Multi-level regulation and metabolic scaling

Metabolic scaling as an emergent outcome of variation in metabolic rate

The allometric scaling of metabolic rate and what drives it are major questions in biology with a long history. Since the metabolic rate at any level of biological organization is an emergent property of its lower-level constituents, it is an outcome of the intrinsic heterogeneity among these units and the interactions among them. However, the influence of lower-level heterogeneity on system-level metabolic rate is difficult to investigate, given the tightly integrated body plan of unitary organisms. In this context, social insects such as honeybees can serve as important model systems because unlike unitary organisms, these superorganisms can be taken apart and reassembled in different configurations to study metabolic rate and its various drivers at different levels of organization. This commentary discusses the background of such an approach and how combining it with artificial selection to generate heterogeneity in metabolic rate with an analytical framework to parse out the different mechanisms that contribute to the effects of heterogeneity can contribute to the various models of metabolic scaling. Finally, the absence of the typical allometric scaling relationship among different species of honeybees is discussed as an important prospect for deciphering the role of top-down ecological factors on metabolic scaling. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Interactive effects of intrinsic and extrinsic factors on metabolic rate

Metabolism energizes all biological processes, and its tempo may importantly influence the ecological success and evolutionary fitness of organisms. Therefore, understanding the broad variation in metabolic rate that exists across the living world is a fundamental challenge in biology. To further the development of a more reliable and holistic picture of the causes of this variation, we review several examples of how various intrinsic (biological) and extrinsic (environmental) factors (including body size, cell size, activity level, temperature, predation and other diverse genetic, cellular, morphological, physiological, behavioural and ecological influences) can interactively affect metabolic rate in synergistic or antagonistic ways. Most of the interactive effects that have been documented involve body size, temperature or both, but future research may reveal additional 'hub factors'. Our review highlights the complex, intimate inter-relationships between physiology and ecology, knowledge of which can shed light on various problems in both disciplines, including variation in physiological adaptations, life histories, ecological niches and various organism-environment interactions in ecosystems. We also discuss theoretical and practical implications of interactive effects on metabolic rate and provide suggestions for future research, including holistic system analyses at various hierarchical levels of organization that focus on interactive proximate (functional) and ultimate (evolutionary) causal networks. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Linear Irreversible Thermodynamics: A Glance at Thermoelectricity and the Biological Scaling Laws

This paper presents so-called thermoelectric generators (TEGs), which are considered thermal engines that transform heat into electricity using the Seebeck effect for this purpose. By using linear irreversible thermodynamics (LIT), it is possible to study the thermodynamic properties of TEGs for three different operating regimes: maximum power output (MPO), maximum ecological function (MEF) and maximum power efficiency (MPE). Then, by considering thermoelectricty, using the correspondence between the heat capacity of a solid and the metabolic rate, and taking the generation of energy by means of the metabolism of an organism as a process out of equilibrium, it is plausible to use linear irreversible thermodynamics (LIT) to obtain some interesting results in order to understand how metabolism is generated by a particle's released energy, which explains the empirically studied allometric laws.

Variable metabolic scaling breaks the law: from 'Newtonian' to 'Darwinian' approaches

Life's size and tempo are intimately linked. The rate of metabolism varies with body mass in remarkably regular ways that can often be described by a simple power function, where the scaling exponent (b, slope in a log-linear plot) is typically less than 1. Traditional theory based on physical constraints has assumed that b is 2/3 or 3/4, following natural law, but hundreds of studies have documented extensive, systematic variation in b. This overwhelming, law-breaking, empirical evidence is causing a paradigm shift in metabolic scaling theory and methodology from ‘Newtonian’ to ‘Darwinian’ approaches. A new wave of studies focuses on the adaptable regulation and evolution of metabolic scaling, as influenced by diverse intrinsic and extrinsic factors, according to multiple context-dependent mechanisms, and within boundary limits set by physical constraints.

White Paper: An Integrated Perspective on the Causes of Hypometric Metabolic Scaling in Animals

