million years ago (Mya). These fluctuations have been hypothesized to constrain many biological patterns, among them the evolution of body size. Here, we review the state of knowledge relating oxygen availability to body size. Laboratory studies increasingly illuminate the mechanisms by which organisms can adapt physiologically to the variation in oxygen availability, but the extent to which these findings can be extrapolated to evolutionary timescales remains poorly understood. Experiments confirm that animal size is limited by experimental hypoxia, but show that plant vegetative growth is enhanced due to reduced photorespiration at lower O(2):CO(2). Field studies of size distributions across extant higher taxa and individual species in the modern provide qualitative support for a correlation between animal and protist size and oxygen availability, but few allow prediction of maximum or mean size from oxygen concentrations in unstudied regions. There is qualitative support for a link between oxygen availability and body size from the fossil record of protists and animals, but there have been few quantitative analyses confirming or refuting this impression. As oxygen transport limits the thickness or volume-to-surface area ratio-rather than mass or volume-predictions of maximum possible size cannot be constructed simply from metabolic rate and oxygen availability. Thus, it remains difficult to confirm that the largest representatives of fossil or living taxa are limited by oxygen transport rather than other factors. Despite the challenges of integrating findings from experiments on model organisms, comparative observations across living species, and fossil specimens spanning millions to billions of years, numerous tractable avenues of research could greatly improve quantitative constraints on the role of oxygen in the macroevolutionary history of organismal size.