Larger animals studied during ontogeny, across populations, or across species, usually have lower mass-specific metabolic rates than smaller animals (hypometric scaling). This pattern is usually observed regardless of physiological state (e.g. basal, resting, field, maximally-active). The scaling of metabolism is usually highly correlated with the scaling of many life history traits, behaviors, physiological variables, and cellular/molecular properties, making determination of the causation of this pattern challenging. For across-species comparisons of resting and locomoting animals (but less so for across populations or during ontogeny), the mechanisms at the physiological and cellular level are becoming clear. Lower mass-specific metabolic rates of larger species at rest are due to a) lower contents of expensive tissues (brains, liver, kidneys), and b) slower ion leak across membranes at least partially due to membrane composition, with lower ion pump ATPase activities. Lower mass-specific costs of larger species during locomotion are due to lower costs for lower-frequency muscle activity, with slower myosin and Ca++ ATPase activities, and likely more elastic energy storage. The evolutionary explanation(s) for hypometric scaling remain(s) highly controversial. One subset of evolutionary hypotheses relies on constraints on larger animals due to changes in geometry with size; for example, lower surface-to-volume ratios of exchange surfaces may constrain nutrient or heat exchange, or lower cross-sectional areas of muscles and tendons relative to body mass ratios would make larger animals more fragile without compensation. Another subset of hypotheses suggests that hypometric scaling arises from biotic interactions and correlated selection, with larger animals experiencing less selection for mass-specific growth or neurolocomotor performance. A additional third type of explanation comes from population genetics. Larger animals with their lower effective population sizes and subsequent less effective selection relative to drift may have more deleterious mutations, reducing maximal performance and metabolic rates. Resolving the evolutionary explanation for the hypometric scaling of metabolism and associated variables is a major challenge for organismal and evolutionary biology. To aid progress, we identify some variation in terminology use that has impeded cross-field conversations on scaling. We also suggest that promising directions for the field to move forward include: 1) studies examining the linkages between ontogenetic, population-level, and cross-species allometries, 2) studies linking scaling to ecological or phylogenetic context, 3) studies that consider multiple, possibly interacting hypotheses, and 4) obtaining better field data for metabolic rates and the life history correlates of metabolic rate such as lifespan, growth rate and reproduction.

How Metabolic Rate Relates to Cell Size

Metabolic rate and its covariation with body mass vary substantially within and among species in little understood ways. Here, I critically review explanations (and supporting data) concerning how cell size and number and their establishment by cell expansion and multiplication may affect metabolic rate and its scaling with body mass. Cell size and growth may affect size-specific metabolic rate, as well as the vertical elevation (metabolic level) and slope (exponent) of metabolic scaling relationships. Mechanistic causes of negative correlations between cell size and metabolic rate may involve reduced resource supply and/or demand in larger cells, related to decreased surface area per volume, larger intracellular resource-transport distances, lower metabolic costs of ionic regulation, slower cell multiplication and somatic growth, and larger intracellular deposits of metabolically inert materials in some tissues. A cell-size perspective helps to explain some (but not all) variation in metabolic rate and its body-mass scaling and thus should be included in any multi-mechanistic theory attempting to explain the full diversity of metabolic scaling. A cell-size approach may also help conceptually integrate studies of the biological regulation of cellular growth and metabolism with those concerning major transitions in ontogenetic development and associated shifts in metabolic scaling.

A quantitative genetics perspective on the body-mass scaling of metabolic rate

Widely observed allometric scaling (log-log slope<1) of metabolic rate (MR) with body mass (BM) in animals has been frequently explained using functional mechanisms, but rarely studied from the perspective of multivariate quantitative genetics. This is unfortunate, given that the additive genetic slope (bA) of the MR-BM relationship represents the orientation of the 'line of least genetic resistance' along which MR and BM may most likely evolve. Here, we calculated bA in eight species. Although most bA values were within the range of metabolic scaling exponents reported in the literature, uncertainty of each bA estimate was large (only one bA was significantly lower than 3/4 and none were significantly different from 2/3). Overall, the weighted average for bA (0.667±0.098 95% CI) is consistent with the frequent observation that metabolic scaling exponents are negatively allometric in animals (b<1). Although bA was significantly positively correlated with the phenotypic scaling exponent (bP) across the sampled species, bP was usually lower than bA, as reflected in a (non-significantly) lower weighted average for bP (0.596±0.100). This apparent discrepancy between bA and bP resulted from relatively shallow MR-BM scaling of the residuals [weighted average residual scaling exponent (be)=0.503±0.128], suggesting regression dilution (owing to measurement error and within-individual variance) causing a downward bias in bP. Our study shows how the quantification of the genetic scaling exponent informs us about potential constraints on the correlated evolution of MR and BM, and by doing so has the potential to bridge the gap between micro- and macro-evolutionary studies of scaling allometry.

Bioenergetics in environmental adaptation and stress tolerance of aquatic ectotherms: linking physiology and ecology in a multi-stressor landscape

Energy metabolism (encompassing energy assimilation, conversion and utilization) plays a central role in all life processes and serves as a link between the organismal physiology, behavior and ecology. Metabolic rates define the physiological and life-history performance of an organism, have direct implications for Darwinian fitness, and affect ecologically relevant traits such as the trophic relationships, productivity and ecosystem engineering functions. Natural environmental variability and anthropogenic changes expose aquatic ectotherms to multiple stressors that can strongly affect their energy metabolism and thereby modify the energy fluxes within an organism and in the ecosystem. This Review focuses on the role of bioenergetic disturbances and metabolic adjustments in responses to multiple stressors (especially the general cellular stress response), provides examples of the effects of multiple stressors on energy intake, assimilation, conversion and expenditure, and discusses the conceptual and quantitative approaches to identify and mechanistically explain the energy trade-offs in multiple stressor scenarios, and link the cellular and organismal bioenergetics with fitness, productivity and/or ecological functions of aquatic ectotherms.

Myonuclear content regulates cell size with similar scaling properties in mice and humans

Muscle fibers are the largest cells in the body, and one of its few syncytia. Individual cell sizes are variable and adaptable, but what governs cell size has been unclear. We find that muscle fibers are DNA scarce compared to other cells, and that the nuclear number (N) adheres to the relationship N = aVb where V is the cytoplasmic volume. N invariably scales sublinearly to V (b < 1), making larger cells even more DNA scarce. N scales linearly to cell surface in adult humans, in adult and developing mice, and in mice with genetically reduced N, but in the latter the relationship eventually fails when they reach adulthood with extremely large myonuclear domains. Another exception is denervation-atrophy where nuclei are not eliminated. In conclusion, scaling exponents are remarkably similar across species, developmental stages and experimental conditions, suggesting an underlying scaling law where DNA-content functions as a limiter of muscle cell size.

Temperature effects on metabolic scaling of a keystone freshwater crustacean depend on fish-predation regime

According to the metabolic theory of ecology, metabolic rate, an important indicator of the pace of life, varies with body mass and temperature as a result of internal physical constraints. However, various ecological factors may also affect metabolic rate and its scaling with body mass. Although reports of such effects on metabolic scaling usually focus on single factors, the possibility of significant interactive effects between multiple factors requires further study. In this study, we show that the effect of temperature on the ontogenetic scaling of resting metabolic rate of the freshwater amphipod Gammarus minus depends critically on habitat differences in predation regime. Increasing temperature tends to cause decreases in the metabolic scaling exponent (slope) in population samples from springs with fish predators, but increases in population samples from springs without fish. Accordingly, the temperature sensitivity of metabolic rate is not only size-specific, but also its relationship to body size shifts dramatically in response to fish predators. We hypothesize that the dampened effect of temperature on the metabolic rate of large adults in springs with fish, and of small juveniles in springs without fish are adaptive evolutionary responses to differences in the relative mortality risk of adults and juveniles in springs with versus without fish predators. Our results demonstrate a complex interaction among metabolic rate, body mass, temperature and predation regime. The intraspecific scaling of metabolic rate with body mass and temperature is not merely the result of physical constraints related to internal body design and biochemical kinetics, but rather is ecologically sensitive and evolutionarily malleable.

Coevolution of body size and metabolic rate in vertebrates: a life-history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non-linearity of the relationship between MR and body mass. This 'statistical' view must be replaced with the life-history perspective that 'allows' organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation 'decisions' that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those 'decisions' form a wealth of life-history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single-cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life-history evolution is the best way forward.

Tumor vascular status controls oxygen delivery facilitated by infused polymerized hemoglobins with varying oxygen affinity

Oxygen (O₂) delivery facilitated by hemoglobin (Hb)-based O₂ carriers (HBOCs) is a promising strategy to increase the effectiveness of chemotherapeutics for treatment of solid tumors. However, the heterogeneous vascular structures present within tumors complicates evaluating the oxygenation potential of HBOCs within the tumor microenvironment. To account for spatial variations in the vasculature and tumor tissue that occur during tumor growth, we used a computational model to develop artificial tumor constructs. With these simulated tumors, we performed a polymerized human hemoglobin (hHb) (PolyhHb) enhanced oxygenation simulation accounting for differences in the physiologic characteristics of human and mouse blood. The results from this model were used to determine the potential effectiveness of different treatment options including a top load (low volume) and exchange (large volume) infusion of a tense quaternary state (T-State) PolyhHb, relaxed quaternary state (R-State) PolyhHb, and a non O₂ carrying control. Principal component analysis (PCA) revealed correlations between the different regimes of effectiveness within the different simulated dosage options. In general, we found that infusion of T-State PolyhHb is more likely to decrease tissue hypoxia and modulate the metabolic rate of O₂ consumption. Though the developed models are not a definitive descriptor of O₂ carrier interaction in tumor capillary networks, we accounted for factors such as non-uniform vascular density and permeability that limit the applicability of O₂ carriers during infusion. Finally, we have used these validated computational models to establish potential benchmarks to guide tumor treatment during translation of PolyhHb mediated therapies into clinical applications.

High rates of oxygen consumption and abnormal vascularization lead to low oxygen levels within solid tumors. The lack of oxygen results in resistance to chemotherapies and increased rates of cancer progression. Hemoglobin-based oxygen carriers have the potential to increase the amount of oxygen delivered to tumors, which may make chemotherapies more effective. Unfortunately, translating experimental results from mice to humans is complicated by allometric scaling between mice and humans. To predict how these therapies may perform differently between human and murine systems, we computationally predicted how hemoglobin-based oxygen delivery varies between the two organisms. Our model accounts for how variations in the tumor vascular network impact the performance of hemoglobin-based oxygen carriers. This model also allows us to assess how the oxygen affinity of hemoglobin-based oxygen carriers affects the oxygenation of hypoxic tissue. The results of these models help us predict how results from murine models may translate to humans. Also, our models help to highlight what clinically-measurable tumor properties should be measured to predict the effectiveness of hemoglobin-based oxygen carriers in biological systems.

Mitochondrial performance of a continually growing marine bivalve, Mytilus edulis, depends on body size

Allometric decline of mass-specific metabolic rate with increasing body size in organisms is a well-documented phenomenon. Despite a long history of research, the mechanistic causes of metabolic scaling with body size remain under debate. Some hypotheses suggest that intrinsic factors such as allometry of cellular and mitochondrial metabolism may contribute to the organismal-level metabolic scaling. The aim of our present study was to determine the metabolic allometry at the mitochondrial level using a continually growing marine ectotherm, the mussel Mytilus edulis, as a model. Mussels from a single cohort that considerably differed in body size were selected, implying faster growth in the larger specimens. We determined the body mass-dependent scaling of the mitochondrial proton leak respiration, respiration in the presence of ADP indicative of the oxidative phosphorylation (OXPHOS), and maximum activity of the mitochondrial electron transport system (ETS) and cytochrome c oxidase (COX). Respiration was measured at normal (15°C), and elevated (27°C) temperatures. The results demonstrated a pronounced allometric increase in both proton leak respiration and OXPHOS activity of mussel mitochondria. Mussels with faster growth (larger body size) showed an increase in OXPHOS rate, proton leak respiration rate, and ETS and COX activity (indicating an overall improved mitochondrial performance) and higher respiratory control ratio (indicating better mitochondrial coupling and potentially lower costs of mitochondrial maintenance at the same OXPHOS capacity) compared with slower growing (smaller) individuals. Our data show that the metabolic allometry at the organismal level cannot be directly explained by mitochondrial functioning.

Size Exponents for Scaling Maximal Oxygen Uptake in Over 6500 Humans: A Systematic Review and Meta-Analysis

BACKGROUND

Maximal oxygen uptake ([Formula: see text] _2max) is conventionally normalized to body size as a simple ratio or using an allometric exponent < 1. Nevertheless, the most appropriate body size variable to use for scaling and the value of the exponent are still enigmatic. Studies tend to be based on small samples and can, therefore, lack precision.

OBJECTIVE

The objective of this systematic review was to provide a quantitative synthesis of reported static allometric exponents used for scaling [Formula: see text] _2max to whole body mass and fat-free mass.

METHODS

Eight electronic databases (CINAHL, Cochrane Central Register of Controlled Trials, EMBASE, MEDLINE, PubMed, Scopus, SPORTDiscus and Web of Science) were searched for relevant studies published up to January 2016. Search terms included 'oxygen uptake', 'cardiorespiratory fitness', '[Formula: see text] _2max', '[Formula: see text] _2peak', 'scaling' and all interchangeable terms. Inclusion criteria included human cardiorespiratory fitness data; cross-sectional study designs; an empirical derivation of the exponent; reported precision statistics; and reported information regarding participant sex, age and sports background, [Formula: see text] _2max protocol, whole body composition protocol and line-fitting methods. A random-effects model was used to quantify weighted pooled exponents and 95% confidence limits (Cls). Heterogeneity was quantified with the tau-statistic (τ). Meta-regression was used to quantify the impact of selected moderator variables on the exponent effect size. A 95% prediction interval was calculated to quantify the likely range of true fat-free mass exponents in similar future studies, with this distribution used to estimate the probability that an exponent would be above theorised universal values of [Formula: see text].

RESULTS

Thirty-six studies, involving 6514 participants, met the eligibility criteria. Whole body mass and fat-free mass were used as the scaling denominator in 27 and 15 studies, respectively. The pooled allometric exponent (95% Cls) was found to be 0.70 (0.64 to 0.76) for whole body mass and 0.90 (0.83 to 0.96) for fat-free mass. The between-study heterogeneity was greater for whole body mass (τ = ±0.15) than for fat-free mass (τ = ±0.11). Participant sex explained 30% of the between-study variability in the whole body mass exponent, but the influence on the fat-free mass exponent was trivial. The whole body mass exponent of 0.52 (0.40 to 0.64) for females was substantially lower than the 0.76 (0.70 to 0.83) for males, whereas the fat-free mass exponent was similar for both sexes. The effects of all other moderators were trivial. The 95% PI for fat-free mass ranged from 0.68 to 1.12. The estimated probability of a true fat-free mass exponent in a future study being greater than [Formula: see text] power scaling is 0.98 (very likely) and 0.92 (likely), respectively.

CONCLUSIONS

In this quantitative synthesis of published studies involving over 6500 humans, the whole body mass exponent was found to be spuriously low and prone to substantial heterogeneity. We conclude that the scaling of [Formula: see text] _2max in humans is consistent with the allometric cascade model with an estimated prediction interval for the fat-free mass exponent not likely to be consistent with the [Formula: see text] power laws.

Individual variation in metabolic reaction norms over ambient temperature causes low correlation between basal and standard metabolic rate

Basal metabolic rate (BMR) is often assumed to be indicative of the energy turnover at ambient temperatures (Ta) below the thermoneutral zone (SMR), but this assumption has remained largely untested. Using a new statistical approach, we quantified the consistency in nocturnal metabolic rate across a temperature range in zebra finches (n=3,213 measurements on 407 individuals) living permanently in eight outdoor aviaries. Foraging conditions were either benign or harsh, and body mass and mass-adjusted BMRm and SMRm were lower in individuals living in a harsh foraging environment. The correlation between SMRm at different Tas was high (r=0.91), independent of foraging environment, showing that individuals are consistently ranked according to their SMRm. However, the correlations between BMRm and SMRm were always lower (average: 0.29; range: 0&lt;r&lt;0.50), in particular in the benign foraging environment. Variation in metabolic response to lower Ta at least in part reflected differential body temperature (Tb) regulation: early morning Tb was lower at low Ta's, and more so in individuals with a weaker metabolic response to lower Ta's. Our findings have implications for the use of BMR in the estimation of time-energy budgets and comparative analyses: we suggest that the use of metabolic rates at ecologically relevant ambient temperatures, such as the easily tractable SMR, will be more informative than the use of BMR as a proxy for energy turnover.

Mouse models of human disease: An evolutionary perspective

The use of mice as model organisms to study human biology is predicated on the genetic and physiological similarities between the species. Nonetheless, mice and humans have evolved in and become adapted to different environments and so, despite their phylogenetic relatedness, they have become very different organisms. Mice often respond to experimental interventions in ways that differ strikingly from humans. Mice are invaluable for studying biological processes that have been conserved during the evolution of the rodent and primate lineages and for investigating the developmental mechanisms by which the conserved mammalian genome gives rise to a variety of different species. Mice are less reliable as models of human disease, however, because the networks linking genes to disease are likely to differ between the two species. The use of mice in biomedical research needs to take account of the evolved differences as well as the similarities between mice and humans.

A model for allometric scaling of mammalian metabolism with ambient heat loss

Background

Allometric scaling, which represents the dependence of biological traits or processes on body size, is a long-standing subject in biological science. However, there has been no study to consider heat loss to the ambient and an insulation layer representing mammalian skin and fur for the derivation of the scaling law of metabolism.

Methods

A simple heat transfer model is proposed to analyze the allometry of mammalian metabolism. The present model extends existing studies by incorporating various external heat transfer parameters and additional insulation layers. The model equations were solved numerically and by an analytic heat balance approach.

Results

A general observation is that the present heat transfer model predicted the 2/3 surface scaling law, which is primarily attributed to the dependence of the surface area on the body mass. External heat transfer effects introduced deviations in the scaling law, mainly due to natural convection heat transfer, which becomes more prominent at smaller mass. These deviations resulted in a slight modification of the scaling exponent to a value < 2/3.

Conclusion

The finding that additional radiative heat loss and the consideration of an outer insulation fur layer attenuate these deviation effects and render the scaling law closer to 2/3 provides in silico evidence for a functional impact of heat transfer mode on the allometric scaling law in mammalian metabolism.

A hierarchy of factors influence discontinuous gas exchange in the grasshopper Paracinema tricolor (Orthoptera: Acrididae)

The evolutionary origin and maintenance of discontinuous gas exchange (DGE) in tracheate arthropods are poorly understood and highly controversial. We investigated prioritization of abiotic factors in the gas exchange control cascade by examining oxygen, water and haemolymph pH regulation in the grasshopper Paracinema tricolor. Using a full-factorial design, grasshoppers were acclimated to hypoxic or hyperoxic (5% O2, 40% O2) gas conditions, or dehydrated or hydrated, whereafter their CO2 release was measured under a range of O2 and relative humidity (RH) conditions (5%, 21%, 40% O2 and 5%, 60%, 90% RH). DGE was significantly less common in grasshoppers acclimated to dehydrating conditions compared with the other acclimations (hypoxia, 98%; hyperoxia, 100%; hydrated, 100%; dehydrated, 67%). Acclimation to dehydrating conditions resulted in a significant decrease in haemolymph pH from 7.0±0.3 to 6.6±0.1 (mean ± s.d., P=0.018) and also significantly increased the open (O)-phase duration under 5% O2 treatment conditions (5% O2, 44.1±29.3 min; 40% O2, 15.8±8.0 min; 5% RH, 17.8±1.3 min; 60% RH, 24.0±9.7 min; 90% RH, 20.6±8.9 min). The observed acidosis could potentially explain the extension of the O-phase under low RH conditions, when it would perhaps seem more useful to reduce the O-phase to lower respiratory water loss. The results confirm that DGE occurrence and modulation are affected by multiple abiotic factors. A hierarchical framework for abiotic factors influencing DGE is proposed in which the following stressors are prioritized in decreasing order of importance: oxygen supply, CO2 excretion and pH modulation, oxidative damage protection and water savings.

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.

Estimating the biological half-life for radionuclides in homoeothermic vertebrates: a simplified allometric approach

The application of allometric, or mass-dependent, relationships within radioecology has increased with the evolution of models to predict the exposure of organisms other than man. Allometry presents a method of addressing the lack of empirical data on radionuclide transfer and metabolism for the many radionuclide-species combinations which may need to be considered. However, sufficient data across a range of species with different masses are required to establish allometric relationships and this is not always available. Here, an alternative allometric approach to predict the biological half-life of radionuclides in homoeothermic vertebrates which does not require such data is derived. Biological half-life values are predicted for four radionuclides and compared to available data for a range of species. All predictions were within a factor of five of the observed values when the model was parameterised appropriate to the feeding strategy of each species. This is an encouraging level of agreement given that the allometric models are intended to provide broad approximations rather than exact values. However, reasons why some radionuclides deviate from what would be anticipated from Kleiber's law need to be determined to allow a more complete exploitation of the potential of allometric extrapolation within radioecological models.

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.

Intraspecific correlations of basal and maximal metabolic rates in birds and the aerobic capacity model for the evolution of endothermy

The underlying assumption of the aerobic capacity model for the evolution of endothermy is that basal (BMR) and maximal aerobic metabolic rates are phenotypically linked. However, because BMR is largely a function of central organs whereas maximal metabolic output is largely a function of skeletal muscles, the mechanistic underpinnings for their linkage are not obvious. Interspecific studies in birds generally support a phenotypic correlation between BMR and maximal metabolic output. If the aerobic capacity model is valid, these phenotypic correlations should also extend to intraspecific comparisons. We measured BMR, M(sum) (maximum thermoregulatory metabolic rate) and MMR (maximum exercise metabolic rate in a hop-flutter chamber) in winter for dark-eyed juncos (Junco hyemalis), American goldfinches (Carduelis tristis; M(sum) and MMR only), and black-capped chickadees (Poecile atricapillus; BMR and M(sum) only) and examined correlations among these variables. We also measured BMR and M(sum) in individual house sparrows (Passer domesticus) in both summer, winter and spring. For both raw metabolic rates and residuals from allometric regressions, BMR was not significantly correlated with either M(sum) or MMR in juncos. Moreover, no significant correlation between M(sum) and MMR or their mass-independent residuals occurred for juncos or goldfinches. Raw BMR and M(sum) were significantly positively correlated for black-capped chickadees and house sparrows, but mass-independent residuals of BMR and M(sum) were not. These data suggest that central organ and exercise organ metabolic levels are not inextricably linked and that muscular capacities for exercise and shivering do not necessarily vary in tandem in individual birds. Why intraspecific and interspecific avian studies show differing results and the significance of these differences to the aerobic capacity model are unknown, and resolution of these questions will require additional studies of potential mechanistic links between minimal and maximal metabolic output.

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.

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.

The bigger they come, the harder they fall: body size and prey abundance influence predator-prey ratios

Large carnivores are highly threatened, yet the processes underlying their population declines are still poorly understood and widely debated. We explored how body mass and prey abundance influence carnivore density using data on 199 populations obtained across multiple sites for 11 carnivore species. We found that relative decreases in prey abundance resulted in a five- to sixfold greater decrease in the largest carnivores compared with the smallest species. We discuss a number of possible causes for this inherent vulnerability, but also explore a possible mechanistic link between predator size, energetics and population processes. Our results have important implications for carnivore ecology and conservation, demonstrating that larger species are particularly vulnerable to anthropogenic threats to their environment, especially those which have an adverse affect on the abundance of their prey.

Allometry of skeletal muscle fine structure allows maintenance of aerobic capacity during ontogenetic growth

Controversy exists over the scaling of oxygen consumption with body mass in vertebrates. A combination of biochemical and structural analyses were used to examine whether individual elements influencing oxygen delivery and demand within locomotory muscle respond similarly during ontogenetic growth of striped bass. Mass-specific metabolic enzyme activity confirmed that glycolytic capacity scaled positively in deep white muscle (regression slope, b=0.1 to 0.8) over a body mass range of ∼20–1500 g, but only creatine phosphokinase showed positive scaling in lateral red muscle(b=0.5). Although oxidative enzymes showed negative allometry in red muscle (b=–0.01 to –0.02), mass-specific myoglobin content scaled positively (b=0.7). Capillary to fibre ratio of red muscle was higher in larger (1.42±0.15) than smaller (1.20±0.15)fish, suggesting progressive angiogenesis. By contrast, capillary density decreased (1989±161 vs 2962±305 mm–2)as a result of larger fibre size (658±31 vs 307±24μm2 in 1595 g and 22.9 g fish, respectively). Thus, facilitated and convective delivery of O2 show opposite allometric trends. Relative mitochondrial content of red muscle (an index of O2demand) varied little with body mass overall, but declined from ∼40% fibre volume in the smallest to ∼30% in the largest fish. However, total content per fibre increased, suggesting that mitochondrial biogenesis supported aerobic capacity during fibre growth. Heterogeneous fibre size indicates both hypertrophic and hyperplastic growth, although positive scaling of fibre myofibrillar content (b=0.085) may enhance specific force generation in larger fish. Modelling intracellular PO2distribution suggests such integrated structural modifications are required to maintain adequate oxygen delivery (calculated PO2 5.15±0.02 kPa and 5.21±0.01 kPa in small and large fish, respectively).

The dynamic transfer of 3H and 14C in mammals: a proposed generic model

Associated with the present debate regarding the potential revival of nuclear energy there is an increased interest in assessing the radiological risk to the public and also the environment. Tritium and (14)C are key radionuclides of interest in many circumstances (e.g. heavy water reactors, waste storage and fusion reactors). Because the stable analogues of these two radionuclides are integral to most biological compounds, their modelling should follow general principles from life sciences. In this paper, a model of the dynamics of (14)C and (3)H in mammals is proposed on the basis of metabolic understanding and of, as far as possible, readily available data (e.g. for organ composition and metabolism). The model is described together with validation tests (without calibration) for a range of farm animals. Despite simplifications, the model tests are encouraging for a range of animal types and products (tissues and milk), and further improvements are suggested.

Energy limitation as a selective pressure on the evolution of sensory systems

Evolution of animal morphology, physiology and behaviour is shaped by the selective pressures to which they are subject. Some selective pressures act to increase the benefits accrued whilst others act to reduce the costs incurred, affecting the cost/benefit ratio. Selective pressures therefore produce a trade-off between costs and benefits that ultimately influences the fitness of the whole organism. The nervous system has a unique position as the interface between morphology, physiology and behaviour; the final output of the nervous system is the behaviour of the animal, which is a product of both its morphology and physiology. The nervous system is under selective pressure to generate adaptive behaviour, but at the same time is subject to costs related to the amount of energy that it consumes. Characterising this trade-off between costs and benefits is essential to understanding the evolution of nervous systems, including our own. Within the nervous system, sensory systems are the most amenable to analysing costs and benefits, not only because their function can be more readily defined than that of many central brain regions and their benefits quantified in terms of their performance, but also because recent studies of sensory systems have begun to directly assess their energetic costs. Our review focuses on the visual system in particular, although the principles we discuss are equally applicable throughout the nervous system. Examples are taken from a wide range of sensory modalities in both vertebrates and invertebrates. We aim to place the studies we review into an evolutionary framework. We combine experimentally determined measures of energy consumption from whole retinas of rabbits and flies with intracellular measurements of energy consumption from single fly photoreceptors and recently constructed energy budgets for neural processing in rats to assess the contributions of various components to neuronal energy consumption. Taken together, these studies emphasize the high costs of maintaining neurons at rest and whilst signalling. A substantial proportion of neuronal energy consumption is related to the movements of ions across the neuronal cell membrane through ion channels, though other processes such as vesicle loading and transmitter recycling also consume energy. Many of the energetic costs within neurons are linked to 3Na(+)/2K(+) ATPase activity, which consumes energy to pump Na(+) and K(+) ions across the cell membrane and is essential for the maintenance of the resting potential and its restoration following signalling. Furthermore, recent studies in fly photoreceptors show that energetic costs can be related, via basic biophysical relationships, to their function. These findings emphasize that neurons are subject to a law of diminishing returns that severely penalizes excess functional capacity with increased energetic costs. The high energetic costs associated with neural tissue favour energy efficient coding and wiring schemes, which have been found in numerous sensory systems. We discuss the role of these efficient schemes in reducing the costs of information processing. Assessing evidence from a wide range of vertebrate and invertebrate examples, we show that reducing energy expenditure can account for many of the morphological features of sensory systems and has played a key role in their evolution.

Uncertainty in allometric exponent estimation: A case study in scaling metabolic rate with body mass

Many factors could influence the allometric scaling exponent beta estimation, but have not been explored systematically. We investigated the influences of three factors on the estimate of beta based on a data set of 626 species of basal metabolic rate and mass in mammals. The influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo method. Small random errors were introduced to measured data to examine their influence on parameter estimations. The influence of analysis method was also evaluated by applying nonlinear and linear regressions to the original data. Results showed that a relative large sample size was required to lower statistical inference errors. When sample size n was 10% of the base population size (n=63), 35% of the samples supported beta=2/3, 39% supported beta=3/4, and 15% rejected beta=0.711, even though the base population had a beta=0.711. The controversy surrounding the estimation of beta in the literature could be partially attributable to such small sample sizes in many studies. Measurement errors in body mass and base metabolic rate, especially in body mass, could largely increase alpha and beta errors. Analysis methods also affected parameter estimations. Nonlinear regressions provided better estimates of the scaling exponent that were significantly higher than these commonly estimated by linear regressions. This study demonstrated the importance of the quantity and quality of data as well as analysis method in power law analysis, raising caution in interpreting power law results. Meta-data synthesis using data from independent studies seems to be a proper approach in the future, but caution should be taken to make sure that such measurements are made using similar protocols.

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.

Suspended animation-like state protects mice from lethal hypoxia

Joseph Priestley observed the high burn rate of candles in pure oxygen and wondered if people would "live out too fast" if we were in the same environment. We hypothesize that sulfide, a natural reducer of oxygen that is made in many cell types, acts as a buffer to prevent unrestricted oxygen consumption. To test this, we administered sulfide in the form of hydrogen sulfide (H2S) to mice (Mus musculus). As we have previously shown, H2S decreases the metabolic rate of mice by approximately 90% and induces a suspended animation-like state. Mice cannot survive for longer than 20 min when exposed to 5% oxygen. However, if mice are first put into a suspended animation-like state by a 20-min pretreatment with H2S and then are exposed to low oxygen, they can survive for more than 6.5 h in 5% oxygen with no apparent detrimental effects. In addition, if mice are exposed to a 20-min pretreatment with H2S followed by 1 h at 5% oxygen, they can then survive for several hours at oxygen tensions as low as 3%. We hypothesize that prior exposure to H2S reduces oxygen demand, therefore making it possible for the mice to survive with low oxygen supply. These results suggest that H2S may be useful to prevent damage associated with hypoxia.

Metabolic rate does not scale with body mass in cultured mammalian cells

The allometric scaling of metabolic rate with organism body mass can be partially accounted for by differences in cellular metabolic rates. For example, hepatocytes isolated from horses consume almost 10-fold less oxygen per unit time as mouse hepatocytes [Porter and Brand, Am J Physiol Regul Integr Comp Physiol 269: R226–R228, 1995]. This could reflect a genetically programmed, species-specific, intrinsic metabolic rate set point, or simply the adaptation of individual cells to their particular in situ environment (i.e., within the organism). We studied cultured cell lines derived from 10 mammalian species with donor body masses ranging from 5 to 600,000 g to determine whether cells propagated in an identical environment (media) exhibited metabolic rate scaling. Neither metabolic rate nor the maximal activities of key enzymes of oxidative or anaerobic metabolism scaled significantly with donor body mass in cultured cells, indicating the absence of intrinsic, species-specific, cellular metabolic rate set points. Furthermore, we suggest that changes in the metabolic rates of isolated cells probably occur within 24 h and involve a reduction of cellular metabolism toward values observed in lower metabolic rate organisms. The rate of oxygen delivery has been proposed to limit cellular metabolic rates in larger organisms. To examine the effect of oxygen on steady-state cellular respiration rates, we grew cells under a variety of physiologically relevant oxygen regimens. Long-term exposure to higher medium oxygen levels increased respiration rates of all cells, consistent with the hypothesis that higher rates of oxygen delivery in smaller mammals might increase cellular metabolic rates.

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.